Determining the Nature of Dark Matter with Astrometry

We show that measurements of stellar proper motions in dwarf spheroidal galaxies provide a powerful probe of the nature of dark matter. Allowing for general dark matter density profiles and stellar velocity anisotropy profiles, we show that the log-slope of the dark matter profile at about twice the stellar core (King) radius can be measured to within \pm 0.2 when the proper motions of 200 stars are added to standard line-of-sight velocity dispersion data. This measurement of the log-slope provides a test of Cold and Warm Dark Matter theories at a sensitivity not possible with line-of-sight velocity dispersion measurements alone. The upcoming SIM PlanetQuest will have the sensitivity to obtain the required number of proper motions in Milky Way dwarf spheroidal galaxies.