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

TL;DR

This work computes the next-to-next-to-leading spin-orbit contributions to the gravitational-wave energy flux and orbital phasing at $3.5$PN for compact binaries with spin, extending previous EOM results into the radiation sector using the multipolar post-Newtonian formalism. The authors derive spin-orbit terms in the source multipole moments in a general frame and reduce them to the center-of-mass frame, then specialize to quasi-circular orbits to obtain the explicit spin-orbit flux contribution $oldsymbol{\\mathcal{F}_S}$ and the corresponding secular phase evolution. Consistency checks include agreement with the test-mass Kerr limit as $ u o 0$ and the boosted Kerr limit for a single moving black hole, validating Lorentz-invariance aspects of the formalism. The results have direct implications for high-precision gravitational-wave templates, aiding parameter estimation for detectors such as LIGO/Virgo and LISA by improving modeling of spin-orbit effects in the late inspiral.

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.