Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation

TL;DR

This paper investigates the fundamental tone and overtones of quasinormal modes in black hole ringdown gravitational waves using numerical simulations and proposes an orthonormalization method to improve modeling accuracy.

Contribution

It introduces a new orthonormalization of quasinormal mode functions for better modeling of black hole ringdown signals.

Findings

Generated low-error ringdown wave data via black hole perturbation simulations.

Proposed an orthonormalization method for quasinormal mode functions.

Discussed implications for gravitational-wave data analysis.

Abstract

Ringdown gravitational waves of compact object binaries observed by ground-based gravitational-wave detectors encapsulate rich information to understand remnant objects after the merger and to test general relativity in the strong field. In this work, we investigate the ringdown gravitational waves in detail to better understand their property, assuming that the remnant objects are black holes. For this purpose, we perform numerical simulations of post-merger phase of binary black holes by using the black hole perturbation scheme with the initial data given under the close-limit approximation, and generate data of ringdown gravitational waves with smaller numerical errors than that associated with currently available numerical relativity simulations. Based on the analysis of the data, we propose an orthonormalization of the quasinormal mode functions describing the fundamental tone and overtones to model ringdown gravitational waves. Finally, through some demonstrations of the proposed model, we briefly discuss the prospects for ringdown gravitational-wave data analysis including the overtones of quasinormal modes.