Gravitational Recoil Velocities from Eccentric Binary Black Hole Mergers

The formation and growth of supermassive black holes is a key issue to unveil the secrets of galaxy formation. In particular, the gravitational recoil produced in the merger of unequal mass black hole binaries could have a number of astrophysical implications, such as the ejection of black holes from the host galaxy or globular cluster. We present estimates of the recoil velocity that include the effect of small eccentricities. The approach is specially suited for the last stage of the merger, where most of the emission of linear momentum in gravitational waves takes place. Supplementing our estimates with post-Newtonian approximations, we obtain lower and upper bounds that constrain previous recoil velocities estimates as well as a best estimate that agrees with numerical simulations in the quasicircular case. For eccentricities e ≤ 0.1, the maximum recoil is found for mass ratios of M1/M2 ∼ 0.38 with a best estimate of ∼ 167 (1 + e), km s and upper and lower bounds of 79 (1 + e) km s and 216 (1 + e) km s respectively. Subject headings: black hole physics — cosmology: theory — galaxies: nuclei — gravitation — gravitational waves — relativity