Recoil velocity at 2PN order for spinning black hole binaries

TL;DR

This paper calculates the linear momentum flux and recoil velocity of spinning black hole binaries at 2PN order, providing new detailed expressions and analyzing the impact of higher-order spin effects on recoil velocities.

Contribution

It introduces explicit 2PN order expressions for momentum flux, including new spin-orbit and spin-spin terms, and extends analysis to generic orbits with validation against existing models.

Findings

Higher-order spin corrections can triple recoil velocities in superkick configurations.

Derived expressions agree with previous perturbation theory results in the extreme mass ratio limit.

Provided accurate 2PN order formulas for energy and angular momentum fluxes for spinning binaries.

Abstract

We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at 2PN order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely next-to-leading order spin-orbit terms at 1.5 PN order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasi-circular orbits, we integrate the linear momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to about a factor 3 with respect to the leading-order PN prediction. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasi-circular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mik\'oczi, Vas\'uth and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka and Sasaki obtained in the context of black hole perturbation theory.