Measuring stellar proper motions in crowded fields with sim

Astrometry in crowded fields is an important component of the science program of the Space Interferometry Mission (SIM). Resolving multiple point sources within the SIM beam, or imaging of complicated, extended source structures requires a (large) number of interferometer baselines. As the spacecraft design keeps evolving, the impact on various key projects needs to be studied. In this paper, we discuss the capabilities of the latest SIM design (with only two baselines available for science measurements) for measuring stellar proper motions in crowded fields. Using the nucleus of the Andromeda Galaxy (M31) as a case study, we quantify the roll angle increment needed to enable such measurements with the reduced SIM baseline set. In particular, we demonstrate that SIM can measure Keplerian motion of luminous stars around the approximate to 3 x 10(7) M-circle dot black hole in M 31, provided that the spacecraft roll angle can be chosen in increments of around 4degrees or smaller.