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.
