Black hole spectroscopy by mode cleaning

TL;DR

This paper introduces a Bayesian mode cleaning framework using rational filters to analyze gravitational wave ringdowns, enabling more precise black hole spectroscopy and tests of the no-hair theorem.

Contribution

It proposes a novel mode cleaning method integrated into Bayesian inference that simplifies parameter estimation without MCMC and enhances mode detection.

Findings

More definitive evidence of the first overtone in GW150914

Efficient constraints on remnant black hole mass and spin

Demonstrated mode cleaning improves mode detection confidence

Abstract

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 ${\it rational~filters}$. 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 (MCMC). 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 MCMC 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.