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Black hole spectroscopy by mode cleaning
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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.
Forward citations
Cited by 8 Pith papers
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Merging black holes with Cauchy-characteristic matching: Computation of late-time tails
First fully nonlinear Cauchy-characteristic matching simulations of binary black hole mergers are stable and accurate, and they expose late-time tails with decay exponents near -3.5 to -3.8.
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Foundations of Direct Waves in Schwarzschild Ringdown
Direct waves in filtered Schwarzschild ringdown are the anti-causal filter-pole contribution sourced by near-horizon trajectory dynamics and do not vanish.
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Probing Direct Waves in Black Hole Ringdowns
Merger gravitational wave signals contain a 'direct wave' from the plunging companions, screened by the remnant's potential, with frequency near the superradiant value for high-spin remnants and SNR above 10 in GW1509...
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LIGO A$^\sharp$: Detector Design and Science Prospects Beyond A+
LIGO A#, a room-temperature upgrade of the LIGO detectors proposed for the 2030s, would broaden sensitivity and increase projected compact-binary detection rates by factors of four to eight relative to A+.
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Computing spectral shifts for Johannsen-Psaltis black holes
Slowly rotating Johannsen–Psaltis black holes have definite-parity quasinormal modes with even/odd frequency shifts split by the deviation parameter, computed here through ℓ=10.
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GW250114 reveals black hole horizon signatures
The merger signal of GW250114 contains a residual 'direct wave' component whose frequency and damping match the remnant horizon's rotation frequency and surface gravity.
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Statistical identification of ringdown modes with rational filters
A frequentist false-alarm framework for rational-filter ringdown analysis is validated on numerical relativity waveforms and shows only marginal evidence for the 221 overtone in GW150914.
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Reanalyzing the ringdown signal of GW150914 using the F-statistic method
Applying the F-statistic method to GW150914's ringdown yields FIC = -0.3 for adding the first overtone, consistent with no overtone, while an injection with an overtone yields FIC = 0.3.
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