A New Estimate of the Milky Way’s Dark Halo Mass

1. A New Estimate of the Milky Way’s Dark Halo Mass Motivation Methods Results Xiangxiang Xue Hans-Walter Rix , G. Zhao, P. Re Fiorentin, T. Naab, M. Steinmetz, E. F. Bell, F. C. van den Bosch, T. C. Beers, R. Wilhelm, Y. S. Lee, C. Rockosi, B. Yanny, H. Newberg, X. Kang, M. C. Smith, D. P. Schneider Dec 3 2008 KIAA-Cambridge Joint Workshop

2. Why to estimate the MW halo mass? Milky Way properties scale with halo mass Mstar /Mhalo  cooled baryon fraction Number of expected sub-halos The poorly known Galactic parameter Recent lit. values 0.8–2.5 x 1012 Mͽ Are all satellites bound?

3. Blitz 1990’s (HI) Dehnen&Binney 1998 15kpc ~200 discrete tracers Battaglia, Helmi et al 2006 How to estimate the MW halo mass? • Basic approach: • Assemble a large and well defined set of distant kinematic tracers from SDSS DR6 • blue Horizontal Branch Stars with • 5% distances to D~60 kpc • dv ~ 10 km/s + Fe/H estimates • Compare to kinematics in simulated halos that have been scaled to different halo mass • derive p(vlos) at different rgc • model it to get vcir(r)

4. Selection of the “clean” BHB sample • Pre-selected by color (Yanny et al 2000) • Measure Balmer line profile parameters • (cfSirko et al 2004, Xue, Rix et al 2008) solid line---BHB Star dotted line---Blue Straggler star SEGUE Survey Spectra Line Shape Parameters • identification >90% • Distances 5-10% • Stars are metal poor 2400 halo BHB stars

5. Spatial, velocity and [Fe/H] distributions of BHBs velocity distribution spatial distribution metallicity distribution velocity dispersion

6. How to estimate the MW halo mass? • Modelling the BHB kinematics with simulations make “mock observations” from within the output of the cosmological (Milky Way-like) galaxy simulations, and then match P(Vlos /Vcir|r) to give Vcir,obs(r), and ultimately Mvir • use simulations from two different groups (Steinmetz, Naab) • same volume as SDSS DR6 • derive P(Vlos/Vcir, r) for simulated halo stars • get P(Vlos/Vcir, r) for observed halo BHB stars • matching the distributions gives estimate of Vcir,obs(r) • [also use good ole’ Jean Eq.]

8. Red dots are halo BHB stars , while Black dots are simulated halo stars Vesc(r) Vesc(r) Vcir(r) Vcir(r) P(Vlos/Vcir) Mhalo ~ 1012 Mͽ Mhalo ~ 2 × 1012 Mͽ

9. Comparison of P(Vl.o.s/Vcir) in radial bin [15.0,20.0] kpc Psim(Vlos, / Vcir),  Construct estimate of Vcir(r) Pobs(Vl.o.s,/Vcir) if vcir(obs)=180km/s P(Vlos/Vcir, obs) = P(Vlos/Vcir, sim)

10. Vcir(r) derived by Jeans Equation • First, relate σlos,obs(r) to σr(r) • Then, use Jeans Equation for • Use observed (photometric) halo profile ρ*~r-3.5 • Estimate Vcir(r) radially anisotropic case, β=0.37 (simulations) radially isotropic case, β=0.0

11. Estimate the DM halo mass • NFW DM halo + Hernquist bulge + exponential disk • Rotation curve matches • Both ‘contracted’ and ‘uncontracted’ halos match • Mvir=1.0± 0.3 × 1012 Mͽ

12. Result • Robust measurement (2sims+Jeans Eq.) M (r<60 kpc) = 4.0±0.7×1011 Mͽ • Vcirc(R) is not constant but gently falling, and matches either contracted or uncontracted NFW profile • If DM halo is NFW then Mvir (~275kpc) = 1.0± 0.3× 1012 Mͽ consistent with previous estimates, but more precise • Imply (high) 40% of baryons end up as stars • LMC and other satellites marginally bound V3D,LMC=378 km/s +- 18km/s (Besla et al 2007)

13. Thank You