MOCCA-SURVEY Database I: Assessing GW kick retention fractions for BH-BH mergers in globular clusters

Anisotropy of gravitational wave (GW) emission results in a net momentum gained by the black hole (BH) merger product, leading to a recoil velocity up to similar to 10(3) km s(-1) , which may kick it out of a globular cluster (GC). We estimate GW kick retention fractions of merger products assuming different models for BH spin magnitude and orientation. We check how they depend on BII-BII merger time and properties of the cluster. We analyse the implications of GW kick retention fractions on intermediate massive BH formation by repeated mergers in a GC. We also calculate final spin of the merger product, and investigate how it correlates with other parameters: effective spin of the binary and gravitational kick velocity. We used data from MOCCA (MOnte Carlo Cluster simulAtor) GC simulations to get a realistic sample of BH-BH mergers, assigned each BH spin value according to a studied model, and calculated recoil velocity and final spin based on most recent theoretical formulas. We discovered that for physically motivated models, GW kick retention fractions are about 30 per cent and display small dependence on assumptions about spin, but are much more prone to cluster properties. In particular, we discovered a strong dependence of GW kick retention fractions on cluster density. We also show that GW kick retention fractions are high in final life stages of the cluster, but low at the beginning. Finally, we derive formulas connecting final spin with effective spin for primordial binaries, and with maximal effective spin for dynamical binaries.