The 2.5PN linear momentum flux and associated recoil from inspiralling compact binaries in quasi-circular orbits: Nonspinning case

Anisotropic emission of gravitational waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasicircular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. We find that the recoil velocity at the end of the inspiral phase (i.e at the innermost stable circular orbit (ISCO)) is maximum for a binary with symmetric mass ratio of \nu~0.2 and is roughly about ~4.58 km/s. Going beyond inspiral, we also provide an estimate of the more important contribution to the recoil velocity from the plunge phase. Again the recoil velocity at the end of the plunge, involving contributions both from inspiral and plunge phase, is maximum for a binary with \nu~0.2 and is of the order of ~180 km/s.