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

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 remain a mystery. One way IMBHs can form is through the collapse of very massive stars produced by stellar collisions in dense stellar environments. However, IMBHs can be ejected from such environments by either dynamical recoil from a three-body scattering or gravitational-wave recoil following a merger with another black hole. Here we conduct Newtonian and post-Newtonian scattering experiments to study dynamical ejection of IMBHs 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. We borrow techniques from survival analysis (commonly used in medicine, epidemiology, engineering, etc.) to develop a model for the probability of IMBH binary ejection versus 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 find that for a typical Milky Way globular cluster, IMBHs with mass ≲10 3 M ⊙ are unlikely to be retained until the present under the assumptions considered in this work. Our results also suggest that IMBH mergers with q ≲ 0.2 may be detectable at higher redshifts with future gravitational-wave observatories such as the Einstein Telescope and Cosmic Explorer.