The Present and Future Mass of the Milky Way Halo

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Abstract
A simple model for the Milky Way halo is presented. It has a flat rotation curve in the inner regions, but the density falls off sharply beyond an outer edge. This truncated, flat rotation curve (TF) model possesses a rich family of simple distribution functions which vary in velocity anisotropy. The model is used to estimate the total mass of the Milky Way halo using the latest data on the motions of satellite galaxies and globular clusters at Galactocentric radii greater than 20 kpc. This comprises a dataset of 27 objects with known distances and radial velocities, of which 6 also possess measured proper motions. Unlike earlier investigations, we find entirely consistent maximum likelihood solutions unaffected by the presence or absence of Leo I, provided both radial and proper motion data are used. The availability of the proper motion data for the satellites is crucial as, without them, the mass estimates with and without Leo I are inconsistent at the 99 % confidence level. All these results are derived from models in which the velocity normalisation of the halo potential is taken as 220 km/s. A detailed analysis of the uncertainties in our estimate is presented, including the effects of the small dataset, possible incompleteness or correlations in the satellite galaxy sample and the measurement errors. The most serious uncertainties come from the size of the dataset, which may cause a systematic underestimate by a factor of two, and the measurement errors, which cause a scatter in the mass of the order of a factor of two. We conclude that the total mass of the halo is 1.9 x 10^12 solar masses, while the mass within 50 kpc is 5.4 x 10^11 solar masses. Future prospects using radial velocity surveys of blue horizontal branch stars and microarcsecond astrometry from the upcoming satellite missions are discussed.

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