Deep HST Imaging in NGC 6397: Stellar Dynamics

Multi-epoch observations with ACS on HST provide a unique and comprehensive probe of stellar dynamics within NGC 6397. We are able to confront analytic models of the globular cluster with the observed stellar proper motions. The measured proper motions probe well along the main sequence from 0.8 to below 0.1 M$_\odot$ as well as white dwarfs younger than one gigayear. The observed field lies just beyond the half-light radius where standard models of globular cluster dynamics (e.g. based on a lowered Maxwellian phase-space distribution) make very robust predictions for the stellar proper motions as a function of mass. The observed proper motions show no evidence for anisotropy in the velocity distribution; furthermore, the observations agree in detail with a straightforward model of the stellar distribution function. We do not find any evidence that the young white dwarfs have received a natal kick in contradiction with earlier results. Using the observed proper motions of the main-sequence stars, we obtain a kinematic estimate of the distance to NGC 6397 of $2.2^{+0.5}_{-0.7}$ kpc and a mass of the cluster of $1.1 \pm 0.1 \times 10^5 \mathrm{M}_\odot$ at the photometric distance of 2.53 kpc. One of the main-sequence stars appears to travel on a trajectory that will escape the cluster, yielding an estimate of the evaporation timescale, over which the number of stars in the cluster decreases by a factor of e, of about 3 Gyr. The proper motions of the youngest white dwarfs appear to resemble those of the most massive main-sequence stars, providing the first direct constraint on the relaxation time of the stars in a globular cluster of greater than or about 0.7 Gyr.