Overtones and Nonlinearities in Binary Black Hole Ringdowns

TL;DR

This paper confirms the presence of multiple overtones and second-order quasinormal modes in binary black hole ringdowns using high-accuracy numerical relativity, supporting perturbation theory's applicability.

Contribution

It provides the first clear evidence of overtones and second-order modes in binary black hole ringdowns, validating perturbation theory in this context.

Findings

Detection of multiple overtones early in ringdown

Identification of second-order quasinormal modes

Validation of perturbation theory for ringdown modeling

Abstract

Using high-accuracy numerical relativity waveforms, we confirm the presence of numerous overtones of the $\ell=2$, $m=2$ quasinormal mode early in the ringdown of binary black hole mergers. We do this by demonstrating the stability of the mode amplitudes at different fit times, ruling out the possibility that a linear superposition of modes unphysically fits a highly nonlinear part of the waveform. We also find a number of previously unidentified subdominant second-order quasinormal modes in the $(2,2)$ mode. Even though these modes are mathematically nonlinear, they nevertheless confirm the validity of perturbation theory as a good approximation for describing much of the ringdown.