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Binary-single and binary-binary encounters play a pivotal role in theevolution of star clusters, as they may lead to the disruption or hardening ofbinaries, a novel prediction of the Hills-Heggie law. Based on our recent {\itChandra} survey of Galactic globular clusters (GCs), we revisit the role ofstellar dynamical interactions in GCs, focusing on main-sequence (MS) binaryencounters as a potential formation channel of the observed X-ray sources inGCs. We show that the cumulative X-ray luminosity ($L_X$), a proxy of the totalnumber of X-ray-emitting binaries (primarily cataclysmic variables andcoronally active binaries) in a given GC, is highly correlated with the MSbinary encounter rate ($\Gamma_{b}$), as $L_X \propto\Gamma_{b}^{0.77\pm0.11}$. We further test the Hills-Heggie law against the{\it binary hardness ratio}, defined as the relative number of X-ray-emittinghard binaries to MS binaries and approximated by $L_{X}/(L_{K}f_{b})$, with$L_{K}$ being the GC K-band luminosity and $f_b$ the MS binary fraction. Wedemonstrate that the binary hardness ratio of most GCs is larger than that ofthe Solar neighborbood stars, and exhibits a positive correlation with thecluster specific encounter rate ($\gamma$), as $L_{X}/(L_{K}f_{b}) \propto\gamma^{0.65\pm0.12}$. We also find a strong correlation between the binaryhardness ratio and cluster velocity dispersion ($\sigma$), with$L_{X}/(L_{K}f_{b}) \propto \sigma^{1.71\pm0.48}$, which is consistent with theHills-Heggie law. We discuss the role of binary encounters in the context ofthe Nuclear Star Cluster, arguing that the X-ray-emitting, close binariesdetected therein could have been predominatly formed in GCs that laterinspiralled to the Galactic center.

A Chandra Survey of Milky Way Globular Clusters II: Testing the Hills-Heggie Law