Ringdown overtones, black hole spectroscopy, and no-hair theorem tests

Abstract

Validating the black-hole no-hair theorem with gravitational-wave observations of compact binary coalescences provides a compelling argument that the remnant object is indeed a black hole as described by the general theory of relativity. This requires performing a spectroscopic analysis of the post-merger signal and resolving the frequencies of either different angular modes or overtones (of the same angular mode). For a nearly-equal mass binary black-hole system, only the dominant angular mode ($l=m=2$) is sufficiently excited and the overtones are instrumental to perform this test. Here we investigate the robustness of modelling the post-merger signal of a binary black hole coalescence as a superposition of overtones. Further, we study the bias expected in the recovered frequencies as a function of the start time of a spectroscopic analysis and provide a computationally cheap procedure to choose it based on the interplay between the expected statistical error due to the detector noise and the systematic errors due to waveform modelling. Moreover, since the overtone frequencies are closely spaced, we find that resolving the overtones is particularly challenging and requires a loud ringdown signal. Rayleigh's resolvability criterion suggests that in an optimistic scenario a ringdown signal-to-noise ratio larger than $\sim 30$ (achievable possibly with LIGO at design sensitivity and routinely with future interferometers such as Einstein Telescope, Cosmic Explorer, and LISA) is necessary to resolve the overtone frequencies. We then conclude by discussing some conceptual issues associated with black-hole spectroscopy with overtones.

19 pages, 18 figures (updated to the version in PRD)

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Cited by in corpus (10)

• Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521
• How does a dark compact object ringdown?
• Spectroscopy of binary black hole ringdown using overtones and angular modes
• Parametrized ringdown spin expansion coefficients: a data-analysis framework for black-hole spectroscopy with multiple events
• Testing General Relativity with Gravitational Waves: An Overview
• Detectable universes inside regular black holes
• Quantum black hole spectroscopy: probing the quantum nature of the black hole area using LIGO-Virgo ringdown detections
• Odd-parity perturbations of the wormhole-like geometries and quasi-normal modes in Einstein-Æther theory
• Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation
• Recent LIGO-Virgo discoveries