1. 次世代位置天文衛星による 銀河系ポテンシャル測定 T. Sumi (Nagoya STE) T. Sumi (Nagoya STE) K.V. Johnston (Columbia) K.V. Johnston (Columbia) S. Tremaine (IAS) S. Tremaine (IAS) D.N. Spergel (Princeton) D.N. Spergel (Princeton) S. Majewski (Virginia) Sumi et al. 2009 S. Majewski (Virginia) Sumi et al. 2009 T. Sumi (Nagoya STE) T. Sumi (Nagoya STE) K.V. Johnston (Columbia) K.V. Johnston (Columbia) S. Tremaine (IAS) S. Tremaine (IAS) D.N. Spergel (Princeton) D.N. Spergel (Princeton) S. Majewski (Virginia) Sumi et al. 2009 S. Majewski (Virginia) Sumi et al. 2009

2. KP ： Taking Measure of the Milky Way: Proposed Scope (1999) o Mass Potential of Galaxy (tidal tails & satellites in halo) o Mass and Mass Distribution (shape, radial profile) of MW o “Lumpiness” of the Halo o Dynamics of the Disk o Surface Mass Density (Oort limit) o Milky Way Rotation Curve o Dynamics of the Central Galaxy o Dynamics of Bulge o Orientation and Motions of the Bar o Fundamental and Legacy Measurements o Proper motions of every known MW satellite galaxy & globular o Proper motions for large number of selected open clusters o Solar rotation speed,  & dynamical distance to GC

3. method 1, generate stars following model density Σ, mean v and dispersion σ, at R=0-25kpc 2, assign observational err in p phot 3, select sample 4, observe p tri, μ, v los with err 5, modeling by MCMC

4. Spiral arms model Φ a : amplitude of spiral arm R 0 : distance to GC m: number of spiral arms k=C/R: radial wave number  p : pattern speed  : epicyclic frequency F: reduction factor 16 parameters in total Potential: Radial verlocity: ~10% of local disk surface density

5. Sampling & observation M-giant: M V =-2 mag Photometric parallax: p phot =0.15p Sample uniform in R In R=4-20kpc p tri =10 μ as μ=0.2+0.6p tri v los =1km/s APOGEE, H-band RVs with <0.5 km/s for 1-2 x 10 5 stars

6. Markov Chain Monte Carlo Conditional probability:P Σ :number density of stars ε : error function V:volume ~p -4 (p -3 ) S: selection function Ux: phase space distribution Likelihood:

7. Recovery by MCMC. (N=850, fit R 0 ) δ phot =15% δ tri =10 μ as

8. Likelihood surface. (N=810) 68%,95%CL.

9. Accuracy vs. Number of stars

10. Accuracy vs. parallax accuracy N=850, fix R 0

11. Disk stars 

12. Accuracy v.s.  N=850

13. Summary Our method is immune to bias in sample selection Our method is immune to bias in sample selection Next generation astrometoric survey can constrain Mass distribution in ~1% at 4-20 kpc (currently ~10% at<8kpc) with N=a few 100~1000 Next generation astrometoric survey can constrain Mass distribution in ~1% at 4-20 kpc (currently ~10% at<8kpc) with N=a few 100~1000 δ M does NOT depend on δ ptri until ~100μas δ M does NOT depend on δ ptri until ~100μas  GAIA does good work.  GAIA does good work. Measure R 0 in ~2% Measure R 0 in ~2%  max should be >60   max should be >60  (Knowing the error distribution is important) (Knowing the error distribution is important)

14. MOA-II1.8m telescope （ New Zealand/Mt. John Observatory at NZ, 44  S ） Mirror : 1.8m CCD : 8k x 10k pix. FOV : 2.2 square deg. Mirror : 1.8m CCD : 8k x 10k pix. FOV : 2.2 square deg.

15. the Galactic Bar structure (face on, from North)  8kpc  G.C. Obs. 1, Microlensing Optical depth,  (Alcock et al. 2000; Afonso et al.2003; Sumi et al. 2003;Popowski et al. 2004; Hamadache et al. 2006;Sumi et al. 2006)  M=1.6  10 10 M , axis ratio (1:0.3:0.2),  ~20  1, Microlensing Optical depth,  (Alcock et al. 2000; Afonso et al.2003; Sumi et al. 2003;Popowski et al. 2004; Hamadache et al. 2006;Sumi et al. 2006)  M=1.6  10 10 M , axis ratio (1:0.3:0.2),  ~20 

16. 2.Red Clump Giants G Metal-rich horizontal branch stars G Small intrinsic width in luminosity function (~0.2mag) Stanek et al. 1997  =20-30 , axis ratio 1:0.4:0.3

17. Streaming motions of the bar Sun faint bright V rot =~50km/s Color Magnitude Diagram