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 KIAA-Cambridge Joint Workshop Motivation Methods Results

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

How to estimate the MW halo mass? Blitz 1990’s (HI) Dehnen&Binney 1998 ~200 discrete tracers Battaglia, Helmi et al kpc Basic approach: a)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  v ~ 10 km/s + Fe/H estimates b)Compare to kinematics in simulated halos that have been scaled to different halo mass derive p(v los ) at different r gc model it to get v cir (r)

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

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

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(V los /V cir |r) to give V cir,obs (r), and ultimately M vir How to estimate the MW halo mass? use simulations from two different groups (Steinmetz, Naab) same volume as SDSS DR6 derive P(V los /V cir, r) for simulated halo stars get P(V los /V cir, r) for observed halo BHB stars matching the distributions gives estimate of V cir,obs (r) [also use good ole’ Jean Eq.]

Red dots are halo BHB stars, while Black dots are simulated halo stars V esc (r) V cir (r) M halo ~ 2 × MM halo ~ M P(V los /V cir )

Comparison of P(V l.o.s /V cir ) in radial bin [15.0,20.0] kpc P sim (V los, / V cir ), P obs (V l.o.s, /V cir ) if v cir (obs)=180km/s  Construct estimate of V cir (r) P(V los /V cir, obs) = P(V los /V cir, sim)

V cir (r) derived by Jeans Equation First, relate σ los,obs (r) to σ r (r) Then, use Jeans Equation for Use observed (photometric) halo profile ρ * ~r -3.5 Estimate V cir (r) 1.radially anisotropic case, β=0.37 (simulations) 2.radially isotropic case, β=0.0

Estimate the DM halo mass NFW DM halo + Hernquist bulge + exponential disk Rotation curve matches Both ‘ contracted ’ and ‘ uncontracted ’ halos match M vir = 1.0± 0.3 × M

Result Robust measurement (2sims+Jeans Eq.) M (r<60 kpc) = 4.0±0.7×10 11 M V circ (R) is not constant but gently falling, and matches either contracted or uncontracted NFW profile If DM halo is NFW then M vir (~275kpc) = 1.0± 0.3 × M consistent with previous estimates, but more precise Imply (high) 40% of baryons end up as stars LMC and other satellites marginally bound V 3D,LMC =378 km/s +- 18km/s (Besla et al 2007)

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