The Space Motion of Leo I: The Mass of the Milky Way's Dark Matter Halo
  We combine our Hubble Space Telescope measurement of the proper motion of the
Leo I dwarf spheroidal galaxy (presented in a companion paper) with the highest
resolution numerical simulations of Galaxy-size dark matter halos in existence
to constrain the mass of the Milky Way's dark matter halo (M_MW). Despite Leo
I's large Galacto-centric space velocity (200 km/s) and distance (261 kpc), we
show that it is extremely unlikely to be unbound if Galactic satellites are
associated with dark matter substructure, as 99.9% of subhalos in the
simulations are bound to their host. The observed position and velocity of Leo
I strongly disfavor a low mass Milky Way: if we assume that Leo I is the least
bound of the Milky Way's classical satellites, then we find that M_MW > 10^{12}
M_sun at 95% confidence for a variety of Bayesian priors on M_MW. In lower mass
halos, it is vanishingly rare to find subhalos at 261 kpc moving as fast as Leo
I. Should an additional classical satellite be found to be less bound than Leo
I, this lower limit on M_MW would increase by 30%. Imposing a mass weighted
LCDM prior, we find a median Milky Way virial mass of M_MW=1.6 x 10^{12} M_sun,
with a 90% confidence interval of [1.0-2.4] x 10^{12} M_sun. We also confirm a
strong correlation between subhalo infall time and orbital energy in the
simulations and show that proper motions can aid significantly in interpreting
the infall times and orbital histories of satellites.
