We test the accuracy of our recently proposed empirical formula to model the recoil velocity imparted to the merger remnant of spinning, unequal-mass black-hole binaries. We study three families of black-hole binary configurations, all with mass ratio $q=3/8$ (to nearly maximize the unequal-mass contribution to the kick) and spins aligned (or counter-aligned) with the orbital angular momentum, two with spin configurations chosen to minimize the spin-induced tangential and radial accelerations of the trajectories, respectively, and a third family where the trajectories are significantly altered by spin-orbit coupling. We find good agreement between the measured and predicted recoil velocities for the first two families, and reasonable agreement for the third. We also reexamine our original generic binary configuration that led to the discovery of extremely large spin-driven recoil velocities and inspired our empirical formula, and find rough agreement between the predicted and measured recoil speeds.

• Received 30 August 2007

DOI:https://doi.org/10.1103/PhysRevD.77.044028