Nicolas NARDETTO – Naples, 2011 1

Nicolas Nardetto et al. Observatoire de la Côte d’Azur (Nice, France)

Nicolas NARDETTO – Naples, 2011 2

Phase

Ang

ular

Diamet

er (mas

)

€

d ∝ ΔRΔθ

with R(t) =radpV∫ dt

A direct linear relation

The Baade-Wesselink methods

Kervella et al., 2004, A&A, 416, 941

Interferometry

IRSB

or €

pulsV

€

radV

€

p = pulsVradV

Nicolas NARDETTO – Naples, 2011 3

The radial velocity definition

β Dor HARPS observations

λm λg λm λc λg λm

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•  A geometric effect (uniform disk) The radial velocity definition

€

pulsV = 30km/s

€

cRV = 20km/s

€

0p =1.5p <= 1.5

•  Limb-darkening effect

€

pulsV = 30km/s

€

cRV = 21.5km/s

€

0p =1.39

po=-0.18uV+1.50 (Nardetto et al. 2006)

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•  Rotation effect The radial velocity definition

€

pulsV = 30km/s

€

cRV = 20km/s

€

0p =1.5

RVc (first moment method) is independent of rotation

•  Line width effect

€

pulsV = 30km/s

€

cRV = 20km/s

€

0p =1.5

RVc (first moment method) is independent of the line width

The first moment method is in principle the best method to use (Burki et al. 1982).

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Static model Initial velocity

Hydro code

Limit cycle

Radiatif transfert

Line profile Intensity distribution (in the continuum and in the

spectral line)

Period

Photometry

Fokin (1990, 1991)

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Self consistent modelling of the projection factor for interferometric distance determination N. Nardetto, A. Fokin, D. Mourard, Ph. Mathias, P. Kervella, D. Bersier, 2004, A&A, 428, 131

€

pulsV photosphere( )

Pulsating atmosphere of δ Cep, numerical model

€

pulsV line formation layer( )

Value including the velocity gradient in the

atmosphere

The dynamical structure of the atmosphere

Result confirmed by HST + CHARA (Mérand et al. 2005)

Nicolas NARDETTO – Naples, 2011

Model of δ Cep

β Dor ζ Gem

8

HARPS observations of 10 Cepheids (P=3j à P=42j) 300 spectra Thousands of spectral lines 17 selected

€

cΔRV = oa D+ ob

Phase

Radi

us (R

s)

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Line depth

Direct measure of the velocity gradient (HARPS)

1 –

2 – geometric p-factor

3 – extrapolation to the photosphere

4 – optical/gas layers : hydro code

Amplitud

e of

the

rad

ial v

eloc

ity

(km/s

)

1

2

3 4

p-factor decomposition : semi-theoretical approach

δ Cep

The p-factor decomposition

€

p =1.39*0.99*0.96 =1.33

2 1

3

4

Nicolas NARDETTO – Naples, 2011 10

The Pp relation High resolution spectroscopy for Cepheids distance determination II. A period-projection factor relation N. Nardetto, D. Mourard, Ph. Mathias, A. Fokin, D. Gillet, 2007, A&A, 471, 661

Geometric model Hydrodynamical modelling

HARPS observations Period (days) Period (days) Period (days)

FeI 4896A

€

p = [−0.06 ± 0.02]logP + [1.38 ± 0.02]

Period (days)

p-fa

ctor

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High resolution spectroscopy for Cepheids distance determination V. Impact of the cross-correlation on the p-factor and the c-velocity N. Nardetto, W. Gieren, P. Kervella, P. Fouqué, J. Storm, G. Pietrzynski, D. Mourard, D. Queloz, 2009, A&A, 502, 951

5%

first moment of the spectral line (RVc)

cross-correlation

And when using the cross-correlation method?

€

p = −[0.08 ± 0.05]logP + [1.31± 0.06]

Conclusions: 1 – the static approach lead to an overestimation of the distances of 10% 2 – consistent with HST parallaxes measurements Mérand et al. 2005 ; Groenewegen 2007 3 – slope PL (Milky Way) = slope PL (LMC) P. Fouqué et al., 2007, A&A, 476, 73

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Synthesis for δ Cep

HST

+LM

C

HST

HST

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PHYSICS OF CEPHEIDS

Conclusion:

THE FONDAMENTAL COSMIC DISTANCE SCALE

Another example : the « K-term » enigma of Cepheids has been resolved using line asymmetry (please refer to Nardetto et al. 2008, A&A, 489, 1255)

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Nicolas NARDETTO – Naples, 2011 15

Impact of the projection factor

Riess et al. 2009, ApJ, 699, 539

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On-going projects related to distances

•  Study of the projection factor of LMC Cepheids.

•  CHARA/FLUOR interferometric observations of 13 ‘new’ Cepheids.

•  CHARA/VEGA observations to determine the LD of δ Cep

•  VEGA observations of Galactic EBs to test the method of LMC EBs distance determination.

•  Calibration of the surface brightness relation of early-type stars (BA) with VEGA/CHARA observations

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Different ways of determining the projection-factor (δ-Cep) : 1/ direct observation (the distance is known, for e.g. HST) : ✚Mérand et al. 2005 ............................................................ ✚Barnes et al. 2003, Benedict et al. 2007 (for T Vul) .................... ✚Groenewegen 2007 (for 7 stars) ............................................. ✚Gieren et al. 2005 (Cepheids in LMC are at the same distance) ........... 2/ toy modelling or static models (Kurucz) : Van Hoof, 1952ApJ, 115, 166 ............................................... Getting, 1934, MNRAS, 95, 139 ............................................ ★Burki et al. 1982, A&A, 109, 258 ......................................... Hindsley & Bell, 1986, PASP, 98, 881; Gieren et al. 1989 .............. Albrow & Cottrell, 1994, MNRAS, 267, 548 .............................. ★N. Nardetto et al. 2006, A&A, 453, 309 ................................. ★Gray & Stevenson, 2007, PASP, 119, 398 ................................. ★Hadrava et al. 2009, A&A, 207, 397 ...................................... 3/ hydrodynamical modelling : Parsons, 1972, ApJ, 174, 5 ................................................. Karp, 1975, ApJ, 201, 641 .................................................. Sabbey at al. 1995, A&A, 446, 205 ........................................ ✖N. Nardetto et al., 2004, A&A, 428, 131 .................................. ★N. Nardetto et al., 2004, A&A, 428, 131 .................................. 4/ semi-theoretical approach using spectroscopy : ★N. Nardetto et al., 2007, A&A, 471, 661 .................................. ✚N. Nardetto et al. 2009, A&A, 502, 951 ................................... :formalism ✚:CC+gaussian ✖:gaussian :bisector ★:centroid

p=1.27+-0.05 p=1.19+-0.16 p=1.27+-0.05 p=1.47+-0.05

p=1.41 (u=0.60) p=1.38 (u=0.80) p=1.36 (u=0.85) p (line width) p (line width) p=1.39 no p needed no p needed

p (line width) p (line width) p=1.34 p=1.27+-0.01 p=1.33+-0.01

p=1.33+-0.02 p=1.25+-0.05

€

geop >hydrop >

CCp

Synthesis

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The enigmatic « K-term » of Cepheids : Joy (1939)

Atmosphere dynamics OR a velocimetrical structure of the Milky Way

A 70 years debate: Parenago (1945), Stibbs (1956), Wielen (1974), Caldwell & Coulson (1987), Moffett & Barnes (1987), Wilson et al. (1991), Pont, Mayor & Burki (1994)

The Milky Way rotation

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High resolution spectroscopy for Cepheids distance determination III. A correlation between c-velocities and c-asymmetries N. Nardetto, A. Stoekl, D. Bersier, T. G. Barnes, 2008, A&A, 489, 1255

γ-Asymmetries (%)

γ-Ve

locities

(km

/s)

+2.0km/s (redshift)

Databases

17 metallic lines

Zero-Point= center-of-mass velocity of the star

The « K-term » is related to the dynamical structure of Cepheids’ atmosphere (ESO press release 2008 & ESO messenger paper)

How can wedisentangle the pulsation and center-of-mass velocities?

There is a period γ-asymmetries relation (convection?)

Period (days)

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