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 theeffective-one-body (EOB) model. This model includes an analyticdescription of the inspiral phase, a short merger, and a superpositionof exponentially damped quasi-normal ring-down modes of a Kerr BH. Byvarying the matching point between inspiral and ring-down, we canestimate the systematic errors generated with this method. Within theseconfidence limits, we find close agreement with previously reportedresults from numerical relativity. Using a Monte Carlo implementation ofthe EOB model, we are able to sample a large volume of BH parameterspace and estimate the distribution of recoil velocities. For a range ofmass ratios 1$\lt$=m$_{1}$/m$_{2}$$\lt$=10, spin magnitudes ofa$_{1,2}$=0.9, and uniform random spin orientations, we find thata fraction f$_{500}$=0.12$^{+0.06}$$_{-0.05}$ ofbinaries have recoil velocities greater than 500 km s$^{-1}$ andthat a fraction f$_{1000}$=0.027$^{+0.021}$$_{-0.014}$of binaries have kicks greater than 1000 km s$^{-1}$. Thesevelocities likely are capable of ejecting the final BH from its hostgalaxy. Limiting the sample to comparable-mass binaries withm$_{1}$/m$_{2}$$\lt$=4, the typical kicks are even larger,with f$_{500}$=0.31$^{+0.13}$$_{-0.12}$ andf$_{1000}$=0.079$^{+0.062}$$_{-0.042}$.