Deep HST Imaging in 47 Tucanae: A Global Dynamical Model

TL;DR

This study uses multi-epoch HST imaging to analyze stellar proper motions in 47 Tucanae, developing a dynamical model that accounts for anisotropy, rotation, and mass segregation, leading to precise estimates of the cluster's mass and distance.

Contribution

The paper introduces a comprehensive dynamical model of 47 Tucanae based on proper motion data, incorporating anisotropy, rotation, and mass segregation effects, with improved estimates of cluster mass and distance.

Findings

Proper motions reveal anisotropy and rotation in the outer field.

Model fits surface brightness and velocity dispersions well.

Mass of the cluster estimated at 1.31 million solar masses.

Abstract

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.