Black-hole Spectroscopy by Making Full Use of Gravitational-Wave Modeling

TL;DR

This paper introduces a new waveform model that uses full gravitational-wave data to improve measurement of black hole quasi-normal modes, enabling tests of general relativity and the black hole no-hair conjecture.

Contribution

The authors develop a parameterized effective-one-body waveform model with free QNM frequencies, enhancing the ability to measure and analyze black hole ringdown signals.

Findings

The pEOBNR model provides stronger constraints on QNM parameters than traditional methods.

It can detect deviations from General Relativity in ringdown signals.

Approximately 30 GW150914-like events are needed to measure QNM frequencies with high accuracy.

Abstract

The Kerr nature of a compact-object-coalescence remnant can be unveiled by observing multiple quasi-normal modes (QNMs) in the post-merger signal. Current methods to achieve this goal rely on matching the data with a superposition of exponentially damped sinusoids with amplitudes fitted to numerical-relativity (NR) simulations of binary black-hole (BBH) mergers. These models presume the ability to correctly estimate the time at which the gravitational-wave (GW) signal starts to be dominated by the QNMs of a perturbed BH. Here we show that this difficulty can be overcome by using multipolar inspiral-merger-ringdown waveforms, calibrated to NR simulations, as already developed within the effective-one-body formalism (EOBNR). We build a parameterized (nonspinning) EOBNR waveform model in which the QNM complex frequencies are free parameters (pEOBNR), and use Bayesian analysis to study its effectiveness in measuring QNMs in GW150914, and in synthetic GW signals of BBHs injected in Gaussian noise. We find that using the pEOBNR model gives, in general, stronger constraints compared to the ones obtained when using a sum of damped sinusoids and using Bayesian model selection, we also show that the pEOBNR model can successfully be employed to find evidence for deviations from General Relativity in the ringdown signal. Since the pEOBNR model properly includes time and phase shifts among QNMs, it is also well suited to consistently combine information from several observations --- e.g., we find on the order of $\sim 30$ GW150914-like BBH events would be needed for Advanced LIGO and Virgo at design sensitivity to measure the fundamental frequencies of both the $(2,2)$ and $(3,3)$ modes, and the decay time of the $(2,2)$ mode with an accuracy of $\lesssim 5\%$ at the $2\mbox{-}\sigma$ level, thus allowing to test the BH's no-hair conjecture.