Quadratic quasi-normal mode dependence on linear mode parity

TL;DR

This paper investigates the nonlinear quadratic quasinormal modes (QQNMs) in black hole ringdowns, revealing that their amplitude ratio to linear QNMs depends on the parity ratio of the linear modes, clarifying previous discrepancies.

Contribution

It introduces a hyperboloidal framework that shows QQNM amplitudes depend on the parity ratio of linear QNMs, resolving prior conflicting results.

Findings

QQNM/QNM ratio depends on black hole parameters and parity ratio.

The parity ratio of linear QNMs influences the nonlinear QQNM amplitudes.

The new framework clarifies the nonlinear mode coupling in black hole ringdowns.

Abstract

Quasinormal modes (QNMs) uniquely describe the dominant piece of the gravitational-wave ringdown of postmerger black holes. While the linear QNM regime has been extensively studied, recent work has highlighted the importance of second-perturbative-order, quadratic QNMs (QQNMs) arising from the nonlinear coupling of linear QNMs. Previous attempts to quantify the magnitude of these QQNMs have shown discrepant results. Using a new hyperboloidal framework, we resolve the discrepancy by showing that the QQNM/QNM ratio is a function not only of the black hole parameters but also of the ratio between even- and odd-parity linear QNMs: the ratio QQNM/QNM depends on what created the ringing black hole, but only through this ratio of even- to odd-parity linear perturbations.