Post-Newtonian prediction for the (2,2) mode of the gravitational wave emitted by compact binaries

TL;DR

This paper computes the 3.5PN order of the (2,2) gravitational wave mode for non-spinning, quasi-circular compact binaries, enhancing the accuracy of waveform models for gravitational wave detection.

Contribution

It extends the multipolar post-Newtonian formalism to 3.5PN order, providing a more precise analytical prediction of the gravitational wave amplitude.

Findings

Achieved 3.5PN order calculation of the (2,2) mode.

Extended the multipolar post-Minkowskian algorithm.

Facilitates improved comparison with numerical relativity.

Abstract

We present our 3.5PN computation of the (2,2) mode of the gravitational wave amplitude emitted by compact binaries, on quasi-circular orbits and in the absence of spins. We use the multipolar post-Newtonian wave generation formalism, extending and building on previous works which computed the 3PN order. This calculation required the extension of the multipolar post-Minkowskian algorithm, as well as the computation of the mass source quadrupole at 3.5PN order. Our result will allow more accurate comparisons to numerical relativity, and is a first step towards the computation of the full 3.5PN waveform amplitude, which would improve the estimation of the source parameters by gravitational wave detectors.