Modeling Kicks from the Merger of Nonprecessing Black Hole Binaries

Several groups have recently computed the gravitational radiation recoilproduced by the merger of two spinning black holes. The results suggest thatspin can be the dominant contributor to the kick, with reported recoil speedsof hundreds to even thousands of kilometers per second. The parameter space ofspin kicks is large, however, and it is ultimately desirable to have a simpleformula that gives the approximate magnitude of the kick given a mass ratio,spin magnitudes, and spin orientations. As a step toward this goal, we performa systematic study of the recoil speeds from mergers of black holes with massratio $q\equiv m_1/m_2=2/3$ 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 theorbital 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, forcurrently reported kicks from aligned or anti-aligned spins, a simple kickformula inspired by post-Newtonian analyses can reproduce the numerical resultsto better than $\sim$10%.Comment: 5 pages, 3 figures. Replaced with published versio