The Masses of the Milky Way and Andromeda galaxies
  We present a family of robust tracer mass estimators to compute the enclosed
mass of galaxy haloes from samples of discrete positional and kinematical data
of tracers, such as halo stars, globular clusters and dwarf satellites. The
data may be projected positions, distances, line of sight velocities or proper
motions. Forms of the estimator tailored for the Milky Way galaxy and for M31
are given. Monte Carlo simulations are used to quantify the uncertainty as a
function of sample size. For the Milky Way, the satellite sample consists of 26
galaxies with line-of-sight velocities. We find that the mass of the Milky Way
within 300 kpc is ~ 0.9 x 10^12 solar masses assuming velocity isotropy.
However, the mass estimate is sensitive to the anisotropy and could plausibly
lie between 0.7 - 3.4 x 10^12 solar masses. Incorporating the proper motions of
6 Milky Way satellites into the dataset, we find ~ 1.4 x 10^12 solar masses.
The range here if plausible anisotropies are used is still broader, from 1.2 -
2.7 x 10^12 solar masses. For M31, there are 23 satellite galaxies with
measured line-of-sight velocities, but only M33 and IC 10 have proper motions.
We use the line of sight velocities and distances of the satellite galaxies to
estimate the mass of M31 within 300 kpc as ~ 1.4 x 10^12 solar masses assuming
isotropy. There is only a modest dependence on anisotropy, with the mass
varying between 1.3 -1.6 x 10^12 solar masses. Given the uncertainties, we
conclude that the satellite data by themselves yield no reliable insights into
which of the two galaxies is actually the more massive.
