A census of orbital properties of the M31 satellites
We present an analysis of the dynamics of the M31 satellite system. Proper motion data exist for only two of the M31 satellites. We account for this incompleteness in velocity data by a statistical analysis using a combination of the timing argument and phase-space distribution functions. These models provide a good fit to the bulk of the M31 satellites and we offer a table of orbital properties, including period, eccentricity and semimajor axis. This enables us to search for evidence of group infall based on orbital similarity rather than propinquity on the sky. Our results favour an association between Cass II and NGC 185, as the orbital parameters are in close agreement, but not for NGC 185 and NGC 147, which have often been associated in the past. Other possible satellite groupings include the pair And I and And XVII; the pair And IX and And X; and the triple And V, And XXV and NGC 147. And XXII has been claimed as a satellite of M33; we find that they are not moving independently along the same orbit, but cannot determine whether they are orbiting each other or are unrelated. Two satellites, And XII and And XIV, have high line-of-sight velocities, consistent with very recent infall from the edge of the Local Group. They are not well described by our underlying smooth phase-space distribution function, and are reanalysed without priors on their orbital parameters. For And XIV, multiple pericentric passages are possible and improved distance information is needed to draw further conclusions. For And XII, orbits which assume at least one pericentric passage can be ruled out and it must be on its first infall into the M31 system.