Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order

TL;DR

This paper derives the third post-Newtonian order quadratic-in-spin effects on the orbital dynamics and gravitational-wave energy flux of compact binaries, providing new insights into their gravitational-wave signals.

Contribution

It introduces the first complete derivation of 3PN spin contributions to gravitational-wave flux, including spin-induced quadrupole effects, using a multipolar post-Minkowskian approach.

Findings

Derived 3PN spin contributions to gravitational-wave energy flux.

Confirmed equivalence with existing equations of motion.

Presented orbital phase calculations for generic and spin-aligned circular orbits.

Abstract

We investigate the dynamics of spinning binaries of compact objects at the next-to-leading order in the quadratic-in-spin effects, which corresponds to the third post-Newtonian order (3PN). Using a Dixon-type multipolar formalism for spinning point particles endowed with spin-induced quadrupoles and computing iteratively in harmonic coordinates the relevant pieces of the PN metric within the near zone, we derive the post-Newtonian equations of motion as well as the equations of spin precession. We find full equivalence with available results. We then focus on the far-zone field produced by those systems and obtain the previously unknown 3PN spin contributions to the gravitational-wave energy flux by means of the multipolar post-Minkowskian (MPM) wave generation formalism. Our results are presented in the center-of-mass frame for generic orbits, before being further specialized to the case of spin-aligned, circular orbits. We derive the orbital phase of the binary based on the energy balance equation and briefly discuss the relevance of the new terms.