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Ringdown analysis of GW250114 with orthonormal modes

Motoki Suzuki1,2, Kei-ichiro Kubota2, Soichiro Morisaki2, Hayato Motohashi3, and Daiki Watarai4

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Phys. Rev. D 114, 044099 – Published 26 August, 2026

DOI: https://doi.org/10.1103/6x5z-q9ml

Abstract

GW250114 is the loudest gravitational wave event to date observed by LIGO-Virgo-KAGRA Collaboration. Owing to its high signal-to-noise ratio (SNR), previous analyses based on quasinormal mode (QNM) superpositions have suggested evidence of the fundamental and the first overtone of the ℓ=m=2 mode in this event. However, QNMs are not orthogonal and the inclusion of multiple QNMs induces correlations among them, which can hinder the robust identification of subdominant QNMs. To address this challenge, we apply an analysis based on orthonormalized QNMs [S. Morisaki et al., Phys. Rev. D 112, 124083 (2025)] to GW250114. We find that, in the model including three ℓ=m=2 QNMs up to the second overtone, the first overtone of the ℓ=m=2 mode is more strongly supported than in previous nonorthogonal analyses, with the inferred significance increasing from 86.2% to 99.9%. Furthermore, we estimate deviations from the Kerr prediction using the orthonormal QNM framework and find no significant deviation, consistent with previous analyses. These results demonstrate that the orthonormal QNM framework provides a more robust way to identify subdominant modes in high-SNR ringdown signals, highlighting its potential for future gravitational wave observations.

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References (94)

  1. 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).
  2. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs, Phys. Rev. X 9, 031040 (2019).
  3. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-2: Compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. X 11, 021053 (2021).
  4. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. D 109, 022001 (2024).
  5. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023).
  6. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Updating the gravitational-wave transient catalog with observations from the first part of the fourth LIGO-Virgo-KAGRA observing run, Astrophys. J. Lett. 1004, L22 (2026).
  7. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1, Phys. Rev. D 100, 104036 (2019).
  8. 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).
  9. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Tests of general relativity with GWTC-3, Phys. Rev. D 112, 084080 (2025).
  10. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Tests of general relativity. I. Overview and general tests, arXiv:2603.19019.
  11. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Tests of general relativity. II. Parameterized tests, arXiv:2603.19020.
  12. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Tests of general relativity. III. Tests of the remnants, arXiv:2603.19021.
  13. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016); (LIGO Scientific and Virgo Collaborations)Phys. Rev. Lett.121, 129902(E) (2018).
  14. 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).
  15. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GW250114: Testing Hawking’s Area Law and the Kerr Nature of Black Holes, Phys. Rev. Lett. 135, 111403 (2025).
  16. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Black hole spectroscopy and tests of general relativity with GW250114, Phys. Rev. Lett. 136, 041403 (2026).
  17. 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).
  18. Emanuele Berti, Vitor Cardoso, and Clifford M. Will, On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA, Phys. Rev. D 73, 064030 (2006).
  19. Emanuele Berti, Jaime Cardoso, Vitor Cardoso, and Marco Cavaglia, Matched-filtering and parameter estimation of ringdown waveforms, Phys. Rev. D 76, 104044 (2007).
  20. Jahed Abedi et al., Black hole spectroscopy: From theory to experiment, Classical Quantum Gravity 43, 123001 (2026).
  21. Sizheng Ma and Huan Yang, Excitation of quadratic quasinormal modes for Kerr black holes, Phys. Rev. D 109, 104070 (2024).
  22. Lionel London, Deirdre Shoemaker, and James Healy, Modeling ringdown: Beyond the fundamental quasinormal modes, Phys. Rev. D 90, 124032 (2014); Phys. Rev. D94, 069902(E) (2016).
  23. Mark Ho-Yeuk Cheung et al., Nonlinear effects in black hole ringdown, Phys. Rev. Lett. 130, 081401 (2023).
  24. N. Khera, A. Ribes Metidieri, B. Bonga, X. Jiménez Forteza, B. Krishnan, E. Poisson, D. Pook-Kolb, E. Schnetter, and H. Yang, Nonlinear ringdown at the black hole horizon, Phys. Rev. Lett. 131, 231401 (2023).
  25. Keefe Mitman et al., Nonlinearities in black hole ringdowns, Phys. Rev. Lett. 130, 081402 (2023).
  26. Neev Khera, Sizheng Ma, and Huan Yang, Quadratic mode couplings in rotating black holes and their detectability, Phys. Rev. Lett. 134, 211404 (2025).
  27. Naritaka Oshita, Sizheng Ma, Yanbei Chen, and Huan Yang, Probing direct waves in black hole ringdowns, arXiv:2509.09165.
  28. Neil Lu, Sizheng Ma, Ornella J. Piccinni, Yanbei Chen, and Ling Sun, GW250114 reveals black hole horizon signatures, Nature (London) 655, 71 (2026).
  29. Roberto Cotesta, Gregorio Carullo, Emanuele Berti, and Vitor Cardoso, Analysis of ringdown overtones in GW150914, Phys. Rev. Lett. 129, 111102 (2022).
  30. Sizheng Ma, Ling Sun, and Yanbei Chen, Black hole spectroscopy by mode cleaning, Phys. Rev. Lett. 130, 141401 (2023).
  31. 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).
  32. Hai-Tian Wang, Ziming Wang, Yiming Dong, Garvin Yim, and Lijing Shao, Reanalyzing the ringdown signal of GW150914 using the F-statistic method, Phys. Rev. D 111, 064037 (2025).
  33. Ke Wang, Retesting the no-hair theorem with GW150914, Eur. Phys. J. C 82, 125 (2022).
  34. Maximiliano Isi and Will M. Farr, Revisiting the ringdown of GW150914, arXiv:2202.02941.
  35. Eliot Finch and Christopher J. Moore, Searching for a ringdown overtone in GW150914, Phys. Rev. D 106, 043005 (2022).
  36. 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).
  37. Koustav Chandra and Juan Calderón Bustillo, Black-hole ringdown analysis with inspiral-merger informed templates and limitations of classical spectroscopy, arXiv:2509.17315.
  38. Neil Lu, Sizheng Ma, Ornella J. Piccinni, Ling Sun, and Eliot Finch, Statistical identification of ringdown modes with rational filters, Phys. Rev. D 112, 064047 (2025).
  39. 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).
  40. M. Giesler, M. Isi, M. A. Scheel, and S. A. Teukolsky, Black hole ringdown: The importance of overtones, Phys. Rev. X 9, 041060 (2019).
  41. Mark Ho-Yeuk Cheung, Emanuele Berti, Vishal Baibhav, and Roberto Cotesta, Extracting linear and nonlinear quasinormal modes from black hole merger simulations, Phys. Rev. D 109, 044069 (2024); Phys. Rev. D110, 049902(E) (2024); Phys. Rev. D112, 049901(E) (2025).
  42. Xisco Jiménez Forteza and Pierre Mourier, High-overtone fits to numerical relativity ringdowns: Beyond the dismissed n=8 special tone, Phys. Rev. D 104, 124072 (2021).
  43. Arnab Dhani, Importance of mirror modes in binary black hole ringdown waveform, Phys. Rev. D 103, 104048 (2021).
  44. Kazuto Takahashi and Hayato Motohashi, Iterative extraction of overtones from black hole ringdown, Classical Quantum Gravity 41, 195023 (2024).
  45. Eliot Finch and Christopher J. Moore, Modeling the ringdown from precessing black hole binaries, Phys. Rev. D 103, 084048 (2021).
  46. Matthew Giesler et al., Overtones and nonlinearities in binary black hole ringdowns, Phys. Rev. D 111, 084041 (2025).
  47. Keefe Mitman et al., Probing the ringdown perturbation in binary black hole coalescences with an improved quasinormal mode extraction algorithm, Phys. Rev. D 112, 064016 (2025).
  48. Swetha Bhagwat, Xisco Jimenez Forteza, Paolo Pani, and Valeria Ferrari, Ringdown overtones, black hole spectroscopy, and no-hair theorem tests, Phys. Rev. D 101, 044033 (2020).
  49. Leda Gao et al., Robustness of extracting quasinormal mode information from black hole merger simulations, Phys. Rev. D 112, 024025 (2025).
  50. 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).
  51. Teagan A. Clarke et al., Toward a self-consistent framework for measuring black hole ringdowns, Phys. Rev. D 109, 124030 (2024).
  52. 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).
  53. 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).
  54. 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).
  55. 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).
  56. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GW231123: A binary black hole merger with total mass 190−265M⊙, Astrophys. J. Lett. 993, L25 (2025).
  57. Imre Bartos and Zoltan Haiman, Accretion is all you need: Black hole spin alignment in merger GW231123 indicates accretion pathway, Astrophys. J. Lett. 996, L44 (2026).
  58. Lavinia Paiella, Cristiano Ugolini, Mario Spera, Marica Branchesi, and Manuel Arca Sedda, Assembling GW231123 in star clusters through the combination of stellar binary evolution and hierarchical mergers, Astrophys. J. Lett. 994, L54 (2025).
  59. Fulya K𝚤roğlu, Kyle Kremer, and Frederic A. Rasio, Beyond hierarchical mergers: Accretion-driven origins of massive, highly spinning black holes in dense star clusters, Astrophys. J. Lett. 994, L37 (2025).
  60. Djuna Croon, Davide Gerosa, and Jeremy Sakstein, Can GW231123 have a stellar origin?, Mon. Not. R. Astron. Soc. 546, stag073 (2026).
  61. Yin-Jie Li, Shao-Peng Tang, Ling-Qin Xue, and Yi-Zhong Fan, GW231123: Likely a product of successive mergers from ∼10 stellar-mass black holes, Astrophys. J. 999, 127 (2026).
  62. Lachlan Passenger, Sharan Banagiri, Eric Thrane, Paul D. Lasky, Angela Borchers, Maya Fishbach, and Claire S. Ye, Is GW231123 a hierarchical merger?, Astrophys. J. 999, 236 (2026).
  63. Shuai Liu, Long Wang, Ataru Tanikawa, Weiwei Wu, and Michiko S. Fujii, On the formation of GW231123 in population III star clusters, Astrophys. J. Lett. 993, L30 (2025).
  64. Jakob Stegmann, Aleksandra Olejak, and Selma E. de Mink, Resolving black hole family issues among the massive ancestors of very High-spin gravitational-wave events like GW231123, Astrophys. J. Lett. 992, L26 (2025).
  65. Guo-Peng Li and Xi-Long Fan, The hierarchical merger scenario for GW231123, arXiv:2509.08298.
  66. Harrison Siegel, Nicole M. Khusid, Maximiliano Isi, and Will M. Farr, GW231123 ringdown: Interpretation as multimodal Kerr signal, Phys. Rev. D 114, 024050 (2026).
  67. Hai-Tian Wang, Shao-Peng Tang, Peng-Cheng Li, and Yi-Zhong Fan, Detection of a higher harmonic quasi-normal mode in the ringdown signal of GW231123, arXiv:2509.02047.
  68. Chen Yuan, Zu-Cheng Chen, and Lang Liu, GW231123 mass gap event and the primordial black hole scenario, Phys. Rev. D 112, L081306 (2025).
  69. Iuliu Cuceu, Marie Anne Bizouard, Nelson Christensen, and Mairi Sakellariadou, GW231123: Binary black hole merger or cosmic string?, Phys. Rev. D 113, L021302 (2026).
  70. Xikai Shan, Huan Yang, and Shude Mao, GW231123: A case for binary microlensing in a strong lensing field, arXiv:2512.19118.
  71. Anarya Ray, Sharan Banagiri, Eric Thrane, and Paul D. Lasky, GW231123: Extreme spins or microglitches?, arXiv:2510.07228.
  72. Qian Hu, Harsh Narola, Jef Heynen, Mick Wright, John Veitch, Justin Janquart, and Chris Van Den Broeck, GW231123: Overlapping gravitational wave signals?, Astrophys. J. 1003, 187 (2026).
  73. Sophie Bini, Krzysztof Król, Katerina Chatziioannou, and Maximiliano Isi, The impact of waveform systematics and Gaussian noise on the interpretation of GW231123, Phys. Rev. D 113, 083036 (2026).
  74. David Reitze et al., Cosmic explorer: The U.S. Contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).https://baas.aas.org/pub/2020n7i035
  75. M. Punturo et al., The Einstein telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  76. Soichiro Morisaki, Hayato Motohashi, Motoki Suzuki, and Daiki Watarai, Analyzing black-hole ringdowns with orthonormal modes, Phys. Rev. D 112, 124083 (2025).
  77. J. Aasi et al. (LIGO Scientific Collaboration), Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  78. F. Acernese et al. (VIRGO Collaboration), Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  79. T Akutsu et al. (KAGRA Collaboration), Overview of KAGRA: Detector design and construction history, Prog. Theor. Exp. Phys. 2021, 05A101 (2021).
  80. 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).
  81. Maximiliano Isi and Will M. Farr, Analyzing black-hole ringdowns, arXiv:2107.05609.
  82. Harrison Siegel, Maximiliano Isi, and Will M. Farr, Analyzing black-hole ringdowns. II. Data conditioning, Phys. Rev. D 111, 044070 (2025).
  83. Hayato Motohashi, Resonant excitation of quasinormal modes of black holes, Phys. Rev. Lett. 134, 141401 (2025).
  84. Hayato Motohashi, Kerr quasinormal mode frequencies and excitation factors (2025), zenodo. Data set.
  85. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Open data from LIGO, Virgo, and KAGRA through the first part of the fourth observing run, Astrophys. J. 1004, 232 (2026).
  86. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Open data from the third observing run of LIGO, Virgo, KAGRA, and GEO, Astrophys. J. Suppl. Ser. 267, 29 (2023).
  87. Rich Abbott et al. (LIGO Scientific, Virgo), Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo, SoftwareX 13, 100658 (2021).
  88. Yuxin Yang, Changfu Shi, and Yi-Ming Hu, Contribution from nonlinear Quasi-normal modes in GW250114, arXiv:2510.16903.
  89. Yi-Fan Wang, Sizheng Ma, Neev Khera, and Huan Yang, A nonlinear voice from GW250114 ringdown, arXiv:2601.05734.
  90. Yiqiu Yang, Emanuele Berti, and Nicola Franchini, Black hole quasinormal mode resonances, Phys. Rev. Lett. 135, 201401 (2025).
  91. gwosc.org
  92. Motoki Suzuki, Kei-ichiro Kubota, Soichiro Morisaki, Hayato Motohashi, and Daiki Watarai, Ringdown analysis of GW250114 with orthonormal modes (2026), zenodo. Dataset. https://zenodo.org/records/19939742.
  93. Hengrui Zhu et al., Black hole spectroscopy for precessing binary black hole coalescences, Phys. Rev. D 111, 064052 (2025).
  94. Xiang Li, Ling Sun, Rico Ka Lok Lo, Ethan Payne, and Yanbei Chen, Angular emission patterns of remnant black holes, Phys. Rev. D 105, 024016 (2022).

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Phys. Rev. D 114, 044099– Published 26 August, 2026
  • Received 14 May 2026
  • Accepted 6 August 2026
Article part of CHORUS
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