Probing the Galactic Potential Using the Probing the Galactic Potential Using the μμarcsecarcsec astrometric astrometric observationsobservations of of Disk Stars Disk Stars

T. T. 　　　　 SumiSumi 　　　　　　 (Nagoya STE)(Nagoya STE) K.V. K.V. Johnston (Columbia)Johnston (Columbia) S.S. 　　　　　　 Tremaine (IAS) Tremaine (IAS) D.N.D.N. Spergel Spergel (Princeton)(Princeton)

MOA-II1.8m telescopeMOA-II1.8m telescope（（ New Zealand/Mt. John Observatory New Zealand/Mt. John Observatory at NZ, 44at NZ, 44SS ））

Mirror : 1.8mMirror : 1.8mCCD : 8kCCD : 8k xx 10k pix. 10k pix. FOV : 2.2 square deg.FOV : 2.2 square deg.

MACHO fraction depends on halo modelMACHO fraction depends on halo model

Proper motionProper motion ~300 I-band frames, 4years ~1mas/yr

Streaming motions of the Streaming motions of the barbar

Sun

faint bright

Vrot=~50km/s

Color Magnitude Diagram

SIM Key Project:SIM Key Project:Taking Measure of the Milky WayTaking Measure of the Milky Way

[John Bahcall (IAS)] [John Bahcall (IAS)] Doug Geisler (ConcepciDoug Geisler (Concepcióón)n)Wolfgang Gieren Wolfgang Gieren (Concepci(Concepcióón)n)Eva Grebel (Basel)Eva Grebel (Basel)Carl Grillmair (Caltech)Carl Grillmair (Caltech)

Kathryn Johnston Kathryn Johnston (Wesleyan)(Wesleyan)Ricky Patterson (Virginia)Ricky Patterson (Virginia)I. Neill Reid (STScI)I. Neill Reid (STScI)David Spergel (Princeton)David Spergel (Princeton)Scott Tremaine (Princeton)Scott Tremaine (Princeton)

Steven Majewski (Virginia)

Takahiro Sumi (Princeton)Jeff Crane (OCIW)Peter Frinchaboy (Virginia)Ricardo Muñoz (Virginia)Clara Moskowitz (Wesleyan)Christina Hampton (Virginia)David Nidever (Virginia)Roberta Johnson (Caltech)Mei-Yin Chou (Virginia)

Cameron Hummels (Wesleyan)Mike Siegel (Texas)Tony Sohn (Korean Astro Obs)Kyle Westfall (Wisconsin)David Law (Caltech)Bill Kunkel (Carnegie)James Bullock (UC-Irvine)Rachael Beaton (Virginia)

SIM Science Team Meeting – Washington 8 January 2006

KP Proposed Scope (1999)KP Proposed Scope (1999)o Mass Potential of Galaxy (tidal tails & Mass Potential of Galaxy (tidal tails & satellites in halo)satellites in halo) o Mass and Mass Distribution (shape, radial profile) Mass and Mass Distribution (shape, radial profile) of MWof MW

o ““Lumpiness” of the HaloLumpiness” of the Haloo Dynamics of the DiskDynamics of the Disk

o Surface Mass Density (Surface Mass Density (Oort limitOort limit))o Milky Way Milky Way Rotation CurveRotation Curve

o Dynamics of the Central GalaxyDynamics of the Central Galaxyo Dynamics of BulgeDynamics of Bulgeo Orientation and Motions of the BarOrientation and Motions of the Bar

o Fundamental and Legacy MeasurementsFundamental and Legacy Measurementso Proper motions of every known MW Proper motions of every known MW satellite galaxy & globularsatellite galaxy & globularo Proper motions for large number of selected Proper motions for large number of selected open clustersopen clusterso Solar rotation speed, Solar rotation speed, & dynamical & dynamical distance to GCdistance to GC

Halo & Disk modelHalo & Disk model

Halo mass:Halo mass:

Disk density:Disk density:

Radial dispersion:Radial dispersion:

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M(R) = MhR2

(R + a)2

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Σ(R) = Σ0 exp −Rh

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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σR2 =σ R ,sun

2 exp R0 − Rhσ

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Hernquist 1990

Spiral arms modelSpiral arms model

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Φ(R,φ, t) = Φa (R)cos m(φ − Ω p t) + c log R8

+ φ0

⎡ ⎣ ⎢

⎤ ⎦ ⎥

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vRa (R,φ, t) = vRa (R)cos m(φ − Ω p t) + c log R8

+ φ0

⎡ ⎣ ⎢

⎤ ⎦ ⎥

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vRa (R) =m(Ω − Ω p )

ΔkΦaF,

Δ = κ 2 − m(Ω − Ω p )[ ]2

m:number of spiralsK=C/R:radial wave numberp:pattern speed:epicyclic frequencyF:reduction factor

Potential:

Radial verlocity:

ParametersParameters

(kpc)

Disk starsDisk stars

SIM Mission SIM Mission time & the time & the number of number of

targetstargets

240hr240hr1010μasμas N=810N=810

Markov Chain Monte CarloMarkov Chain Monte Carlo

n:number density of starsV:volume ~p-4(p-3)

Likelihood:

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L(x) = Πi=1

NP(μo

i ,voi | po

i , loi ,x)

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P(μo,vo | po,lo,x) = n(p)V (p,l)ε(p, po)Pμ (μo)P(vo)0

∞∫ dp,

ε(p, po) =Gauss(p, po), Q P(po, p) =Gauss(po, p)

Provability distribution of pProvability distribution of p

V~p-3

Recovery by MCMC. Recovery by MCMC. (N=810)(N=810)

Consistency Consistency CheckCheck

10 MCMC runs10 MCMC runs

Accuracy v.s. Numer of starsAccuracy v.s. Numer of stars

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log(δM /1010MSun ) = 0.55 − 0.49log(N)

Accuracy v.s. parallax accuracyAccuracy v.s. parallax accuracy

Disk starsDisk stars

Accuracy v.s. Accuracy v.s.

SummarySummary

SIM can constrain Rotation curve in 3% SIM can constrain Rotation curve in 3% up to 20 kpcup to 20 kpc

δδMMNN-1/2-1/2

δδM M do NOT depnd on δdo NOT depnd on δp p until 500μasuntil 500μas should be >60should be >60

Knowing the error distribution is Knowing the error distribution is importantimportant

APOGEE, APOGEE, RVs with <0.5 km/s for 1-2 x 10^5 starsRVs with <0.5 km/s for 1-2 x 10^5 stars

Likelihood surface. Likelihood surface. (N=810)(N=810)

68%,95%68%,95%CL.CL.

2005: Satellite Galaxy Tails2005: Satellite Galaxy Tailso Extensive new data on Sgr Extensive new data on Sgr tidal streamstidal streamso 2 new wraps of debris (Pakzad 2 new wraps of debris (Pakzad et al. 2005)et al. 2005)

o Evidence for interaction w/LMC Evidence for interaction w/LMC 2 Gyrs ago2 Gyrs ago

(Majewski, Nidever et al., (Majewski, Nidever et al., in prep)in prep)

o Proper motion predictions for Proper motion predictions for the LMC-Sgrthe LMC-Sgrinteraction made. interaction made.

o Extensive RV survey of Sgr Extensive RV survey of Sgr core (~1500 stars)core (~1500 stars)