Black Hole Spectroscopy by Mode Cleaning.

We formulate a Bayesian framework to analyze ringdown gravitational waves from colliding binary black holes and test the no-hair theorem. The idea hinges on mode cleaning-revealing subdominant oscillation modes by removing dominant ones using newly proposed "rational filters." By incorporating the filter into Bayesian inference, we construct a likelihood function that depends only on the mass and spin of the remnant black hole (no dependence on mode amplitudes and phases) and implement an efficient pipeline to constrain the remnant mass and spin without Markov chain Monte Carlo. We test ringdown models by cleaning combinations of different modes and evaluating the consistency between the residual data and pure noise. The model evidence and Bayes factor are used to demonstrate the presence of a particular mode and to infer the mode starting time. In addition, we design a hybrid approach to estimate the remnant black hole properties exclusively from a single mode using Markov chain Monte Carlo after mode cleaning. We apply the framework to GW150914 and demonstrate more definitive evidence of the first overtone by cleaning the fundamental mode. This new framework provides a powerful tool for black hole spectroscopy in future gravitational-wave events.

Nonlinearities in Black Hole Ringdowns.

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter, we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain's (ℓ,m)=(4,4) angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic (4,4) mode's amplitude exhibits quadratic scaling with the fundamental (2,2) mode-its parent mode. The nonlinear mode's amplitude is comparable to or even larger than that of the linear (4,4) mode. Therefore, correctly modeling the ringdown of higher harmonics-improving mode mismatches by up to 2 orders of magnitude-requires the inclusion of nonlinear effects.