Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit

TL;DR

This work shows that individual spin-weighted gravitational-wave modes can be computed to higher PN order by directly relating them to radiative multipole moments, rather than projecting from truncated polarization waveforms. By deriving and summing the radiative moments $U_L$ and $V_L$, including nonlinear tail, tail-of-tail, and memory terms, the dominant $h^{22}$ mode is obtained up to 3PN for non-spinning binaries, facilitating more precise PN–NR comparisons across the whole sky. The paper provides detailed expressions for numerous ${h}^{\ell m}$ components, analyzes hereditary contributions, and demonstrates how amplitude terms can be absorbed into the phase to simplify comparisons with NR while preserving essential PN structure. The results argue for computing higher PN corrections to radiative moments to improve detection and parameter estimation in gravitational-wave astronomy, as supported by NR studies showing improved agreement when 3PN amplitudes are included.

Abstract

The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN polarization waveforms. In particular, the dominant (l = 2, m = 2) mode can be computed to 3PN order. Individual modes are computed to as high a post-Newtonian order as possible given previous post-Newtonian results.