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

TL;DR

This work advances gravitational-wave modeling by completing the 3.5PN amplitude accuracy for inspiralling binaries through non-linear multipole couplings, including tails, tail-of-tail, and memory effects, and by deriving the 3PN mass octupole moment to obtain the (3,3) and (3,1) octupole modes. It integrates dimensional regularization with center-of-mass reductions to produce a gauge-consistent, IR-log-resummed octupole waveform, and demonstrates consistency with known quadrupole results and the test-mass limit. The results feed into improved PN templates and EOB-based waveform models, enabling more accurate comparisons with numerical relativity and data analysis for subdominant modes. Overall, the paper tightens the theoretical underpinnings of waveform amplitudes at high PN order and provides practical expressions for octupole contributions and resummed tails that enhance gravitational-wave data analysis and theory-experiment cross-checks.

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.