  We use particle data from the Illustris simulation, combined with individual
kinematic constraints on the mass of the Milky Way (MW) at specific distances
from the Galactic center, to infer the radial distribution of the MW's dark
matter halo mass. Our method allows us to convert any constraint on the mass of
the MW within a fixed distance to a full circular velocity profile to the MW's
virial radius. As primary examples, we take two recent (and discrepant)
measurements of the total mass within 50 kpc of the Galaxy and find they imply
very different mass profiles and stellar masses for the Galaxy. The
dark-matter-only version of the Illustris simulation enables us to compute the
effects of galaxy formation on such constraints on a halo-by-halo basis; on
small scales, galaxy formation enhances the density relative to
dark-matter-only runs, while the total mass density is approximately 20% lower
at large Galactocentric distances. We are also able to quantify how current and
future constraints on the mass of the MW within specific radii will be
reflected in uncertainties on its virial mass: even a measurement of M(<50 kpc)
with essentially perfect precision still results in a 20% uncertainty on the
virial mass of the Galaxy, while a future measurement of M(<100 kpc) with 10%
errors would result in the same level of uncertainty. We expect that our
technique will become even more useful as (1) better kinematic constraints
become available at larger distances and (2) cosmological simulations provide
even more faithful representations of the observable Universe.
