Deep HST Imaging in 47 Tucanae: A Global Dynamical Model
  Multi-epoch observations with ACS and WFC3 on HST provide a unique and
comprehensive probe of stellar dynamics within 47 Tucanae. We confront analytic
models of the globular cluster with the observed stellar proper motions that
probe along the main sequence from just above 0.8 to 0.1M$_\odot$ as well as
white dwarfs younger than one gigayear. One field lies just beyond the
half-light radius where dynamical models (\eg lowered Maxwellian distributions)
make robust predictions for the stellar proper motions. The observed proper
motions in this outer field show evidence for anisotropy in the velocity
distribution as well as skewness; the latter is evidence of rotation. The
measured velocity dispersions and surface brightness distributions agree in
detail with a rotating, anisotropic model of the stellar distribution function
with mild dependence of the proper-motion dispersion on mass. However, the best
fitting models under-predict the rotation and skewness of the stellar
velocities. In the second field, centered on the core of the cluster, the mass
segregation in proper motion is much stronger. Nevertheless the model developed
in the outer field can be extended inward by taking this mass segregation into
account in a heuristic fashion. The proper motions of the main-sequence stars
yield a mass estimate of the cluster of $1.31 \pm 0.02 \times 10^6
\mathrm{M}_\odot$ at a distance of 4.7 kpc. By comparing the proper motions of
a sample of giant and sub-giant stars with the observed radial velocities we
estimate the distance to the cluster kinematically to be $4.29 \pm 0.47$ kpc.
