Using rational filters to uncover the first ringdown overtone in GW150914
There have been debates in the literature about the existence of the first overtone in the ringdown of GW150914. We develop a novel Bayesian framework to reanalyze the data of this event, by incorporating a new technique, the "rational filter" that can clean particular modes from the ringdown signal. We examine the existence of the first overtone in GW150914 from multiple novel perspectives. First, we confirm that the estimates of the remnant black hole mass and spin are more consistent with those obtained from the full inspiral-merger-ringdown signal when including the first overtone at an early stage of the ringdown (right after the inferred signal peak); such improvement fades away at later times. Second, we formulate a new way to compare the ringdown models with and without the first overtone by calculating the Bayes factor at different times during the ringdown. We obtain a Bayes factor of 600 at the time when the signal amplitude reaches its peak. The Bayes factor decreases sharply when moving away from the peak time and eventually oscillates around a small value when the overtone signal is expected to have decayed. Third, we clean the fundamental mode from the ringdown of GW150914 and estimate the amplitudes of the modes using the filtered data with Markov chain Monte Carlo (MCMC). The inferred amplitude of the fundamental mode is ∼0 whereas the amplitude of the first overtone remains almost unchanged, implying that the filtered data is consistent with a first-overtone-only template. Similarly, if we remove the first overtone from the GW150914 data, the filtered data are consistent with a fundamental-mode-only template. Finally, after removing the fundamental mode, we use MCMC to infer the remnant black hole mass and spin from the first overtone alone. We find the posteriors are still informative and consistent with those inferred from the fundamental mode. The conclusions are also verified through simulations in Gaussian noise using a GW150914-like numerical relativity waveform.
© 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 Number 568762), and by NSF Grants No. PHY-2011961, No. PHY-2011968, No. 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 - PhysRevD.107.084010.pdf