Complete gravitational-waveform amplitude modes for quasi-circular compact binaries to the 3.5PN order

TL;DR

This paper completes the calculation of gravitational waveform amplitude modes for non-spinning compact binaries in quasi-circular orbits up to 3.5PN order, aiding gravitational wave data analysis.

Contribution

It provides the full 3.5PN order amplitude modes including spin effects, using a spherical harmonics decomposition and formalism suitable for EOB models.

Findings

Amplitude modes computed to 3.5PN order

Includes non-spinning and spinning effects

Provides expressions for waveform modeling

Abstract

We complete the computation of the gravitational waveform amplitude for non-spinning compact binaries to the third and a half post-Newtonian (PN) order in the quasi-circular case. This is done by performing a spin-weighted spherical harmonics decomposition of the amplitude. This computation is achieved using the post-Newtonian-Multipolar-post-Minkowskian formalism. The amplitude modes are written in a PN expanded way as well as a factorized form suitable for EOB template building. Combining this work with previous ones, we provide in the supplemental materials the expressions of the modes including all non-spinning and spinning effects to the 3.5PN order for non-precessing quasi-circular binaries.