Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the...

23
arXiv:1111.2226v1 [astro-ph.SR] 9 Nov 2011 Mon. Not. R. Astron. Soc. 000, 1–23 (2011) Printed 29 April 2018 (MN L A T E X style file v2.2) Constraining the Absolute Orientation of η Carinae’s Binary Orbit: A 3-D Dynamical Model for the Broad [Fe III ] Emission T. I. Madura 1 , T. R. Gull 2 , S. P. Owocki 3 , J. H. Groh 1 , A. T. Okazaki 4 , and C. M. P. Russell 3 1 Max-Planck-Institut f¨ ur Radioastronomie, Auf dem H¨ ugel 69, D-53121 Bonn, Germany 2 Astrophysics Science Division, Code 667, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 3 Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA 4 Faculty of Engineering, Hokkai-Gakuen University, Toyohira-ku, Sapporo 062-8605, Japan 29 April 2018 ABSTRACT We present a three-dimensional (3-D) dynamical model for the broad [Fe III] emission ob- served in η Carinae using the Hubble Space Telescope/Space Telescope Imaging Spectro- graph (HST/STIS). This model is based on full 3-D Smoothed Particle Hydrodynamics (SPH) simulations of η Car’s binary colliding winds. Radiative transfer codes are used to generate synthetic spectro-images of [Fe III] emission line structures at various observed orbital phases and STIS slit position angles (PAs). Through a parameter study that varies the orbital inclina- tion i, the PA θ that the orbital plane projection of the line-of-sight makes with the apastron side of the semi-major axis, and the PA on the sky of the orbital axis, we are able, for the first time, to tightly constrain the absolute 3-D orientation of the binary orbit. To simultaneously re- produce the blue-shifted emission arcs observed at orbital phase 0.976, STIS slit PA = +38 , and the temporal variations in emission seen at negative slit PAs, the binary needs to have an i 130 to 145 , θ ≈-15 to +30 , and an orbital axis projected on the sky at a PA 302 to 327 east of north. This represents a system with an orbital axis that is closely aligned with the inferred polar axis of the Homunculus nebula, in 3-D. The companion star, η B , thus orbits clockwise on the sky and is on the observer’s side of the system at apastron. This orientation has important implications for theories for the formation of the Homunculus and helps lay the groundwork for orbital modeling to determine the stellar masses. Key words: hydrodynamics – binaries: close – stars: individual: Eta Carinae – stars: mass- loss – stars: winds, outflows – line: formation 1 INTRODUCTION η Carinae is the most luminous, evolved stellar object that can be closely studied (Davidson & Humphreys 1997). Its immense lu- minosity (L 5 × 10 6 L, Cox et al. 1995) and relative prox- imity (D =2.3 ± 0.1 kpc, Smith 2006b) make it possible to test and constrain specific theoretical models of extremely massive stars ( 60 M) using high-quality data (Hillier et al. 2001, 2006; Smith & Owocki 2006). η Car is thus one of the most intensely observed stellar systems in the Galaxy, having been the focus of numerous ground- and space-based observing campaigns at mul- tiple wavelengths from radio (Duncan & White 2003; White et al. 2005) to gamma-rays (Tavani et al. 2009; Abdo et al. 2010). Based on observations made with the NASA/ESA Hubble Space Tele- scope. Support for programs 7302, 8036, 8483, 8619, 9083, 9337, 9420, 9973, 10957 and 11273 was provided by NASA directly to the STIS Sci- ence Team and through grants from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in As- tronomy, Inc., under NASA contract NAS 5-26555. Email: [email protected] Unfortunately, the dusty Homunculus nebula that formed dur- ing η Car’s “Great Eruption” in the 1840s enshrouds the system, complicating direct observations of the central stellar source (Smith 2009). Nevertheless, ground- and space-based, multi-wavelength observations obtained over the past two decades strongly indicate that η Car is a highly eccentric (e 0.9) colliding wind binary (CWB) with a 5.54-year orbital period (Damineli 1996; Feast et al. 2001; Duncan & White 2003; Whitelock et al. 2004; Smith et al. 2004; Corcoran 2005; Verner et al. 2005; van Genderen et al. 2006; Damineli et al. 2008a,b; Fern´ andez-Laj´ us et al. 2010; Corcoran 2011, hereafter C11). The consensus view is that the primary star, ηA, is a Luminous Blue Variable (LBV) (Hillier & Allen 1992; Davidson & Humphreys 1997; Hillier et al. 2001, 2006). Radia- tive transfer modeling of Hubble Space Telescope/Space Tele- scope Imaging Spectrograph (HST/STIS) spatially-resolved spec- troscopic observations suggests that ηA has a current mass 90 M, and a current-day stellar wind with a mass-loss rate of 10 3 Myr 1 and terminal speed of 500 600 km s 1 (Hillier et al. 2001, 2006, hereafter H01, H06). The companion star, ηB, continues to evade direct detection since ηA dwarfs its emission

Transcript of Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the...

Page 1: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

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Mon Not R Astron Soc000 1ndash23 (2011) Printed 29 April 2018 (MN LATEX style file v22)

Constraining the Absolute Orientation of η Carinaersquos Binary OrbitA 3-D Dynamical Model for the Broad [Fe III] Emission⋆

T I Madura1dagger T R Gull2 S P Owocki3 J H Groh1 A T Okazaki4 and C M P Russell3

1 Max-Planck-Institut fur Radioastronomie Auf dem Hugel69 D-53121 Bonn Germany2 Astrophysics Science Division Code 667 NASA Goddard Space Flight Center Greenbelt MD 20771 USA3 Bartol Research Institute Department of Physics and Astronomy University of Delaware Newark DE 19716 USA4 Faculty of Engineering Hokkai-Gakuen University Toyohira-ku Sapporo 062-8605 Japan

29 April 2018

ABSTRACTWe present a three-dimensional (3-D) dynamical model for the broad [FeIII ] emission ob-served inη Carinae using theHubble Space TelescopeSpace Telescope Imaging Spectro-graph (HSTSTIS) This model is based on full 3-D Smoothed Particle Hydrodynamics (SPH)simulations ofη Carrsquos binary colliding winds Radiative transfer codes areused to generatesynthetic spectro-images of [FeIII ] emission line structures at various observed orbital phasesand STIS slit position angles (PAs) Through a parameter study that varies the orbital inclina-tion i the PAθ that the orbital plane projection of the line-of-sight makes with the apastronside of the semi-major axis and the PA on the sky of the orbital axis we are able for the firsttime to tightly constrain the absolute 3-D orientation of the binary orbit To simultaneously re-produce the blue-shifted emission arcs observed at orbitalphase 0976 STIS slitPA = +38and the temporal variations in emission seen at negative slit PAs the binary needs to have ani asymp 130 to 145 θ asymp minus15 to+30 and an orbital axis projected on the sky at aPA asymp 302

to 327 east of north This represents a system with an orbital axis that is closely aligned withthe inferred polar axis of the Homunculus nebula in 3-D Thecompanion starηB thus orbitsclockwise on the sky and is on the observerrsquos side of the system at apastron This orientationhas important implications for theories for the formation of the Homunculus and helps lay thegroundwork for orbital modeling to determine the stellar masses

Key words hydrodynamics ndash binaries close ndash stars individual Eta Carinae ndash stars mass-loss ndash stars winds outflows ndash line formation

1 INTRODUCTION

η Carinae is the most luminous evolved stellar object that can beclosely studied (Davidson amp Humphreys 1997) Its immense lu-minosity (L amp 5 times 106 L⊙ Cox et al 1995) and relative prox-imity (D = 23 plusmn 01 kpc Smith 2006b) make it possible totest and constrain specific theoretical models of extremelymassivestars (amp 60M⊙) using high-quality data (Hillier et al 2001 2006Smith amp Owocki 2006)η Car is thus one of the most intenselyobserved stellar systems in the Galaxy having been the focus ofnumerous ground- and space-based observing campaigns at mul-tiple wavelengths from radio (Duncan amp White 2003 White et al2005) to gamma-rays (Tavani et al 2009 Abdo et al 2010)

⋆ Based on observations made with the NASAESAHubble Space Tele-scope Support for programs 7302 8036 8483 8619 9083 9337 94209973 10957 and 11273 was provided by NASA directly to the STIS Sci-ence Team and through grants from the Space Telescope Science Institutewhich is operated by the Association of Universities for Research in As-tronomy Inc under NASA contract NAS 5-26555dagger Email tmadurampifr-bonnmpgde

Unfortunately the dusty Homunculus nebula that formed dur-ing η Carrsquos ldquoGreat Eruptionrdquo in the 1840s enshrouds the systemcomplicating direct observations of the central stellar source (Smith2009) Nevertheless ground- and space-based multi-wavelengthobservations obtained over the past two decades strongly indicatethat η Car is a highly eccentric (e sim 09) colliding wind binary(CWB) with a 554-year orbital period (Damineli 1996 Feastet al2001 Duncan amp White 2003 Whitelock et al 2004 Smith et al2004 Corcoran 2005 Verner et al 2005 van Genderen et al 2006Damineli et al 2008ab Fernandez-Lajus et al 2010 Corcoran2011 hereafter C11) The consensus view is that the primarystarηA is a Luminous Blue Variable (LBV) (Hillier amp Allen 1992Davidson amp Humphreys 1997 Hillier et al 2001 2006) Radia-tive transfer modeling ofHubble Space TelescopeSpace Tele-scope Imaging Spectrograph (HSTSTIS) spatially-resolved spec-troscopic observations suggests thatηA has a current massamp90 M⊙ and a current-day stellar wind with a mass-loss rate ofsim 10minus3M⊙ yrminus1 and terminal speed ofsim 500 minus 600 km sminus1

(Hillier et al 2001 2006 hereafter H01 H06) The companion starηB continues to evade direct detection sinceηA dwarfs its emission

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2 Madura et al

at most wavelengths (Damineli et al 2000 H01 H06 Smith etal2004 C11) As a resultηBrsquos stellar parameters evolutionary stateorbit and influence on the evolution ofηA are poorly known

Currently the best constraints on the stellar properties ofηB come from photoionization modeling of the ldquoWeigelt blobsrdquodense slow-moving ejecta in the vicinity of the binary system(Weigelt amp Ebersberger 1986) Verner et al (2005) initially char-acterizedηB as a mid-O to WN supergiant More recent workby Mehner et al (2010) tightly constrains the effective tempera-ture of ηB (Teff sim 37 000 minus 43 000 K) but not its luminosity(logLL⊙ sim 5 minus 6) resulting in a larger range of allowed stellarparameters

Constraints on the wind parameters ofηB come from ex-tended X-ray monitoring by theRossi X-ray Timing Explorer(RXTE) Chandra XMM and Suzakusatellites (Ishibashi et al1999 Corcoran 2005 Hamaguchi et al 2007 Corcoran et al2010) The periodic nature minimum around periastron andhard-ness (up to 10 keV) ofη CarrsquosRXTElight curve are all character-istics of a highly eccentric CWB the variable X-ray emission aris-ing in a wind-wind collision (WWC) zone formed between the twostars (Pittard amp Corcoran 2002 Okazaki et al 2008 Parkin et al2009 2011 Corcoran et al 2010 hereafter PC02 O08 P09 P11and C10 respectively) The hardness of the X-rays requiresthatηBhave a high wind terminal speed ofsim 3000 km sminus1 and detailedmodeling of the momentum balance between the two shock frontssuggests a mass-loss rate ofsim 10minus5M⊙ yrminus1 (PC02 O08 P09P11)

Proper numerical modeling ofη Carrsquos WWC remains a chal-lenge mainly because it requires a full three-dimensional(3-D)treatment since orbital motion especially during periastron can beimportant or even dominant affecting the shape and dynamics ofthe WWC region (O08 P09 P11) Most hydrodynamical simula-tions of η Car have been two-dimensional (2-D) neglecting theeffects of orbital motion for simplicity (Pittard 1998 2000 PC02Henley 2005) Until very recently (O08 P11) fully 3-D simula-tions were computationally impractical

When it comes to reproducing observational diagnostics ofη Car from hydrodynamical simulations of its colliding winds thefocus has been almost exclusively on X-rays One drawback ofthisis that models forη Car at other wavelengths have been mostly phe-nomenological offering only qualitative explanations for the vastarray of complicated observations This makes it difficult to test andrefine models or quantitatively constrain the physical parameters ofthe system An excellent example is the lack of consensus regard-ing η Carrsquos orbital orientation The majority favor an orbit in whichηB is behindηA during periastron (Damineli 1996 PC02 Corco-ran 2005 Hamaguchi et al 2007 Nielsen et al 2007a Damineli etal 2008b Henley et al 2008 O08 P09 P11 Groh et al 2010bRichardson et al 2010) But others placeηB on the near side ofηAat periastron (Falceta-Goncalves et al 2005 Abraham et al 2005bAbraham amp Falceta-Goncalves 2007 Kashi amp Soker 2007 2008Falceta-Goncalves amp Abraham 2009) Some claim that the orienta-tion is not well established at all (Mehner et al 2011)

A more fundamental drawback of focusing purely on X-raysor other spatially-unresolved data is that any derived orbit is am-biguous with respect to itsabsoluteorientation on the skyany or-bital orientation derived solely from fitting the X-ray datacan berotated on the sky about the observerrsquos line-of-sight and still matchthe observations A degeneracy also exists in the orbital inclinationwith models that assumei asymp 45 andi asymp 135 both capable of fit-ting the observedRXTElight curve However high-resolution spa-tial information is not enough moderate-resolution spectral data is

needed to determine the velocity structure of the emitting gas andthus fully constrain the orbital orientation As a result using X-raydata alone it is impossible to determine the 3-D alignment or mis-alignment of the orbital axis with the Homunculus polar axis orthe direction of the orbit It is commonlyassumedthat the orbitalaxis is aligned with the Homunculus polar axis but to date neithermodeling nor observations have unambiguously demonstrated thatthis is the case Knowing the orbitrsquos orientation is key to constrain-ing theories for the cause of the Great Eruption and formation of theHomunculus (ie single star versus binary interactionmerger sce-narios Iben 1999 Dwarkadas amp Owocki 2002 Smith et al 2003aSoker 2007 Smith 2009 2011 Smith amp Frew 2011) Furthermorea precise set of orbital parameters would lay the groundworkfororbital modeling to determine the stellar masses

In a recent attempt to characterizeη Carrsquos interactingwinds Gull et al (2009 hereafter G09) presented an analysis ofHSTSTIS observations taken between 1998 and 2004 identifyingspatially-extended (up to08primeprime) velocity-resolved forbidden emis-sion lines from low- and high-ionization1 speciesHSTSTIS imag-ing spectroscopy is ideal for moving beyond X-ray signatures as ituniquely provides the spatial (sim 01primeprime) and spectral (R sim 8 000)resolution necessary to separate the spectra ofη Carrsquos centralsource and nearby circumstellar ejecta from those of the Homuncu-lus and other surrounding material Moreover this high-ionizationforbidden emission is phase-locked which strongly suggests it isregulated by the orbital motion ofηB Observed spectro-images arealso highly dependent on the PA2 of the HSTSTIS slit implyingthat they contain valuable geometrical information This opens upthe possibility of obtainingηBrsquos orbital stellar and wind parame-ters through proper modeling of the extended forbidden lineemis-sion

This paper presents a detailed 3-D dynamical model for thebroad components of the high-ionization forbidden line emissionobserved inη Car using theHSTSTIS Our model is based on theresults of full 3-D Smoothed Particle Hydrodynamics (SPH) simu-lations ofη Carrsquos colliding winds (sect 32 and41) Radiative trans-fer calculations performed with a modified version of the SPLASHcode (Price 2007) are used with IDL routines to generate syntheticspectro-images of [FeIII ] emission line structures at various orbitalphases and STIS slit PAs (sect 34) Through a parameter study thatvaries the orbital inclination the angle that the line-of-sight makeswith the apastron side of the semi-major axis and the PA on thesky of the projected orbital axis we are able to tightly constrainfor the first time theabsolute(3-D) orientation and direction ofη Carrsquos orbit (sect 4) showing in particular that the orbital axis isclosely aligned in 3-D with the inferred polar axis of the Homuncu-lus nebula A discussion of the results and this derived orientationare insect 5 sect 6 summarizes our conclusions and outlines the direc-tion of future work We begin (sect 2) with a brief summary of theobservations used in this paper

2 THE OBSERVATIONS

This paper uses the sameHSTSTIS data described in G09 (see theirTable 1) Extracted portions of observations recorded fromMarch1998 to March 2004 with the STIS CCD (00507primeprime pixelminus1 scale)with medium dispersion gratings (R sim 8 000) in combination

1 Low- and high-ionization refer here to atomic species with ionizationpotentials (IPs) below and above the IP of hydrogen 136 eV2 Position Angle measured in degrees from north to east

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Constraining the 3-D Orientation ofη Carrsquos Orbit 3

Figure 1 Examples of theHSTSTIS spatially-resolved [FeIII ] spectra Top Left AnHSTAdvanced Camera for Surveys (ACS) High Resolution Camera(HRC) image of the Homunculus andη Car with a20primeprime field of view Bottom Left Enlarged central2primeprime field of view with the52primeprime times 01primeprime slit positionedat PA = +69 and directional labels (NW = northwest etc) included for reference in the text Spectro-images in the middle and right-hand columns wererecorded from the central2primeprime times 01primeprime portion of the slit as drawn between labels I and II Top Center Spatially-resolved line profile of [FeIII ] λ4659 inoriginal form recorded atPA = +69 in 2002 July (φ = 082) Top Right The same spectro-image with the continuum subtracted on a spatial row-by-rowbasis The velocity scale referenced to the vacuum rest wavelength of the line isplusmn600 km sminus1 and the color level is proportional to the square root of theintensity Bottom Center Spectro-image of [FeII ] λ4815 shifted by400 km sminus1 used as a template to determine the spatial and spectral ranges where the[Fe III ] image is contaminated by [FeII ] λ4666 emission Bottom Right Same spectro-image as the top right panel but with masks that remove the narrowline contamination and the contamination to the red from nearby [FeII ] λ4666 (see text)

with the52primeprime times01primeprime slit from 1640 to 10100A were used to sam-ple the spectrum of the central core ofη Car Phases of the obser-vationsφ are relative to theRXTEX-ray minimum at 19979604(Corcoran 2005)JDobs = JD 2450799792 + 20240 times φ Solarpanel orientation requirements constrained the STIS slit PAs Thereduced STIS CCD spectra available through the STScI archives(httparchivestscieduprepdsetacar) wereused Compass directions (NW = north-west etc) describe the spa-tial extent of the emission All wavelengths are in vacuum and ve-locities are heliocentric For details see G09 and references therein

Figure 1 shows examples of resolved broad emission from[Fe III ] λ4659 In the top center panel faint spatially- and velocity-resolved emission can be seen against bright nebular emission anddust-scattered stellar radiation Strong narrow line emission fromthe SW ofη Car is also seen The bright continuum close to thewavelength of the wind line of interest is subtracted on a spatialrow-by-row basis in order to isolate the fainter broad forbiddenline emission (top right panel of Figure 1) All spectro-images inthis paper have been processed identically using a portion of thespectrum with no bright narrow- or broad-line contamination Row-by-row subtraction across the stellar position is less successful dueto insufficient correction in the data reduction for small tilts of thespectrum on the CCD (G09)

The bottom right panel of Figure 1 contains the same spectro-image of [FeIII ] λ4659 as the top right panel but with masks thatremove narrow line contamination from the Weigelt blobs and con-

tamination to the red due to the nearby [FeII ] λ4666 wind lineThe masks are intended to remove ldquodistractingrdquo emission featuresnot relevant to the work in this paper displaying only the observedbroad structures that are the focus of the modeling (outlined inwhite) To determine the spatial and spectral ranges where [FeII ]λ4666 contaminates the [FeIII ] λ4659 image we use as a tem-plate the uncontaminated spectro-image of the bright [FeII ] λ4815line (bottom center panel of Figure 1) We also compare the [Fe III ]λ4659 images to those of the [FeIII ] λ4702 and [NII ] λ5756 lineswhich form in nearly identical conditions as they have very similarcritical densities and IPs (Table 3 of G09) A detailed discussionof the observations and masking procedure for all spectro-imagesmodeled in this paper is in Appendix A (available in the onlineversion of this paper - see Supporting Information)

21 The Key Observational Constraints Modeled

Three key features observed in spectro-images of the high-ionization forbidden line emission can be used to constrainthe 3-Dorientation ofη Carrsquos orbit Each provides important clues aboutthe nature and orbital variation ofη Carrsquos interacting winds Webriefly summarize these below

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4 Madura et al

211 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

Figure 2 displays observed spectro-images of [FeIII ] λ4659recorded at slit PA = +38 on 2003 May 5 (φ = 0976) show-ing spatially-extended (up tosim 035primeprime) emission in the form ofvery distinct nearly complete arcs that are entirely blue-shiftedup to sim minus475 km sminus1 Several weaker [FeIII ] lines nearby inthe spectrum while blended show no evidence of a spatially-extended (gt 01primeprime) red component and no other high-ionizationforbidden lines show an extended red component at this position(G09) To illustrate this the bottom right panel of Figure 2containsa continuum-subtracted spectro-image of [NII ] λ5756 taken at thesame orbital phase and slit PA The IP (145 eV) and critical density(3 times 107 cmminus3) of [N II ] λ5756 are very similar to that of [FeIII ]λ4659 (162 eV andsim 107 cmminus3) meaning that their spatially-extended emission forms in nearly identical regions and viathesame physical mechanism The [NII ] λ5756 line is strong and lo-cated in a spectral region with very few other lines Unlike [FeIII ]λ4659 there is no contamination to the red of [NII ] λ5756 mak-ing it ideal for demonstrating that there is no spatially-extendedred-shifted broad high-ionization forbidden line emission

Of particular importance are the asymmetric shape and inten-sity of these emission arcs Both arcs extend to nearly the samespatial distance from the central core but the upper arc is notice-ably dimmer and stretches farther to the blue tosim minus475 km sminus1The lower arc is brighter but only extends tosim minus400 km sminus1 Ev-ery high-ionization forbidden line observed at this orbital phase andslit PA exhibits these asymmetries in intensity and velocity (figures6 minus 9 of G09) indicating that they are independent of the IP andcritical density of the line and intrinsic to the shape and distributionof the photoionized extended wind material in which the lines formAs such the shape and asymmetry of the blue-shifted emission arcsmay be used to help constrain the orbital orientation

212 Constraint 2 Variations with Orbital Phase at ConstantSlit PA =minus28

Let us focus next on shifts of the high-ionization forbiddenemis-sion with orbital phase Figure 11 of G09 shows sets of six spec-tra of [FeIII ] λ4659 andλ4702 recorded at select phases at slitPA = minus28 During the two minima atφ = 0045 and 1040 (rows1 and 5 of figure 11 of G09) the broad [FeIII ] emission is absentBy φ = 0213 (row 2) andφ = 1122 (row 6sim 8 months after theX-ray minimum) it strongly reappears Images atφ = 0407 aresimilar to those atφ = 0213 and 1122 Byφ = 0952 emissionabovesim 150 km sminus1 disappears This phase dependence in the[Fe III ] emission especially the disappearance during periastronstrongly indicates that it is tied to the orbital motion ofηB

Another important observational feature is the presence ofspatially-extendedred-shiftedemission to the NW in addition toextended blue-shifted emission to the SE at phases far frompe-riastron This is in contrast to the entirely blue-shifted arcs seenfor slit PA = +38 indicating that the STIS slit at PA =minus28

is sampling different emitting portions ofη Carrsquos extended windstructures even at similar orbital phases

213 Constraint 3 Doppler Shift Correlations with OrbitalPhase and Slit PA

The final set of observations focuses on changes with slit PA lead-ing up to periastron Figures 12 and 13 of G09 illustrate the be-havior of the [FeIII ] emission for various slit PAs at select phases

Figure 2 Spectro-images recorded 2003 May 5 (φ = 0976) Top LeftPanelHSTACS HRC image of the central2primeprime of η Car with the2primeprime longportion of the STIS slit at PA = +38 overlaid The locations of Weigeltblobs B C and D are indicated as is the direction of north Top Right PanelContinuum-subtracted spectro-image of [FeIII ] λ4659 Emission appearsas a pair of completely blue-shifted arcs Color is proportional to the squareroot of the intensity and the velocity scale isplusmn600 km sminus1 Weak emissionto the red is entirely due to contamination by [FeII ] λ4666 while weaknarrow emission is centered atsim minus40 km sminus1 Bottom Left Panel Samespectro-image but with masks that remove the line contamination BottomRight Panel Continuum-subtracted spectro-image of [NII ] λ5756 includedto demonstrate that at this phase and STIS PA the high-ionization forbiddenlines show no evidence of broad spatially-extended red-shifted emission

The key point to take away from this particular data set is that awayfrom periastron the spatially-extended [FeIII ] emission is almostentirely blue-shifted for positive slit PAs =+22 to +70 but ispartially red-shifted for negative PAs most notably PA =minus82

3 A 3-D DYNAMICAL MODEL FOR THE BROADHIGH-IONIZATION FORBIDDEN LINE EMISSION

31 Why Model [Fe III] λ4659 Emission

Table 3 of G09 lists the various forbidden emission lines observedin η Car However there are several important reasons to focus par-ticular attention on [FeIII ] λ4659 emission

First the physical mechanism for the formation of forbiddenlines is well understood (Appendix B online version) Moreoveremission from forbidden lines is optically thin Thus forbidden lineradiation can escape from a nebula much more easily than radiationfrom an optically thick resonance line which is emitted andreab-sorbed many times (Hartman 2003) This is of great value whenstudying an object so enshrouded by circumstellar materialsinceone does not have to model complicated radiative transfer effects

[Fe III ] is considered rather than a lower ionization line of[Fe II ] becausethe bulk of the[Fe III ] emission arises in regions thatare directly photoionized byηB (Verner et al 2005 G09 Mehner etal 2010) No intrinsic [FeIII ] emission is expected fromηA Thisis based on detailed theoretical models by H01 and H06 whichshow that inηArsquos envelope Fe2+ only exists in regions where theelectron density is two-to-four orders of magnitude higherthan the

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Constraining the 3-D Orientation ofη Carrsquos Orbit 5

critical density of the [FeIII ] λ4659 line Since Fe0 needs162 eVradiation (or collisions) to reach the Fe2+ state most of the [FeIII ]emission arises in areas directly photoionized byηB

In comparison Fe0 only needs 79 eV radiation or collisions toionize to Fe+ which can form in the wind ofηA (without ηBrsquos in-fluence) andor near the wind-wind interaction regions in areas ex-cited by mid-UV radiation filtered byηArsquos dense wind Collisionsand photoexcitation to upper Fe+ energy levels can also populatemany metastable levels As a result [FeII ] emission is far morecomplicated and originates from lower excitation lower density re-gions on much larger spatial scales (H01 H06 G09 Mehner etal2010) Because of this complexity the modeling of [FeII ] emissionis deferred to future work

The IP of 162 eV required for Fe2+ also means that the[Fe III ] emission forms in regions where hydrogen is ionized buthelium is still neutral In contrast both Ar2+ and Ne2+ have IPsgreater than246 eV Therefore [ArIII ] and [NeIII ] emission arisein areas where helium is singly ionized Modeling [FeIII ] is thusmore straightforward as one does not have to worry about the twodifferent types of ionization structure possible (one due to H andone due to He) which depend on the spectrum of ionizing radia-tion and the abundance of helium (Osterbrock 1989)

[Fe III ] λ4659 is chosen over the similar emission line of [NII ]λ5756 in order to avoid potential complications due to intrinsic[N II ] emission in the extended wind ofηA [N II ] emission canform in a broad zone between 100 and 1000Rlowast (sim 30 minus 300 AU)of ηA and is sensitive to its wind temperature and mass-loss rate(H01) By focusing on [FeIII ] one avoids having to include anyintrinsic forbidden line emission fromηA

The modeling in this paper focuses solely on thebroad[Fe III ]emission features that are thought to arise in the dense mod-erate velocity (sim 100 minus 600 km sminus1) extended primary windand WWC regions The much narrower ( 50 km sminus1) emis-sion features that form in the Weigelt blobs and other denseslow-moving equatorial ejecta fromη Carrsquos smaller eruptionin the 1890s (Weigelt amp Ebersberger 1986 Davidson et al 19951997 Ishibashi et al 2003 Smith et al 2004 Gull et al 2009Mehner et al 2010) are not modeled Any possible effects of localdust formation are neglected for simplicity as not enough informa-tion is available to realistically include them at this time(Williams2008 Mehner et al 2010)

As all observed high-ionization forbidden lines show the samebasic spatial and temporal features in their broad emission with anydifferences in size or location attributable to differences in the IPand critical density of the specific line of interest focusing solelyon [FeIII ] λ4659 should not significantly bias the overall conclu-sions which should extend to the other high-ionization forbiddenlines as well Values of the transition probability (A21 = 044 sminus1)statistical weights (g1 = g2 = 9) and line transition frequency(ν21 = 6435 times 1014 sminus1) for [Fe III ] λ4659 all come fromNahar amp Pradhan (1996) Values for the collision strengths (Ω12)come from Zhang (1996) A solar abundance of iron is also usedconsistent with the works of H01 Verner et al (2005) and H06

32 The 3-D SPH Code and General Problem Setup

The numerical simulations in this paper were performed withthesame 3-D SPH code used in O08 The stellar winds are modeledby an ensemble of gas particles that are continuously ejected witha given outward velocity at a radius just outside each star For sim-plicity both winds are taken to be adiabatic with the same initialtemperature (35 000 K) at the stellar surfaces and coasting with-

Table 1 Stellar Wind and Orbital Parameters of the 3-D SPH Simulation

Parameter ηA ηB

Mass (M⊙) 90 30Radius (R⊙) 90 30Mass-Loss Rate (M⊙ yrminus1) 10minus3 10minus5

Wind Terminal Velocity (km sminus1) 500 3000Orbital Period (days) 2024Orbital Eccentricitye 09Semi-major Axis Lengtha (AU) 154

out any net external forces assuming that gravitational forces areeffectively canceled by radiative driving terms (O08) Thegas hasnegligible self-gravity and adiabatic cooling is included

In a standardxyz Cartesian coordinate system the binary or-bit is set in thexy plane with the origin at the system center-of-mass and the orbital major axis along thex-axis The two starsorbit counter-clockwise when looking down on the orbital planealong the+z axis Simulations are started with the stars at apas-tron and run for multiple consecutive orbits By convention t = 0(φ = 0) is defined to be at periastron passage

To match thesim plusmn07primeprime scale of the STIS observations at theadopted distance of 23 kpc to theη Car system (Smith 2006b) theouter simulation boundary is set atr = plusmn105a from the systemcenter-of-mass wherea is the length of the orbital semi-major axis(a = 154 AU) Particles crossing this boundary are removed fromthe simulation We note that the SPH formalism is ideally suitedfor such large-scale 3-D simulations as compared to grid-basedhydrodynamics codes (Price 2004 Monaghan 2005)

Table 1 summarizes the stellar wind and orbital parametersused in the modeling which are consistent with those derived fromthe observations (PC02 H01 H06 C11) with the exception of thewind temperature ofηA The effect of the wind temperature on thedynamics of the high-velocity wind collision is negligible(O08)Note that the simulation adopts the higher mass-loss rate for ηAderived by Davidson et al (1995) Cox et al (1995) H01 andH06rather than the factor of four lower mass-loss rate assumed whenanalyzing X-ray signatures (PC02 O08 P09 P11 C11) Effects ofthe adopted value of the primary mass-loss rate on the forbiddenline emission will be the subject of a future paper

The publicly available software SPLASH (Price 2007) is usedto visualize the 3-D SPH code output SPLASH differs from othertools because it is designed to visualize SPH data using SPH algo-rithms There are a number of benefits to using SPLASH and thereader is referred to Price (2007) and the SPLASH userguide forthese and discussions on the interpolation algorithms

33 Generation of Synthetic Slit Spectro-Images

The 3-D SPH simulation provides the time-dependent 3-D den-sity and temperature structure ofη Carrsquos interacting winds on spa-tial scales comparable to those of theHSTSTIS observations Thisforms the basis of our 3-D dynamical model Unfortunately it iscurrently not possible to perform full 3-D simulations ofη Car inwhich the radiative transfer is properly coupled to the hydrodynam-ics (Paardekooper 2010) Instead the radiative transfer calculationshere are performed as post-processing on the 3-D SPH simulationoutput This should not strongly affect the results so long as the ma-terial that is photoionized byηB responds nearly instantaneously toits UV flux In other words as long as the timescale for the recom-

ccopy 2011 RAS MNRAS000 1ndash23

6 Madura et al

bination ofe + Fe2+ rarr Fe+ is very small relative to the orbitaltimescale the calculations should be valid

The recombination timescale isτrec = 1(αrecne) secondswhereαrec(T ) is the recombination rate coefficient (in units ofcm3 sminus1) at temperatureT andne is the electron number densityFor T sim 104 K αrec(T ) asymp 4 times 10minus12 cm3 sminus1 (Nahar 1997)Since densities near the critical density of the line are theprimaryfocusne sim 107 cmminus3 this givesτrec asymp 7 hours which is muchsmaller than the orbital timescale even during periastronpassagewhich takes approximately one month Any possible time-delay ef-fects should not strongly affect the results as the light-travel-timeto material at distances ofsim 05primeprime in η Car is only about one week

331 Summary of the Basic Procedure

Synthetic slit spectro-images are generated using a combination ofInteractive Data Language (IDL) routines and radiative transfer cal-culations performed with a modified version of the SPLASH (Price2007) code Here we outline the basic procedure with the specificsdiscussed in the following subsections

Nearly all of the required calculations are performed withinSPLASH which reads in the 3-D SPH code output for a specificorbital phase rotates the data to a desired orbital orientation on thesky and computes the line-of-sight velocity for all of the materialNext is the computation of the ionization volume created byηBwhere Fe+ is photoionized to Fe2+ It is assumed that any materialwithin this volume is in collisional ionization equilibrium and thatno material withT gt 250 000 K emits All other material in thephotoionization volume has its forbidden line emissivity calculatedusing Equation (13) derived below Material located outside thephotoionization volume does not emit

The intensityI is computed by performing a line-of-sight in-tegration of the emissivity at each pixel resulting in an image ofthe spatial distribution of the [FeIII ] intensity projected on the skyThis is done for each velocityvbin used along the dispersion axisof the synthetic slit in the velocity range of interest resulting ina set of intensity images The individual [FeIII ] λ4659 intensityimages are then combined and convolved with theHSTSTIS re-sponse using IDL routines in order to create a synthetic positionversus velocity spectro-image for comparison to the observations

332 Defining the Binary Orientation Relative to the Observer

With the two stars orbiting in thexy plane the 3-D orientation ofthe binary relative to the observer is defined by the orbital inclina-tion i the prograde direction angleθ that the orbital plane projec-tion of the observerrsquos line-of-sight makes with the apastron side ofthe semi-major axis3 and the position angleon the skyof the+zorbital axis PAz (Figure 3)

Following the standard definition for binary systemsi is theangle that the line-of-sight makes with the+z axis An i = 0 isa face-on orbit with the observerrsquos line-of-sight along the+z axisand the two stars orbiting counter-clockwise on the sky Ani = 90

places the line-of-sight in the orbitalxy plane whilei = 180 is aface-on orbit with the two stars orbiting clockwise on the sky

For i = 90 a value ofθ = 0 has the observer looking alongthe+x axis (along the semi-major axis on the apastron side of thesystem) while aθ = 90 has the observer looking along the+y

3 θ is the same as the angleφ defined in figure 3 of O08

Figure 3 Diagrams illustrating the observerrsquos position Top Schematicdefining the inclination anglei that the observerrsquos line-of-sight makes withthe +z orbital axis and the equatorial projection angleθ of the line-of-sight relative to the apastron side of the semi-major axisx The backgroundorthogonal planes show slices of density from the 3-D SPH simulation atapastron in thexy orbital plane and theyz plane perpendicular to the or-bital plane and major axis Bottom Diagram defining the position angle onthe skyPAz of the+z orbital axis (blue) measured in degrees counter-clockwise of north (N) The binary orbit projected on the skyis shown inyellow as are the semi-major (red) and semi-minor (green) axes The smallinset to the left is aHSTWFPC2 image of the Homunculus (Credit NASAESA and the Hubble SM4 ERO Team) included for reference

axis In the conventional notation of binary orbits the lsquoargument ofperiapsisrsquoω = 270 minus θ

PAz defines the position angle on the sky of the+z orbital axisand is measured in degrees counter-clockwise of N APAz = 312

aligns the projected orbital axis with the Homunculus polaraxis(Davidson et al 2001 Smith 2006b 2009) and has+z pointingNW on the sky APAz = 42 places the orbital axis perpen-dicular to the Homunculus polar axis with+z pointing NE APAz = 132 (222) is also aligned with (perpendicular to) theHomunculus polar axis and has+z pointing SE (SW) on the sky

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

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14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

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Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

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16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

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Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

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18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 2: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

2 Madura et al

at most wavelengths (Damineli et al 2000 H01 H06 Smith etal2004 C11) As a resultηBrsquos stellar parameters evolutionary stateorbit and influence on the evolution ofηA are poorly known

Currently the best constraints on the stellar properties ofηB come from photoionization modeling of the ldquoWeigelt blobsrdquodense slow-moving ejecta in the vicinity of the binary system(Weigelt amp Ebersberger 1986) Verner et al (2005) initially char-acterizedηB as a mid-O to WN supergiant More recent workby Mehner et al (2010) tightly constrains the effective tempera-ture of ηB (Teff sim 37 000 minus 43 000 K) but not its luminosity(logLL⊙ sim 5 minus 6) resulting in a larger range of allowed stellarparameters

Constraints on the wind parameters ofηB come from ex-tended X-ray monitoring by theRossi X-ray Timing Explorer(RXTE) Chandra XMM and Suzakusatellites (Ishibashi et al1999 Corcoran 2005 Hamaguchi et al 2007 Corcoran et al2010) The periodic nature minimum around periastron andhard-ness (up to 10 keV) ofη CarrsquosRXTElight curve are all character-istics of a highly eccentric CWB the variable X-ray emission aris-ing in a wind-wind collision (WWC) zone formed between the twostars (Pittard amp Corcoran 2002 Okazaki et al 2008 Parkin et al2009 2011 Corcoran et al 2010 hereafter PC02 O08 P09 P11and C10 respectively) The hardness of the X-rays requiresthatηBhave a high wind terminal speed ofsim 3000 km sminus1 and detailedmodeling of the momentum balance between the two shock frontssuggests a mass-loss rate ofsim 10minus5M⊙ yrminus1 (PC02 O08 P09P11)

Proper numerical modeling ofη Carrsquos WWC remains a chal-lenge mainly because it requires a full three-dimensional(3-D)treatment since orbital motion especially during periastron can beimportant or even dominant affecting the shape and dynamics ofthe WWC region (O08 P09 P11) Most hydrodynamical simula-tions of η Car have been two-dimensional (2-D) neglecting theeffects of orbital motion for simplicity (Pittard 1998 2000 PC02Henley 2005) Until very recently (O08 P11) fully 3-D simula-tions were computationally impractical

When it comes to reproducing observational diagnostics ofη Car from hydrodynamical simulations of its colliding winds thefocus has been almost exclusively on X-rays One drawback ofthisis that models forη Car at other wavelengths have been mostly phe-nomenological offering only qualitative explanations for the vastarray of complicated observations This makes it difficult to test andrefine models or quantitatively constrain the physical parameters ofthe system An excellent example is the lack of consensus regard-ing η Carrsquos orbital orientation The majority favor an orbit in whichηB is behindηA during periastron (Damineli 1996 PC02 Corco-ran 2005 Hamaguchi et al 2007 Nielsen et al 2007a Damineli etal 2008b Henley et al 2008 O08 P09 P11 Groh et al 2010bRichardson et al 2010) But others placeηB on the near side ofηAat periastron (Falceta-Goncalves et al 2005 Abraham et al 2005bAbraham amp Falceta-Goncalves 2007 Kashi amp Soker 2007 2008Falceta-Goncalves amp Abraham 2009) Some claim that the orienta-tion is not well established at all (Mehner et al 2011)

A more fundamental drawback of focusing purely on X-raysor other spatially-unresolved data is that any derived orbit is am-biguous with respect to itsabsoluteorientation on the skyany or-bital orientation derived solely from fitting the X-ray datacan berotated on the sky about the observerrsquos line-of-sight and still matchthe observations A degeneracy also exists in the orbital inclinationwith models that assumei asymp 45 andi asymp 135 both capable of fit-ting the observedRXTElight curve However high-resolution spa-tial information is not enough moderate-resolution spectral data is

needed to determine the velocity structure of the emitting gas andthus fully constrain the orbital orientation As a result using X-raydata alone it is impossible to determine the 3-D alignment or mis-alignment of the orbital axis with the Homunculus polar axis orthe direction of the orbit It is commonlyassumedthat the orbitalaxis is aligned with the Homunculus polar axis but to date neithermodeling nor observations have unambiguously demonstrated thatthis is the case Knowing the orbitrsquos orientation is key to constrain-ing theories for the cause of the Great Eruption and formation of theHomunculus (ie single star versus binary interactionmerger sce-narios Iben 1999 Dwarkadas amp Owocki 2002 Smith et al 2003aSoker 2007 Smith 2009 2011 Smith amp Frew 2011) Furthermorea precise set of orbital parameters would lay the groundworkfororbital modeling to determine the stellar masses

In a recent attempt to characterizeη Carrsquos interactingwinds Gull et al (2009 hereafter G09) presented an analysis ofHSTSTIS observations taken between 1998 and 2004 identifyingspatially-extended (up to08primeprime) velocity-resolved forbidden emis-sion lines from low- and high-ionization1 speciesHSTSTIS imag-ing spectroscopy is ideal for moving beyond X-ray signatures as ituniquely provides the spatial (sim 01primeprime) and spectral (R sim 8 000)resolution necessary to separate the spectra ofη Carrsquos centralsource and nearby circumstellar ejecta from those of the Homuncu-lus and other surrounding material Moreover this high-ionizationforbidden emission is phase-locked which strongly suggests it isregulated by the orbital motion ofηB Observed spectro-images arealso highly dependent on the PA2 of the HSTSTIS slit implyingthat they contain valuable geometrical information This opens upthe possibility of obtainingηBrsquos orbital stellar and wind parame-ters through proper modeling of the extended forbidden lineemis-sion

This paper presents a detailed 3-D dynamical model for thebroad components of the high-ionization forbidden line emissionobserved inη Car using theHSTSTIS Our model is based on theresults of full 3-D Smoothed Particle Hydrodynamics (SPH) simu-lations ofη Carrsquos colliding winds (sect 32 and41) Radiative trans-fer calculations performed with a modified version of the SPLASHcode (Price 2007) are used with IDL routines to generate syntheticspectro-images of [FeIII ] emission line structures at various orbitalphases and STIS slit PAs (sect 34) Through a parameter study thatvaries the orbital inclination the angle that the line-of-sight makeswith the apastron side of the semi-major axis and the PA on thesky of the projected orbital axis we are able to tightly constrainfor the first time theabsolute(3-D) orientation and direction ofη Carrsquos orbit (sect 4) showing in particular that the orbital axis isclosely aligned in 3-D with the inferred polar axis of the Homuncu-lus nebula A discussion of the results and this derived orientationare insect 5 sect 6 summarizes our conclusions and outlines the direc-tion of future work We begin (sect 2) with a brief summary of theobservations used in this paper

2 THE OBSERVATIONS

This paper uses the sameHSTSTIS data described in G09 (see theirTable 1) Extracted portions of observations recorded fromMarch1998 to March 2004 with the STIS CCD (00507primeprime pixelminus1 scale)with medium dispersion gratings (R sim 8 000) in combination

1 Low- and high-ionization refer here to atomic species with ionizationpotentials (IPs) below and above the IP of hydrogen 136 eV2 Position Angle measured in degrees from north to east

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 3

Figure 1 Examples of theHSTSTIS spatially-resolved [FeIII ] spectra Top Left AnHSTAdvanced Camera for Surveys (ACS) High Resolution Camera(HRC) image of the Homunculus andη Car with a20primeprime field of view Bottom Left Enlarged central2primeprime field of view with the52primeprime times 01primeprime slit positionedat PA = +69 and directional labels (NW = northwest etc) included for reference in the text Spectro-images in the middle and right-hand columns wererecorded from the central2primeprime times 01primeprime portion of the slit as drawn between labels I and II Top Center Spatially-resolved line profile of [FeIII ] λ4659 inoriginal form recorded atPA = +69 in 2002 July (φ = 082) Top Right The same spectro-image with the continuum subtracted on a spatial row-by-rowbasis The velocity scale referenced to the vacuum rest wavelength of the line isplusmn600 km sminus1 and the color level is proportional to the square root of theintensity Bottom Center Spectro-image of [FeII ] λ4815 shifted by400 km sminus1 used as a template to determine the spatial and spectral ranges where the[Fe III ] image is contaminated by [FeII ] λ4666 emission Bottom Right Same spectro-image as the top right panel but with masks that remove the narrowline contamination and the contamination to the red from nearby [FeII ] λ4666 (see text)

with the52primeprime times01primeprime slit from 1640 to 10100A were used to sam-ple the spectrum of the central core ofη Car Phases of the obser-vationsφ are relative to theRXTEX-ray minimum at 19979604(Corcoran 2005)JDobs = JD 2450799792 + 20240 times φ Solarpanel orientation requirements constrained the STIS slit PAs Thereduced STIS CCD spectra available through the STScI archives(httparchivestscieduprepdsetacar) wereused Compass directions (NW = north-west etc) describe the spa-tial extent of the emission All wavelengths are in vacuum and ve-locities are heliocentric For details see G09 and references therein

Figure 1 shows examples of resolved broad emission from[Fe III ] λ4659 In the top center panel faint spatially- and velocity-resolved emission can be seen against bright nebular emission anddust-scattered stellar radiation Strong narrow line emission fromthe SW ofη Car is also seen The bright continuum close to thewavelength of the wind line of interest is subtracted on a spatialrow-by-row basis in order to isolate the fainter broad forbiddenline emission (top right panel of Figure 1) All spectro-images inthis paper have been processed identically using a portion of thespectrum with no bright narrow- or broad-line contamination Row-by-row subtraction across the stellar position is less successful dueto insufficient correction in the data reduction for small tilts of thespectrum on the CCD (G09)

The bottom right panel of Figure 1 contains the same spectro-image of [FeIII ] λ4659 as the top right panel but with masks thatremove narrow line contamination from the Weigelt blobs and con-

tamination to the red due to the nearby [FeII ] λ4666 wind lineThe masks are intended to remove ldquodistractingrdquo emission featuresnot relevant to the work in this paper displaying only the observedbroad structures that are the focus of the modeling (outlined inwhite) To determine the spatial and spectral ranges where [FeII ]λ4666 contaminates the [FeIII ] λ4659 image we use as a tem-plate the uncontaminated spectro-image of the bright [FeII ] λ4815line (bottom center panel of Figure 1) We also compare the [Fe III ]λ4659 images to those of the [FeIII ] λ4702 and [NII ] λ5756 lineswhich form in nearly identical conditions as they have very similarcritical densities and IPs (Table 3 of G09) A detailed discussionof the observations and masking procedure for all spectro-imagesmodeled in this paper is in Appendix A (available in the onlineversion of this paper - see Supporting Information)

21 The Key Observational Constraints Modeled

Three key features observed in spectro-images of the high-ionization forbidden line emission can be used to constrainthe 3-Dorientation ofη Carrsquos orbit Each provides important clues aboutthe nature and orbital variation ofη Carrsquos interacting winds Webriefly summarize these below

ccopy 2011 RAS MNRAS000 1ndash23

4 Madura et al

211 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

Figure 2 displays observed spectro-images of [FeIII ] λ4659recorded at slit PA = +38 on 2003 May 5 (φ = 0976) show-ing spatially-extended (up tosim 035primeprime) emission in the form ofvery distinct nearly complete arcs that are entirely blue-shiftedup to sim minus475 km sminus1 Several weaker [FeIII ] lines nearby inthe spectrum while blended show no evidence of a spatially-extended (gt 01primeprime) red component and no other high-ionizationforbidden lines show an extended red component at this position(G09) To illustrate this the bottom right panel of Figure 2containsa continuum-subtracted spectro-image of [NII ] λ5756 taken at thesame orbital phase and slit PA The IP (145 eV) and critical density(3 times 107 cmminus3) of [N II ] λ5756 are very similar to that of [FeIII ]λ4659 (162 eV andsim 107 cmminus3) meaning that their spatially-extended emission forms in nearly identical regions and viathesame physical mechanism The [NII ] λ5756 line is strong and lo-cated in a spectral region with very few other lines Unlike [FeIII ]λ4659 there is no contamination to the red of [NII ] λ5756 mak-ing it ideal for demonstrating that there is no spatially-extendedred-shifted broad high-ionization forbidden line emission

Of particular importance are the asymmetric shape and inten-sity of these emission arcs Both arcs extend to nearly the samespatial distance from the central core but the upper arc is notice-ably dimmer and stretches farther to the blue tosim minus475 km sminus1The lower arc is brighter but only extends tosim minus400 km sminus1 Ev-ery high-ionization forbidden line observed at this orbital phase andslit PA exhibits these asymmetries in intensity and velocity (figures6 minus 9 of G09) indicating that they are independent of the IP andcritical density of the line and intrinsic to the shape and distributionof the photoionized extended wind material in which the lines formAs such the shape and asymmetry of the blue-shifted emission arcsmay be used to help constrain the orbital orientation

212 Constraint 2 Variations with Orbital Phase at ConstantSlit PA =minus28

Let us focus next on shifts of the high-ionization forbiddenemis-sion with orbital phase Figure 11 of G09 shows sets of six spec-tra of [FeIII ] λ4659 andλ4702 recorded at select phases at slitPA = minus28 During the two minima atφ = 0045 and 1040 (rows1 and 5 of figure 11 of G09) the broad [FeIII ] emission is absentBy φ = 0213 (row 2) andφ = 1122 (row 6sim 8 months after theX-ray minimum) it strongly reappears Images atφ = 0407 aresimilar to those atφ = 0213 and 1122 Byφ = 0952 emissionabovesim 150 km sminus1 disappears This phase dependence in the[Fe III ] emission especially the disappearance during periastronstrongly indicates that it is tied to the orbital motion ofηB

Another important observational feature is the presence ofspatially-extendedred-shiftedemission to the NW in addition toextended blue-shifted emission to the SE at phases far frompe-riastron This is in contrast to the entirely blue-shifted arcs seenfor slit PA = +38 indicating that the STIS slit at PA =minus28

is sampling different emitting portions ofη Carrsquos extended windstructures even at similar orbital phases

213 Constraint 3 Doppler Shift Correlations with OrbitalPhase and Slit PA

The final set of observations focuses on changes with slit PA lead-ing up to periastron Figures 12 and 13 of G09 illustrate the be-havior of the [FeIII ] emission for various slit PAs at select phases

Figure 2 Spectro-images recorded 2003 May 5 (φ = 0976) Top LeftPanelHSTACS HRC image of the central2primeprime of η Car with the2primeprime longportion of the STIS slit at PA = +38 overlaid The locations of Weigeltblobs B C and D are indicated as is the direction of north Top Right PanelContinuum-subtracted spectro-image of [FeIII ] λ4659 Emission appearsas a pair of completely blue-shifted arcs Color is proportional to the squareroot of the intensity and the velocity scale isplusmn600 km sminus1 Weak emissionto the red is entirely due to contamination by [FeII ] λ4666 while weaknarrow emission is centered atsim minus40 km sminus1 Bottom Left Panel Samespectro-image but with masks that remove the line contamination BottomRight Panel Continuum-subtracted spectro-image of [NII ] λ5756 includedto demonstrate that at this phase and STIS PA the high-ionization forbiddenlines show no evidence of broad spatially-extended red-shifted emission

The key point to take away from this particular data set is that awayfrom periastron the spatially-extended [FeIII ] emission is almostentirely blue-shifted for positive slit PAs =+22 to +70 but ispartially red-shifted for negative PAs most notably PA =minus82

3 A 3-D DYNAMICAL MODEL FOR THE BROADHIGH-IONIZATION FORBIDDEN LINE EMISSION

31 Why Model [Fe III] λ4659 Emission

Table 3 of G09 lists the various forbidden emission lines observedin η Car However there are several important reasons to focus par-ticular attention on [FeIII ] λ4659 emission

First the physical mechanism for the formation of forbiddenlines is well understood (Appendix B online version) Moreoveremission from forbidden lines is optically thin Thus forbidden lineradiation can escape from a nebula much more easily than radiationfrom an optically thick resonance line which is emitted andreab-sorbed many times (Hartman 2003) This is of great value whenstudying an object so enshrouded by circumstellar materialsinceone does not have to model complicated radiative transfer effects

[Fe III ] is considered rather than a lower ionization line of[Fe II ] becausethe bulk of the[Fe III ] emission arises in regions thatare directly photoionized byηB (Verner et al 2005 G09 Mehner etal 2010) No intrinsic [FeIII ] emission is expected fromηA Thisis based on detailed theoretical models by H01 and H06 whichshow that inηArsquos envelope Fe2+ only exists in regions where theelectron density is two-to-four orders of magnitude higherthan the

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 5

critical density of the [FeIII ] λ4659 line Since Fe0 needs162 eVradiation (or collisions) to reach the Fe2+ state most of the [FeIII ]emission arises in areas directly photoionized byηB

In comparison Fe0 only needs 79 eV radiation or collisions toionize to Fe+ which can form in the wind ofηA (without ηBrsquos in-fluence) andor near the wind-wind interaction regions in areas ex-cited by mid-UV radiation filtered byηArsquos dense wind Collisionsand photoexcitation to upper Fe+ energy levels can also populatemany metastable levels As a result [FeII ] emission is far morecomplicated and originates from lower excitation lower density re-gions on much larger spatial scales (H01 H06 G09 Mehner etal2010) Because of this complexity the modeling of [FeII ] emissionis deferred to future work

The IP of 162 eV required for Fe2+ also means that the[Fe III ] emission forms in regions where hydrogen is ionized buthelium is still neutral In contrast both Ar2+ and Ne2+ have IPsgreater than246 eV Therefore [ArIII ] and [NeIII ] emission arisein areas where helium is singly ionized Modeling [FeIII ] is thusmore straightforward as one does not have to worry about the twodifferent types of ionization structure possible (one due to H andone due to He) which depend on the spectrum of ionizing radia-tion and the abundance of helium (Osterbrock 1989)

[Fe III ] λ4659 is chosen over the similar emission line of [NII ]λ5756 in order to avoid potential complications due to intrinsic[N II ] emission in the extended wind ofηA [N II ] emission canform in a broad zone between 100 and 1000Rlowast (sim 30 minus 300 AU)of ηA and is sensitive to its wind temperature and mass-loss rate(H01) By focusing on [FeIII ] one avoids having to include anyintrinsic forbidden line emission fromηA

The modeling in this paper focuses solely on thebroad[Fe III ]emission features that are thought to arise in the dense mod-erate velocity (sim 100 minus 600 km sminus1) extended primary windand WWC regions The much narrower ( 50 km sminus1) emis-sion features that form in the Weigelt blobs and other denseslow-moving equatorial ejecta fromη Carrsquos smaller eruptionin the 1890s (Weigelt amp Ebersberger 1986 Davidson et al 19951997 Ishibashi et al 2003 Smith et al 2004 Gull et al 2009Mehner et al 2010) are not modeled Any possible effects of localdust formation are neglected for simplicity as not enough informa-tion is available to realistically include them at this time(Williams2008 Mehner et al 2010)

As all observed high-ionization forbidden lines show the samebasic spatial and temporal features in their broad emission with anydifferences in size or location attributable to differences in the IPand critical density of the specific line of interest focusing solelyon [FeIII ] λ4659 should not significantly bias the overall conclu-sions which should extend to the other high-ionization forbiddenlines as well Values of the transition probability (A21 = 044 sminus1)statistical weights (g1 = g2 = 9) and line transition frequency(ν21 = 6435 times 1014 sminus1) for [Fe III ] λ4659 all come fromNahar amp Pradhan (1996) Values for the collision strengths (Ω12)come from Zhang (1996) A solar abundance of iron is also usedconsistent with the works of H01 Verner et al (2005) and H06

32 The 3-D SPH Code and General Problem Setup

The numerical simulations in this paper were performed withthesame 3-D SPH code used in O08 The stellar winds are modeledby an ensemble of gas particles that are continuously ejected witha given outward velocity at a radius just outside each star For sim-plicity both winds are taken to be adiabatic with the same initialtemperature (35 000 K) at the stellar surfaces and coasting with-

Table 1 Stellar Wind and Orbital Parameters of the 3-D SPH Simulation

Parameter ηA ηB

Mass (M⊙) 90 30Radius (R⊙) 90 30Mass-Loss Rate (M⊙ yrminus1) 10minus3 10minus5

Wind Terminal Velocity (km sminus1) 500 3000Orbital Period (days) 2024Orbital Eccentricitye 09Semi-major Axis Lengtha (AU) 154

out any net external forces assuming that gravitational forces areeffectively canceled by radiative driving terms (O08) Thegas hasnegligible self-gravity and adiabatic cooling is included

In a standardxyz Cartesian coordinate system the binary or-bit is set in thexy plane with the origin at the system center-of-mass and the orbital major axis along thex-axis The two starsorbit counter-clockwise when looking down on the orbital planealong the+z axis Simulations are started with the stars at apas-tron and run for multiple consecutive orbits By convention t = 0(φ = 0) is defined to be at periastron passage

To match thesim plusmn07primeprime scale of the STIS observations at theadopted distance of 23 kpc to theη Car system (Smith 2006b) theouter simulation boundary is set atr = plusmn105a from the systemcenter-of-mass wherea is the length of the orbital semi-major axis(a = 154 AU) Particles crossing this boundary are removed fromthe simulation We note that the SPH formalism is ideally suitedfor such large-scale 3-D simulations as compared to grid-basedhydrodynamics codes (Price 2004 Monaghan 2005)

Table 1 summarizes the stellar wind and orbital parametersused in the modeling which are consistent with those derived fromthe observations (PC02 H01 H06 C11) with the exception of thewind temperature ofηA The effect of the wind temperature on thedynamics of the high-velocity wind collision is negligible(O08)Note that the simulation adopts the higher mass-loss rate for ηAderived by Davidson et al (1995) Cox et al (1995) H01 andH06rather than the factor of four lower mass-loss rate assumed whenanalyzing X-ray signatures (PC02 O08 P09 P11 C11) Effects ofthe adopted value of the primary mass-loss rate on the forbiddenline emission will be the subject of a future paper

The publicly available software SPLASH (Price 2007) is usedto visualize the 3-D SPH code output SPLASH differs from othertools because it is designed to visualize SPH data using SPH algo-rithms There are a number of benefits to using SPLASH and thereader is referred to Price (2007) and the SPLASH userguide forthese and discussions on the interpolation algorithms

33 Generation of Synthetic Slit Spectro-Images

The 3-D SPH simulation provides the time-dependent 3-D den-sity and temperature structure ofη Carrsquos interacting winds on spa-tial scales comparable to those of theHSTSTIS observations Thisforms the basis of our 3-D dynamical model Unfortunately it iscurrently not possible to perform full 3-D simulations ofη Car inwhich the radiative transfer is properly coupled to the hydrodynam-ics (Paardekooper 2010) Instead the radiative transfer calculationshere are performed as post-processing on the 3-D SPH simulationoutput This should not strongly affect the results so long as the ma-terial that is photoionized byηB responds nearly instantaneously toits UV flux In other words as long as the timescale for the recom-

ccopy 2011 RAS MNRAS000 1ndash23

6 Madura et al

bination ofe + Fe2+ rarr Fe+ is very small relative to the orbitaltimescale the calculations should be valid

The recombination timescale isτrec = 1(αrecne) secondswhereαrec(T ) is the recombination rate coefficient (in units ofcm3 sminus1) at temperatureT andne is the electron number densityFor T sim 104 K αrec(T ) asymp 4 times 10minus12 cm3 sminus1 (Nahar 1997)Since densities near the critical density of the line are theprimaryfocusne sim 107 cmminus3 this givesτrec asymp 7 hours which is muchsmaller than the orbital timescale even during periastronpassagewhich takes approximately one month Any possible time-delay ef-fects should not strongly affect the results as the light-travel-timeto material at distances ofsim 05primeprime in η Car is only about one week

331 Summary of the Basic Procedure

Synthetic slit spectro-images are generated using a combination ofInteractive Data Language (IDL) routines and radiative transfer cal-culations performed with a modified version of the SPLASH (Price2007) code Here we outline the basic procedure with the specificsdiscussed in the following subsections

Nearly all of the required calculations are performed withinSPLASH which reads in the 3-D SPH code output for a specificorbital phase rotates the data to a desired orbital orientation on thesky and computes the line-of-sight velocity for all of the materialNext is the computation of the ionization volume created byηBwhere Fe+ is photoionized to Fe2+ It is assumed that any materialwithin this volume is in collisional ionization equilibrium and thatno material withT gt 250 000 K emits All other material in thephotoionization volume has its forbidden line emissivity calculatedusing Equation (13) derived below Material located outside thephotoionization volume does not emit

The intensityI is computed by performing a line-of-sight in-tegration of the emissivity at each pixel resulting in an image ofthe spatial distribution of the [FeIII ] intensity projected on the skyThis is done for each velocityvbin used along the dispersion axisof the synthetic slit in the velocity range of interest resulting ina set of intensity images The individual [FeIII ] λ4659 intensityimages are then combined and convolved with theHSTSTIS re-sponse using IDL routines in order to create a synthetic positionversus velocity spectro-image for comparison to the observations

332 Defining the Binary Orientation Relative to the Observer

With the two stars orbiting in thexy plane the 3-D orientation ofthe binary relative to the observer is defined by the orbital inclina-tion i the prograde direction angleθ that the orbital plane projec-tion of the observerrsquos line-of-sight makes with the apastron side ofthe semi-major axis3 and the position angleon the skyof the+zorbital axis PAz (Figure 3)

Following the standard definition for binary systemsi is theangle that the line-of-sight makes with the+z axis An i = 0 isa face-on orbit with the observerrsquos line-of-sight along the+z axisand the two stars orbiting counter-clockwise on the sky Ani = 90

places the line-of-sight in the orbitalxy plane whilei = 180 is aface-on orbit with the two stars orbiting clockwise on the sky

For i = 90 a value ofθ = 0 has the observer looking alongthe+x axis (along the semi-major axis on the apastron side of thesystem) while aθ = 90 has the observer looking along the+y

3 θ is the same as the angleφ defined in figure 3 of O08

Figure 3 Diagrams illustrating the observerrsquos position Top Schematicdefining the inclination anglei that the observerrsquos line-of-sight makes withthe +z orbital axis and the equatorial projection angleθ of the line-of-sight relative to the apastron side of the semi-major axisx The backgroundorthogonal planes show slices of density from the 3-D SPH simulation atapastron in thexy orbital plane and theyz plane perpendicular to the or-bital plane and major axis Bottom Diagram defining the position angle onthe skyPAz of the+z orbital axis (blue) measured in degrees counter-clockwise of north (N) The binary orbit projected on the skyis shown inyellow as are the semi-major (red) and semi-minor (green) axes The smallinset to the left is aHSTWFPC2 image of the Homunculus (Credit NASAESA and the Hubble SM4 ERO Team) included for reference

axis In the conventional notation of binary orbits the lsquoargument ofperiapsisrsquoω = 270 minus θ

PAz defines the position angle on the sky of the+z orbital axisand is measured in degrees counter-clockwise of N APAz = 312

aligns the projected orbital axis with the Homunculus polaraxis(Davidson et al 2001 Smith 2006b 2009) and has+z pointingNW on the sky APAz = 42 places the orbital axis perpen-dicular to the Homunculus polar axis with+z pointing NE APAz = 132 (222) is also aligned with (perpendicular to) theHomunculus polar axis and has+z pointing SE (SW) on the sky

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Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

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14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

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Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

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Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

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18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

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Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

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Davidson K 1999 Eta Carinae at The Millennium 179 304

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Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

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Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

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Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

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This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 3: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 3

Figure 1 Examples of theHSTSTIS spatially-resolved [FeIII ] spectra Top Left AnHSTAdvanced Camera for Surveys (ACS) High Resolution Camera(HRC) image of the Homunculus andη Car with a20primeprime field of view Bottom Left Enlarged central2primeprime field of view with the52primeprime times 01primeprime slit positionedat PA = +69 and directional labels (NW = northwest etc) included for reference in the text Spectro-images in the middle and right-hand columns wererecorded from the central2primeprime times 01primeprime portion of the slit as drawn between labels I and II Top Center Spatially-resolved line profile of [FeIII ] λ4659 inoriginal form recorded atPA = +69 in 2002 July (φ = 082) Top Right The same spectro-image with the continuum subtracted on a spatial row-by-rowbasis The velocity scale referenced to the vacuum rest wavelength of the line isplusmn600 km sminus1 and the color level is proportional to the square root of theintensity Bottom Center Spectro-image of [FeII ] λ4815 shifted by400 km sminus1 used as a template to determine the spatial and spectral ranges where the[Fe III ] image is contaminated by [FeII ] λ4666 emission Bottom Right Same spectro-image as the top right panel but with masks that remove the narrowline contamination and the contamination to the red from nearby [FeII ] λ4666 (see text)

with the52primeprime times01primeprime slit from 1640 to 10100A were used to sam-ple the spectrum of the central core ofη Car Phases of the obser-vationsφ are relative to theRXTEX-ray minimum at 19979604(Corcoran 2005)JDobs = JD 2450799792 + 20240 times φ Solarpanel orientation requirements constrained the STIS slit PAs Thereduced STIS CCD spectra available through the STScI archives(httparchivestscieduprepdsetacar) wereused Compass directions (NW = north-west etc) describe the spa-tial extent of the emission All wavelengths are in vacuum and ve-locities are heliocentric For details see G09 and references therein

Figure 1 shows examples of resolved broad emission from[Fe III ] λ4659 In the top center panel faint spatially- and velocity-resolved emission can be seen against bright nebular emission anddust-scattered stellar radiation Strong narrow line emission fromthe SW ofη Car is also seen The bright continuum close to thewavelength of the wind line of interest is subtracted on a spatialrow-by-row basis in order to isolate the fainter broad forbiddenline emission (top right panel of Figure 1) All spectro-images inthis paper have been processed identically using a portion of thespectrum with no bright narrow- or broad-line contamination Row-by-row subtraction across the stellar position is less successful dueto insufficient correction in the data reduction for small tilts of thespectrum on the CCD (G09)

The bottom right panel of Figure 1 contains the same spectro-image of [FeIII ] λ4659 as the top right panel but with masks thatremove narrow line contamination from the Weigelt blobs and con-

tamination to the red due to the nearby [FeII ] λ4666 wind lineThe masks are intended to remove ldquodistractingrdquo emission featuresnot relevant to the work in this paper displaying only the observedbroad structures that are the focus of the modeling (outlined inwhite) To determine the spatial and spectral ranges where [FeII ]λ4666 contaminates the [FeIII ] λ4659 image we use as a tem-plate the uncontaminated spectro-image of the bright [FeII ] λ4815line (bottom center panel of Figure 1) We also compare the [Fe III ]λ4659 images to those of the [FeIII ] λ4702 and [NII ] λ5756 lineswhich form in nearly identical conditions as they have very similarcritical densities and IPs (Table 3 of G09) A detailed discussionof the observations and masking procedure for all spectro-imagesmodeled in this paper is in Appendix A (available in the onlineversion of this paper - see Supporting Information)

21 The Key Observational Constraints Modeled

Three key features observed in spectro-images of the high-ionization forbidden line emission can be used to constrainthe 3-Dorientation ofη Carrsquos orbit Each provides important clues aboutthe nature and orbital variation ofη Carrsquos interacting winds Webriefly summarize these below

ccopy 2011 RAS MNRAS000 1ndash23

4 Madura et al

211 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

Figure 2 displays observed spectro-images of [FeIII ] λ4659recorded at slit PA = +38 on 2003 May 5 (φ = 0976) show-ing spatially-extended (up tosim 035primeprime) emission in the form ofvery distinct nearly complete arcs that are entirely blue-shiftedup to sim minus475 km sminus1 Several weaker [FeIII ] lines nearby inthe spectrum while blended show no evidence of a spatially-extended (gt 01primeprime) red component and no other high-ionizationforbidden lines show an extended red component at this position(G09) To illustrate this the bottom right panel of Figure 2containsa continuum-subtracted spectro-image of [NII ] λ5756 taken at thesame orbital phase and slit PA The IP (145 eV) and critical density(3 times 107 cmminus3) of [N II ] λ5756 are very similar to that of [FeIII ]λ4659 (162 eV andsim 107 cmminus3) meaning that their spatially-extended emission forms in nearly identical regions and viathesame physical mechanism The [NII ] λ5756 line is strong and lo-cated in a spectral region with very few other lines Unlike [FeIII ]λ4659 there is no contamination to the red of [NII ] λ5756 mak-ing it ideal for demonstrating that there is no spatially-extendedred-shifted broad high-ionization forbidden line emission

Of particular importance are the asymmetric shape and inten-sity of these emission arcs Both arcs extend to nearly the samespatial distance from the central core but the upper arc is notice-ably dimmer and stretches farther to the blue tosim minus475 km sminus1The lower arc is brighter but only extends tosim minus400 km sminus1 Ev-ery high-ionization forbidden line observed at this orbital phase andslit PA exhibits these asymmetries in intensity and velocity (figures6 minus 9 of G09) indicating that they are independent of the IP andcritical density of the line and intrinsic to the shape and distributionof the photoionized extended wind material in which the lines formAs such the shape and asymmetry of the blue-shifted emission arcsmay be used to help constrain the orbital orientation

212 Constraint 2 Variations with Orbital Phase at ConstantSlit PA =minus28

Let us focus next on shifts of the high-ionization forbiddenemis-sion with orbital phase Figure 11 of G09 shows sets of six spec-tra of [FeIII ] λ4659 andλ4702 recorded at select phases at slitPA = minus28 During the two minima atφ = 0045 and 1040 (rows1 and 5 of figure 11 of G09) the broad [FeIII ] emission is absentBy φ = 0213 (row 2) andφ = 1122 (row 6sim 8 months after theX-ray minimum) it strongly reappears Images atφ = 0407 aresimilar to those atφ = 0213 and 1122 Byφ = 0952 emissionabovesim 150 km sminus1 disappears This phase dependence in the[Fe III ] emission especially the disappearance during periastronstrongly indicates that it is tied to the orbital motion ofηB

Another important observational feature is the presence ofspatially-extendedred-shiftedemission to the NW in addition toextended blue-shifted emission to the SE at phases far frompe-riastron This is in contrast to the entirely blue-shifted arcs seenfor slit PA = +38 indicating that the STIS slit at PA =minus28

is sampling different emitting portions ofη Carrsquos extended windstructures even at similar orbital phases

213 Constraint 3 Doppler Shift Correlations with OrbitalPhase and Slit PA

The final set of observations focuses on changes with slit PA lead-ing up to periastron Figures 12 and 13 of G09 illustrate the be-havior of the [FeIII ] emission for various slit PAs at select phases

Figure 2 Spectro-images recorded 2003 May 5 (φ = 0976) Top LeftPanelHSTACS HRC image of the central2primeprime of η Car with the2primeprime longportion of the STIS slit at PA = +38 overlaid The locations of Weigeltblobs B C and D are indicated as is the direction of north Top Right PanelContinuum-subtracted spectro-image of [FeIII ] λ4659 Emission appearsas a pair of completely blue-shifted arcs Color is proportional to the squareroot of the intensity and the velocity scale isplusmn600 km sminus1 Weak emissionto the red is entirely due to contamination by [FeII ] λ4666 while weaknarrow emission is centered atsim minus40 km sminus1 Bottom Left Panel Samespectro-image but with masks that remove the line contamination BottomRight Panel Continuum-subtracted spectro-image of [NII ] λ5756 includedto demonstrate that at this phase and STIS PA the high-ionization forbiddenlines show no evidence of broad spatially-extended red-shifted emission

The key point to take away from this particular data set is that awayfrom periastron the spatially-extended [FeIII ] emission is almostentirely blue-shifted for positive slit PAs =+22 to +70 but ispartially red-shifted for negative PAs most notably PA =minus82

3 A 3-D DYNAMICAL MODEL FOR THE BROADHIGH-IONIZATION FORBIDDEN LINE EMISSION

31 Why Model [Fe III] λ4659 Emission

Table 3 of G09 lists the various forbidden emission lines observedin η Car However there are several important reasons to focus par-ticular attention on [FeIII ] λ4659 emission

First the physical mechanism for the formation of forbiddenlines is well understood (Appendix B online version) Moreoveremission from forbidden lines is optically thin Thus forbidden lineradiation can escape from a nebula much more easily than radiationfrom an optically thick resonance line which is emitted andreab-sorbed many times (Hartman 2003) This is of great value whenstudying an object so enshrouded by circumstellar materialsinceone does not have to model complicated radiative transfer effects

[Fe III ] is considered rather than a lower ionization line of[Fe II ] becausethe bulk of the[Fe III ] emission arises in regions thatare directly photoionized byηB (Verner et al 2005 G09 Mehner etal 2010) No intrinsic [FeIII ] emission is expected fromηA Thisis based on detailed theoretical models by H01 and H06 whichshow that inηArsquos envelope Fe2+ only exists in regions where theelectron density is two-to-four orders of magnitude higherthan the

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 5

critical density of the [FeIII ] λ4659 line Since Fe0 needs162 eVradiation (or collisions) to reach the Fe2+ state most of the [FeIII ]emission arises in areas directly photoionized byηB

In comparison Fe0 only needs 79 eV radiation or collisions toionize to Fe+ which can form in the wind ofηA (without ηBrsquos in-fluence) andor near the wind-wind interaction regions in areas ex-cited by mid-UV radiation filtered byηArsquos dense wind Collisionsand photoexcitation to upper Fe+ energy levels can also populatemany metastable levels As a result [FeII ] emission is far morecomplicated and originates from lower excitation lower density re-gions on much larger spatial scales (H01 H06 G09 Mehner etal2010) Because of this complexity the modeling of [FeII ] emissionis deferred to future work

The IP of 162 eV required for Fe2+ also means that the[Fe III ] emission forms in regions where hydrogen is ionized buthelium is still neutral In contrast both Ar2+ and Ne2+ have IPsgreater than246 eV Therefore [ArIII ] and [NeIII ] emission arisein areas where helium is singly ionized Modeling [FeIII ] is thusmore straightforward as one does not have to worry about the twodifferent types of ionization structure possible (one due to H andone due to He) which depend on the spectrum of ionizing radia-tion and the abundance of helium (Osterbrock 1989)

[Fe III ] λ4659 is chosen over the similar emission line of [NII ]λ5756 in order to avoid potential complications due to intrinsic[N II ] emission in the extended wind ofηA [N II ] emission canform in a broad zone between 100 and 1000Rlowast (sim 30 minus 300 AU)of ηA and is sensitive to its wind temperature and mass-loss rate(H01) By focusing on [FeIII ] one avoids having to include anyintrinsic forbidden line emission fromηA

The modeling in this paper focuses solely on thebroad[Fe III ]emission features that are thought to arise in the dense mod-erate velocity (sim 100 minus 600 km sminus1) extended primary windand WWC regions The much narrower ( 50 km sminus1) emis-sion features that form in the Weigelt blobs and other denseslow-moving equatorial ejecta fromη Carrsquos smaller eruptionin the 1890s (Weigelt amp Ebersberger 1986 Davidson et al 19951997 Ishibashi et al 2003 Smith et al 2004 Gull et al 2009Mehner et al 2010) are not modeled Any possible effects of localdust formation are neglected for simplicity as not enough informa-tion is available to realistically include them at this time(Williams2008 Mehner et al 2010)

As all observed high-ionization forbidden lines show the samebasic spatial and temporal features in their broad emission with anydifferences in size or location attributable to differences in the IPand critical density of the specific line of interest focusing solelyon [FeIII ] λ4659 should not significantly bias the overall conclu-sions which should extend to the other high-ionization forbiddenlines as well Values of the transition probability (A21 = 044 sminus1)statistical weights (g1 = g2 = 9) and line transition frequency(ν21 = 6435 times 1014 sminus1) for [Fe III ] λ4659 all come fromNahar amp Pradhan (1996) Values for the collision strengths (Ω12)come from Zhang (1996) A solar abundance of iron is also usedconsistent with the works of H01 Verner et al (2005) and H06

32 The 3-D SPH Code and General Problem Setup

The numerical simulations in this paper were performed withthesame 3-D SPH code used in O08 The stellar winds are modeledby an ensemble of gas particles that are continuously ejected witha given outward velocity at a radius just outside each star For sim-plicity both winds are taken to be adiabatic with the same initialtemperature (35 000 K) at the stellar surfaces and coasting with-

Table 1 Stellar Wind and Orbital Parameters of the 3-D SPH Simulation

Parameter ηA ηB

Mass (M⊙) 90 30Radius (R⊙) 90 30Mass-Loss Rate (M⊙ yrminus1) 10minus3 10minus5

Wind Terminal Velocity (km sminus1) 500 3000Orbital Period (days) 2024Orbital Eccentricitye 09Semi-major Axis Lengtha (AU) 154

out any net external forces assuming that gravitational forces areeffectively canceled by radiative driving terms (O08) Thegas hasnegligible self-gravity and adiabatic cooling is included

In a standardxyz Cartesian coordinate system the binary or-bit is set in thexy plane with the origin at the system center-of-mass and the orbital major axis along thex-axis The two starsorbit counter-clockwise when looking down on the orbital planealong the+z axis Simulations are started with the stars at apas-tron and run for multiple consecutive orbits By convention t = 0(φ = 0) is defined to be at periastron passage

To match thesim plusmn07primeprime scale of the STIS observations at theadopted distance of 23 kpc to theη Car system (Smith 2006b) theouter simulation boundary is set atr = plusmn105a from the systemcenter-of-mass wherea is the length of the orbital semi-major axis(a = 154 AU) Particles crossing this boundary are removed fromthe simulation We note that the SPH formalism is ideally suitedfor such large-scale 3-D simulations as compared to grid-basedhydrodynamics codes (Price 2004 Monaghan 2005)

Table 1 summarizes the stellar wind and orbital parametersused in the modeling which are consistent with those derived fromthe observations (PC02 H01 H06 C11) with the exception of thewind temperature ofηA The effect of the wind temperature on thedynamics of the high-velocity wind collision is negligible(O08)Note that the simulation adopts the higher mass-loss rate for ηAderived by Davidson et al (1995) Cox et al (1995) H01 andH06rather than the factor of four lower mass-loss rate assumed whenanalyzing X-ray signatures (PC02 O08 P09 P11 C11) Effects ofthe adopted value of the primary mass-loss rate on the forbiddenline emission will be the subject of a future paper

The publicly available software SPLASH (Price 2007) is usedto visualize the 3-D SPH code output SPLASH differs from othertools because it is designed to visualize SPH data using SPH algo-rithms There are a number of benefits to using SPLASH and thereader is referred to Price (2007) and the SPLASH userguide forthese and discussions on the interpolation algorithms

33 Generation of Synthetic Slit Spectro-Images

The 3-D SPH simulation provides the time-dependent 3-D den-sity and temperature structure ofη Carrsquos interacting winds on spa-tial scales comparable to those of theHSTSTIS observations Thisforms the basis of our 3-D dynamical model Unfortunately it iscurrently not possible to perform full 3-D simulations ofη Car inwhich the radiative transfer is properly coupled to the hydrodynam-ics (Paardekooper 2010) Instead the radiative transfer calculationshere are performed as post-processing on the 3-D SPH simulationoutput This should not strongly affect the results so long as the ma-terial that is photoionized byηB responds nearly instantaneously toits UV flux In other words as long as the timescale for the recom-

ccopy 2011 RAS MNRAS000 1ndash23

6 Madura et al

bination ofe + Fe2+ rarr Fe+ is very small relative to the orbitaltimescale the calculations should be valid

The recombination timescale isτrec = 1(αrecne) secondswhereαrec(T ) is the recombination rate coefficient (in units ofcm3 sminus1) at temperatureT andne is the electron number densityFor T sim 104 K αrec(T ) asymp 4 times 10minus12 cm3 sminus1 (Nahar 1997)Since densities near the critical density of the line are theprimaryfocusne sim 107 cmminus3 this givesτrec asymp 7 hours which is muchsmaller than the orbital timescale even during periastronpassagewhich takes approximately one month Any possible time-delay ef-fects should not strongly affect the results as the light-travel-timeto material at distances ofsim 05primeprime in η Car is only about one week

331 Summary of the Basic Procedure

Synthetic slit spectro-images are generated using a combination ofInteractive Data Language (IDL) routines and radiative transfer cal-culations performed with a modified version of the SPLASH (Price2007) code Here we outline the basic procedure with the specificsdiscussed in the following subsections

Nearly all of the required calculations are performed withinSPLASH which reads in the 3-D SPH code output for a specificorbital phase rotates the data to a desired orbital orientation on thesky and computes the line-of-sight velocity for all of the materialNext is the computation of the ionization volume created byηBwhere Fe+ is photoionized to Fe2+ It is assumed that any materialwithin this volume is in collisional ionization equilibrium and thatno material withT gt 250 000 K emits All other material in thephotoionization volume has its forbidden line emissivity calculatedusing Equation (13) derived below Material located outside thephotoionization volume does not emit

The intensityI is computed by performing a line-of-sight in-tegration of the emissivity at each pixel resulting in an image ofthe spatial distribution of the [FeIII ] intensity projected on the skyThis is done for each velocityvbin used along the dispersion axisof the synthetic slit in the velocity range of interest resulting ina set of intensity images The individual [FeIII ] λ4659 intensityimages are then combined and convolved with theHSTSTIS re-sponse using IDL routines in order to create a synthetic positionversus velocity spectro-image for comparison to the observations

332 Defining the Binary Orientation Relative to the Observer

With the two stars orbiting in thexy plane the 3-D orientation ofthe binary relative to the observer is defined by the orbital inclina-tion i the prograde direction angleθ that the orbital plane projec-tion of the observerrsquos line-of-sight makes with the apastron side ofthe semi-major axis3 and the position angleon the skyof the+zorbital axis PAz (Figure 3)

Following the standard definition for binary systemsi is theangle that the line-of-sight makes with the+z axis An i = 0 isa face-on orbit with the observerrsquos line-of-sight along the+z axisand the two stars orbiting counter-clockwise on the sky Ani = 90

places the line-of-sight in the orbitalxy plane whilei = 180 is aface-on orbit with the two stars orbiting clockwise on the sky

For i = 90 a value ofθ = 0 has the observer looking alongthe+x axis (along the semi-major axis on the apastron side of thesystem) while aθ = 90 has the observer looking along the+y

3 θ is the same as the angleφ defined in figure 3 of O08

Figure 3 Diagrams illustrating the observerrsquos position Top Schematicdefining the inclination anglei that the observerrsquos line-of-sight makes withthe +z orbital axis and the equatorial projection angleθ of the line-of-sight relative to the apastron side of the semi-major axisx The backgroundorthogonal planes show slices of density from the 3-D SPH simulation atapastron in thexy orbital plane and theyz plane perpendicular to the or-bital plane and major axis Bottom Diagram defining the position angle onthe skyPAz of the+z orbital axis (blue) measured in degrees counter-clockwise of north (N) The binary orbit projected on the skyis shown inyellow as are the semi-major (red) and semi-minor (green) axes The smallinset to the left is aHSTWFPC2 image of the Homunculus (Credit NASAESA and the Hubble SM4 ERO Team) included for reference

axis In the conventional notation of binary orbits the lsquoargument ofperiapsisrsquoω = 270 minus θ

PAz defines the position angle on the sky of the+z orbital axisand is measured in degrees counter-clockwise of N APAz = 312

aligns the projected orbital axis with the Homunculus polaraxis(Davidson et al 2001 Smith 2006b 2009) and has+z pointingNW on the sky APAz = 42 places the orbital axis perpen-dicular to the Homunculus polar axis with+z pointing NE APAz = 132 (222) is also aligned with (perpendicular to) theHomunculus polar axis and has+z pointing SE (SW) on the sky

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

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12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

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14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

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Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

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Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 4: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

4 Madura et al

211 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

Figure 2 displays observed spectro-images of [FeIII ] λ4659recorded at slit PA = +38 on 2003 May 5 (φ = 0976) show-ing spatially-extended (up tosim 035primeprime) emission in the form ofvery distinct nearly complete arcs that are entirely blue-shiftedup to sim minus475 km sminus1 Several weaker [FeIII ] lines nearby inthe spectrum while blended show no evidence of a spatially-extended (gt 01primeprime) red component and no other high-ionizationforbidden lines show an extended red component at this position(G09) To illustrate this the bottom right panel of Figure 2containsa continuum-subtracted spectro-image of [NII ] λ5756 taken at thesame orbital phase and slit PA The IP (145 eV) and critical density(3 times 107 cmminus3) of [N II ] λ5756 are very similar to that of [FeIII ]λ4659 (162 eV andsim 107 cmminus3) meaning that their spatially-extended emission forms in nearly identical regions and viathesame physical mechanism The [NII ] λ5756 line is strong and lo-cated in a spectral region with very few other lines Unlike [FeIII ]λ4659 there is no contamination to the red of [NII ] λ5756 mak-ing it ideal for demonstrating that there is no spatially-extendedred-shifted broad high-ionization forbidden line emission

Of particular importance are the asymmetric shape and inten-sity of these emission arcs Both arcs extend to nearly the samespatial distance from the central core but the upper arc is notice-ably dimmer and stretches farther to the blue tosim minus475 km sminus1The lower arc is brighter but only extends tosim minus400 km sminus1 Ev-ery high-ionization forbidden line observed at this orbital phase andslit PA exhibits these asymmetries in intensity and velocity (figures6 minus 9 of G09) indicating that they are independent of the IP andcritical density of the line and intrinsic to the shape and distributionof the photoionized extended wind material in which the lines formAs such the shape and asymmetry of the blue-shifted emission arcsmay be used to help constrain the orbital orientation

212 Constraint 2 Variations with Orbital Phase at ConstantSlit PA =minus28

Let us focus next on shifts of the high-ionization forbiddenemis-sion with orbital phase Figure 11 of G09 shows sets of six spec-tra of [FeIII ] λ4659 andλ4702 recorded at select phases at slitPA = minus28 During the two minima atφ = 0045 and 1040 (rows1 and 5 of figure 11 of G09) the broad [FeIII ] emission is absentBy φ = 0213 (row 2) andφ = 1122 (row 6sim 8 months after theX-ray minimum) it strongly reappears Images atφ = 0407 aresimilar to those atφ = 0213 and 1122 Byφ = 0952 emissionabovesim 150 km sminus1 disappears This phase dependence in the[Fe III ] emission especially the disappearance during periastronstrongly indicates that it is tied to the orbital motion ofηB

Another important observational feature is the presence ofspatially-extendedred-shiftedemission to the NW in addition toextended blue-shifted emission to the SE at phases far frompe-riastron This is in contrast to the entirely blue-shifted arcs seenfor slit PA = +38 indicating that the STIS slit at PA =minus28

is sampling different emitting portions ofη Carrsquos extended windstructures even at similar orbital phases

213 Constraint 3 Doppler Shift Correlations with OrbitalPhase and Slit PA

The final set of observations focuses on changes with slit PA lead-ing up to periastron Figures 12 and 13 of G09 illustrate the be-havior of the [FeIII ] emission for various slit PAs at select phases

Figure 2 Spectro-images recorded 2003 May 5 (φ = 0976) Top LeftPanelHSTACS HRC image of the central2primeprime of η Car with the2primeprime longportion of the STIS slit at PA = +38 overlaid The locations of Weigeltblobs B C and D are indicated as is the direction of north Top Right PanelContinuum-subtracted spectro-image of [FeIII ] λ4659 Emission appearsas a pair of completely blue-shifted arcs Color is proportional to the squareroot of the intensity and the velocity scale isplusmn600 km sminus1 Weak emissionto the red is entirely due to contamination by [FeII ] λ4666 while weaknarrow emission is centered atsim minus40 km sminus1 Bottom Left Panel Samespectro-image but with masks that remove the line contamination BottomRight Panel Continuum-subtracted spectro-image of [NII ] λ5756 includedto demonstrate that at this phase and STIS PA the high-ionization forbiddenlines show no evidence of broad spatially-extended red-shifted emission

The key point to take away from this particular data set is that awayfrom periastron the spatially-extended [FeIII ] emission is almostentirely blue-shifted for positive slit PAs =+22 to +70 but ispartially red-shifted for negative PAs most notably PA =minus82

3 A 3-D DYNAMICAL MODEL FOR THE BROADHIGH-IONIZATION FORBIDDEN LINE EMISSION

31 Why Model [Fe III] λ4659 Emission

Table 3 of G09 lists the various forbidden emission lines observedin η Car However there are several important reasons to focus par-ticular attention on [FeIII ] λ4659 emission

First the physical mechanism for the formation of forbiddenlines is well understood (Appendix B online version) Moreoveremission from forbidden lines is optically thin Thus forbidden lineradiation can escape from a nebula much more easily than radiationfrom an optically thick resonance line which is emitted andreab-sorbed many times (Hartman 2003) This is of great value whenstudying an object so enshrouded by circumstellar materialsinceone does not have to model complicated radiative transfer effects

[Fe III ] is considered rather than a lower ionization line of[Fe II ] becausethe bulk of the[Fe III ] emission arises in regions thatare directly photoionized byηB (Verner et al 2005 G09 Mehner etal 2010) No intrinsic [FeIII ] emission is expected fromηA Thisis based on detailed theoretical models by H01 and H06 whichshow that inηArsquos envelope Fe2+ only exists in regions where theelectron density is two-to-four orders of magnitude higherthan the

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 5

critical density of the [FeIII ] λ4659 line Since Fe0 needs162 eVradiation (or collisions) to reach the Fe2+ state most of the [FeIII ]emission arises in areas directly photoionized byηB

In comparison Fe0 only needs 79 eV radiation or collisions toionize to Fe+ which can form in the wind ofηA (without ηBrsquos in-fluence) andor near the wind-wind interaction regions in areas ex-cited by mid-UV radiation filtered byηArsquos dense wind Collisionsand photoexcitation to upper Fe+ energy levels can also populatemany metastable levels As a result [FeII ] emission is far morecomplicated and originates from lower excitation lower density re-gions on much larger spatial scales (H01 H06 G09 Mehner etal2010) Because of this complexity the modeling of [FeII ] emissionis deferred to future work

The IP of 162 eV required for Fe2+ also means that the[Fe III ] emission forms in regions where hydrogen is ionized buthelium is still neutral In contrast both Ar2+ and Ne2+ have IPsgreater than246 eV Therefore [ArIII ] and [NeIII ] emission arisein areas where helium is singly ionized Modeling [FeIII ] is thusmore straightforward as one does not have to worry about the twodifferent types of ionization structure possible (one due to H andone due to He) which depend on the spectrum of ionizing radia-tion and the abundance of helium (Osterbrock 1989)

[Fe III ] λ4659 is chosen over the similar emission line of [NII ]λ5756 in order to avoid potential complications due to intrinsic[N II ] emission in the extended wind ofηA [N II ] emission canform in a broad zone between 100 and 1000Rlowast (sim 30 minus 300 AU)of ηA and is sensitive to its wind temperature and mass-loss rate(H01) By focusing on [FeIII ] one avoids having to include anyintrinsic forbidden line emission fromηA

The modeling in this paper focuses solely on thebroad[Fe III ]emission features that are thought to arise in the dense mod-erate velocity (sim 100 minus 600 km sminus1) extended primary windand WWC regions The much narrower ( 50 km sminus1) emis-sion features that form in the Weigelt blobs and other denseslow-moving equatorial ejecta fromη Carrsquos smaller eruptionin the 1890s (Weigelt amp Ebersberger 1986 Davidson et al 19951997 Ishibashi et al 2003 Smith et al 2004 Gull et al 2009Mehner et al 2010) are not modeled Any possible effects of localdust formation are neglected for simplicity as not enough informa-tion is available to realistically include them at this time(Williams2008 Mehner et al 2010)

As all observed high-ionization forbidden lines show the samebasic spatial and temporal features in their broad emission with anydifferences in size or location attributable to differences in the IPand critical density of the specific line of interest focusing solelyon [FeIII ] λ4659 should not significantly bias the overall conclu-sions which should extend to the other high-ionization forbiddenlines as well Values of the transition probability (A21 = 044 sminus1)statistical weights (g1 = g2 = 9) and line transition frequency(ν21 = 6435 times 1014 sminus1) for [Fe III ] λ4659 all come fromNahar amp Pradhan (1996) Values for the collision strengths (Ω12)come from Zhang (1996) A solar abundance of iron is also usedconsistent with the works of H01 Verner et al (2005) and H06

32 The 3-D SPH Code and General Problem Setup

The numerical simulations in this paper were performed withthesame 3-D SPH code used in O08 The stellar winds are modeledby an ensemble of gas particles that are continuously ejected witha given outward velocity at a radius just outside each star For sim-plicity both winds are taken to be adiabatic with the same initialtemperature (35 000 K) at the stellar surfaces and coasting with-

Table 1 Stellar Wind and Orbital Parameters of the 3-D SPH Simulation

Parameter ηA ηB

Mass (M⊙) 90 30Radius (R⊙) 90 30Mass-Loss Rate (M⊙ yrminus1) 10minus3 10minus5

Wind Terminal Velocity (km sminus1) 500 3000Orbital Period (days) 2024Orbital Eccentricitye 09Semi-major Axis Lengtha (AU) 154

out any net external forces assuming that gravitational forces areeffectively canceled by radiative driving terms (O08) Thegas hasnegligible self-gravity and adiabatic cooling is included

In a standardxyz Cartesian coordinate system the binary or-bit is set in thexy plane with the origin at the system center-of-mass and the orbital major axis along thex-axis The two starsorbit counter-clockwise when looking down on the orbital planealong the+z axis Simulations are started with the stars at apas-tron and run for multiple consecutive orbits By convention t = 0(φ = 0) is defined to be at periastron passage

To match thesim plusmn07primeprime scale of the STIS observations at theadopted distance of 23 kpc to theη Car system (Smith 2006b) theouter simulation boundary is set atr = plusmn105a from the systemcenter-of-mass wherea is the length of the orbital semi-major axis(a = 154 AU) Particles crossing this boundary are removed fromthe simulation We note that the SPH formalism is ideally suitedfor such large-scale 3-D simulations as compared to grid-basedhydrodynamics codes (Price 2004 Monaghan 2005)

Table 1 summarizes the stellar wind and orbital parametersused in the modeling which are consistent with those derived fromthe observations (PC02 H01 H06 C11) with the exception of thewind temperature ofηA The effect of the wind temperature on thedynamics of the high-velocity wind collision is negligible(O08)Note that the simulation adopts the higher mass-loss rate for ηAderived by Davidson et al (1995) Cox et al (1995) H01 andH06rather than the factor of four lower mass-loss rate assumed whenanalyzing X-ray signatures (PC02 O08 P09 P11 C11) Effects ofthe adopted value of the primary mass-loss rate on the forbiddenline emission will be the subject of a future paper

The publicly available software SPLASH (Price 2007) is usedto visualize the 3-D SPH code output SPLASH differs from othertools because it is designed to visualize SPH data using SPH algo-rithms There are a number of benefits to using SPLASH and thereader is referred to Price (2007) and the SPLASH userguide forthese and discussions on the interpolation algorithms

33 Generation of Synthetic Slit Spectro-Images

The 3-D SPH simulation provides the time-dependent 3-D den-sity and temperature structure ofη Carrsquos interacting winds on spa-tial scales comparable to those of theHSTSTIS observations Thisforms the basis of our 3-D dynamical model Unfortunately it iscurrently not possible to perform full 3-D simulations ofη Car inwhich the radiative transfer is properly coupled to the hydrodynam-ics (Paardekooper 2010) Instead the radiative transfer calculationshere are performed as post-processing on the 3-D SPH simulationoutput This should not strongly affect the results so long as the ma-terial that is photoionized byηB responds nearly instantaneously toits UV flux In other words as long as the timescale for the recom-

ccopy 2011 RAS MNRAS000 1ndash23

6 Madura et al

bination ofe + Fe2+ rarr Fe+ is very small relative to the orbitaltimescale the calculations should be valid

The recombination timescale isτrec = 1(αrecne) secondswhereαrec(T ) is the recombination rate coefficient (in units ofcm3 sminus1) at temperatureT andne is the electron number densityFor T sim 104 K αrec(T ) asymp 4 times 10minus12 cm3 sminus1 (Nahar 1997)Since densities near the critical density of the line are theprimaryfocusne sim 107 cmminus3 this givesτrec asymp 7 hours which is muchsmaller than the orbital timescale even during periastronpassagewhich takes approximately one month Any possible time-delay ef-fects should not strongly affect the results as the light-travel-timeto material at distances ofsim 05primeprime in η Car is only about one week

331 Summary of the Basic Procedure

Synthetic slit spectro-images are generated using a combination ofInteractive Data Language (IDL) routines and radiative transfer cal-culations performed with a modified version of the SPLASH (Price2007) code Here we outline the basic procedure with the specificsdiscussed in the following subsections

Nearly all of the required calculations are performed withinSPLASH which reads in the 3-D SPH code output for a specificorbital phase rotates the data to a desired orbital orientation on thesky and computes the line-of-sight velocity for all of the materialNext is the computation of the ionization volume created byηBwhere Fe+ is photoionized to Fe2+ It is assumed that any materialwithin this volume is in collisional ionization equilibrium and thatno material withT gt 250 000 K emits All other material in thephotoionization volume has its forbidden line emissivity calculatedusing Equation (13) derived below Material located outside thephotoionization volume does not emit

The intensityI is computed by performing a line-of-sight in-tegration of the emissivity at each pixel resulting in an image ofthe spatial distribution of the [FeIII ] intensity projected on the skyThis is done for each velocityvbin used along the dispersion axisof the synthetic slit in the velocity range of interest resulting ina set of intensity images The individual [FeIII ] λ4659 intensityimages are then combined and convolved with theHSTSTIS re-sponse using IDL routines in order to create a synthetic positionversus velocity spectro-image for comparison to the observations

332 Defining the Binary Orientation Relative to the Observer

With the two stars orbiting in thexy plane the 3-D orientation ofthe binary relative to the observer is defined by the orbital inclina-tion i the prograde direction angleθ that the orbital plane projec-tion of the observerrsquos line-of-sight makes with the apastron side ofthe semi-major axis3 and the position angleon the skyof the+zorbital axis PAz (Figure 3)

Following the standard definition for binary systemsi is theangle that the line-of-sight makes with the+z axis An i = 0 isa face-on orbit with the observerrsquos line-of-sight along the+z axisand the two stars orbiting counter-clockwise on the sky Ani = 90

places the line-of-sight in the orbitalxy plane whilei = 180 is aface-on orbit with the two stars orbiting clockwise on the sky

For i = 90 a value ofθ = 0 has the observer looking alongthe+x axis (along the semi-major axis on the apastron side of thesystem) while aθ = 90 has the observer looking along the+y

3 θ is the same as the angleφ defined in figure 3 of O08

Figure 3 Diagrams illustrating the observerrsquos position Top Schematicdefining the inclination anglei that the observerrsquos line-of-sight makes withthe +z orbital axis and the equatorial projection angleθ of the line-of-sight relative to the apastron side of the semi-major axisx The backgroundorthogonal planes show slices of density from the 3-D SPH simulation atapastron in thexy orbital plane and theyz plane perpendicular to the or-bital plane and major axis Bottom Diagram defining the position angle onthe skyPAz of the+z orbital axis (blue) measured in degrees counter-clockwise of north (N) The binary orbit projected on the skyis shown inyellow as are the semi-major (red) and semi-minor (green) axes The smallinset to the left is aHSTWFPC2 image of the Homunculus (Credit NASAESA and the Hubble SM4 ERO Team) included for reference

axis In the conventional notation of binary orbits the lsquoargument ofperiapsisrsquoω = 270 minus θ

PAz defines the position angle on the sky of the+z orbital axisand is measured in degrees counter-clockwise of N APAz = 312

aligns the projected orbital axis with the Homunculus polaraxis(Davidson et al 2001 Smith 2006b 2009) and has+z pointingNW on the sky APAz = 42 places the orbital axis perpen-dicular to the Homunculus polar axis with+z pointing NE APAz = 132 (222) is also aligned with (perpendicular to) theHomunculus polar axis and has+z pointing SE (SW) on the sky

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

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12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

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14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

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Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

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Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 5: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 5

critical density of the [FeIII ] λ4659 line Since Fe0 needs162 eVradiation (or collisions) to reach the Fe2+ state most of the [FeIII ]emission arises in areas directly photoionized byηB

In comparison Fe0 only needs 79 eV radiation or collisions toionize to Fe+ which can form in the wind ofηA (without ηBrsquos in-fluence) andor near the wind-wind interaction regions in areas ex-cited by mid-UV radiation filtered byηArsquos dense wind Collisionsand photoexcitation to upper Fe+ energy levels can also populatemany metastable levels As a result [FeII ] emission is far morecomplicated and originates from lower excitation lower density re-gions on much larger spatial scales (H01 H06 G09 Mehner etal2010) Because of this complexity the modeling of [FeII ] emissionis deferred to future work

The IP of 162 eV required for Fe2+ also means that the[Fe III ] emission forms in regions where hydrogen is ionized buthelium is still neutral In contrast both Ar2+ and Ne2+ have IPsgreater than246 eV Therefore [ArIII ] and [NeIII ] emission arisein areas where helium is singly ionized Modeling [FeIII ] is thusmore straightforward as one does not have to worry about the twodifferent types of ionization structure possible (one due to H andone due to He) which depend on the spectrum of ionizing radia-tion and the abundance of helium (Osterbrock 1989)

[Fe III ] λ4659 is chosen over the similar emission line of [NII ]λ5756 in order to avoid potential complications due to intrinsic[N II ] emission in the extended wind ofηA [N II ] emission canform in a broad zone between 100 and 1000Rlowast (sim 30 minus 300 AU)of ηA and is sensitive to its wind temperature and mass-loss rate(H01) By focusing on [FeIII ] one avoids having to include anyintrinsic forbidden line emission fromηA

The modeling in this paper focuses solely on thebroad[Fe III ]emission features that are thought to arise in the dense mod-erate velocity (sim 100 minus 600 km sminus1) extended primary windand WWC regions The much narrower ( 50 km sminus1) emis-sion features that form in the Weigelt blobs and other denseslow-moving equatorial ejecta fromη Carrsquos smaller eruptionin the 1890s (Weigelt amp Ebersberger 1986 Davidson et al 19951997 Ishibashi et al 2003 Smith et al 2004 Gull et al 2009Mehner et al 2010) are not modeled Any possible effects of localdust formation are neglected for simplicity as not enough informa-tion is available to realistically include them at this time(Williams2008 Mehner et al 2010)

As all observed high-ionization forbidden lines show the samebasic spatial and temporal features in their broad emission with anydifferences in size or location attributable to differences in the IPand critical density of the specific line of interest focusing solelyon [FeIII ] λ4659 should not significantly bias the overall conclu-sions which should extend to the other high-ionization forbiddenlines as well Values of the transition probability (A21 = 044 sminus1)statistical weights (g1 = g2 = 9) and line transition frequency(ν21 = 6435 times 1014 sminus1) for [Fe III ] λ4659 all come fromNahar amp Pradhan (1996) Values for the collision strengths (Ω12)come from Zhang (1996) A solar abundance of iron is also usedconsistent with the works of H01 Verner et al (2005) and H06

32 The 3-D SPH Code and General Problem Setup

The numerical simulations in this paper were performed withthesame 3-D SPH code used in O08 The stellar winds are modeledby an ensemble of gas particles that are continuously ejected witha given outward velocity at a radius just outside each star For sim-plicity both winds are taken to be adiabatic with the same initialtemperature (35 000 K) at the stellar surfaces and coasting with-

Table 1 Stellar Wind and Orbital Parameters of the 3-D SPH Simulation

Parameter ηA ηB

Mass (M⊙) 90 30Radius (R⊙) 90 30Mass-Loss Rate (M⊙ yrminus1) 10minus3 10minus5

Wind Terminal Velocity (km sminus1) 500 3000Orbital Period (days) 2024Orbital Eccentricitye 09Semi-major Axis Lengtha (AU) 154

out any net external forces assuming that gravitational forces areeffectively canceled by radiative driving terms (O08) Thegas hasnegligible self-gravity and adiabatic cooling is included

In a standardxyz Cartesian coordinate system the binary or-bit is set in thexy plane with the origin at the system center-of-mass and the orbital major axis along thex-axis The two starsorbit counter-clockwise when looking down on the orbital planealong the+z axis Simulations are started with the stars at apas-tron and run for multiple consecutive orbits By convention t = 0(φ = 0) is defined to be at periastron passage

To match thesim plusmn07primeprime scale of the STIS observations at theadopted distance of 23 kpc to theη Car system (Smith 2006b) theouter simulation boundary is set atr = plusmn105a from the systemcenter-of-mass wherea is the length of the orbital semi-major axis(a = 154 AU) Particles crossing this boundary are removed fromthe simulation We note that the SPH formalism is ideally suitedfor such large-scale 3-D simulations as compared to grid-basedhydrodynamics codes (Price 2004 Monaghan 2005)

Table 1 summarizes the stellar wind and orbital parametersused in the modeling which are consistent with those derived fromthe observations (PC02 H01 H06 C11) with the exception of thewind temperature ofηA The effect of the wind temperature on thedynamics of the high-velocity wind collision is negligible(O08)Note that the simulation adopts the higher mass-loss rate for ηAderived by Davidson et al (1995) Cox et al (1995) H01 andH06rather than the factor of four lower mass-loss rate assumed whenanalyzing X-ray signatures (PC02 O08 P09 P11 C11) Effects ofthe adopted value of the primary mass-loss rate on the forbiddenline emission will be the subject of a future paper

The publicly available software SPLASH (Price 2007) is usedto visualize the 3-D SPH code output SPLASH differs from othertools because it is designed to visualize SPH data using SPH algo-rithms There are a number of benefits to using SPLASH and thereader is referred to Price (2007) and the SPLASH userguide forthese and discussions on the interpolation algorithms

33 Generation of Synthetic Slit Spectro-Images

The 3-D SPH simulation provides the time-dependent 3-D den-sity and temperature structure ofη Carrsquos interacting winds on spa-tial scales comparable to those of theHSTSTIS observations Thisforms the basis of our 3-D dynamical model Unfortunately it iscurrently not possible to perform full 3-D simulations ofη Car inwhich the radiative transfer is properly coupled to the hydrodynam-ics (Paardekooper 2010) Instead the radiative transfer calculationshere are performed as post-processing on the 3-D SPH simulationoutput This should not strongly affect the results so long as the ma-terial that is photoionized byηB responds nearly instantaneously toits UV flux In other words as long as the timescale for the recom-

ccopy 2011 RAS MNRAS000 1ndash23

6 Madura et al

bination ofe + Fe2+ rarr Fe+ is very small relative to the orbitaltimescale the calculations should be valid

The recombination timescale isτrec = 1(αrecne) secondswhereαrec(T ) is the recombination rate coefficient (in units ofcm3 sminus1) at temperatureT andne is the electron number densityFor T sim 104 K αrec(T ) asymp 4 times 10minus12 cm3 sminus1 (Nahar 1997)Since densities near the critical density of the line are theprimaryfocusne sim 107 cmminus3 this givesτrec asymp 7 hours which is muchsmaller than the orbital timescale even during periastronpassagewhich takes approximately one month Any possible time-delay ef-fects should not strongly affect the results as the light-travel-timeto material at distances ofsim 05primeprime in η Car is only about one week

331 Summary of the Basic Procedure

Synthetic slit spectro-images are generated using a combination ofInteractive Data Language (IDL) routines and radiative transfer cal-culations performed with a modified version of the SPLASH (Price2007) code Here we outline the basic procedure with the specificsdiscussed in the following subsections

Nearly all of the required calculations are performed withinSPLASH which reads in the 3-D SPH code output for a specificorbital phase rotates the data to a desired orbital orientation on thesky and computes the line-of-sight velocity for all of the materialNext is the computation of the ionization volume created byηBwhere Fe+ is photoionized to Fe2+ It is assumed that any materialwithin this volume is in collisional ionization equilibrium and thatno material withT gt 250 000 K emits All other material in thephotoionization volume has its forbidden line emissivity calculatedusing Equation (13) derived below Material located outside thephotoionization volume does not emit

The intensityI is computed by performing a line-of-sight in-tegration of the emissivity at each pixel resulting in an image ofthe spatial distribution of the [FeIII ] intensity projected on the skyThis is done for each velocityvbin used along the dispersion axisof the synthetic slit in the velocity range of interest resulting ina set of intensity images The individual [FeIII ] λ4659 intensityimages are then combined and convolved with theHSTSTIS re-sponse using IDL routines in order to create a synthetic positionversus velocity spectro-image for comparison to the observations

332 Defining the Binary Orientation Relative to the Observer

With the two stars orbiting in thexy plane the 3-D orientation ofthe binary relative to the observer is defined by the orbital inclina-tion i the prograde direction angleθ that the orbital plane projec-tion of the observerrsquos line-of-sight makes with the apastron side ofthe semi-major axis3 and the position angleon the skyof the+zorbital axis PAz (Figure 3)

Following the standard definition for binary systemsi is theangle that the line-of-sight makes with the+z axis An i = 0 isa face-on orbit with the observerrsquos line-of-sight along the+z axisand the two stars orbiting counter-clockwise on the sky Ani = 90

places the line-of-sight in the orbitalxy plane whilei = 180 is aface-on orbit with the two stars orbiting clockwise on the sky

For i = 90 a value ofθ = 0 has the observer looking alongthe+x axis (along the semi-major axis on the apastron side of thesystem) while aθ = 90 has the observer looking along the+y

3 θ is the same as the angleφ defined in figure 3 of O08

Figure 3 Diagrams illustrating the observerrsquos position Top Schematicdefining the inclination anglei that the observerrsquos line-of-sight makes withthe +z orbital axis and the equatorial projection angleθ of the line-of-sight relative to the apastron side of the semi-major axisx The backgroundorthogonal planes show slices of density from the 3-D SPH simulation atapastron in thexy orbital plane and theyz plane perpendicular to the or-bital plane and major axis Bottom Diagram defining the position angle onthe skyPAz of the+z orbital axis (blue) measured in degrees counter-clockwise of north (N) The binary orbit projected on the skyis shown inyellow as are the semi-major (red) and semi-minor (green) axes The smallinset to the left is aHSTWFPC2 image of the Homunculus (Credit NASAESA and the Hubble SM4 ERO Team) included for reference

axis In the conventional notation of binary orbits the lsquoargument ofperiapsisrsquoω = 270 minus θ

PAz defines the position angle on the sky of the+z orbital axisand is measured in degrees counter-clockwise of N APAz = 312

aligns the projected orbital axis with the Homunculus polaraxis(Davidson et al 2001 Smith 2006b 2009) and has+z pointingNW on the sky APAz = 42 places the orbital axis perpen-dicular to the Homunculus polar axis with+z pointing NE APAz = 132 (222) is also aligned with (perpendicular to) theHomunculus polar axis and has+z pointing SE (SW) on the sky

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

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Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

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Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

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18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

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Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

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Davidson K 1999 Eta Carinae at The Millennium 179 304

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

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Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

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Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

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Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

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This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 6: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

6 Madura et al

bination ofe + Fe2+ rarr Fe+ is very small relative to the orbitaltimescale the calculations should be valid

The recombination timescale isτrec = 1(αrecne) secondswhereαrec(T ) is the recombination rate coefficient (in units ofcm3 sminus1) at temperatureT andne is the electron number densityFor T sim 104 K αrec(T ) asymp 4 times 10minus12 cm3 sminus1 (Nahar 1997)Since densities near the critical density of the line are theprimaryfocusne sim 107 cmminus3 this givesτrec asymp 7 hours which is muchsmaller than the orbital timescale even during periastronpassagewhich takes approximately one month Any possible time-delay ef-fects should not strongly affect the results as the light-travel-timeto material at distances ofsim 05primeprime in η Car is only about one week

331 Summary of the Basic Procedure

Synthetic slit spectro-images are generated using a combination ofInteractive Data Language (IDL) routines and radiative transfer cal-culations performed with a modified version of the SPLASH (Price2007) code Here we outline the basic procedure with the specificsdiscussed in the following subsections

Nearly all of the required calculations are performed withinSPLASH which reads in the 3-D SPH code output for a specificorbital phase rotates the data to a desired orbital orientation on thesky and computes the line-of-sight velocity for all of the materialNext is the computation of the ionization volume created byηBwhere Fe+ is photoionized to Fe2+ It is assumed that any materialwithin this volume is in collisional ionization equilibrium and thatno material withT gt 250 000 K emits All other material in thephotoionization volume has its forbidden line emissivity calculatedusing Equation (13) derived below Material located outside thephotoionization volume does not emit

The intensityI is computed by performing a line-of-sight in-tegration of the emissivity at each pixel resulting in an image ofthe spatial distribution of the [FeIII ] intensity projected on the skyThis is done for each velocityvbin used along the dispersion axisof the synthetic slit in the velocity range of interest resulting ina set of intensity images The individual [FeIII ] λ4659 intensityimages are then combined and convolved with theHSTSTIS re-sponse using IDL routines in order to create a synthetic positionversus velocity spectro-image for comparison to the observations

332 Defining the Binary Orientation Relative to the Observer

With the two stars orbiting in thexy plane the 3-D orientation ofthe binary relative to the observer is defined by the orbital inclina-tion i the prograde direction angleθ that the orbital plane projec-tion of the observerrsquos line-of-sight makes with the apastron side ofthe semi-major axis3 and the position angleon the skyof the+zorbital axis PAz (Figure 3)

Following the standard definition for binary systemsi is theangle that the line-of-sight makes with the+z axis An i = 0 isa face-on orbit with the observerrsquos line-of-sight along the+z axisand the two stars orbiting counter-clockwise on the sky Ani = 90

places the line-of-sight in the orbitalxy plane whilei = 180 is aface-on orbit with the two stars orbiting clockwise on the sky

For i = 90 a value ofθ = 0 has the observer looking alongthe+x axis (along the semi-major axis on the apastron side of thesystem) while aθ = 90 has the observer looking along the+y

3 θ is the same as the angleφ defined in figure 3 of O08

Figure 3 Diagrams illustrating the observerrsquos position Top Schematicdefining the inclination anglei that the observerrsquos line-of-sight makes withthe +z orbital axis and the equatorial projection angleθ of the line-of-sight relative to the apastron side of the semi-major axisx The backgroundorthogonal planes show slices of density from the 3-D SPH simulation atapastron in thexy orbital plane and theyz plane perpendicular to the or-bital plane and major axis Bottom Diagram defining the position angle onthe skyPAz of the+z orbital axis (blue) measured in degrees counter-clockwise of north (N) The binary orbit projected on the skyis shown inyellow as are the semi-major (red) and semi-minor (green) axes The smallinset to the left is aHSTWFPC2 image of the Homunculus (Credit NASAESA and the Hubble SM4 ERO Team) included for reference

axis In the conventional notation of binary orbits the lsquoargument ofperiapsisrsquoω = 270 minus θ

PAz defines the position angle on the sky of the+z orbital axisand is measured in degrees counter-clockwise of N APAz = 312

aligns the projected orbital axis with the Homunculus polaraxis(Davidson et al 2001 Smith 2006b 2009) and has+z pointingNW on the sky APAz = 42 places the orbital axis perpen-dicular to the Homunculus polar axis with+z pointing NE APAz = 132 (222) is also aligned with (perpendicular to) theHomunculus polar axis and has+z pointing SE (SW) on the sky

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 7: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 7

333 Volume of Material Photoionized byηB

Based on the models ofηArsquos envelope by H01 and H06 it is as-sumed that Fe+ is initially the dominant ionization state of ironin primary wind material locatedr gt 50 AU from ηA and thathydrogen and helium are initially neutral in the primary wind fordistances ofr gt 155 AU andgt 37 AU respectively The cal-culation of the volume of material photoionized from Fe+ to Fe2+

by ηB follows that presented in Nussbaumer amp Vogel (1987) forsymbiotic star systems For cases where hydrogen or helium alonedetermine the ionization structure the boundary between neutralhydrogen (H0) and ionized hydrogen (H+) can be expressed ana-lytically As ηArsquos extended wind consists mostly of hydrogen andhelium (figure 9 of H01) and because the [FeIII ] emission arisesin regions where hydrogen is ionized but helium is not such acal-culation should provide a reasonable approximation for thesizeand shape of the photoionization boundary between Fe+ and Fe2+This however is an upper limit for the photoionization volumesince the IP of 162 eV required for Fe2+ is slightly larger thanthe 136 eV needed to ionize H0

In our calculation the primary star is separated by a dis-tancep from a hot companion star that emits spherically sym-metrically LH photons sminus1 that are capable of ionizing H0 Theprimary has a standard spherically symmetric mass-loss rate ofM1 = 4πr2micromHn(r)vinfin wheren(r) is the hydrogen numberdensitymicro is the mean molecular weightmH is the mass of a hy-drogen atom andvinfin is the terminal speed of the primary wind

In a small angle∆θ around the directionθ the equilibriumcondition for recombination-ionization balance is

LH

∆θ

4π= ∆θ

int sθ

0

n(s)ne(s)αB(H Te) s2 ds (1)

wheres measures the distance from the ionizing secondary starin the directionθ sθ is the boundary between H0 and H+ αB

is the total hydrogenic recombination coefficient in case B atelectron temperatureTe andne is the electron number density(Nussbaumer amp Vogel 1987) The electron density can be writtenas

ne(r) = (1 + a(He))n(r) (2)

where

n(r) =M1

4πr2micromHvinfin (3)

and a(He) is the abundance by number of He relative to HExpressing boths and r in units of p defining u equiv spand making the further approximation thatαB is constant(Nussbaumer amp Vogel 1987) Equation (1) can be written as

XH+

= f(u θ) (4)

where

XH+

=4πmicro2m2

H

αB(1 + a(He))pLH

(

vinfin

M1

)2

(5)

and

f(u θ) =

int u

0

x2

(x2 minus 2x cos θ + 1)2dx (6)

In the modified SPLASH routine Equation (4) is solved for aspecifiedLH However since Equation (4) does not account for theeffects of the WWC we assume that mass is conserved and that allprimary wind material normally within the cavity created byηB iscompressed into the walls of the WWC region with the ionizationstate of the WWC zone walls before being photoionized the sameas that of the primary wind (ie iron is in the Fe+ state)

The stellar separation is computed directly from the 3-D SPHsimulation We use the same value for the abundance by numberof He to H as H01 and H06a(He) = 02 A constant value ofαB = 256 times 10minus13 cm3 sminus1 at Te = 10 000 K is also used(Osterbrock 1989) Based on Mehner et al (2010) and Verner et al(2005) the value ofLH is chosen to be that of an O5 giant withTeff asymp 40 000 K which according to Martins et al (2005) hasa hydrogen ionizing flux of104948 photons sminus1 Any shieldingeffects due to the presence of the Weigelt blobs or other denseslow-moving equatorial ejecta are not presently included

The third column of Figure 6 illustrates the time variabilityof the photoionization region created byηB for slices in thexyorbital plane The region is largest around apastron whenηB isfarthest fromηArsquos dense wind AsηB moves closer toηA the pho-toionization zone becomes smaller and more wedge-shaped4 dueto the gradual embedding ofηB in ηArsquos wind During periastronηB becomes completely enshrouded inηA rsquos thick wind preventingmaterial at large distances (amp 10a) from being photoionized AsηB emerges after periastron the photoionization region is restoredand grows asηB moves back toward apastron This plunging intoand withdrawal fromηArsquos wind byηB leads to the illumination ofdistant material in very specific directions as a function ofphase

334 The Emissivity Equation

For a simple two-level atom the volume emissivityj (erg cmminus3

sminus1 srminus1) of a forbidden line is

j =1

4πhν21N2A21 (7)

whereN2 is the number density of atoms in the excited upper levelandν21 is the frequency of the line transition (Dopita amp Sutherland2003) Using the total number density of element of interestE inionization statei niE asymp N1 + N2 (Ignace amp Brimeyer 2006)together with Equation (B5) one finds

N2 =

(

neq12neq21 + A21

)

(niE minusN2) (8)

Solving forN2 and using Equation (B4) forq21q12 gives

N2 = niE

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(9)

wherenc defined in Equation (B6) is the critical density of theline By definingQiE equiv niEnE as the fraction of elementEin ionization statei AE equiv nEnN as the abundance of element

4 The outer edge looks circular only because this marks the edge of thespherical computational domain of the SPH simulation

ccopy 2011 RAS MNRAS000 1ndash23

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

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14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

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Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

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Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

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18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

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Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

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Davidson K 1999 Eta Carinae at The Millennium 179 304

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Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

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Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

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Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

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This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 8: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

8 Madura et al

E relative to all nucleonsnN andγe equiv nNne as the ratio ofnucleons to electrons (Ignace amp Brimeyer 2006)niE becomes

niE = QiEAEγene (10)

Therefore using Equations (9) and (10)

j =hν21A21QiEAEγene

times

1 +g1g2

exp

(

hν21kT

)[

1 +nc

ne

]minus1

(11)

Based on Equation (11) emission from a specific forbiddenline is concentrated only in regions that (1) contain the right ion-ization state of the element of interest (in our case Fe2+) (2) arenear the critical density of the line (for [FeIII ] sim 107 cmminus3) and(3) are near the right temperature (for [FeIII ] T asymp 32 000 K)This important point is crucial to understanding the forbidden lineemission observed inη Car

To compute the emissivity using SPLASH the line profiles areassumed to have a Gaussian thermal broadening so that Equation(11) is weighted by an exponential with the form

j =hν21A21QiEAEγene

4πexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12

βΩ12ne

]minus1

(12)

where Equation (B8) has been used fornc vlos is the line-of-sightvelocity of material in the 3-D SPH simulation for a specifiedori-entation of the binary orbit relative to the observervth is a thermalvelocity dispersion (taken to be 25 km sminus1) andvbin is the bin sizeused along the dispersion axis of the synthetic slit in the wavelengthrange of interest expressed in thermal velocity units (25 km sminus1)

To relate the physical density in the SPH simulation to theelectron number density we usene = ρsph(microemH) with microe themean molecular weight per free electron As the focus is on forbid-den lines of trace metals the value ofne should not be impactedby the ionization balance of the metals (Ignace amp Brimeyer 2006)Moreover since far-UV radiation (or high-energy collisions) is nec-essary for the formation of the high-ionization forbidden lineswherever [FeIII ] emission occurs hydrogen should also be ionizedFor such regions dominated by H+ we thus takemicroe = γe = 1 Thevolume emissivity then takes the final general form

j =hν21A21QiEAEρsph

4πmHexp

[

minus

(

vbin minusvlosvth

)2]

times

1 + exp

(

hν21kT

)[

g1g2

+A21g1T

12mH

βΩ12ρsph

]minus1

(13)

The appropriate value ofQiE is found assuming collisionalionization equilibrium with the fraction of Fe2+ as a function ofTbased on the ion fraction data from Bryans et al (2006) These datashow that atT sim 250 000 K the fractional abundance of Fe2+

is 10minus5453 with the remaining Fe being collisionally ionized tohigher states The amount of Fe2+ decreases even more at higher

temperatures The model therefore assumes zero [FeIII ] emissionfrom material withT gt 250 000 K

335 The Intensity and Synthetic Slit Spectro-Images

Since the [FeIII ] emission is optically thin the intensityI is simplythe integral of the volume emissivityj along the line-of-sight

I =

int

j dl (14)

(Mihalas 1978) The intensity is computed in SPLASH by perform-ing a line-of-sight integration ofj through the entire 3-D simulationat each pixel resulting in an image of the intensity in the [Fe III ]λ4659 line centered at a particular velocity (wavelength) as an ob-server would see it projected on the sky This is done for multiplevelocities (vbin) in 25 km sminus1 intervals for line-of-sight velocitiesfrom minus600 km sminus1 to+600 km sminus1

The resulting series of [FeIII ] intensity images are combinedusing IDL routines to create a synthetic position versus velocityspectro-image The IDL code reads in the SPLASH images and ro-tates them to a specified PA on the sky corresponding to a desiredPA of the HSTSTIS slit assuming that the orbital axis is eitheraligned with the Homunculus polar axis at aPAz = 312 or ro-tated relative to the Homunculus axis by some specified angle Eachimage is cropped to match the01primeprime width of the STIS slit with theslit assumed centered exactly on theη Car central source Since po-sition information is only available along one direction each imagehas its intensity values integrated along each row of pixelswithinthe slit width This produces a single lsquoslicersquo of the [FeIII ] λ4659intensity along the slit centered at a specific velocity These slicesare combined to create the synthetic spectro-image

The resulting model spectro-images have spatial (sim 0003primeprime)and spectral (25 km sminus1) resolutions that are better than theHSTobservations The synthetic spectro-images are thereforecon-volved with the response ofHSTSTIS in order to match its spa-tial (01primeprime) and spectral (375 km sminus1) resolutions Point-spreadfunctions (PSFs) for STIS generated using the Tiny Tim program(Krist amp Hook 1999) are used for the convolution in the spatial di-rection while a gaussian is used for the convolution in the spectraldirection Color in the model spectro-images scales as the squareroot of the intensity with the colorbar ranging from 0 to14 of themaximum intensity the same as used for displaying the observa-tions

Figure 4 shows that there is a noticeable difference be-tween the unconvolved (left) and convolved (right) model spectro-images especially in the centralplusmn015primeprime Details in the uncon-volved spectro-images that arise near the inner WWC zone arecompletely unresolved in the convolved images resulting in abright central streak of emission extending from negativeto pos-itive velocities This is consistent with the observationsand indi-cates thatHSTSTIS lacks the spatial resolution needed to resolvethe details ofη Carrsquos inner WWC zone

4 RESULTS FROM THE 3-D DYNAMICAL MODEL

In the discussions below it is assumed for simplicity that phase zeroof the spectroscopic cycle (from the observations) coincides withphase zero of the orbital cycle (periastron passage) In a highly-eccentric binary system likeη Car the two values are not expectedto be shifted by more than a few weeks (Groh et al 2010a) Sucha

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

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Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

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Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

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Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

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Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

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Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 9: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 9

Figure 4 Example synthetic spectro-images of [FeIII ] λ4659 both uncon-volved (left) and convolved with the response ofHSTSTIS (right) assum-ing i = 138 θ = 0 andPAz = 312 Roman numerals I and IIindicate the top and bottom of the slit respectively Coloris proportional tothe square root of the intensity and the velocity scale isplusmn600 km sminus1

time shift would only cause a small change ofsim 10 in the derivedbest value ofθ which will not affect the overall conclusions

41 Hydrodynamics of the Extended WWC Region

The first two columns of Figures 5 and 6 show respectively thedensity and temperature in thexy orbital plane from the 3-D SPHsimulation The binary system has undergone multiple orbits as in-dicated by the dense arcs of wind material in the outer (gt 20a) re-gions On theminusx (periastron) side of the system are narrow cavitiescarved byηB in ηArsquos dense wind during each periastron passageThe cavities are most easily seen in the temperature plots astheycontain warm (sim 104 minus 105 K) low-density wind material fromηB Bordering these cavities are compressed high-density shells ofprimary wind that form as a result of the WWC

The insets of Figure 6 illustrate the creation of one of thesenarrow wind cavities and its bordering dense shell of primary windTheir spiral shape is due to the increased orbital speeds of the starsduring periastron This is in contrast to phases around apastron(rows b c and d) when orbital speeds are much lower and the cur-rent WWC zone maintains a simple axisymmetric conical shape(O08 P09 P11) The increasing orbital speeds when approachingperiastron causes the postshock gas in the leading arm of theWWCzone to be heated to higher temperatures than the gas in the trailingarm (insets of rows d and e) an affect also found by P11

Following periastronηB moves back to the+x (apastron)side of the system its wind colliding with and heating the denseprimary wind that flows unimpeded in the+xminusy direction Aspointed out by P11 the arms of the WWC region shortly after this(φ asymp 01) are so distorted by orbital motion that the leading armcollides with the trailing arm from before periastron leading to ad-ditional heating of the postshock gas in the trailing arm (compareφ asymp 1122 Figure 6 row f) The leading arm of the WWC zone(including the portion that collides with the trailing arm)helps toform a dense compressed shell of primary wind that flows in the+x andminusy directions after periastron passage Because the wind ofηB collides with a dense wall of postshock primary wind with highinertia the primary wind controls the overall rate of expansion ofthe resulting spiral (P11)

The overall stability of the expanding shell of primary windon the apastron side of the system depends on the shock thickness(Vishniac 1983 Wunsch et al 2010 P11) Portions of the shellmoving in theminusy direction appear to be the most stable due to the

increased amount of primary wind that borders it in this directionHowever our simulations show that atφ asymp 03 the upper portionof the shell expanding in the+x+y direction starts to fragmentEventually the wind ofηB is able to plough through the shell caus-ing it to separate from the leading arm of the WWC zone (φ asymp 04row c of Figure 6) This produces a pair of dense lsquoarcsrsquo of primarywind on the apastron side of the system The arc expanding in the+xminusy direction is the remnant of the leading arm of the WWCregion from the previous periastron passage The arc in the+x+ydirection is the remnant of the trailing arm of the WWC regionfromjustprior to the previous periastron passage Multiple pairs of thesearcs are visible in Figures 5 and 6 They are also quite spatially ex-tended by the time the system is back at periastron the arcsfromthe previous periastron are up to70a from the central stars (in thexy plane) As the arcs expand further they gradually mix with thesurrounding low-density wind material fromηB

The fragmentation of the shell and formation of the arcs ismainly due to the above-mentioned collision of the leading arm ofthe WWC zone with the trailing arm just after periastron This col-lision produces instabilities at the interface between thetwo arms(P11) which together with the shellrsquos expansion the pressure fromηBrsquos high-velocity wind and the lack of bordering primary windmaterial for support causes the shell to break apart in the+x+ydirectionsim 17 years after periastron

While the term lsquoshellrsquo is used to describe the layer of com-pressed primary wind that flows in the direction of apastron fol-lowing periastron passage this is not related to the lsquoshellejectionrsquoevent discussed in the pastη Car literature (Zanella et al 1984Davidson 1999 Davidson et al 1999 Smith et al 2003a Davidson2005) The scenario proposed by Zanella et al (1984) and advo-cated by Davidson (1999) to explainη Carrsquos spectroscopic eventsis a qualitative single-star model wherein some sort of thermal orsurface instability is presumed to induce significant mass loss fromη Car approximately every 554 years A shell ejection as the resultof a latitude-dependent disturbance in the wind of a single star hasalso been proposed (Smith et al 2003a Davidson 2005) Davidson(2005) suggested that the shell event may be triggered by thecloseapproach of a secondary star but this is still mainly a single-starscenario requiring some kind of surface instability in the primary

In contrast to these ideas the formation of the outflowing shellof primary wind seen in the 3-D SPH simulations is a natural un-avoidable consequence in any high-eccentricity massive CWB inwhich the primary star has a significant mass-loss rate (significantboth in terms of overall mass-loss rate and mass-loss rate relativeto the companion star) It is not so much an lsquoejectionrsquo event as itis a chance for the normal primary wind to flow in the directionof apastron for a brief time (sim 3 minus 5 months) whileηB performsperiastron passage EventuallyηB returns to the apastron side andits high-velocity wind collides with and compresses this primarywind material forming a dense shell that continues to propagate inthe direction of apastron until it breaks apart at its weakest pointresulting in a pair of dense lsquoarcsrsquo as described above

42 Physical Origin and Location of the BroadHigh-Ionization Forbidden Line Emission

Figure 5 presents slices in the orbital plane from the 3-D SPHsim-ulation atφ = 0976 used to model the blue-shifted emission arcsseen at STIS slitPA = +38 The colors show log density logtemperature photoionization zone created byηB and square rootof the modeled emissivity of the [FeIII ] λ4659 line The photoion-ization region is confined to the same side of the system asηB the

ccopy 2011 RAS MNRAS000 1ndash23

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

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12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

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Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

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Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 10: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

10 Madura et al

Figure 5 Snapshots in the orbitalxy plane from the 3-D SPH simulation ofη Car atφ = 0976 used to model the observed blue-shifted emission arcs ofFigure 2 Color shows from left to right log density log temperature photoionization volume created byηB (white = ionized) and square root of the modeledemissivity of the [FeIII ] λ4659 line The color bar in the last panel has been adjusted tomake faint emission more visible The box size isplusmn105a asymp plusmn1622AU

asymp plusmn07primeprime (D = 23 kpc) Axis tick marks correspond to an increment of10a asymp 154 AU asymp 0067primeprime In the last panel [FeIII ] emission only originates frommaterial within the photoionization volume that is near thecritical density of the [FeIII ] line (sim 107 cmminus3) and at the appropriate temperature

dense wind ofηA preventing the far (minusx) side of the system frombeing photoionized All of the [FeIII ] emission is thus concentratedin two spatially-distinct regions on the apastron side of the system

bull The strongest [FeIII ] emission originates near the walls of thecurrent WWC zone in the innersim 30a asymp 02primeprime of η Carbull Faint spatially-extended (out tosim 60a asymp 04primeprime) [Fe III ] emis-

sion arises in the arcs of dense primary wind formed during theprevious periastron passage

The [FeIII ] emission occurs in these two areas because they are theregions within the photoionization zone that are near the criticaldensity of the [FeIII ] line and at the appropriate temperature

Figure 6 illustrates how the density temperature photoion-ization region and [FeIII ] λ4659 emissivity change with orbitalphase The six phases shown correspond to those observed in figure11 of G09 During periastron passage (φ = 0045 and 1040 rowsa and e)ηB becomes deeply embedded in the dense wind ofηAand the photoionization region shrinks considerably downto onlya few semi-major axes across This leads to an effective lsquoshutting-offrsquo of the forbidden line emission at large distances (amp 10a) Byφ = 0213 and 1122 (rows b and f)ηB has moved far enough fromηA to re-establish the large photoionization zone and spatially-extended forbidden line emission The photoionization region islargest and the [FeIII ] most spatially extended around apastron(row cφ = 0407) By φ = 0952 (row d) ηB starts to becomeembedded in the dense wind ofηA the photoionization region inthe+xminusy quadrant decreasing slightly in size

Far-UV radiation fromηB leads to highly ionized regions thatextend outward from its low density wind cavity in the direction ofsystem apastron During periastron passage the disappearance ofthe extended high-ionization forbidden emission can be attributedto the wrapping of the dense primary wind aroundηB which trapsits far-UV radiation and prevents it from photoionizing theouterwind structures responsible for the observed emission While ηB isembedded inηArsquos wind the latter flows unimpeded in the directionof apastron eventually forming dense arcs of material thatexpandoutward asηB completes periastron passage and the inner regionsof the WWC zone regain their near conical shape These coolerdense arcs of expanding primary wind also produce high-ionizationforbidden line emission when photoionized byηB

Observed temporal variations of the high-ionization forbiddenlines can thus be linked to the orbital motion ofηB in its highlyeccentric orbit which causes different portions of the WWCre-gions and extended arcs of primary wind from earlier cycles tobe photoionized As the two stars move closer to or farther fromeach other orbital motion also leads to changes in the density andtemperature of the inner WWC zone which in turn modifies thesize and shape ofηBrsquos photoionization volume and thus the over-all shape location and intensity of the high-ionization forbiddenline emission even at phases away from periastron (rows b c dand f of Figure 6) Forbidden line emission from the compressedinner WWC region increases in intensity until the critical densityis reached or the temperature exceeds that at which the appropriateions can exist Forbidden emission from the extended arcs ofpri-mary wind decreases in intensity as the arcs gradually expand andmix with the surrounding low-density wind material fromηB

43 Synthetic Slit Spectro-images and Constraining theOrbital Orientation

431 Constraint 1 Emission Arcs at Slit PA =+38 φ = 0976

The blue-shifted emission arcs in Figure 2 represent distinct well-defined structures observed at a specific orbital phase and slit PAAs such they provide a natural basis for modeling and can be usedto constrain the orbital orientation We have performed a parameterstudy ini θ andPAz with the goal of determining which set(s)if any of orientation parameters result in synthetic spectro-imagesthat closely match the observations in Figure 2 The value ofθ wasvaried in15 increments for values of0 6 θ 6 360 with i variedin 5 increments over the range0 6 i 6 180 for eachθ valueandPAz varied in5 increments over the range0 6 PAz 6 360

for each pair ofi θ valuesWe find that only synthetic spectro-images generated for

minus15 6 θ 6 +45 are able to reasonably match the observationstaken atφ = 0976 PA = 38 However an ambiguity exists ini andPAz with values of30 6 i 6 50 PAz = 272 to 332

(top row of Figure 7) and130 6 i 6 150 PAz = 282 to 342

(bottom row of Figure 7) both capable of producing entirely blue-shifted arcs that resemble those observed Our best morphological

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Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

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Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

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Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

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Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 11: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 11

Figure 6 Same as Figure 5 but forφ = 0045 0213 0407 0952 1040 and 1122 (rows top to bottom) which correspond to phases at whichHSTSTISobservations were accomplished (figure 11 of G09) Insets inthe first two columns are a zoom of the inner10a included to illustrate the complex dynamicsof the lsquocurrentrsquo WWC region

ccopy 2011 RAS MNRAS000 1ndash23

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

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Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

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Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

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16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

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Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

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18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 12: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

12 Madura et al

Figure 7 2-D spatial distribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line and synthetic spectro-images for orbitalorientationsi = 42 θ = 7 PAz = 302 (top row) andi = 138 θ = 7 PAz = 317 (bottom row) which lie near the centers of the two derivedbest-fit ranges of orientation parameters for matching the observations taken atφ = 0976 PA = 38 in Figure 2 Columns are from left to right 2-Ddistribution on the sky of the square root of the modeled intensity in the [FeIII ] λ4659 line for blue-shifted material withvlos betweenminus500 km sminus1 andminus100 km sminus1 same as first column but for red-shifted material withvlos between+100 km sminus1 and+500 km sminus1 model spectro-image convolved withthe response ofHSTSTIS and observed spectro-image with mask The projectedx y andz axes are shown for reference in the 2-D images of the intensityon the sky as is the direction of north The01primeprime wide STIS slit atPA = +38 is also overlaid Roman numerals I and II indicate the top andbottom ofthe slit respectively All following 2-D projections of the modeled [FeIII ] intensity in this paper use this same labeling conventionThe color scale in thespectro-images is proportional to the square root of the intensity and the velocity scale isplusmn600 km sminus1 Lengths are in arcseconds

fits are obtained using values ofi = 42 θ = 7 PAz = 302

or i = 138 θ = 7 PAz = 317 which lie near the centers ofthese two derived ranges of best-fit orientation parameters

The observed morphology and asymmetries in brightness andvlos of the spatially-extended emission arcs determine the allowedranges of the orbital orientation parameters The parameters i andPAz primarily control the brightness asymmetry and spatial orien-tation of the blue- and red-shifted emission components on the skyFigure 7 shows that the synthetic spectro-images at slitPA = 38

for i = 42 and138 (at nearly identicalθ andPAz) are remark-ably similar Yet the two orbital orientations are drastically dif-ferent resulting in unique distributions on the sky of the blue- andred-shifted emission The red component is the most notable whichextends to the SE fori = 42 but to the NW fori = 138 Theasymmetry in brightness between the two blue-shifted arcs is alsocontrolled byi Only values of30 6 i 6 50 or130 6 i 6 150

produce a brightness asymmetry with otheri resulting in arcs thatare approximately equal in brightness

The value ofPAz determines the final orientation of the pro-jectedz axis and thus of the individual emission components Be-cause the lower blue-shifted arc in the observations is brighter thanthe upper arc the extended blue emission projected on the sky mustbe brighter in directions to the SW (where the lower half of the slitis located position II in Figure 7) and dimmer in directions to theNE (position I) This limitsPAz to values between272 and342

More importantlyi andPAz determine the 3-D orientationof the orbital axis Ifi = 42 andPAz = 272 to 342 theorbital axis is inclined toward the observer andis not alignedwith the Homunculus polar axis The two stars would also orbitcounter-clockwise on the sky However ifi = 138 then because

PAz asymp 312 the orbital axisis closely alignedin 3-D with theHomunculus polar axis and the stars orbit clockwise on the sky

Figure 8 shows that the value ofθ (for fixed i = 138

and PAz = 312) determines thevlos of the material exhibit-ing [FeIII ] emission According to our 3-D model the spatially-extended [FeIII ] emission originates in the expanding arcs of denseprimary wind formed during the previous periastron passage Whenθ asymp 0 (top row of Figure 8) this emission is mostly blue-shiftedbecause the emitting material withinηBrsquos photoionization zoneis moving mostly toward the observer The model spectro-imageconsists of spatially-extended blue-shifted arcs because the slit atPA = 38 primarily samples the blue component which stretchesfrom NE to SW on the sky In contrast the extended red componentis not sampled only a small amount of red-shifted emission in thevery centralplusmn01primeprime core falls within the slit Moreover only valuesof minus15 6 θ 6 +45 produce significant amounts of spatially-extended (sim 07primeprime in total length) blue-shifted emission with thecorrect observed asymmetry invlos wherein the dimmer upper arcextendssim 75 km sminus1 more to the blue than the brighter lower arc

Figure 7 demonstrates that our 3-D dynamical model and de-rived best-fit orbital orientation(s) reproduce all of the key featuresin the observations taken atφ = 0976 PA = 38 Both syn-thetic and observed spectro-images contain concentratedvelocity-extended emission in the centralplusmn01primeprime core The completely blue-shifted emission arcs extend to roughly the same spatial distances(sim plusmn035primeprime) The asymmetry in brightness between the upper andlower arcs is matched as well The asymmetry invlos is also repro-duced and of the same magnitude However the arcs in the modelimages stretch a bit farther to the blue tosim minus550 km sminus1 (upperarc) andminus475 km sminus1 (lower arc) versussim minus475 km sminus1 andminus400 km sminus1 in the observations The synthetic images thus show

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 13: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 13

Figure 8 Same as Figure 7 but for values ofθ = 0 90 180 and 270 (rows top to bottom) assumingi = 138 andPAz = 312

emission at velocities slightly above the value used in the SPH sim-ulation forηArsquos wind terminal speed This is a minor discrepancythough likely due to the extended emitting material receiving anextra lsquopushrsquo from the fast wind ofηB (see subsection 434)

4311 Results for Orbital Orientations with a θ asymp 180

Returning back to Figure 8 one sees that the spectro-image forθ = 180 fails to match the observations There is a distinct lackof any spatially-extended blue-shifted emission Instead the ex-tended emission arcs are entirelyred-shifteddue to the quite dif-ferent vlos of the emitting material Whenθ = 180 ηA is be-tween the observer andηB during most of the orbit Therefore allof the emitting material withinηBrsquos photoionization zone is on thefar side of the system and movingaway fromthe observer The ex-tended forbidden line emission is thus mostly red-shiftedThe slit atPA = 38 now primarily samples this red component producing aspectro-image consisting of entirely red-shifted spatially-extendedarcs the directoppositeof the observations

Changing the value ofi andorPAz when θ = 180 does

not result in a better match to the observations since most ofthe material photoionized byηB and exhibiting forbidden lineemission is still moving away from the observer This is truefor all values ofθ near 180 none of the model images gener-ated for 135 6 θ 6 225 regardless of the assumedi andPAz matches theφ = 0976 PA = 38 observations Ex-ample model spectro-images for these orientations can be foundin Madura (2010) We therefore find that an orbital orientationthat placesηB on the near side ofηA at periastron such asthat favored by Falceta-Goncalves et al (2005) Abraham et al(2005b) Abraham amp Falceta-Goncalves (2007) Kashi amp Soker(2007 2008) Falceta-Goncalves amp Abraham (2009) and others isexplicitly ruled out

4312 Results for Orientations with θ asymp 90 and 270

Model spectro-images forθ = 90 and 270 also fail to matchthe observations The 2-D images of the modeled [FeIII ] intensityon the sky in Figure 8 show that in both cases one half of the STISslit is empty (from center to position II forθ = 90 and from I

ccopy 2011 RAS MNRAS000 1ndash23

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

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Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

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Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

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Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

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Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 14: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

14 Madura et al

Figure 9 Same as Figure 7 but forφ = 0952 slit PA = minus28 Note that the red- and blue-shifted emission in the model spectro-image that assumesi = 42 (top row) spatially extends in the wrong directions compared to the observationsη Carrsquos orbital orientation parameters are thus constrainedto valuesof i asymp 130 to 145 θ asymp 0 to 15 PAz asymp 302 to 327 (see text)

to the center forθ = 270) Therefore emission is absent to oneside spatially in the spectro-images Changing the value ofi has noeffect on this since a change ini at theseθ values is equivalent toa rotation about thex axis in the 2-D intensity images Instead arotation of nearly90 in PAz is needed in order to place emittingmaterial in both halves of the slit However such a rotationdoesnot result in a match to the observations Synthetic spectro-imagesfor 45 lt θ lt 135 and225 lt θ lt 345 all suffer from thesame problems namely either no blue-shifted ring-like emissionfeature (ifPAz asymp 132 or 312) or arc-like emission to only oneside spatially (ifPAz asymp 42 or 222) (Madura 2010) This is trueregardless of thei andPAz assumed

432 Constraint 2 Variations with Phase at Slit PA =minus28

Using the 3-D dynamical model we generated synthetic spectro-images for a slitPA = minus28 at each of the phases in figure 11of G09φ = 0045 0213 0407 0952 1040 and 1122 Themain goals were to determine if the binary scenario and 3-D modelcould explain the phase dependence observed in the high-ionizationforbidden lines and whether the set ofPA = minus28 observationscould resolve the ambiguity between the sets ofi = 35 minus 50 andi = 130minus145 best-fit orientations found in the above subsection

Figure 9 illustrates the results of investigating the two best-fit i regimes It is clear that synthetic spectro-images fori asymp 30

to 50 do not match the observations taken at slitPA = minus28

(top row of Figure 9) There are a number of discrepancies butthe most important and obvious is that the blue- and red-shiftedemission components in the synthetic spectro-image extendin thewrong spatial directions with the blue emission stretching to theNW and the red to the SE theoppositeof the observations

In contrast synthetic images generated fori asymp 130 to 150

(bottom row of Figure 9)arecapable of matching the observationsThe morphology of thePA = minus28 observations breaks the de-generacy ini and fully constrains in 3-Dη Carrsquos orbit Becausered-shifted emission is observed to extend spatially in directions to

the NW the red emission component of [FeIII ] on the sky must beoriented such that it too stretches NW and falls within the top halfof thePA = minus28 slit The synthetic images of the [FeIII ] inten-sity on the sky (first two columns of Figures 9 and 10) illustratehow the slit atPA = minus28 samples the emitting regions ofη Carrsquosextended interacting winds in very different directions compared toslit PA = 38 This is why the observed spectro-images are so dif-ferent between the two slit PAs even at similar orbital phases Wefind thatonly orbital orientations withi asymp 130 to 145 θ asymp 0

to 15 PAz asymp 302 to 327 are able to simultaneously match theobservations taken at both slitPA = 38 andminus28

Figure 10 shows that the 3-D dynamical model and derived or-bital orientation reproduce the overall observed shape andvelocitystructure of the [FeIII ] emission at each phase for slitPA = minus28Figure 10 further illustrates howη Carrsquos extended interacting windschange with time The orientation of the blue component doesnotappear to change always stretching from NE to SW on the skyHowever the spatial extent does change growing larger going fromperiastron to apastron as the wind structures flow outward Movingfrom apastron back to periastron the intensity and spatialextent ofthe blue component eventually start to decrease as the expandingarcs of primary wind drop in density and mix with the surroundingwind from ηB The red-shifted emission changes in a way similarto that of the blue component but points mainly NW

433 Constraint 3 Observed Variations withφ and Slit PA

Synthetic spectro-images were generated at the ten combinations ofphase and slit PA in Table 2 assuming the best-fit orientation i =138 θ = 7 andPAz = 317 The goal was to determine howwell the 3-D model and derived binary orientation could reproduceobservations at a variety of other phases and slit PAs Modelimagesfor φ = 1001 and1013 are nearly identical to those atφ = 0045and1040 in Figure 10 and add no new information We thereforefocus this discussion on the phases before and after periastron

Figure 11 presents the results The overall match between syn-

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 15: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 15

Figure 10 Same as Figure 7 but for phases (rows top to bottom)φ = 0045 0213 0407 0952 1040 and 1122 with the STIS slit atPA = minus28 (as infigure 11 of G09) and assumingi = 138 θ = 7 PAz = 317

ccopy 2011 RAS MNRAS000 1ndash23

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

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Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 16: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

16 Madura et al

Table 2 Phases and slit PAs from figures 12 and 13 of G09 modeled inSection 433 and shown in Figure 11

φ PA Figure

0601 +22 11a0738 minus82 11b0820 +69 11c0930 minus57 11d0970 +27 11e0984 +62 11f0995 +70 11g1001 +69 minus

1013 +105 minus

1068 minus142 11h

thetic and observed spectro-images is quite good The modelrepro-duces all of the key spatial features namely extended (gt plusmn01primeprime)[Fe III ] emission that is almost entirely blue-shifted for positive slitPAs but that is partially red-shifted for negative slit PAs Observedvariations in emission with phase are also reproduced

Model images atφ = 0601 (11a) and0738 (11b) demon-strate how a large change in slit PA results in very differentspectro-images The spatial distributions of the emission on the skyare verysimilar at these two phases as expected since the system is nearapastron when orbital velocities are their lowest However the slitat PA = minus82 samples the emission in very different directionscompared toPA = 22 producing a spectro-image that resemblesthose taken atPA = minus28 in Figure 10

The partial ring of emission observed atφ = 0984 PA =62 (11f) is also noteworthy The match between model and ob-servations is very good the emission arc to the SW present inbothas well as the much shorter arc to the NE betweensim minus500 km sminus1

andminus350 km sminus1 Two effects appear to be causing the NE arc tobe shorter First due to their outward expansion the extended arcsof primary wind have dropped in density and started to mix withthe surrounding low-density wind fromηB Second the photoion-ization of material in directions to the NE byηB has diminisheddue to its clockwise orbital motion and gradual embedding inηA rsquoswind These lead to a decrease in the amount of extended [FeIII ]emission to the NE This combined with the slit PA producesapartial arc of blue-shifted emission to the NE in the spectro-image

By φ = 0995 (11g) the extended emission has vanished im-plying that the ionizing flux of photons fromηB shuts off sometimebetweenφ = 0984 and 0995 Atφ = 1068 (11h) there is still noobserved spatially-extended emission Yet the 2-D model imagesof the intensity on the sky show that the extended [FeIII ] emissionhas started to return in directions to the NE This is visiblein themodel spectro-image as a bright blue-shifted bulge that points NEUnfortunately the observational data in the centralplusmn015primeprime is ofinsufficient quality to tell if such an emission bulge was detectedNevertheless the 3-D model predicts thatηB should start to emergefrom ηA rsquos dense wind and begin to restore the spatially-extendedhigh-ionization forbidden line emission atφ asymp 1068

434 Discrepancies Between the Observations and 3-D Model

During most of the orbit the wind ofηB collides with the densearcs of primary wind on the apastron side of the system where

the spatially-extended forbidden line emission forms (seerows bthrough d of Figure 6) Because the arcs are bordered by a largelow-density wind cavity created earlier byηB they have almost nosupport againstηBrsquos high-velocity wind which is able to drive por-tions of the arcs into the cavity at velocities just above their outflowspeed the terminal speed of the primary wind An orientation thatplaces the observer on the apastron side of the system thus resultsin model spectro-images containing blue-shifted emissionat veloc-ities slightly higher than the wind terminal velocity of theprimary

Because the observations do not contain blue-shifted emissionat speeds more thansim 500 km sminus1 the wind speed(s) ofηA andorηB used in the SPH simulation may be a bit too large The launch-ing of the two winds at their terminal velocity in the simulationmay also be having a small effect on the results Better constraintson ηBrsquos wind terminal speed and improved 3-D simulations withproper driving of the stellar winds should help resolve these is-sues Improved modeling coupled with future observations of theextended forbidden emission inη Carrsquos central arcsecond also hasthe potential to further constrain the wind terminal velocity of ηA

The main discrepancies between synthetic spectro-images as-sumingi = 138 θ = 7 PAz = 317 and the observationsfor slit PA = minus28 are (1) the extended blue-shifted componentis locatedsim 100 km sminus1 farther to the blue in the model imagesthan in the observations and (2) the red-shifted componentin themodel images issim 75 km sminus1 broader than observed Both issuesare likely due to the reasons discussed above concerning thewindterminal velocities ofηA andηB

5 DISCUSSION

51 The Orientation and Direction of η Carrsquos Binary Orbit

There has been much speculation about the binary orientation andmany papers published offering suggestions (see Section1) Thedetailed modeling of Section4 tightly constrains the observerrsquosline-of-sight to angles ofθ asymp 0 minus 15 prograde of the semi-majoraxis on the apastron side of the system placingηB behindηA dur-ing periastron Given the uncertainties in the stellar and wind pa-rameters ofηB used in the 3-D simulations and the assumption thatphase zero of the orbital and spectroscopic periods coincide valuesof minus15 θ +30 may also be possible A study in the stel-larwind parameters ofηB or improved observational constraintsis needed to further refine the value ofθ

More importantly the results bound for the first time theorientation ofη Carrsquos orbital plane with the orbital axis closelyaligned in 3-D with the inferred polar axis of the Homunculusatan i asymp 130 minus 145 andPAz asymp 302 minus 327 Figure 12 illus-trates the orientation ofη Carrsquos binary orbit on the sky relative tothe Homunculus Withi asymp 138 θ asymp 7 andPAz asymp 317 the re-sulting projected orbit on the sky hasηB movingclockwiserelativeto ηA with ηB approachingηA from the SW prior to periastronand receding to the NE afterward

In their recent work modelingη CarrsquosRXTElight curve O08and P09 investigated values ofi in the range0 lt i lt 90 andeach obtained a best-fit value ofi asymp 42 which they state is consis-tent with the orbital axis of theη Car binary being aligned with theHomunculus polar axis However the inclination angle of the Ho-munculus as defined in Davidson et al (2001) and Smith (2006b)corresponds to the tilt of the polar axis out of the line of sight (fig-ure 5 of Davidson et al 2001) Since this is the same quantityasthe inclination defined for binary orbits the polar axis of the Ho-munculus is tilted from the plane of the sky bysim 48 Therefore

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

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Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

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Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 17: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 17

Figure 11 A Same as Figure 10 but for the observed orbital phases and STIS slit PAs listed in Table 2 Phases are (top to bottom)φ = 0601 0738 0820and 0930 The01primeprime wide STIS slit is shown overlaid at the appropriate PA in the 2-D images of the modeled intensity on the sky Roman numeralsI and IIindicate the top and bottom of the slit respectively

an i asymp 138 is required in order for theη Car orbital axis to bealigned with the Homunculus polar axisnot 42

The spatially-unresolved nature of the X-ray observationsandoverall top-bottom symmetry of the problem are what allowedO08and P09 to reasonably reproduce theRXTElight curve using ani asymp42 However ani asymp 138 works as well Moreover with eitherianyPA on the sky of the orbital axis produces a good fit to theRXTElight curve Unfortunately this ambiguity ini and PA of the orbitalaxis has not been sufficiently discussed in theη Car literature andmost have simply assumed that the orbital and Homunculus polaraxes are aligned Yet knowing the value ofi is crucial for properinterpretation of spatially-resolved observational diagnostics andmost importantly determining the stellar masses

Taking into account this ambiguity ini inherent to 3-D mod-els of X-ray data our derived ranges ofi and θ agree very wellwith those of O08 P09 and P11 They are also consistent withthei andω values derived by Groh et al (2010b) in their attempts to

understand the origin of the high-velocity (up tominus1900 km sminus1)absorption wing detected in HeI λ10830 during η Carrsquos 2009periastron passage Our binary orientation is in complete agree-ment with simple models proposed to explain the available ra-dio (Duncan amp White 2003 White et al 2005) and HeII λ4686(Teodoro et al 2011) observations as well

Further support for our results and derived orbital orientationcomes from recent work by Mehner et al (2010) who mapped theflux of the broad blue-shifted component of [FeIII ] λ4659 andfound that most of the emission originates in the inner015primeprime re-gion ofη Car (see their figure 8) The synthetic spectro-images and2-D spatial maps of [FeIII ] λ4659 in Section4 show that most ofthe emission should indeed originate in the inner015primeprime Accordingto our 3-D model this emission forms innear the current WWCzone in regions photoionized byηB and manifests itself in spectro-images as a bright central streak in the innerplusmn015primeprime that spans awide range of velocities from blue to red This emission appears

ccopy 2011 RAS MNRAS000 1ndash23

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 18: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

18 Madura et al

Figure 11 B Same as Figure 11A but at phases (top to bottom)φ = 0970 0984 0995 and 1068

as a bright central streak becauseHSTSTIS lacks the resolutionnecessary to resolve the inner WWC regionrsquos complex features

Mehner et al (2010) additionally found that the spatial distri-bution of the blue-shifted component of [FeIII ] λ4659 in the cen-tral 01primeprime of η Car is not as sharp as a stellar point source and isdetectably elongated to the NE and SW (see their figures 8 and 9)Model images displaying the 2-D spatial distribution on thesky ofthe blue-shifted component of [FeIII ] λ4659 (first column of Fig-ures 7 10 and 11) show that the emissionis elongated to the NEand SW for our suggested orbital orientation even in the central01primeprime While detailed mapping withHSTSTIS is needed to verifythe results of Mehner et al (2010) they do strongly suggestthatour 3-D model and binary orientation are correct

All other orbital orientations such as that withθ asymp 180 fa-vored by Falceta-Goncalves et al (2005) Abraham et al (2005b)Abraham amp Falceta-Goncalves (2007) Kashi amp Soker (20072008) Falceta-Goncalves amp Abraham (2009) and Kashi amp Soker(2009) produce spectro-images that are in strong disagreementwith the φ = 0976 PA = 38 observations lacking any

spatially-extended blue-shifted emission and containing signifi-cant amounts of extended red-shifted emission WithηB the mainsource of photons capable of producing high-ionization forbiddenline emission there is no realistic situation withθ asymp 180 for anyi andPAz that can produce spectro-images like those observedsince there will always be an extended red-shifted componentHypothesizing some method to absorb or diminish the red-shiftedemission does not help since there would then be almostnospatially-extended emission detected at slitPA = 38

There is no known source of ionizing photons in theη Carsystem that permits aθ asymp 180 orientation Photons generated inthe WWC region will not work simply because the WWC zone ison the opposite side of the system during most of the orbit andηArsquosdense wind would easily absorb any such photons before they reachthe periastron side Even if some contrived process could producesignificant amounts of spatially-extended blue-shifted emission onthe periastron side of the system this would not result in a match tothe observations as the spectro-images would then contain both red-andblue-shifted extended emission There would have to be some

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 19: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 19

Figure 12 Illustration of η Carrsquos binary orbit (inset yellow) on the skyrelative to the Homunculus nebula for a binary orientation with i = 138θ = 7 andPAz = 317 which lies near the center of our best-fit rangeof orbital parameters The+z orbital axis (blue) is closely aligned with theHomunculus polar axis in 3-DηB orbits clockwise on the sky relative toηA(black arrows in inset) and apastron is on the observerrsquos side of the systemThe semi-major axis (+x-axis red) runs from NW to SE on the sky whilethe semi-minor axis (+y-axis green) runs from SW to NE North is up

way to absorb or diminish the extended optically-thin red-shiftedemission while allowing the blue-shifted emission component toreach the observer The problem is that extended red-shifted emis-sion is observed at other slit PAs even for similar orbital phasesTherefore the absorptiondiminution would have to be restricted tovery specific extended regions on the sky which seems unrealisticGiven all of these issues as well as those concerning the observedphase dependence of the emission an orientation that places apas-tron on our side of the system seems unavoidable

511 Observational Support from the Weigelt Blobs

While a detailed review ofη Carrsquos spectral variability is beyond thescope of this paper it now seems well established that observedphase-dependent narrow ( 50 km sminus1) high-ionization forbiddenemission lines form in Weigelt blobs B C and D (Davidson et al1995 Zethson 2001 Zethson et al 2011 Damineli et al 2008abMehner et al 2010) Illumination of the Weigelt blobs byηB is re-quired for the formation of these narrow lines which are presentduring most ofη Carrsquos 55-year orbit and fade during perias-tron passage gradually returning to their lsquonormalrsquo strength a fewmonths afterward (Verner et al 2005 Mehner et al 2010)

Our proposed orientation and direction forη Carrsquos binary or-bit are consistent with and provide an explanation for thetimevariability of the narrow-line emission features seen in the Weigeltblobs Davidson et al (1995 1997) found that Weigelt blobsB Cand D are located within015primeprime to 03primeprime NW of the central stel-lar source near the Homunculus equatorial plane (see Figure2)

Based on proper motions and observed blue-shifted emission theWeigelt blobs are located on the same side ofη Car as the ob-server and are thought to have been ejected sometime around thesmaller eruption of 1890 that also formed the Little Homuncu-lus (Davidson amp Humphreys 1997 Zethson 2001 Ishibashi et al2003 Smith et al 2004 Nielsen et al 2007a Mehner et al 2010)Since the Weigelt blobs are on the same side of the system as theobserver and becauseηB is required for the formation of the nar-row high-ionization forbidden lines that form in the blobsduringmost of the orbit one easily concludes thatηB must be on the sameside of the system as the observer during most of the orbit

Moreover the Weigelt blobs are located in the NW quadrant ofthe system For our proposed orbital orientation during most of theorbit the low-density wind cavity created byηB is open toward andpointing NW in the direction of the blobs The low-density cavitythus provides a path for the ionizing photons fromηB to reach theWeigelt blobs and produce the high-ionization emission Over thecourse of the 55-year orbitηB gradually moves from SE to NW onthe sky when going from periastron to apastron and then fromtheNW back to the SE when moving from apastron to periastron Theorbital motion ofηB and gradual embedding in the wind ofηA closeto periastron leads to changes in the spatial extent and directionof the photoionization region which causes observed variations inthe narrow high-excitation emission in the blobs During periastronpassage the ionizing flux fromηB shuts off and the high-excitationemission from the blobs fades It takes several months afterperias-tron for ηB to restore the large photoionization volume that facesNW and thus the high-excitation emission in the blobs

While omitting some of the details this qualitative picture isconsistent with the known behavior of the Weigelt blobs Thepro-posed clockwise direction ofηBrsquos orbit is further supported by theimages of Smith et al (2004) which show excess UV emission tothe SW ofη Car just before periastron and to the NE just after Acomplete review of all of the available observations ofη Car andhow they support the derived orientation and direction of the binaryorbit is obviously not possible here However we note that the ori-entation shown in Figure 12 and clockwise motion on the sky ofηBare consistent with all known observations ofη Car to date

52 Implications for Theories for the Formation of theHomunculus Nebula and the Nature of ηArsquos Wind

A variety of models ranging from the interaction of stellarwindswith differing speeds and densities to binary interactions andeven a binary merger have been proposed for explaining boththeGreat Eruption and the bipolar shape of the resulting nebula(Smith2009) Observational studies of the Homunculus have firmly estab-lished that its polar axis is orientated on the sky at aPA ≃ 312and that its inclination is42 plusmn 1 (Davidson et al 2001 Smith2006b 2009) As shown in Figure 12 the orbital axis of theη Carbinary for our best-fit range of orientation parameters is closelyaligned in 3-D with the Homunculus polar axis Such an alignmenthas important implications for theories for the formation of the Ho-munculus andor the present-day shape ofηArsquos wind

HSTSTIS long-slit spectral observations of the Homunculusby Smith et al (2003a) indicate that the reflected stellar spectrumover the poles has stronger and broader absorption in Hα implyinga denser polar outflow Very Large Telescope (VLT)Very LargeTelescope Interferometer (VLTI) observations of the optically thickstellar wind ofηA by van Boekel et al (2003) and Weigelt et al(2007) also indicate thatηArsquos wind could be prolate in shape andaligned at the same PA on the sky as the Homunculus Many have

ccopy 2011 RAS MNRAS000 1ndash23

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 20: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

20 Madura et al

interpreted these observational studies as evidence for the current-day wind ofηA being prolate with a bipolar form and orientationsimilar to the Homunculus Thus one explanation offered for boththe Homunculusrsquo formation and the nature of the present-daywindis thatηA is a rapid rotator (Owocki amp Gayley 1997 Maeder ampMeynet 2000 Dwarkadas amp Owocki 2002 Smith et al 2003aOwocki Gayley amp Shaviv 2004) the effects of gravity darken-ing on radiation-driven wind outflows from a rapidly rotating starsuggested as a way of explaining both the high polar densities andvelocities inferred inηArsquos extended wind

However using 2-D radiative transfer models Groh et al(2010a) and Groh (2011) find that the density structure ofηA rsquoswind can be sufficiently disturbed byηB thus strongly affectingthe observed UV spectrum optical hydrogen lines and mimick-ing the effects of fast rotation in the interferometric observablesGroh et al (2010a) further show that even ifηA is a fast rotatormodels of the interferometric data are not unique and both prolate-and oblate-wind models can reproduce the interferometric observa-tions These prolate- and oblate-wind models additionallysuggestthat the rotation axis ofηA would not be aligned with the Homuncu-lus polar axis Further complicating the situation are the recent re-sults of Mehner et al (2011) who find no evidence for higher windvelocities at high stellar latitudes in Hδ P Cygni profiles obtainedduring η Carrsquos normal state (see their Section 5) Together thesenew results challenge the idea that the present-day wind ofηA islatitudinally-dependent and prolate in shape

In this context it is noteworthy that the results in Section4match the observations so well given that the winds from both starsare assumed to be spherical in the 3-D simulations New 3-D simu-lations with a latitudinal-dependent wind forηA and comparison ofthe resulting spectro-images to the observations may provide addi-tional clues as to the nature ofηArsquos present-day wind It is impor-tant to keep in mind though that these new results do not necessar-ily mean thatηArsquos wind was not latitudinally-dependent in the pastLatitudinal-dependent mass-loss from a rapidly-rotatingηA couldhave played a role in the formation of the Homunculus Howeverthe argument for this possibility should not be made based ontheabove-mentioned observations ofηArsquos current-day wind

If ηArsquos rotation axis is aligned with the orbital axis and thestar is a rapid rotator then the extended wind should be prolateand aligned at nearly the same PA as the Homunculus Howeverthe orbital axis and rotation axis ofηA do not have to be alignedThis is another common assumption with important implicationsfor theories proposed to explainη Carrsquos spectroscopic events(Davidson amp Humphreys 1997 Smith et al 2003a Mehner et al2011) Future observations using diagnostics that are not signifi-cantly affected byηB are needed to determine whether or notηAis a rapid rotator and whether its rotation axis is aligned with theorbital axis

Alignment of the orbital and Homunculus polar axes stronglysuggests that binarity played a role in the Great Eruption and pos-sibly the smaller eruption that later formed the Little HomunculusA binary merger seems unlikely given the multiple known largeeruptions of the system (Smith 2009) The most likely situation in-volves some sort of interaction betweenηA andηB at periastronSmith et al (2003a) suggested a scenario in which a rotatingηAloses mass due to increased angular momentum caused by an in-teraction withηB Models for the periastron-passage triggering ofη Carrsquos massive eruptions and the requirement of a binary to ex-plain the bipolar shape of the Homunculus have also been proposedby Soker and colleagues (Kashi amp Soker 2010 Soker 2004 2007)

More recently Smith amp Frew (2011) presented a revised his-

torical light curve forη Car showing that two 100-day peaks ob-served in 1838 and 1843 just before the Great Eruption coincideto within weeks of periastron provided the orbital period then wasshorter than the current period bysim 5 The beginning ofη Carrsquoslesser outburst in 1890 also seems to have occurred around perias-tron (Smith amp Frew 2011) Based on these findings and other con-siderations Smith (2011) proposes that a stellar collision occurredat periastron before and duringη Carrsquos Great Eruption withηBplunging deeply into the bloated photosphere ofηA Is close align-ment of the orbital axis and polar axis of the Homunculus evidencefor such a scenario Only detailed theoretical modeling cananswerthis question but given the now apparent alignment of the two axesbinary interaction scenarios should be seriously considered as pos-sible explanations forη Carrsquos multiple massive eruptions

53 Probing Changes in η Carrsquos Stellar and WindParameters via Long-Term Monitoring of the ForbiddenLine Emission

The η Car system not only has a centuries-long history of vari-ation including two major eruptions it exhibits shorter-termvariability with a 55-year period (Davidson amp Humphreys 1997Humphreys et al 2008 Smith amp Frew 2011) This implies thatη Carrsquos numerous spectroscopic events are also related to periastronpassage (Damineli et al 2008ab) Contrary to many expectationsη Carrsquos 20090 spectroscopic event was considerably different thanthat of earlier cycles (C11 Mehner et al 2011) The observed X-ray minimum in 2009 was substantially shorter than the minimain 1998 and 2003 by approximately one month (C10 C11) Theemission strength of Hα and various X-ray lines also appears tohave decreased by factors of order two (C11) RecentHSTWFPC2observations by Mehner et al (2011) show that the minimum intheUV was much deeper (again by about a factor of two) for the 2009event than for the 2003 event While still the subject of debatethe behavior of [HeII ] λ4686 might have been different in 2009 aswell with a second lsquooutburstrsquo occurringsim 30 days after the first(Teodoro et al 2011 Mehner et al 2011)

The cause of this sudden change in the behavior ofη Carrsquosspectroscopic event is still poorly understood One proposed expla-nation is that the mass-loss rate ofηA has suddenly decreased byat least a factor of two (C10 C11 Mehner et al 2011) Howeverthis is far from confirmed and the exact reasons for such a dropare unknown The results in this paper suggest a possible waytoobservationally test the idea thatηArsquos mass-loss rate has recentlychanged All of theHSTSTIS observations modeled were taken inor before 2004 The model in this paper assumes a mass-loss rate of10minus3 M⊙ yrminus1 for ηA which is based on earlier observational andmodeling studies (Davidson amp Humphreys 1997 H01 H06) Thegood match between the synthetic spectro-images and the observa-tions suggests that the mass-loss rate ofηA wassim 10minus3 M⊙ yrminus1

at the time the observations were takenThe results in Section 4 though are strongly dependent on the

mass-loss rate assumed forηA and the ionizing flux of photonsassumed forηB If the ionizing flux of photons fromηB remainsconstant but the mass-loss rate ofηA drops by a factor of two ormore the size of the photoionization region should increase consid-erably Therefore the spatial extent and flux of the observed high-ionization forbidden lines should also drastically change The phasedependence of the forbidden emission would likely differ with thehigh-ionization emission vanishing at later phases (compared toearlier orbital cycles) when going into periastron and reappearingat earlier phases afterward Observed variations with slitPA should

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

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Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 21: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 21

be different too possibly showing longer spatially-extended struc-tures and even new components at differentvlos Changes in thewind terminal velocity ofηA could be similarly investigated usingthe maximum observedvlos of the spatially-extended emission

Multi-epoch observations coupled with improved 3-D radia-tive transfer modeling of the high-ionization forbidden line emis-sion would also help in determining if there is a significant changein ηBrsquos ionizing flux of photons mass-loss rate or wind terminalspeed Constraints on the ionizing flux of photons fromηB couldbe compared to stellar models for a range of O (Martins et al 2005)and WR (Crowther 2007) stars allowing one to obtain a luminosityand temperature forηB

6 SUMMARY AND CONCLUSIONS

A major goal of this paper has been to use the 3-D dynamicalmodel and availableHSTSTIS observations of high-ionization for-bidden lines to constrain the absolute 3-D orientation and directionof η Carrsquos binary orbit The spatially-resolved spectroscopicobser-vations obtained with theHSTSTIS provide the crucial spatialandvelocity information needed to help accomplish this Sincethe for-bidden lines do not have an absorption component they providea clear view throughoutη Carrsquos extended interacting winds Eachhigh-ionization forbidden line arisesonly in regions where (1) pho-toionization byηB can produce the required ion (2) the density isnear the linersquos critical density and (3) the material is at the appro-priate temperature Our results are therefore not as dependent onthe many complicated details and effects encountered when mod-eling other forms of emission andor absorption such as X-rays orspectral features of HI HeI or other species (H01 H06 Nielsenet al 2007b P11)

Synthetic spectro-images of [FeIII ] emission line structuresgenerated using 3-D SPH simulations ofη Carrsquos binary WWC andradiative transfer codes were compared to the availableHSTSTISobservations for a variety of orbital phases and STIS slit PAs Themodel spectro-images provide important details about the physicalmechanisms responsible for the observed high-ionization forbiddenline emission as well as the location and orientation of theobservedemitting structures Below we summarize our key conclusions andoutline the direction of future work

(i) Large-scale (sim 1600 AU) 3-D SPH simulations ofη Carrsquosbinary colliding winds show that during periastron passage thedense wind ofηA flows unimpeded in the direction of system apas-tron (Figure 6) Following periastronηBrsquos high-velocity wind col-lides with this primary wind material creating dense shells thatexpand outward duringη Carrsquos 55-year orbital cycle These shellseventually fragment forming a pair of dense spatially-extendedlsquoarcsrsquo of primary wind on the apastron side of the system Afterseveral orbital cycles the arcs drop in density and mix withthesurrounding low-density wind material fromηB

(ii) During most ofη Carrsquos orbit far-UV radiation fromηB pho-toionizes a significant spatially-extended region on the apastronside of the system including portions of the dense arcs of primarywind formed following periastron (Figure 6) Portions of the cur-rent WWC region and primary wind just beyond it are also pho-toionized byηB The density and temperature of the material inthese regions are ideal for producing [FeIII ] emission (Figure 6)

(iii) During periastron passageηB becomes enveloped in thedense wind ofηA This significantly reduces the size of the pho-toionization region to approximately a few semi-major axes in di-ameter Since the large photoionization region has lsquocollapsedrsquo the

spatially-extended (gt 01primeprime) high-ionization forbidden line emis-sion vanishes during periastron passage (φ asymp 099minus 107) It doesnot reappear untilηB completes periastron passage and restores theextended photoionization region which can take several months

(iv) Synthetic spectro-images of [FeIII ] λ4659 show that mostof the [FeIII ] emission originates in the central015primeprime in agree-ment with figure 8 of Mehner et al (2010) Our 3-D model showsthat this emission forms in photoionized material near the cur-rent WWC zone which is not spatially-resolved byHSTSTISSpatially-extended (gt 015primeprime) [Fe III ] emission arises in photoion-ized portions of the expanding arcs of primary wind formed justafter periastron passage

(v) Only spectro-images generated for lines-of-sight angledθ =minus15 to +30 prograde of the semi-major axis on the apastronside of the system are able to match the observations taken atφ =0976 slitPA = 38 However there is an ambiguity in the orbitalinclinationi with models fori = 35 to50PAz = 272 to332

andi = 130 to 145 PAz = 282 to 342 both able to produceentirely blue-shifted arcs (Figure 7)

(vi) Model spectro-images of multi-phase observations obtainedat slit PA = minus28 break the above degeneracy ini fully con-strainingη Carrsquos orbital orientation parameters Given the uncer-tainties in some of the stellarwind parameters used in the 3-D mod-elingour suggested best-fit range of orientation parameters for theη Car binary system arei asymp 130 to 145 θ asymp minus15 to +30PAz asymp 302 to 327 Thereforethe orbital axis of theη Car bi-nary system is closely aligned in 3-D with the Homunculus polaraxis with apastron on the observerrsquos side of the system andηBorbiting clockwise on the sky relative toηA (Figure 12)

(vii) All other orbital orientations including that in whichηB isin front of ηA at periastron (θ = 180) are explicitly ruled out asthey produce model spectro-images that lack entirely blue-shiftedspatially-extended arcs containing instead significant amounts ofunobserved spatially-extended red-shifted emission atφ = 0976slit PA = 38 (Figure 8)

(viii) The 3-D model predicts that the orientation on the skyofthe blue-shifted component of [FeIII ] λ4659 should not vary muchduringη Carrsquos orbit stretching from NE to SW However the spa-tial extent of the emission should grow larger as the system movesfrom periastron to apastron and decrease in size close to perias-tron The orientation and spatial extent of the red-shiftedcompo-nent should behave in a way similar to that of the blue-shifted com-ponent but pointing NW on the sky

(ix) The apparent alignment of the orbital axis and Homunculuspolar axis implies a link between binarity andη Carrsquos numerousmassive eruptions Binary interaction scenarios should beseriouslyconsidered as possible explanations for the Great Eruptionand for-mation of the bipolar Homunculus and possibly the smaller erup-tion in 1890 that formed the Little Homunculus

(x) Future detailed 3-D simulations and radiative transfercalcu-lations together with high-resolution spatial mapping ofthe high-ionization forbidden line emission withHSTSTIS have the poten-tial to further constrain the temperature and luminosity ofηB Thestrong dependence of the forbidden line emission on the mass-lossrate ofηA and ionizing flux of photons fromηB may provide cluesas to the nature ofη Carrsquos long-term variability specifically thecycle-to-cycle variations of the spectroscopic events

The 3-D dynamical modeling in this paper and the availableHSTSTIS spectral observations have increased our understandingof theη Car system Much work remains however Efforts are un-derway to improve both the 3-D hydrodynamical modeling and 3-D

ccopy 2011 RAS MNRAS000 1ndash23

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 22: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

22 Madura et al

radiative transfer approach New 3-D simulations that include ra-diative cooling radiation-driven stellar winds gravity and effectslike radiative inhibition and braking are on the horizon Prelim-inary results of detailed 3-D radiative transfer calculations usingSimpleX (Paardekooper 2010) are promising as well With thesenew tools at our disposal it should be possible to further constrainthe stellar wind and orbital parameters ofη Car setting the stagefor orbital modeling to determine the stellar masses

ACKNOWLEDGEMENTS

T I M and C M P R were supported through the NASA Grad-uate Student Researchers Program T I M and J H G alsothank the Max Planck Society for financial support for this workAll SPH simulations were performed on NASA Advanced Su-percomputing (NAS) facilities using NASA High End Computing(HEC) time S P O acknowledges partial support from NASAATP grant NNK11AC40G T R G acknowledges the hospitalityof the MPIfR during the completion of this paper

REFERENCES

Abdo A A et al 2010 ApJ 723 649Abraham Z Falceta-Goncalves D Dominici T P Nyman L-A Durouchoux P McAuliffe F Caproni A and Jatenco-Pereira V 2005a AampA 437 977

Abraham Z Falceta-Goncalves D Dominici T Caproni A andJatenco-Pereira V 2005b MNRAS 364 922

Abraham Z and Falceta-Goncalves D 2007 MNRAS 378 309Abraham Z and Damineli A 1999 Eta Carinae at The Millen-nium 179 263

Bate M R and Bonnell I A 1997 MNRAS 285 33Bate M R Bonnell I A and Price N M 1995 MNRAS 277362

Benz W Cameron A G W Press W H and Bowers R L1990 ApJ 348 647

Bryans P Badnell N R Gorczyca T W Laming J M Mit-thumsiri W and Savin D W 2006 ApJS 167 343

Corcoran M F 2011 Bulletin de la Societe Royale des Sciencesde Liege 80 578 (C11)

Corcoran M F Hamaguchi K Pittard J M Russell C M POwocki S P ParkinE R and Okazaki A 2010 ApJ 7251528 (C10)

Corcoran MF 2005 ApJ 129 2018Corcoran M F et al 2004 ApJ 613 381Corcoran M F Fredericks A C Petre R Swank J H andDrake S A 2000 ApJ 545 420

Cox P Mezger P G Sievers A Najarro F Bronfman LKreysa E and Haslam G 1995 AampA 297 168

Crowther P A 2007 ARAampA 45 177Damineli A et al 2008a MNRAS 384 1649Damineli A et al 2008b MNRAS 386 2330Damineli A Kaufer A Wolf B Stahl O Lopes D F and deAraujo F X 2000 ApJL 528 L101

Damineli A 1996 ApJL 460 L49Davidson K 2005 The Fate of the Most Massive Stars 332 101Davidson K Smith N Gull T R Ishibashi K and HillierD J 2001 AJ 121 1569

Davidson K 1999 Eta Carinae at The Millennium 179 304

Davidson K Ishibashi K Gull T R and Humphreys R M1999 Eta Carinae at The Millennium 179 227

Davidson K 1997 NewA 2 387Davidson K et al 1997 AJ 113 335Davidson K and Humphreys RM 1997 ARAampA 35 1Davidson K Ebbets D Weigelt G Humphreys R M Hajian AR Walborn N R and Rosa M 1995 ApJ 109 1784

Dopita M A and Sutherland R S 2003 Diffuse Matter in theUniverse Springer Heidelberg

Duncan R A and White S M 2003 MNRAS 338 425Dwarkadas V and Owocki SP 2002 ApJ 581 1337Falceta-Goncalves D and Abraham Z 2009 MNRAS 399 1441Falceta-Goncalves D Jatenco-Pereira V and Abraham Z2005MNRAS 357 895

Feast M Whitelock P and Marang F 2001 MNRAS 322 741Fernandez-Lajus E et al 2010 New Astronomy 15 108Groh J 2011 Bulletin de la Societe Royale des Sciences deLiege 80 590

Groh J H et al 2010b AampA 517 A9Groh J H Madura T I Owocki S P Hillier D J amp WeigeltG 2010a ApJL 716 L223

Gull TR et al 2009 MNRAS 396 1308 (G09)Hamaguchi K et al 2007 ApJ 663 522Hartman H 2003 PhD Dissertation Lund Observatory LundUniversity Sweden

Henley D B Corcoran M F Pittard J M Stevens I R Ham-aguchi K and Gull T R 2008 ApJ 680 705

Henley DB 2005 PhD Dissertation University of BirminghamHillier D J et al 2006 ApJ 642 1098 (H06)Hillier D J Davidson K Ishibashi K and Gull T 2001 ApJ553 837 (H01)

Hillier D J and Miller D L 1998 ApJ 496 407Hillier DJ and Allen DA 1992 AampA 262 153Hillier D J 1988 ApJ 327 822Humphreys R M Davidson K and Koppelman M 2008 AJ135 1249

Iben I Jr 1999 Eta Carinae at The Millennium 179 367Ignace R Bessey R and Price C S 2009 MNRAS 395 962Ignace R and Brimeyer A 2006 MNRAS 371 343Ishibashi K et al 2003 AJ 125 3222Ishibashi K Corcoran M F Davidson K Swank J H PetreR Drake S A Damineli A and White S 1999 ApJ 524983

Kashi A and Soker N 2010 ApJ 723 602Kashi A and Soker N 2009 MNRAS 397 1426Kashi A and Soker N 2008 MNRAS 390 1751Kashi A and Soker N 2007 NewA 12 590Krist J and Hook R 1999 The Tiny Tim Userrsquos Guide (Balti-more STScI)

Madura T I 2010 PhD Dissertation University of DelawareMaeder A and Meynet G 2000 ARAampA 38 143Martins F Schaerer D and Hillier D J 2005 AampA 4361049Mehner A Davidson K Martin J C Humphreys R MIshibashi K and Ferland G J 2011 arXiv11065869

Mehner A Davidson K Ferland G J and Humphreys R M2010 ApJ 710 729

Mihalas D 1978 Stellar Atmospheres (New York W H Free-man)

Monaghan J J 2005 Reports on Progress in Physics 68 1703Nahar S N 1997 PhRvA 55 1980Nahar S N and Pradhan A K 1996 AampAS 119 509Nielsen K E Ivarsson S and Gull T R 2007a ApJS 168 289

ccopy 2011 RAS MNRAS000 1ndash23

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

Wunsch R Dale JE Palous J and Whitworth AP 2010 MN-RAS 407 1963

Zanella R Wolf B and Stahl O 1984 AampA 137 79Zethson T Johansson S Hartman H and Gull TR 2011AampA submitted

Zethson T 2001 PhD Dissertation Lunds Universitet SwedenZhang H 1996 AampAS 119 523

This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions
Page 23: Constraining the Absolute Orientation of ηCarinae’s · PDF fileConstraining the Absolute Orientation of ηCarinae ... hereafter G09) presented ... fer calculations performed with

Constraining the 3-D Orientation ofη Carrsquos Orbit 23

Nielsen K E Corcoran M F Gull T R Hillier D J Ham-aguchi K Ivarsson S and Lindler D J 2007b ApJ 660669

Nussbaumer H and Vogel M 1987 AampA 182 51Okazaki A T Owocki S P Russell C M P and Corcoran MF 2008 MNRAS 388 L39 (O08)

Osterbrock D E 1989 Astrophysics of Gaseous Nebulae andActive Galactic Nuclei University Science Books California

Owocki S P Gayley K G and Shaviv N J 2004 ApJ 616525

Owocki S P and Gayley K G 1995 ApJ 454 L145Paardekooper J-P 2010 PhD Dissertation Leiden ObservatoryLeiden University Netherlands

Parkin E R Pittard J M Corcoran M F and Hamaguchi K2011 ApJ 726 105 (P11)

Parkin E R Pittard J M Corcoran M F Hamaguchi K andStevens I R 2009 MNRAS 394 1758 (P09)

Pittard JM and Corcoran MF 2003 RMxAC 15 81Pittard JM and Corcoran MF 2002 AampA 383 636 (PC02)Pittard JM 2000 PhD Dissertation University of BirminghamPittard J M 1998 MNRAS 300 479Price D J 2007 Publications of the Astronomical SocietyofAustralia 24 159

Price D J 2004 PhD Dissertation Institute of Astronomy ampChurchill College University of Cambridge

Richardson N D Gies D R Henry T J Fernandez-Lajus Eand Okazaki A T 2010 AJ 139 1534

Smith N and Frew D J 2011 MNRAS 415 2009Smith N 2011 MNRAS 415 2020Smith N 2009 arXiv09062204Smith N 2006b ApJ 644 1151Smith N and Owocki S 2006 ApJ 645 L45Smith N et al 2004 ApJ 605 405Smith N Davidson K Gull T R Ishibashi K and HillierD J 2003a ApJ 586 432

Smith N Gehrz R D Hinz P M Hoffmann W F Hora JLMamajek E E and Meyer M R 2003b AJ 125 1458

Soker N 2007 ApJ 661 490Soker N 2004 ApJ 612 1060Tavani M et al 2009 ApJL 698 L142Teodoro M et al 2011 arXiv11042276van Boekel R et al 2003 AampA 410 L37van Genderen A M Sterken C Allen W H and WalkerW S G 2006 Journal of Astronomical Data 12 3

Verner E Bruhweiler F and Gull T 2005 ApJ 624 973Vishniac ET 1983 ApJ 274 152Weigelt G et al 2007 AampA 464 87Weigelt G and Ebersberger J 1986 AampA 163 L5White S M Duncan R A Chapman J M and Koribalski B2005 The Fate of the Most Massive Stars 332 126

Whitelock P A Feast M W Marang F and Breedt E 2004MNRAS 352 447

Williams P M 2008 Revista Mexicana de Astronomia y As-trofisica Conference Series 33 71

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This paper has been typeset from a TEX LATEX file prepared by theauthor

ccopy 2011 RAS MNRAS000 1ndash23

  • 1 Introduction
  • 2 The Observations
    • 21 The Key Observational Constraints Modeled
      • 3 A 3-D Dynamical Model for the Broad High-Ionization Forbidden Line Emission
        • 31 Why Model [Feiii] 4659 Emission
        • 32 The 3-D SPH Code and General Problem Setup
        • 33 Generation of Synthetic Slit Spectro-Images
          • 4 Results from the 3-D Dynamical Model
            • 41 Hydrodynamics of the Extended WWC Region
            • 42 Physical Origin and Location of the Broad High-Ionization Forbidden Line Emission
            • 43 Synthetic Slit Spectro-images and Constraining the Orbital Orientation
              • 5 Discussion
                • 51 The Orientation and Direction of Cars Binary Orbit
                • 52 Implications for Theories for the Formation of the Homunculus Nebula and the Nature of As Wind
                • 53 Probing Changes in Cars Stellar and Wind Parameters via Long-Term Monitoring of the Forbidden Line Emission
                  • 6 Summary and Conclusions