Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order

TL;DR

This paper enhances the accuracy of gravitational waveform models for inspiralling compact binaries by calculating non-linear multipole interactions and octupole modes up to 3.5PN order, improving data analysis and theoretical comparisons.

Contribution

It provides detailed calculations of non-linear multipole couplings and the source octupole moment at 3PN, completing the 3.5PN waveform expressions for inspiralling binaries.

Findings

Derived non-linear multipole interactions up to 3.5PN

Computed source octupole moment at 3PN order

Confirmed quadrupole moment results independently

Abstract

This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between post-Newtonian approximations and numerical relativity computations. It presents: (i) the non-linear couplings between multipole moments of general post-Newtonian matter sources up to order 3.5PN, including all contributions from tails, tails-of-tails and the non-linear memory effect; and (ii) the source mass-type octupole moment of (non-spinning) compact binaries up to order 3PN, which permits to complete the expressions of the octupole modes (3,3) and (3,1) of the gravitational waveform to order 3.5PN. At this occasion we reconfirm by means of independent calculations our earlier results concerning the source mass-type quadrupole moment to order 3PN. Related discussions on factorized resummed waveforms and the occurence of logarithmic contributions to high order are also included.