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 $\sim10^3\text{ km s}^{-1}$, 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 (MS0 - random, MS1 -
spin as a function of mass and metalicity, MS2 - constant value of $0.5$). We
check how they depend on BH-BH merger time and properties of the cluster. We
analyze the implications of GW kick retention fractions on intermediate massive
BH (IMBH) formation by repeated mergers in a GC. We also calculate final spin
of the merger product, and investigate how it correlates with effective spin of
the binary. 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 $30\%$ 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.
