THE NUCLEUS OF M33

We have obtained high-resolution surface photometry and velocity dispersion measurements of the semistellar nucleus of M33 to study its structure and to look for a central black hole. The images were obtained with the DAO/CFHT HR Camera; this uses a tip-tilt mirror to correct the motion component of seeing. Our best images have resolution sigma* = 0.''186 in the B band and sigma* = 0.''177 in R (sigma* = Gaussian dispersion radius of the point spread function). The nucleus is unresolved. Its true core radius is r(c) less than or similar to 0.''10 congruent-to 0.39 pc; this is as small as in core-collapsed globular clusters. The true central surface brightness is mu0 less than or similar to 11.3 R mag arcsec-2, and the central density is rho0 greater than or similar to 5 X 10(5) M. pc-3. Except for M32 and the nucleus of our Galaxy, this is the most compact galactic core known. The velocity dispersion of the nucleus was measured using the Ca II infrared triplet; sigma = 21 +/- 3 km s - 1. The seeing-corrected mass-to-light ratio is small, M/L(V) less than or similar to 0.4. Also, there is a substantial color gradient inside 0.''5 radius: the center is DELTA(B-R) = 0.44 mag bluer than the rest of the nucleus. These observations and the F-type integrated spectrum imply that the nucleus contains young stars concentrated to the center. It may have been built out of gas funneled to the center from the rest of the disk. The small mass-to-light ratio leaves little room to hide dark matter. We derive a strict limit on the mass of a central black hole, M. less than or equal to 5 X 10(4) M.. The central relaxation time T(r) less than or equal to 2 X 10(7.) yr is so short that core collapse has probably occurred. We estimate how core properties changed during the collapse, and compare the M33 nucleus with M32 and a globular cluster. If a black hole formed in M33, it is likely to have M. approximately 10(2) to 10(3) M.. Evidently it did not grow monstrous by accretion. M33 is the first high-luminosity galaxy in which we can rule out the presence of a dead quasar.