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.
© 2023 American Physical Society. We thank Maximiliano Isi and Will M. Farr for their helpful suggestions and comments. We also thank Eric Thrane, Paul Lasky, Emanuele Berti, Mark Ho-Yeuk Cheung, Roberto Cotesta, and all the attendees of the ringdown workshop held at CCA, Flatiron Institute for useful discussions. Computations for this work were performed with the Wheeler cluster at Caltech. Y. C. and S. M. acknowledge support from the Brinson Foundation, the Simons Foundation (Award No. 568762), and by NSF Grants PHY-2011961, PHY-2011968, PHY–1836809. L. S. acknowledges the support of the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), Project No. CE170100004. This material is based upon work supported by NSF's LIGO Laboratory, which is a major facility fully funded by the National Science Foundation.
Published - PhysRevLett.130.141401.pdf
Supplemental Material - Supplemental_Material.pdf