PLANETARY CAMERA OBSERVATIONS OF THE CENTRAL PARSEC OF M32

Analysis of V band HST Planetary Camera images of the elliptical galaxy M32 shows that its nucleus is extremely dense and remains unresolved at even the HST diffraction limit. A combined approach of image deconvolution and model fitting is used to investigate the starlight distribution into limiting radii of 0."04 (0.14 pc at 700 kpc). The logarithmic slope of the brightness profile smoothly flattens from gamma = - 1.2 at 3.4 pc to gamma = - 0.5 at 0.34 pc; interior to this radius the profile is equally consistent with a singular mu(r) is-proportional-to r-1/2 cusp or a small nonisothermal core with r(c) less-than-or-equal-to 0.37 pc. The isophotes maintain constant ellipticity into the center, and there is no evidence for a central point source, disk, dust, or any other substructures. The cusp model implies central mass densities rho-0 > 3 X 10(7) M . pc-3 at the resolution limit and is consistent with a central M . = 3 X 10(6) M . black hole; the core model implies rho-0 almost-equal-to 4 X 10(6) M . pc-3. From the viewpoint of long-term stability, we argue that a starlight cusp surrounding a central black hole is the more plausible interpretation of the observations. A core at the implied density and size without a black hole has a relaxation time of only approximately 7 X 10(7) yr and a short stellar collision timescale implying wholesale stellar merging over the age of the universe. The core would be strongly vulnerable to collapse and concomitant runaway stellar merging. Collapse may lead to formation of a massive black hole in any case if it cannot be reversed by formation of a binary from high-mass merger products. Regardless of the ultimate fate of the core, however, structural evolution of the core will always be accompanied by strong evolution of the core population-the constant isophote shape and absence of a central color gradient appear to show that such evolution has not occurred. In contrast, the high velocities around a black hole imply long relaxation and stellar collision times for the cusp population compared to the age of the universe.