On the ease of excitation of black hole ringing: Quantifying the importance of overtones by the excitation factors

TL;DR

This paper calculates the excitation factors of Kerr black hole overtones, demonstrating that higher overtones are more easily excited, which supports their significance in gravitational wave signals.

Contribution

It provides the first comprehensive calculation of excitation factors for overtones up to the 20th order in Kerr black holes, highlighting the prominence of specific overtones.

Findings

Overtones 4, 5, and 6 have the highest excitation factors for certain spins.

Excitation factors are independent of the perturbation source.

Results confirm the importance of overtones in gravitational wave analysis.

Abstract

The excitation factors of black hole quasinormal modes quantify the $\textit{ease of excitation}$ of the quasinormal modes and are independent of the source of perturbation. We compute the excitation factors of Kerr black holes up to the 20th overtone and find that the 4th, 5th, and 6th overtones have the first three highest excitation factors for intermediate and high spin parameters. This provides an independent confirmation of the importance of overtones that has been confirmed by the fitting data analysis of numerical relativity waveforms beginning around the strain peak amplitude.