A Chandra Survey of Milky Way Globular Clusters II: Testing the
  Hills-Heggie Law
  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 {\it
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 ($\Gamma_{b}$), 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-emitting
hard 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. 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 ($\gamma$), as $L_{X}/(L_{K}f_{b}) \propto
\gamma^{0.65\pm0.12}$. We also find a strong correlation between the binary
hardness ratio and cluster velocity dispersion ($\sigma$), with
$L_{X}/(L_{K}f_{b}) \propto \sigma^{1.71\pm0.48}$, 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 predominatly formed in GCs that later
inspiralled to the Galactic center.
