Black holes or dark clusters in M31 and M32?

Recent spectroscopic data and dynamical modeling indicate the presence of dark matter within the nuclei of M31 and M32. If these nuclei do not contain massive black holes, the most likely alternative form for the dark matter is a cluster of low-mass stars or degenerate remnants. Here we show that simple physical considerations place lower limits ~0.1" on the half-mass radii of such clusters if they have survived in their present form over much of the age of the universe. Therefore, Space Telescope observations should rule out such clusters, or resolve them.