Constraints on the mass distribution near the centers of M31 and M32

We have reinterpreted spectroscopic data on the motions of stars near the centers of M31 and M32. The mass distribution near the centers of each of these galaxies must be more concentrated than the light. We have constructed models containing black holes in the mass range 4-5 x 10⁷^ Mₛun_ for M31 and 0. 7-3 x 10⁶^ Mₛun_ for M32. Extended models of the unseen mass must have core radii less than 0. 4" and must contain ~ 10⁸^ Mₛun_ for M31 and ~ 10⁷^ Mₛun_ for M32. There are two astrophysical constraints on extended models. First, the objects that comprise them must not collide frequently. Second, the two- body relaxation time must be long enough that the nuclei have not already collapsed. These constraints are not particularly interesting at present but are likely to become so if Space Telescope observations reduce the maximum core radii of the mass distributions in the two galaxies.