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

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.