A Chandra Survey of Milky Way Globular Clusters. II. Testing the Hills–Heggie Law

Abstract

Abstract Binary–single and binary–binary encounters play a pivotal role in the evolution of star clusters, as they may lead to the disruption or hardening of binaries, a novel prediction of the Hills–Heggie law. Based on our recent Chandra survey of Galactic globular clusters (GCs), we revisit the role of stellar dynamical interactions in GCs, focusing on main-sequence (MS) binary encounters as a potential formation channel of the observed X-ray sources in GCs. We show that the cumulative X-ray luminosity (L X), a proxy of the total number of X-ray-emitting binaries (primarily cataclysmic variables and coronally active binaries) in a given GC, is highly correlated with the MS binary encounter rate (Γ b ), as . We further test the Hills–Heggie law against the binary hardness ratio, defined as the relative number of X-ray-emitting hard binaries to MS binaries and approximated by , with L K being the GC K-band luminosity and f b the MS binary fraction. We demonstrate that the binary hardness ratio of most GCs is larger than that of the solar neighborbood stars, and exhibits a positive correlation with the cluster specific encounter rate (γ), as . We also find a strong correlation between the binary hardness ratio and cluster velocity dispersion (σ), with , which is consistent with the Hills–Heggie law. We discuss the role of binary encounters in the context of the Nuclear Star Cluster, arguing that the X-ray-emitting, close binaries detected therein could have been predominantly formed in GCs that later inspiralled to the Galactic center.