The Distribution of Recoil Velocities from Merging Black Holes

Abstract

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 ≤ m1/m2 ≤ 10, spin magnitudes of a1, 2 = 0.9, and uniform random spin orientations, we find that a fraction f500 = 0.12 of binaries have recoil velocities greater than 500 km s-1 and that a fraction f1000 = 0.027 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 m1/m2 ≤ 4, the typical kicks are even larger, with f500 = 0.31 and f1000 = 0.079.