Mass estimates from stellar proper motions: The mass of $\omega$ Centauri

TL;DR

This paper develops and applies methods to estimate the mass of star clusters using proper motion data, demonstrating that accounting for flattening affects mass estimates and providing a precise mass measurement for omega Centauri.

Contribution

It introduces a likelihood-based approach for dynamical mass estimation from proper motions and compares spherical and flattened models, showing flattening impacts mass estimates.

Findings

Mass of omega Centauri estimated at ~4.55 million solar masses.

Including flattening reduces the mass estimate by about 10%.

Proper motion data precision improves mass estimate accuracy.

Abstract

We lay out and apply methods to use proper motions of individual kinematic tracers for estimating the dynamical mass of star clusters. We first describe a simple projected mass estimator and then develop an approach that evaluates directly the likelihood of the discrete kinematic data given the model predictions. Those predictions may come from any dynamical modelling approach, and we implement an analytic King model, a spherical isotropic Jeans equation model and an axisymmetric, anisotropic Jeans equation model.We apply these approaches to the enigmatic globular cluster omega Centauri, combining the proper motion from van Leeuwen et al (2000) with improved photometric cluster membership probabilities. We show that all mass estimates based on spherical isotropic models yield $(4.55\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, where our modelling allows us to show how the statistical precision of this estimate improves as more proper motion data of lower signal-to-noise are included. MLM predictions, based on an anisotropic axisymmetric Jeans model, indicate for $\omega$ Cen that the inclusion of anisotropies is not important for the mass estimates, but that accounting for the flattening is: flattened models imply $(4.05\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, 10% lower than when restricting the analysis to a spherical model. The best current distance estimates imply an additional uncertainty in the mass estimate of 12%.