Binary black holes: Spin dynamics and gravitational recoil

Abstract

We present a study of spinning black hole binaries focusing on the spin dynamics of the individual black holes as well as on the gravitational recoil acquired by the black hole produced by the merger. We consider two series of initial spin orientations away from the binary orbital plane. In one of the series, the spins are antialigned; for the second series, one of the spins points away from the binary along the line separating the black holes. We find a remarkable agreement between the spin dynamics predicted at 2nd post-Newtonian order and those from numerical relativity. For each configuration, we compute the kick of the final black hole. We use the kick estimates from the series with antialigned spins to fit the parameters in the Kidder kick formula, and verify that the recoil in the direction of the orbital angular momentum is $\propto \sin \theta$ and on the orbital plane $\propto \cos \theta$, with $\theta$ the angle between the spin directions and the orbital angular momentum. We also find that the black hole spins can be well estimated by evaluating the isolated horizon spin on spheres of constant coordinate radius.