Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux

TL;DR

This work advances gravitational‑wave modeling for binaries in quasi‑elliptical orbits by delivering the complete instantaneous 3PN energy flux, requiring the 3PN mass quadrupole and 2PN mass octupole/current quadrupole moments, and employing the 3PN quasi‑Keplerian orbital representation to average over eccentric orbits. By evaluating the flux in standard harmonic coordinates and recasting it in modified harmonic and ADM coordinates, the authors remove logarithmic artifacts and obtain gauge‑invariant expressions suitable for constructing accurate GW templates. The analysis combines instantaneous flux with hereditary tails (tails, tails‑of‑tails, and tails squared) computed in a companion paper to yield the full 3PN energy flux, with rigorous checks including the circular‑orbit limit and the test‑particle limit against perturbative results. The results provide a robust framework for modeling eccentric compact binaries in both LISA and ground‑based detector bands, and culminate in explicit, gauge‑invariant formulas for the averaged flux and its dependence on eccentricity and PN parameters.

Abstract

The instantaneous contributions to the 3PN gravitational wave luminosity from the inspiral phase of a binary system of compact objects moving in a quasi elliptical orbit is computed using the multipolar post-Minkowskian wave generation formalism. The necessary inputs for this calculation include the 3PN accurate mass quadrupole moment for general orbits and the mass octupole and current quadrupole moments at 2PN. Using the recently obtained 3PN quasi-Keplerian representation of elliptical orbits the flux is averaged over the binary's orbit. Supplementing this by the important hereditary contributions arising from tails, tails-of-tails and tails squared terms calculated in a previous paper, the complete 3PN energy flux is obtained. The final result presented in this paper would be needed for the construction of ready-to-use templates for binaries moving on non-circular orbits, a plausible class of sources not only for the space based detectors like LISA but also for the ground based ones.