Black-hole spectroscopy by making full use of gravitational-wave modeling

The Kerr nature of a compact-object-coalescence remnant can be unveiled by observing multiple quasinormal modes 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 mergers. These models presume the ability to correctly estimate the time at which the gravitational-wave signal starts to be dominated by the quasinormal modes of a perturbed black hole. 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 quasinormal mode complex frequencies are free parameters (pEOBNR), and use Bayesian analysis to study its effectiveness in measuring quasinormal modes in GW150914, and in synthetic gravitational-wave signals of binary black holes 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 quasinormal modes, it is also well suited to consistently combine information from several observations-e.g., we find on the order of similar to 30 GW150914-like binary black-hole 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 less than or similar to 5% at the 2-sigma level, thus allowing to test the black hole's no-hair conjecture.