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 ring-down modes of a Kerr BH. By varying the matching point between inspiral and ring-down, 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 of f(500) = 0.12-(+0.06)(0.05) of binaries have recoil velocities greater then 500 km s(-1) and that a fraction f(1000) = 0.027(-0.014)(+0.021) of binaries have kicks greater than 1000 km s(-1). 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 f1000 = 0.079-(+0.062)(0.042).