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Gating-and-inpainting perspective on GW150914 ringdown overtone: Understanding the data analysis systematics

Yi-Fan Wang (王一帆)1,2,3,*, Collin D. Capano4,5, Jahed Abedi6,7,2,3, Shilpa Kastha8,9,10,2,3, Badri Krishnan11,2,3, Alex B. Nielsen7, Alexander H. Nitz4, and Julian Westerweck2,3,12

  • *Contact author: yifan.wang@aei.mpg.de
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Phys. Rev. D 112, 083023 – Published 10 October, 2025

DOI: https://doi.org/10.1103/3gqn-297f

Abstract

We revisit the recent debate on the evidence for an overtone in the black hole ringdown of GW150914 using an independent data-analysis pipeline. By gating and inpainting the data, we discard the contamination from earlier parts of the gravitational wave signal before ringdown. This enables parameter estimation to be conducted in the frequency domain, which is mathematically equivalent to the time domain method. We keep the settings as similar as possible to the previous studies by Cotesta et al. [Phys. Rev. Lett. 129, 111102 (2022)] and Isi et al. [Phys. Rev. Lett. 123, 111102 (2019); arXiv:2202.02941] which yielded conflicting results on the Bayes factor of the overtone. Our aim is to understand how different data analysis systematics, including sampling rates, erroneous timestamps, and the frequency resolution of the noise power spectrum, would influence the statistical significance of an overtone. Our main results indicate the following: (i) a low-resolution estimation of the noise power spectrum tends to diminish the significance of overtones, (ii) adjusting the start time to a later digitized point reduces the significance of overtones, and (iii) overtone evidence varies with different sampling rates if the start time is too early, indicating that the overtone is a poor model, hence we propose a convergence test to verify the validity of an overtone model. With these issues addressed, we find the Bayes factors for the overtone to range from 10 to 26 in a range of times centered at the best-fit merger time of GW150914, which supports the existence of an overtone in agreement with the conclusions of Isi et al. in the above papers. These results are obtained by keeping the start time and sky location fixed, enabling a direct comparison with other work. Marginalizing over these parameters would lower the Bayes factor to 1 for the evidence of an overtone.

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References (65)

  1. C. V. Vishveshwara, Scattering of gravitational radiation by a schwarzschild black-hole, Nature (London) 227, 936 (1970).
  2. Werner Israel, Event horizons in static vacuum space-times, Phys. Rev. 164, 1776 (1967).
  3. B. Carter, Axisymmetric black hole has only two degrees of freedom, Phys. Rev. Lett. 26, 331 (1971).
  4. Olaf Dreyer, Bernard J. Kelly, Badri Krishnan, Lee Samuel Finn, David Garrison, and Ramon Lopez-Aleman, Black hole spectroscopy: Testing general relativity through gravitational wave observations, Classical Quantum Gravity 21, 787 (2004).
  5. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  6. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016); 121, 129902(E) (2018).
  7. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021).
  8. Miriam Cabero, Julian Westerweck, Collin D. Capano, Sumit Kumar, Alex B. Nielsen, and Badri Krishnan, Black hole spectroscopy in the next decade, Phys. Rev. D 101, 064044 (2020).
  9. J. Aasi et al. (LIGO Scientific Collaboration), Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  10. F. Acernese et al. (VIRGO Collaboration), Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  11. Homare Abe et al. (KAGRA Collaboration), The current status and future prospects of kagra, the large-scale cryogenic gravitational wave telescope built in the kamioka underground, Galaxies 10, 3 (2022).
  12. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW190521: A binary black hole merger with a total mass of 150M⊙, Phys. Rev. Lett. 125, 101102 (2020).
  13. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Properties and astrophysical implications of the 150M⊙ binary black hole merger GW190521, Astrophys. J. Lett. 900, L13 (2020).
  14. Collin D. Capano, Miriam Cabero, Julian Westerweck, Jahed Abedi, Shilpa Kastha, Alexander H. Nitz, Yi-Fan Wang, Alex B. Nielsen, and Badri Krishnan, Multimode quasinormal spectrum from a perturbed black hole, Phys. Rev. Lett. 131, 221402 (2023).
  15. Collin D. Capano, Jahed Abedi, Shilpa Kastha, Alexander H. Nitz, Julian Westerweck, Yi-Fan Wang, Miriam Cabero, Alex B. Nielsen, and Badri Krishnan, Estimating false alarm rates of sub-dominant quasi-normal modes in GW190521, Classical Quantum Gravity 41, 245009 (2024).
  16. Xisco Jiménez Forteza, Swetha Bhagwat, Sumit Kumar, and Paolo Pani, Novel ringdown amplitude-phase consistency test, Phys. Rev. Lett. 130, 021001 (2023).
  17. Jahed Abedi, Collin D. Capano, Shilpa Kastha, Alexander H. Nitz, Yi-Fan Wang, Julian Westerweck, Alex B. Nielsen, and Badri Krishnan, Spectroscopy for asymmetric binary black hole mergers, Phys. Rev. D 108, 104009 (2023).
  18. Harrison Siegel, Maximiliano Isi, and Will M. Farr, Ringdown of GW190521: Hints of multiple quasinormal modes with a precessional interpretation, Phys. Rev. D 108, 064008 (2023).
  19. Matthew Giesler, Maximiliano Isi, Mark A. Scheel, and Saul Teukolsky, Black hole ringdown: The importance of overtones, Phys. Rev. X 9, 041060 (2019).
  20. Matthew Giesler et al., Overtones and nonlinearities in binary black hole ringdowns, Phys. Rev. D 111, 084041 (2025).
  21. Vishal Baibhav, Mark Ho-Yeuk Cheung, Emanuele Berti, Vitor Cardoso, Gregorio Carullo, Roberto Cotesta, Walter Del Pozzo, and Francisco Duque, Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory, Phys. Rev. D 108, 104020 (2023).
  22. Maximiliano Isi, Matthew Giesler, Will M. Farr, Mark A. Scheel, and Saul A. Teukolsky, Testing the no-hair theorem with GW150914, Phys. Rev. Lett. 123, 111102 (2019).
  23. Roberto Cotesta, Gregorio Carullo, Emanuele Berti, and Vitor Cardoso, Analysis of ringdown overtones in GW150914, Phys. Rev. Lett. 129, 111102 (2022).
  24. Maximiliano Isi and Will M. Farr, Revisiting the ringdown of GW150914, arXiv:2202.02941.
  25. Gregorio Carullo, Walter Del Pozzo, and John Veitch, Observational black hole spectroscopy: A time-domain multimode analysis of GW150914, Phys. Rev. D 99, 123029 (2019); 100, 089903(E) (2019).
  26. Maximiliano Isi and Will M. Farr, Analyzing black-hole ringdowns, arXiv:2107.05609.
  27. M. Isi and W. M. Farr, Comment on analysis of ringdown overtones in GW150914, Phys. Rev. Lett. 131, 169001 (2023).
  28. Gregorio Carullo, Roberto Cotesta, Emanuele Berti, and Vitor Cardoso, Carullo et al. reply:, Phys. Rev. Lett. 131, 169002 (2023).
  29. Juan Calderón Bustillo, Paul D. Lasky, and Eric Thrane, Black-hole spectroscopy, the no-hair theorem, and GW150914: Kerr versus Occam, Phys. Rev. D 103, 024041 (2021).
  30. Eliot Finch and Christopher J. Moore, Searching for a ringdown overtone in GW150914, Phys. Rev. D 106, 043005 (2022).
  31. Sizheng Ma, Ling Sun, and Yanbei Chen, Using rational filters to uncover the first ringdown overtone in GW150914, Phys. Rev. D 107, 084010 (2023).
  32. Sizheng Ma, Ling Sun, and Yanbei Chen, Black hole spectroscopy by mode cleaning, Phys. Rev. Lett. 130, 141401 (2023).
  33. Marco Crisostomi, Kallol Dey, Enrico Barausse, and Roberto Trotta, Neural posterior estimation with guaranteed exact coverage: The ringdown of GW150914, Phys. Rev. D 108, 044029 (2023).
  34. Hai-Tian Wang and Lijing Shao, Effect of noise estimation in time-domain ringdown analysis: A case study with GW150914, Phys. Rev. D 108, 123018 (2023).
  35. Barak Zackay, Tejaswi Venumadhav, Javier Roulet, Liang Dai, and Matias Zaldarriaga, Detecting gravitational waves in data with non-stationary and non-Gaussian noise, Phys. Rev. D 104, 063034 (2021).
  36. C. M. Biwer, Collin D. Capano, Soumi De, Miriam Cabero, Duncan A. Brown, Alexander H. Nitz, and V. Raymond, pycbcinference: A Python-based parameter estimation toolkit for compact binary coalescence signals, Publ. Astron. Soc. Pac. 131, 024503 (2019).
  37. P. D. Welch, The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Trans. Audio Electroacoust. 15, 70 (1967).
  38. Bruce Allen, Warren G. Anderson, Patrick R. Brady, Duncan A. Brown, and Jolien D. E. Creighton, FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries, Phys. Rev. D 85, 122006 (2012).
  39. Alexander H. Nitz, Collin D. Capano, Sumit Kumar, Yi-Fan Wang, Shilpa Kastha, Marlin Schäfer, Rahul Dhurkunde, and Miriam Cabero, 3-OGC: Catalog of gravitational waves from compact-binary mergers, Astrophys. J. 922, 76 (2021).
  40. Alexander H. Nitz, Sumit Kumar, Yi-Fan Wang, Shilpa Kastha, Shichao Wu, Marlin Schäfer, Rahul Dhurkunde, and Collin D. Capano, 4-OGC: Catalog of gravitational waves from compact binary mergers, Astrophys. J. 946, 59 (2023).
  41. Alex Correia, Yi-Fan Wang, Julian Westerweck, and Collin D. Capano, Low evidence for ringdown overtone in GW150914 when marginalizing over time and sky location uncertainty, Phys. Rev. D 110, L041501 (2024).
  42. Rich Abbott et al. (LIGO Scientific and Virgo Collaborations), Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo, SoftwareX 13, 100658 (2021).
  43. Subrahmanyan Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon Press, 1988).
  44. Emanuele Berti, Vitor Cardoso, and Marc Casals, Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions, Phys. Rev. D 73, 024013 (2006); 73, 109902(E) (2006).
  45. Joshua S Speagle, dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences, Mon. Not. R. Astron. Soc. 493, 3132 (2020).
  46. Sascha Husa, Sebastian Khan, Mark Hannam, Michael Pürrer, Frank Ohme, Xisco Jiménez Forteza, and Alejandro Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal, Phys. Rev. D 93, 044006 (2016).
  47. Sebastian Khan, Sascha Husa, Mark Hannam, Frank Ohme, Michael Pürrer, Xisco Jiménez Forteza, and Alejandro Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era, Phys. Rev. D 93, 044007 (2016).
  48. Benjamin P. Abbott et al. (LIGO Scientific and Virgo Collaborations), A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals, Classical Quantum Gravity 37, 055002 (2020).
  49. Bruce Allen, χ2 time-frequency discriminator for gravitational wave detection, Phys. Rev. D 71, 062001 (2005).
  50. https://github.com/rcotesta/GW150914_ringdown.
  51. Neil J. Cornish and Tyson B. Littenberg, Bayeswave: Bayesian inference for gravitational wave bursts and instrument glitches, Classical Quantum Gravity 32, 135012 (2015).
  52. Tyson B. Littenberg and Neil J. Cornish, Bayesian inference for spectral estimation of gravitational wave detector noise, Phys. Rev. D 91, 084034 (2015).
  53. Neil J. Cornish, Tyson B. Littenberg, Bence Bécsy, Katerina Chatziioannou, James A. Clark, Sudarshan Ghonge, and Margaret Millhouse, BayesWave analysis pipeline in the era of gravitational wave observations, Phys. Rev. D 103, 044006 (2021).
  54. Power Spectral Densities (PSD) release for GWTC-1, https://dcc.ligo.org/LIGO-P1900011/public.
  55. Vijay Varma, Scott E. Field, Mark A. Scheel, Jonathan Blackman, Davide Gerosa, Leo C. Stein, Lawrence E. Kidder, and Harald P. Pfeiffer, Surrogate models for precessing binary black hole simulations with unequal masses, Phys. Rev. Res. 1, 033015 (2019).
  56. Héctor Estellés, Marta Colleoni, Cecilio García-Quirós, Sascha Husa, David Keitel, Maite Mateu-Lucena, Maria de Lluc Planas, and Antoni Ramos-Buades, New twists in compact binary waveform modeling: A fast time-domain model for precession, Phys. Rev. D 105, 084040 (2022).
  57. Geraint Pratten et al., Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys. Rev. D 103, 104056 (2021).
  58. Michael Boyle et al., The SXS Collaboration catalog of binary black hole simulations, Classical Quantum Gravity 36, 195006 (2019).
  59. Mark A. Scheel et al., The SXS Collaboration’s third catalog of binary black hole simulations, arXiv:2505.13378.
  60. Patricia Schmidt, Ian W. Harry, and Harald P. Pfeiffer, Numerical relativity injection infrastructure, arXiv:1703.01076.
  61. Peter James Nee, Sebastian H. Völkel, and Harald P. Pfeiffer, Role of black hole quasinormal mode overtones for ringdown analysis, Phys. Rev. D 108, 044032 (2023).
  62. Data release for “Gating-and-inpainting perspective on GW150914 ringdown overtone: Understanding the data analysis systematics” systematics, https://github.com/gwastro/gw150914-overtone.
  63. Norman Levinson, The wiener (root mean square) error criterion in filter design and prediction, J. Math. Phys. (N.Y.) 25, 261 (1946).
  64. James Durbin, The fitting of time-series models, Revue de l’Institut International de Statistique (1960), p. 233.
  65. Pauli Virtanen et al., scipy1.0–Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).

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Phys. Rev. D 112, 083023– Published 10 October, 2025
  • Received 7 November 2023
  • Accepted 22 September 2025
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