Decoding mode-mixing in black-hole merger ringdown

TL;DR

This paper investigates the complex behavior of higher-order gravitational-wave modes in black-hole mergers, revealing that mode-mixing arises mainly from basis mismatch, which affects waveform analysis and parameter estimation.

Contribution

It identifies the primary cause of mode-mixing in merger waveforms as basis mismatch between spherical and spheroidal harmonics, improving understanding of waveform modeling.

Findings

Mode-mixing in the (3,2) harmonic mode is mainly due to basis mismatch.

Other causes like gauge ambiguities are minor for studied waveforms.

Understanding mode-mixing aids in more accurate gravitational-wave data analysis.

Abstract

Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multi-mode template of merger waveforms is the apparently complicated behavior of some of these modes; instead of settling down to a simple quasinormal frequency with decaying amplitude, some $|m| \neq \ell$ modes show periodic bumps characteristic of mode-mixing. We analyze the strongest of these modes -- the anomalous $(3,2)$ harmonic mode -- measured in a set of binary black-hole merger waveform simulations, and show that to leading order, they are due to a mismatch between the spherical harmonic basis used for extraction in 3D numerical relativity simulations, and the spheroidal harmonics adapted to the perturbation theory of Kerr black holes. Other causes of mode-mixing arising from gauge ambiguities and physical properties of the quasinormal ringdown modes are also considered and found to be small for the waveforms studied here.