M32+ -1

Multicolor HST WFPC2 images are used to study the central structure of the three Local Group galaxies M31, M32, and M33. PSF deconvolution a nd modeling of image aliasing are required to recover accurate brightn ess profiles within r < 0.'' 5. The data present a study in contrasts that suggests different evolutionary histories. In M31, the nucleus is double-peaked, as found by WFPC1 and confirmed by WFPC2. The dimmer p eak, P2, is closely centered on the bulge isophotes to 0.'' 1, implyin g that it is the dynamical center of the galaxy. Directly on P2 lies a UV-bright compact source that was discovered by King, Stanford, & Cra ne at 1700 Angstrom, WFPC2 images now show that this source is resolve d, with r(1/2) approximate to 0.2 pc. It dominates the nucleus at 3000 Angstrom and its spectral energy distribution is consistent with late B-early A stars. This probable nuclear star cluster may consist of yo ung stars and be an older version of the central cluster of hot stars that now sits at the center of the Milky Way, or it may consist of hea vier stars built up from collisions in a possible cold disk of stars o rbiting P2. Aspects of its formation remain highly problematic. In M32 , new images show that the central cusp continues to rise into the HST limit with slope gamma approximate to 0.5 and the central density rho (0) > 10(7) M. pc(-3). The V-I and U-V color profiles are essentially flat, and there is no sign of an inner disk, dust, or any other struct ure. This total lack of features seems at variance with a nominal stel lar collision time of 2 x 10(10) yr, which implies that a significant fraction of the light in the central pixel should come from blue strag glers. This discrepancy is eased but not completely removed if the ste llar population is young (2 x 10(9) yr). The stubborn normalcy of M32 at tiny radii may be emerging as an important puzzle. In M33, the nucl eus has an extremely steep gamma = 1.49 power-law profile for 0.'' 05 < r < 0.'' 2 that appears to become somewhat shallower as the HST reso lution limit is approached. The profile for r < 0.'' 04 can be describ ed as having either a gamma approximate to 0.8 cusp or a small core wi th r(c) approximate to 0.13 pc. The central density is rho(0) > 2 x 10 (6) M. pc(-3), and the implied central relaxation time is only similar to 3 x 106 yr, indicating that the nucleus is highly relaxed. The acc ompanying short collision time of 7 x 109 yr predicts a central blue s traggler component that is quantitatively consistent with the strong V -I and B-R color gradients seen with HST and from the ground. When com bined with the Galaxy, the nuclei of the Local Group show surprisingly similar radial density profiles but divide into two classes according to velocity dispersion and black hole content: M31, M32, and the Milk y Way are dominated dynamically (and stabilized against relaxation) by massive central black holes, while M33 lacks a dominant black hole. A n obvious hypothesis is that a sizable stellar spheroid (which M33 lac ks) is necessary to grow a massive black hole. A further implication i s that the black hole growth in M31, M32, and the Milky Way was accomp anied by evolution in the stellar density profiles, stellar population s, and dynamical structure of these nuclei such that their past appear ance may have differed significantly from what they look like today. I n short, HST observations are taking us to scales where understanding the central structure of galactic nuclei is intimately connected to th e detailed interactions among their central stellar populations.