C

Abstract

We analyze data from the Hubble Space Telescope’s (HST) Advanced Camera for Surveys of the globular cluster (GC) Omega Cen. We construct a photometric catalog of 1.2×106 stars over a 10′ ×10′ central field down to below BF435W = 25 (M ∼ 0.35 M ). The 2.5 to 4 year baseline between observations yields a catalog of some 105 proper motions over a smaller area, with 53,382 “high-quality” measurements in a central R 2′ field. Artificial-star tests characterize the photometric incompleteness. We determine the cluster center to ∼1′′ accuracy from star counts using two different methods, one based on isodensity contours and the other on “pie slices.” We independently confirm the result by determining also the kinematical center of the HST proper motions, as well as the center of unresolved light seen in Two Micron All Sky Survey data. All results agree to within their 1′′–2′′ levels of uncertainty. The proper-motion dispersion of the cluster increases gradually inward, but there is no variation in kinematics with position within the central ∼15′′: there is no dispersion cusp and no stars with unusually high velocities. We measure for the first time in any GC the variation in internal kinematics along the main sequence. The variation of proper-motion dispersion with mass shows that the cluster is not yet in equipartition. There are no differences in proper-motion kinematics between the different stellar populations of Omega Cen. Our results do not confirm the arguments put forward by Noyola, Gebhardt, and Bergmann to suspect an intermediate-mass black hole (IMBH) in Omega Cen. They determined line-of-sight velocity dispersions in two 5′′ × 5′′ fields, and reported higher motions in their central field. We find the proper-motion kinematics to be the same in both fields. Also, we find that they (as well as other previous studies) did not accurately identify the cluster center, so that both of their fields are in fact 12′′ from the true center. We also do not confirm the central density cusp they reported (in part due to the different center, and in part due to biases induced by their use of unresolved light). The surface number-density distribution near the center does not differ strongly from a single-mass King model, although a shallow cusp may not be ruled out. In the companion paper, which is Paper II in this series, we present new dynamical models for the high-quality data presented here, with the aim of putting quantitative constraints on the mass of any possible IMBH.