The Distribution of Recoil Velocities from Merging Black Holes

We calculate the linear momentum flux from merging black holes (BHs) with arbitrary masses and spin orientations, using the effective-one-body (EOB) model. This model includes an analytic description of the inspiral phase, a short merger, and a superposition of exponentially damped quasi-normal ringdown modes of a Kerr BH. By varying the matching point between inspiral and ringdown, we can estimate the systematic errors generated with this method. Within these confidence limits, we find close agreement with previously reported results from numerical relativity. Using a Monte Carlo implementation of the EOB model, we are able to sample a large volume of BH parameter space and estimate the distribution of recoil velocities. For a range of mass ratios 1 <= m_1/m_2 <= 10, spin magnitudes of a_{1,2}=0.9, and uniform random spin orientations, we find that a fraction f_{500}=0.12^{+0.06}_{-0.05} of binaries have recoil velocities greater than 500 km/s and f_{1000}=0.027^{+0.021}_{-0.014} have kicks greater than 1000 km/s. These velocities likely are capable of ejecting the final BH from its host galaxy. Limiting the sample to comparable-mass binaries with m_1/m_2 <= 4, the typical kicks are even larger, with f_{500}=0.31_{-0.12}^{+0.13} and f_{1000}=0.079^{+0.062}_{-0.042}