2018ApJ...869...52C

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 L_X∝Γ_b^0.77±0.11^. 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 L_X/(L_Kf_b), 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 L_X/(L_Kf_b)∝γ^0.65±0.12^. We also find a strong correlation between the binary hardness ratio and cluster velocity dispersion (σ), with L_X/(L_Kf_b)∝σ ^1.71±0.48^, 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.