The present and future mass of the Milky Way halo

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 data set of 27 objects with known distances and radial velocities, of which six 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 per cent confidence level. All these results are derived from models in which the velocity normalization of the halo potential is taken as ∼220 km s−1. A detailed analysis of the uncertainties in our estimate is presented, including the effects of the small data set, possible incompleteness or correlations in the satellite galaxy sample and the measurement errors. The most serious uncertainties come from the size of the data set, which may cause a systematic underestimate by a factor of 2, and the measurement errors, which cause a scatter in the mass of the order of a factor of 2. We conclude that the total mass of the halo is , while the mass within 50 kpc is . In the near future, ground-based radial velocity surveys of samples of blue horizontal branch (BHB) stars are a valuable way to augment the sparse data set. A data set of ∼200 radial velocities of BHB stars will reduce the uncertainty in the mass estimate to ∼20 per cent. In the coming decade, microarcsecond astrometry will be possible with the Space Interferometry Mission (SIM) and the Global Astrometry Interferometer for Astrophysics (GAIA) satellites. For example, GAIA can provide the proper motions of the distant dwarfs like Leo I to within ±15 km s−1 and the nearer dwarfs like Ursa Minor to within ±1 km s−1. This will also allow the total mass of the Milky Way to be found to ∼20 per cent. SIM and GAIA will also provide an accurate estimate of the velocity normalization of the halo potential at large radii.