Comparison of subdominant gravitational wave harmonics between post-Newtonian and numerical relativity calculations and construction of multi-mode hybrids

TL;DR

This paper compares post-Newtonian and numerical relativity gravitational waveforms, focusing on subdominant modes, and develops methods to create accurate hybrid waveforms for binary black hole mergers.

Contribution

It introduces a systematic approach for aligning and combining waveforms from different methods, including higher-order modes, to improve gravitational wave modeling.

Findings

Successful hybridization of waveforms with higher-order modes

Identification of finite radius errors in numerical simulations

Enhanced understanding of waveform alignment procedures

Abstract

Gravitational waveforms which describe the inspiral, merger and ringdown of coalescing binaries are usually constructed by synthesising information from perturbative descriptions, in particular post-Newtonian theory and black-hole perturbation theory, with numerical solutions of the full Einstein equations. In this paper we discuss the "glueing" of numerical and post-Newtonian waveforms to produce hybrid waveforms which include subdominant spherical harmonics ("higher order modes"), and focus in particular on the process of consistently aligning the waveforms, which requires a comparison of both descriptions and a discussion of their imprecisions. We restrict to the non-precessing case, and illustrate the process using numerical waveforms of up to mass ratio $q=18$ produced with the BAM code, and publicly available waveforms from the SXS catalogue. The results also suggest new ways of analysing finite radius errors in numerical simulations.