Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order

TL;DR

This paper advances the theoretical modeling of gravitational waveforms from spin-aligned binary systems by extending the post-Newtonian calculations to 3.5PN order, including detailed spin contributions and mode decompositions.

Contribution

The authors derive the complete 3.5PN order spin contributions to gravitational waveform modes for aligned binaries, improving waveform accuracy for gravitational wave detection.

Findings

Derived full waveform decomposed in spin-weighted spherical harmonics.

Extended previous models with higher multipolar order and non-linear interactions.

Corrected and improved mode terms used in effective-one-body waveform models.

Abstract

We complete the post-Newtonian (PN) prediction at the 3.5PN order for the spin contributions to the gravitational waveforms emitted by inspiraling compact binaries, in the case of quasi-circular, equatorial orbits, where both spins are aligned with the orbital angular momentum. Using results from the multipolar post-Minkowskian wave generation formalism, we extend previous works that derived the dynamics and gravitational-wave energy flux and phasing, by computing the full waveform decomposed in spin-weighted spherical harmonics. This new calculation requires the computation of multipolar moments of higher multipolar order, new quadratic-in-spin contributions to the hereditary tail terms entering at the 3.5PN order, as well as other non-linear interactions between moments. When specialized to the test-mass limit, our results are equivalent to those obtained in the literature for the waveform emitted by a test-mass in equatorial, circular orbits around a Kerr black hole. We also compute the factorized modes for use in effective-one-body waveform models, correcting the 2.5PN nonspinning and 3PN quadratic-in-spin terms in the (2,1) mode used in current models.