Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries

TL;DR

This paper calculates advanced spin-orbit effects at 3.5PN order in gravitational wave flux from compact binaries, improving models for gravitational wave detection and parameter estimation.

Contribution

It provides the next-to-next-to-leading order spin-orbit contributions to gravitational wave flux and multipole moments for compact binaries, extending previous work to higher precision.

Findings

Results agree with Kerr black hole perturbation in the test-mass limit

Multipole moments reduce to those of a boosted Kerr black hole in one-body case

Implications for gravitational wave phase evolution and detection accuracy

Abstract

We compute the next-to-next-to-leading order spin-orbit contributions in the total energy flux emitted in gravitational waves by compact binary systems. Such contributions correspond to the post-Newtonian order 3.5PN for maximally spinning compact objects. Continuing our recent work on the next-to-next-to-leading spin-orbit terms at 3.5PN order in the equations of motion, we obtain the spin-orbit terms in the multipole moments of the compact binary system up to the same order within the multipolar post-Newtonian wave generation formalism. Our calculation of the multipole moments is valid for general orbits and in an arbitrary frame; the moments are then reduced to the center-of-mass frame and the resulting energy flux is specialized to quasi-circular orbits. The test-mass limit of our final result for the flux agrees with the already known Kerr black hole perturbation limit. Furthermore the various multipole moments of the compact binary reduce in the one-body case to those of a single boosted Kerr black hole. We briefly discuss the implications of our result for the gravitational-wave flux in terms of the binary's phase evolution, and address its importance for the future detection and parameter estimation of signals in gravitational wave detectors.