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

Norichika Sago,Hiroyuki Nakano,Soichiro Isoyama

doi:10.3390/universe7100357

Norichika Sago, Hiroyuki Nakano + Show 1 more

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https://doi.org/10.3390/universe7100357

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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 we 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.

Highlights

The remnant of merging black holes (BHs) is a perturbed compact object characterized by the set of complex frequencies known as quasinormal modes (QNMs), and the gravitational radiation from this remnant is called the ringdown phase of gravitational waves (GWs)
An accurate measurement of QNMs encoded in the ringdown signal, offers various GR tests regarding the compact object, for example, to disclose the remnant property (the ergo region of Kerr geometry [4,5,6], ringdown test of general relativity (GR) [7], etc.), and to verify GR itself in the strong-field regime; we refer readers to Ref. [8] for a review of the BH QNMs, and Ref. [9] for that of the ringdown GWs
We examined in detail the ringdown GWs of binary BHs with QNM fits including overtones in Equations (25) and (37), using the accurate close-limit waveform in the BH perturbation theory as a test bed

Summary

Introduction

The remnant of merging black holes (BHs) is a perturbed compact object (a Kerr BH [1], or even something more exotic) characterized by the set of complex frequencies known as quasinormal modes (QNMs), and the gravitational radiation from this remnant is called the ringdown phase of gravitational waves (GWs). An accurate measurement of QNMs encoded in the ringdown signal, offers various GR tests regarding the compact object, for example, to disclose the remnant property (the ergo region of Kerr geometry [4,5,6], ringdown test of general relativity (GR) [7], etc.), and to verify GR itself in the strong-field regime; we refer readers to Ref. Leaver [16] gave a standard method to calculate the QNM frequencies very accurately ( see, e.g., Refs. [17,18,19], for more modern techniques to compute QNMs, motivated by the recent development in the BH perturbation theory or high-energy physics)

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