Gravitational recoil during binary black hole coalescence using the effective one body approach

During the coalescence of binary black holes, gravitational waves carry linear momentum away from the source, which results in the recoil of the center of mass. Using the effective one body approach, which includes nonperturbative resummed estimates for the damping and conservative parts of the compact binary dynamics, we compute the recoil during the late inspiral and the subsequent plunge of nonspinning black holes of comparable masses moving in quasicircular orbits. Further, using a prescription that smoothly connects the plunge phase to a perturbed single black hole, we obtain an estimate for the total recoil associated with the binary black hole coalescence. We show that the crucial physical feature which determines the magnitude of the terminal recoil is the presence of a burst of linear-momentum flux emitted slightly before coalescence. When using the most natural expression for the linear-momentum flux during the plunge, together with a Taylor-expanded (v/c)(4) correction factor, we find that the maximum value of the terminal recoil is similar to 74 km/s and occurs for eta=(m(1)m(2))/(m(1)+m(2))(2)similar or equal to 0.2, i.e., for a mass ratio m(2)/m(1)similar or equal to 0.38. Away from this optimal mass ratio, the recoil velocity decreases approximately proportionally to the scaling function f(eta)=eta(2)(1-4 eta)(1/2)(1.0912-1.04 eta+2.92 eta(2)). We comment, however, on the fact that the above best-bet estimate is subject to strong uncertainties because the location and amplitude of the crucial peak of linear-momentum flux happens at a moment during the plunge where most of the simplifying analytical assumptions underlying the effective one body approach are no longer justified. Changing the analytical way of estimating the linear-momentum flux, we find maximum recoils that range between 49 and 172 km/s.