Modeling kicks from the merger of non-precessing black-hole binaries

Several groups have recently computed the gravitational radiation recoil produced by the merger of two spinning black holes. The results suggest that spin can be the dominant contributor to the kick, with reported recoil speeds of hundreds to even thousands of kilometers per second. The parameter space of spin kicks is large, however, and it is ultimately desirable to have a simple formula that gives the approximate magnitude of the kick given a mass ratio, spin magnitudes, and spin orientations. As a step toward this goal, we perform a systematic study of the recoil speeds from mergers of black holes with mass ratio $q\equiv m_1/m_2=2/3$ and dimensionless spin parameters of $a_1/m_1$ and $a_2/m_2$ equal to 0 or 0.2, with directions aligned or anti-aligned with the orbital angular momentum. We also run an equal-mass $a_1/m_1=-a_2/m_2=0.2$ case, and find good agreement with previous results. We find that, for currently reported kicks from aligned or anti-aligned spins, a simple kick formula inspired by post-Newtonian analyses can reproduce the numerical results to better than $\sim$10%.