Gravitational Recoil from Binary Black Hole Mergers: the Close-Limit Approximation

[abridged] The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. We present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of ~ 64 km/s for a symmetric mass ratio eta = M_1 M_2/(M_1+M_2)^2 ~ 0.19 and an initial proper separation of 4 M, where M is the total ADM mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. If we supplement this estimate with PN calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around 84 km/s. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of 220-265 km/s. We also provide non-linear fits to these estimated upper and lower bounds. These estimates are subject to uncertainties related to issues such as the choice of initial data and higher effects in perturbation theory. Nonetheless, our estimates are consistent with previous results in the literature and suggest a narrower range of possible recoil velocities.