- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Black-hole ringdown with templates capturing spin precession: A reanalysis of GW190521

Chiara Anselmo1,2,*, Costantino Pacilio1,2,3,4, and Davide Gerosa1,2

  • *Contact author: c.anselmo@campus.unimib.it
PDF

Phys. Rev. D 113, 124047 – Published 15 June, 2026

DOI: https://doi.org/10.1103/52cd-81m5

Abstract

The ringdown stage of a binary black-hole merger provides a clean probe of strong-field gravity, as it can be modeled with minimal assumptions. The quasi–normal-mode frequencies encode the mass and spin of the Kerr black hole remnant, while the mode excitation depends on the progenitor binary. In this paper, we implement a recently developed amplitude model that captures spin precession in a simulation-based inference pipeline that specifically targets ringdown signals. We present a reanalysis of GW190521—a short-duration, merger-dominated event with conflicting interpretations. Spin-aligned and precessing analyses at two ringdown start times show that precession induces modest but systematic shifts in inferred parameters and subdominant mode amplitudes, although such ringdown-only analyses provide no strong evidence for precession. Our results demonstrate the feasibility of physics-informed precessing ringdown modeling, paving the way for the identification of spin precession in gravitational-wave events using solely their ringdown stages, where waveform systematics are expected to be substantially less prominent.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (106)

  1. R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).
  2. S. A. Teukolsky, Classical Quantum Gravity 32, 124006 (2015).
  3. S. A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).
  4. S. A. Teukolsky, Astrophys. J. 185, 635 (1973).
  5. E. Berti, V. Cardoso, and A. O. Starinets, Classical Quantum Gravity 26, 163001 (2009).
  6. K. D. Kokkotas and B. G. Schmidt, Living Rev. Relativity 2, 2 (1999).
  7. C. V. Vishveshwara, Nature (London) 227, 936 (1970).
  8. W. H. Press, Astrophys. J. Lett. 170, L105 (1971).
  9. W. H. Press and S. A. Teukolsky, Astrophys. J. 185, 649 (1973).
  10. E. Berti, V. Cardoso, G. Carullo et al., arXiv:2505.23895.
  11. S. Detweiler, Astrophys. J. 239, 292 (1980).
  12. O. Dreyer, B. Kelly, B. Krishnan, L. S. Finn, D. Garrison, and R. Lopez-Aleman, Classical Quantum Gravity 21, 787 (2004).
  13. E. Berti, K. Yagi, H. Yang, and N. Yunes, Gen. Relativ. Gravit. 50, 49 (2018).
  14. B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016).
  15. B. P. Abbott et al., Phys. Rev. X 9, 031040 (2019).
  16. R. Abbott et al., Phys. Rev. X 11, 021053 (2021).
  17. R. Abbott et al., Phys. Rev. D 109, 022001 (2024).
  18. R. Abbott et al., Phys. Rev. X 13, 041039 (2023).
  19. A. G. Abac et al., arXiv:2508.18082.
  20. R. Abbott et al., Phys. Rev. Lett. 125, 101102 (2020).
  21. A. G. Abac et al., Astrophys. J. Lett. 993, L25 (2025).
  22. C. J. Moore, E. Finch, R. Buscicchio, and D. Gerosa, iScience 24, 102577 (2021).
  23. A. Gupta et al., SciPost Phys. Commun. Rep. 5, 11 (2025).
  24. Q. Hu and J. Veitch, Phys. Rev. D 106, 044042 (2022).
  25. A. Borchers and F. Ohme, Classical Quantum Gravity 40, 095008 (2023).
  26. D. Fernando, R. O’Shaughnessy, and D. Williams, Phys. Rev. D 112, 084004 (2025).
  27. H. Siegel, N. M. Khusid, M. Isi, and W. M. Farr, arXiv:2511.02691.
  28. C. D. Capano, M. Cabero, J. Westerweck, J. Abedi, S. Kastha, A. H. Nitz, Y.-F. Wang, A. B. Nielsen, and B. Krishnan, Phys. Rev. Lett. 131, 221402 (2023).
  29. H. Siegel, M. Isi, and W. M. Farr, Phys. Rev. D 108, 064008 (2023).
  30. I. Kamaretsos, M. Hannam, and B. S. Sathyaprakash, Phys. Rev. Lett. 109, 141102 (2012).
  31. L. London, D. Shoemaker, and J. Healy, Phys. Rev. D 90, 124032 (2014).
  32. V. Baibhav, E. Berti, V. Cardoso, and G. Khanna, Phys. Rev. D 97, 044048 (2018).
  33. L. T. London, Phys. Rev. D 102, 084052 (2020).
  34. S. Borhanian, K. G. Arun, H. P. Pfeiffer, and B. S. Sathyaprakash, Classical Quantum Gravity 37, 065006 (2020).
  35. X. J. Forteza, S. Bhagwat, S. Kumar, and P. Pani, Phys. Rev. Lett. 130, 021001 (2023).
  36. M. H.-Y. Cheung, E. Berti, V. Baibhav, and R. Cotesta, Phys. Rev. D 109, 044069 (2024).
  37. G. Carullo, J. Cosmology Astropart. Phys. 10 (2024) 061.
  38. C. Pacilio, S. Bhagwat, F. Nobili, and D. Gerosa, Phys. Rev. D 110, 103037 (2024).
  39. L. Magaña Zertuche, L. C. Stein, K. Mitman et al., Phys. Rev. D 112, 024077 (2025).
  40. F. Nobili, S. Bhagwat, C. Pacilio, and D. Gerosa, Phys. Rev. D 112, 044058 (2025).
  41. H. Estellés, S. Husa, M. Colleoni et al., Astrophys. J. 924, 79 (2022).
  42. I. Romero-Shaw, P. D. Lasky, E. Thrane, and J. Calderón Bustillo, Astrophys. J. Lett. 903, L5 (2020).
  43. R. Gamba, M. Breschi, G. Carullo et al., Nat. Astron. 7, 11 (2023).
  44. V. Gayathri, J. Healy, J. Lange, B. O’Brien, M. Szczepańczyk, I. Bartos, M. Campanelli, S. Klimenko, C. O. Lousto, and R. O’Shaughnessy, Nat. Astron. 6, 344 (2022).
  45. R. Abbott et al., Astrophys. J. Lett. 900, L13 (2020).
  46. K. Cranmer, J. Brehmer, and G. Louppe, Proc. Natl. Acad. Sci. U.S.A. 117, 30055 (2020).
  47. M. Deistler, J. Boelts, P. Steinbach, G. Moss, T. Moreau, M. Gloeckler, P. L. C. Rodrigues, J. Linhart, J. K. Lappalainen, B. K. Miller, P. J. Gonçalves, J.-M. Lueckmann, C. Schröder, and J. H. Macke, arXiv:2508.12939.
  48. M. Crisostomi, K. Dey, E. Barausse, and R. Trotta, Phys. Rev. D 108, 044029 (2023).
  49. C. Pacilio, S. Bhagwat, and R. Cotesta, Phys. Rev. D 110, 083010 (2024).
  50. C. T. Cunningham, R. H. Price, and V. Moncrief, Astrophys. J. 224, 643 (1978).
  51. M. De Amicis, H. R. Rüter, G. Carullo, S. Albanesi, C. Melize Ferrus, K. Mitman, L. C. Stein, V. Cardoso, S. Bernuzzi, M. Boyle, N. Deppe, L. E. Kidder, J. Moxon, A. Nagar, K. C. Nelli, H. P. Pfeiffer, M. A. Scheel, W. Throwe, N. L. Vu, and A. Zenginoğlu, Phys. Rev. Lett. 135, 171401 (2025).
  52. S. Ma, M. A. Scheel, J. Moxon, K. C. Nelli, N. Deppe, L. E. Kidder, W. Throwe, and N. L. Vu, Phys. Rev. D 112, 024003 (2025).
  53. E. Berti and A. Klein, Phys. Rev. D 90, 064012 (2014).
  54. B. S. Sathyaprakash and B. F. Schutz, Living Rev. Relativity 12, 2 (2009).
  55. M. Isi, Classical Quantum Gravity 40, 203001 (2023).
  56. C. Pacilio and F. Nobili, github.com/cpacilio/postmerger (2025).
  57. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (MIT, Cambridge, MA, 2006).
  58. M. Boyle, D. Hemberger, D. A. B. Iozzo et al., Classical Quantum Gravity 36, 195006 (2019).
  59. E. Finch and C. J. Moore, Phys. Rev. D 103, 084048 (2021).
  60. E. Berti, V. Cardoso, J. A. Gonzalez, U. Sperhake, M. Hannam, S. Husa, and B. Brügmann, Phys. Rev. D 76, 064034 (2007).
  61. H. Zhu, H. Siegel, K. Mitman et al., Phys. Rev. D 111, 064052 (2025).
  62. E. P. Wigner and U. Fano, Am. J. Phys. 28, 408 (1960).
  63. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
  64. P. Schmidt, M. Hannam, S. Husa, and P. Ajith, Phys. Rev. D 84, 024046 (2011).
  65. M. Deistler, P. J. Goncalves, and J. H. Macke, arXiv:2210.04815.
  66. G. Papamakarios and I. Murray, arXiv:1605.06376.
  67. D. S. Greenberg, M. Nonnenmacher, and J. H. Macke, arXiv:1905.07488.
  68. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, arXiv:1912.01703.
  69. J. Boelts, M. Deistler, M. Gloeckler et al., J. Open Source Software 10, 7754 (2025).
  70. G. Papamakarios, E. Nalisnick, D. Jimenez Rezende, S. Mohamed, and B. Lakshminarayanan, J. Mach. Learn. Res. 22, 2617 (2021), https://arxiv.org/abs/1912.02762.
  71. C. Durkan, A. Bekasov, I. Murray, and G. Papamakarios, arXiv:1906.04032.
  72. S. R. Green and J. Gair, Mach. Learn. Sci. Technol. 2, 03LT01 (2021).
  73. M. Isi and W. M. Farr, arXiv:2107.05609.
  74. E. Finch and C. J. Moore, Phys. Rev. D 104, 123034 (2021).
  75. V. Gennari, G. Carullo, and W. Del Pozzo, Eur. Phys. J. C 84, 233 (2024).
  76. A. Nitz et al., github.com/gwastro/pycbc (2025).
  77. G. Carullo, L. van der Schaaf, L. London, P. T. H. Pang, K. W. Tsang, O. A. Hannuksela, J. Meidam, M. Agathos, A. Samajdar, A. Ghosh, T. G. F. Li, W. Del Pozzo, and C. Van Den Broeck, Phys. Rev. D 98, 104020 (2018).
  78. R. Abbott et al., Phys. Rev. D 103, 122002 (2021).
  79. R. Abbott et al., Phys. Rev. D 112, 084080 (2025).
  80. A. Toubiana and J. R. Gair, arXiv:2401.06845.
  81. H. Siegel, M. Isi, and W. M. Farr, Phys. Rev. D 111, 044070 (2025).
  82. A. G. Abac et al., Phys. Rev. Lett. 135, 111403 (2025).
  83. C. Capano, github.com/cdcapano/pykerr (2023).
  84. V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, and H. P. Pfeiffer, Phys. Rev. Res. 1, 033015 (2019).
  85. S. J. Miller, M. Isi, K. Chatziioannou, V. Varma, and I. Mandel, Phys. Rev. D 109, 024024 (2024).
  86. S. J. Miller, M. Isi, V. Varma, and K. Chatziioannou, 10.5281/zenodo.8349282 (2023).
  87. M. Mould and D. Gerosa, Phys. Rev. D 105, 024076 (2022).
  88. V. Baibhav, M. H.-Y. Cheung, E. Berti, V. Cardoso, G. Carullo, R. Cotesta, W. Del Pozzo, and F. Duque, Phys. Rev. D 108, 104020 (2023).
  89. A. G. Abac et al., Phys. Rev. Lett. 136, 041403 (2026).
  90. S. Kastha, J. Westerweck, Y.-F. Wang, and C. Capano, github.com/gwastro/BH-Spectroscopy-GW190521 (2023).
  91. H. Jeffreys, The Theory of Probability (Oxford University Press, Oxford, 1939).
  92. S. Biscoveanu, M. Isi, V. Varma, and S. Vitale, Phys. Rev. D 104, 103018 (2021).
  93. E. Hamilton, L. London, and M. Hannam, Phys. Rev. D 107, 104035 (2023).
  94. A. Dhani, Phys. Rev. D 103, 104048 (2021).
  95. J. Hermans, A. Delaunoy, F. Rozet, A. Wehenkel, V. Begy, and G. Louppe, arXiv:2110.06581.
  96. J.-M. Lueckmann, J. Boelts, D. S. Greenberg, P. J. Gonçalves, and J. H. Macke, arXiv:2101.04653.
  97. S. Bhagwat, M. Okounkova, S. W. Ballmer, D. A. Brown, M. Giesler, M. A. Scheel, and S. A. Teukolsky, Phys. Rev. D 97, 104065 (2018).
  98. S. H. Völkel and A. Dhani, Phys. Rev. D 112, 084076 (2025).
  99. F. Crescimbeni, G. Carullo, E. Berti, G. Caneva Santoro, M. Ho-Yeuk Cheung, and P. Pani, arXiv:2511.02915.
  100. M. A. Scheel, M. Boyle, K. Mitman et al., Classical Quantum Gravity 42, 195017 (2025).
  101. G. Fumagalli, I. Romero-Shaw, D. Gerosa, V. De Renzis, K. Kritos, and A. Olejak, Phys. Rev. D 110, 063012 (2024).
  102. R. Dyer and C. J. Moore, arXiv:2510.13954.
  103. R. Dyer and C. J. Moore, arXiv:2510.11783.
  104. C. Anselmo, github.com/chiaranselmo17/ringdown_GW190521 (2025), 10.5281/zenodo.17857210.
  105. L. Liu and M. T. Özsu, Encyclopedia of Database Systems (Springer, New York, 2009).
  106. J. Lange, R. O’Shaughnessy, and M. Rizzo, arXiv:1805.10457.

Outline

Information

Phys. Rev. D 113, 124047– Published 15 June, 2026
  • Received 4 December 2025
  • Accepted 13 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation