The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries

TL;DR

This paper calculates the 3.5 post-Newtonian order quadrupole gravitational wave mode for inspiralling compact binaries on quasi-circular orbits, improving waveform models for gravitational wave detection.

Contribution

It introduces the 3.5PN terms in the mass quadrupole moment and refines hereditary integral corrections, advancing the accuracy of gravitational waveform modeling.

Findings

Provides the (2,2) quadrupolar mode at 3.5PN order

Enhances waveform models for better source parameter estimation

Lays groundwork for full 3.5PN waveform computation

Abstract

We compute the quadrupole mode of the gravitational waveform of inspiralling compact binaries at the third and a half post-Newtonian (3.5PN) approximation of general relativity. The computation is performed using the multipolar post-Newtonian formalism, and restricted to binaries without spins moving on quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the mass quadrupole moment of the source, and the control of required subdominant corrections to the contributions of hereditary integrals (tails and non-linear memory effect). The result is given in the form of the quadrupolar mode (2,2) in a spin-weighted spherical harmonic decomposition of the waveform, and may be used for comparison with the counterpart quantity computed in numerical relativity. It is a step towards the computation of the full 3.5PN waveform, whose knowledge is expected to reduce the errors on the location parameters of the source.