2021ApJ...918L..31M

When binary black holes merge in dense star clusters, their remnants can pair up with other black holes in the cluster, forming heavier and heavier black holes in a process called hierarchical merger. The most important condition for hierarchical merger to occur is that remnants formed by mergers are retained by the host star cluster. Using the publicly available gravitational-wave event database, we infer the magnitudes of kick velocities imparted to the remnant black holes due to anisotropic emission of gravitational waves and use that to quantify the retention probability of each event as a function of the escape speed of the star cluster. Among the second gravitational-wave transient catalog (GWTC-2) events, GW190814 provides the tightest constraint on the kick magnitude with V_kick=74_–7⁺¹⁰ km s^–1 at the 90% credible level. We find that star clusters with escape speeds of 200 km s^–1 can retain about 50% of the events in the GWTC-2. Using the escape speed distributions of nuclear star clusters and globular clusters, we find that ∼17 (2) remnants of GWTC-2 may be retained by the host star cluster if all GWTC-2 events occurred in nuclear (globular) clusters. Our study demonstrates the importance of folding in kick velocity inferences in future studies of hierarchical mergers.