Gravitational Wave Capture in Spinning Black Hole Encounters

The orbits of two black holes which are initially unbound can be transformed into bound orbits by emitting gravitational waves during close encounters in a star cluster, which is called a gravitational wave (GW) capture. The effects of spin of black holes on GW capture are investigated in the context of numerical relativity. The radiated energy during the encounter is dependent on the effective spin when the black holes have the equal masses as expected from post-Newtonian approximation. The strongest emission is produced when the spins of both black holes are anti-aligned to the orbital angular momentum in the case of fly-by encounters. But the opposite is true in the case of direct merging: the strongest emission comes from the black holes with aligned spins to the orbital angular momentum. The fraction of direct merging among the GW captures increases in proportional to $v^{4/7}$ assuming the uniform distribution of pericenter distances in the encounters, where $v$ is the velocity dispersion of cluster, which means about 5 % of GW capture leads to the direct merging for star clusters with $v=150$ km s$^{-1}$.