Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order

TL;DR

This paper derives third post-Newtonian order gravitational waveforms and fluxes for spinning eccentric binaries, including new spin-orbit and spin-spin effects, to improve waveform modeling for gravitational wave detection.

Contribution

It provides the first derivation of next-to-leading order spin contributions to waveforms and fluxes for eccentric binaries at third post-Newtonian order, including hereditary effects.

Findings

Derived spin-orbit and spin-spin contributions to waveforms.

Included hereditary tail and memory effects for eccentric orbits.

Resummed small-eccentricity expansion for large eccentricities.

Abstract

Compact binaries can have non-negligible orbital eccentricities in the frequency band of ground-based gravitational-wave detectors, depending on their astrophysical formation channels. To accurately determine the parameters of such systems, waveform models need to incorporate eccentricity effects. In this paper, we consider an eccentric binary of spinning nonprecessing compact objects, and derive the energy and angular momentum fluxes at infinity, as well as the gravitational waveform modes to the third post-Newtonian order. The novel results of this paper include the next-to-leading order instantaneous spin-orbit and spin-spin contributions to the waveform modes, in addition to the hereditary (tail and memory) contributions to the modes and fluxes for eccentric orbits. The instantaneous contributions are derived for generic motion, while the hereditary contributions are computed in a small-eccentricity expansion, but we consider a resummation that makes them valid for large eccentricities. We employ a quasi-Keplerian parametrization of the motion using harmonic coordinates and the covariant spin-supplementary condition, which complements some results in the literature in other coordinates. Our results can be useful in improving the accuracy of waveform models for spinning binaries on eccentric orbits.