Hubble Space Telescope Proper Motions and Stellar Dynamics in the Core of the Globular Cluster 47 Tucanae

We have used HST imaging of the central regions of the globular cluster 47 Tucanae (=NGC 104), taken with the WFPC2 and ACS instruments between 1995 and 2002, to derive proper motions and U- and V-band magnitudes for 14,366 stars within 100" (about 5 core radii) of the cluster center. This represents the largest set of member velocities collected for any globular cluster. The stars involved range in brightness from just fainter than the horizontal branch of the cluster to more than 2.5 mag below the main-sequence turnoff In the course of obtaining these kinematic data, we also use a recent set of ACS images to define a list of astrometrically calibrated positions (and F475W magnitudes) for nearly 130,000 stars in a larger, 3' x 3' central area. We describe our data reduction procedures in some detail and provide the full position, photometric, and velocity data in the form of downloadable electronic tables. We have used the star counts to obtain anew estimate for the position of the cluster center and to define the density profile of main-sequence turnoff and giant branch stars in to essentially zero radius, thus constraining the global spatial structure of the cluster better than before. A single-mass, isotropic King model fit to it is then used as a rough point of reference against which to compare the gross characteristics of our proper-motion data. We search in particular for any evidence of very fast-moving stars, in significantly greater numbers than expected for the extreme tails of the velocity distribution in a sample of our size. We find that likely fewer than 0.1%, and no more than about 0.3%, of stars with measured proper motions have total speeds above the nominal central escape velocity of the cluster. At lower speeds, the proper-motion velocity distribution very closely matches that of a regular King model (which is itself nearly Gaussian given the high stellar density) at all observed radii. Considerations of only the velocity dispersion then lead to a number of results: (1) Blue stragglers in the core of 47 Tuc have a velocity dispersion sk smaller than that of the cluster giants by a factor of :2, consistent with the former being on average twice as massive as normal, main-sequence turnoff stars. (2) The velocity distribution in the inner 5 core radii of the cluster is essentially isotropic, and the detailed dependence of sk on R for the brighter stars suggests that heavy remnants contribute only a fraction of a percent to the total clust