Hubble Space Telescope Proper Motion (HSTPROMO) Catalogs of Galactic Globular Clusters. VII. Energy Equipartition

TL;DR

This study measures the degree of energy equipartition in nine Galactic globular clusters using Hubble Space Telescope proper motions, finding partial equipartition correlated with relaxation times and no significant radial variation.

Contribution

It provides the first energy equipartition analysis for most of these clusters and introduces a large, cleaned dataset for future dynamical studies.

Findings

All clusters show partial, not full, energy equipartition.

The degree of equipartition correlates with relaxation times.

No significant radial trend in equipartition was observed.

Abstract

We examine the degree of energy equipartition in 9 Galactic globular clusters using proper motions measured with the Hubble Space Telescope. For most clusters in the sample, this is the first energy equipartition study ever performed. This study is also the largest of its kind, albeit with only 9 clusters. We begin by rigorously cleaning the catalogues to remove poor-quality measurements and to ensure high signal-to-noise for the study. Using the cleaned catalogues, we investigate how velocity dispersion $\sigma$ changes with stellar mass $m$. We fit two functional forms: the first, a classic power-law of the form $\sigma \propto m^{-\eta}$ where $\eta$ is the degree of energy equipartition, and the second from Bianchini et al. (2016) parameterised by an equipartition mass $m_{eq}$ where $\eta$ changes with stellar mass. We find that both functions fit well but cannot distinguish with statistical significance which function provides the best fit. All clusters exhibit varying degrees of partial equipartition; no cluster is at or near full equipartition. We search for correlations of $\eta$ and $m_{eq}$ with various cluster properties. The most significant correlation is observed with the number of core or median relaxation times ($N_{core}$ or $N_{half}$) the cluster has experienced. Finally, we determine the radial equipartition profile for each cluster, that is, how the degree of equipartition changes with projected distance from the cluster centre. We do not detect statistically significant trends in the degree of equipartition with radius. Overall, our observational findings are in broad agreement with theoretical predictions from N-body models published in recent years.