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

TL;DR

This paper derives an analytical expression for the gravitational recoil velocity of nonspinning compact binaries in quasi-circular orbits at 2.5PN order, estimating maximum recoil velocities during inspiral and plunge phases.

Contribution

It provides the first 2.5PN order analytical formula for recoil velocity in nonspinning binaries, including estimates for the plunge phase.

Findings

Maximum recoil velocity during inspiral is about 4.58 km/s for symmetric mass ratio ~0.2.

Maximum recoil velocity after plunge is about 180 km/s for the same mass ratio.

Recoil velocity depends strongly on the binary's mass ratio and phase of evolution.

Abstract

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.