Gravitational-wave Capture in Spinning Black Hole Encounters

The orbits of two black holes (BHs) that are initially unbound can be transformed into bound orbits by emitting gravitational waves during close encounters in a star cluster, which is called gravitational-wave (GW) capture. The effects of spin of BHs 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 BHs have equal masses, as expected from post-Newtonian approximation. The strongest emission is produced when the spins of both BHs 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 BHs with aligned spins to the orbital angular momentum. The fraction of direct merging among the GW captures increases in proportion to v4/7, assuming the uniform distribution of pericenter distances in the encounters, where v is the velocity dispersion of the cluster, which means about 5% of GW capture leads to the direct merging for star clusters with v = 150 km s−1.