Survival Analysis of Intermediate-Mass Black Holes in Dense Star Clusters

Abstract

Recently, an intermediate-mass black hole (IMBH) candidate was announced in the Galactic globular cluster Omega Centauri. IMBHs at the lower end of the traditional mass range have also been detected through gravitational-wave transients, though their formation and subsequent growth linking the two mass scales remains a mystery. One way IMBHs may be produced is through the collapse of very massive stars produced by stellar collisions in dense stellar environments. However, IMBHs may be ejected from such environments by either dynamical recoil from binary-single scattering or gravitational-wave recoil following the merger of two black holes. We conduct Newtonian and post-Newtonian binary-single scattering experiments to study dynamical ejection in greater detail. We obtain fits to the probabilities for dynamical ejection, gravitational wave capture, and per-encounter hardening as a function of the binary mass ratio and hardness with respect to its environment. We borrow techniques from survival analysis (commonly used in studies of medicine, epidemiology, engineering, etc.) to develop a model to calculate the probability of IMBH binary ejection vs in-cluster merger. We confirm that the dynamical ejection probability strongly depends on both the mass ratio of the IMBH compared to other BHs in its environment and on the environment's velocity dispersion. We estimate that for a typical Milky Way globular cluster, IMBHs with mass $\lesssim10^3\,\mathrm{M}_\odot$ are unlikely to be retained until the present. Our results also suggest that IMBH mergers with $q\lesssim0.2$ may be detectable at higher redshifts with future gravitational wave instruments such as the Einstein Telescope and Cosmic Explorer.