The mass of the Andromeda galaxy

This paper argues that the Milky Way galaxy is probably the largest member of the Local Group. The evidence comes from estimates of the total mass of the Andromeda galaxy (M31) derived from the three-dimensional positions and radial velocities of its satellite galaxies, as well as the projected positions and radial velocities of its distant globular clusters and planetary nebulae. The available data set comprises 10 satellite galaxies, 17 distant globular clusters and nine halo planetary nebulae with radial velocities. We find that the halo of Andromeda has a mass of ~ 12.3⁺¹⁸_-6 x 10¹¹ M_sun, together with a scalelength of ~90kpc and a predominantly isotropic velocity distribution. For comparison, our earlier estimate for the Milky Way halo is 19⁺³⁶_-17 x 10¹¹ M_sun. Although the error bars are admittedly large, this suggests that the total mass of M31 is probably less than that of the Milky Way. We verify the robustness of our results to changes in the modelling assumptions and to errors caused by the small size and incompleteness of the data set. Our surprising claim can be checked in several ways in the near future. The numbers of satellite galaxies, planetary nebulae and globular clusters with radial velocities can be increased by ground-based spectroscopy, while the proper motions of the companion galaxies and the unresolved cores of the globular clusters can be measured using the astrometric satellites Space Interferometry Mission (SIM) and Global Astrometric Interferometer for Astrophysics (GAIA). Using 100 globular clusters at projected radii 20<~R<~50kpc with both radial velocities and proper motions, it will be possible to estimate the mass within 50kpc to an accuracy of ~20per cent. Measuring the proper motions of the companion galaxies with SIM and GAIA will reduce the uncertainty in the total mass caused by the small size of the data set to ~22per cent.