Exploring the Mass Segregation Effect of X-ray Sources in Globular Clusters. IV. Evidence of Black Hole Burning in $\omega$ Centauri

Abstract

Using X-ray sources as sensitive probes of stellar dynamical interactions in globular clusters (GCs), we study the mass segregation and binary burning processes in $\omega$ Cen. We show that the mass segregation of X-ray sources is quenched in $\omega$ Cen, while the X-ray source abundance of $\omega$ Cen is much smaller than other GCs, and the binary hardness ratio (defined as $L_{\rm X}/(L_{\rm K}f_{b})$, with $f_{b}$ the binary fraction, $L_{\rm X}$ and $L_{\rm K}$ the cumulative X-ray and K band luminosity of GCs, respectively) of $\omega$ Cen is located far below the $L_{\rm X}/(L_{\rm K}f_{b})-\sigma_{c}$ correlation line of the dynamically normal GCs. These evidences suggest that the binary burning processes are highly suppressed in $\omega$ Cen, and other "heating mechanisms", very likely a black hole subsystem (BHS), are essential in the dynamical evolution of $\omega$ Cen. Through the "black hole burning" processes (i.e., dynamical hardening of the BH binaries), the BHS is dominating the energy production of $\omega$ Cen, which also makes $\omega$ Cen a promising factory of gravitational-wave sources in the Galaxy.