Remnant recoil and host environments of GWTC-4.0 binary black-hole mergers
Determining the astrophysical origin of binary black holes and whether merger remnants are retained in their birth environments is essential for understanding hierarchical mergers and the growth of intermediate-mass black holes. We identified gravitational-wave events most consistent with dense-cluster origin and assessed whether their merger remnants are retained in globular clusters, nuclear star clusters, or galactic potentials. We considered 84 events consistent with binary-black-hole mergers from the first part of the fourth observing run (O4a) of the LIGO-Virgo-KAGRA detector network, and 3 selected events from the second part (O4b). We compared parameter-estimation posteriors with synthetic population models for field and cluster binaries using Bayes factors, accounting for the relative abundances of these formation channels. We computed recoil-velocity posteriors for all events using the IMRPhenomXPNR waveform model. We identified five events whose intrinsic parameters show preference for the adopted dense-cluster models over the considered field-binary populations, including the most massive O4a event GW231123_135430, while finding no robust preference for a dense-cluster origin for the high-spinning O4b event GW241011_233834. Typical recoil velocities are a few hundred km/s, with extended high-velocity tails. These kicks suggest merger remnants are likely ejected from typical globular clusters, while retention in nuclear star clusters remains possible but not guaranteed. Within the adopted models, efficient hierarchical growth may be challenging in typical globular clusters, whereas nuclear star clusters remain viable environments for repeated mergers. Although results depend on the adopted population models, this analysis highlights the importance of improved population models and higher-quality detections enabled by future GW detectors.