- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

High-precision ringdown surrogate model for nonprecessing binary black holes

Lorena Magaña Zertuche1,2,*, Leo C. Stein1, Keefe Mitman3, Scott E. Field4,5, Vijay Varma4, Michael Boyle6, Nils Deppe7,8,6, Lawrence E. Kidder6, Jordan Moxon3 et al.

Harald P. Pfeiffer9, Mark A. Scheel3, Kyle C. Nelli3, William Throwe6, and Nils L. Vu3

  • *Contact author: lorena.zertuche@nbi.ku.dk
PDF

Phys. Rev. D 112, 024077 – Published 30 July, 2025

DOI: https://doi.org/10.1103/q7sy-g3kl

Abstract

Highly precise and robust waveform models are required as improvements in detector sensitivity enable us to test general relativity with more precision than ever before. In this work, we introduce a spin-aligned surrogate ringdown model. This ringdown surrogate, nrsur3dq8_rd, is built with numerical waveforms produced using Cauchy-characteristic evolution. In addition, these waveforms are in the super-rest frame of the remnant black hole allowing us to do a correct analysis of the ringdown spectrum. The novel prediction of our surrogate model is complex-valued quasinormal mode (QNM) amplitudes, with median relative errors of 10−2−10−3 over the parameter space. Like previous remnant surrogates, we also predict the remnant black hole’s mass and spin. The QNM mode amplitude errors translate into median errors on ringdown waveforms of ∼10−4. The high accuracy and QNM mode content provided by our surrogate will enable high-precision ringdown analyses such as tests of general relativity. Our ringdown model is publicly available through the python package surfinbh.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (70)

  1. S. A. Teukolsky, Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations, Astrophys. J. 185, 635 (1973).
  2. S. L. Detweiler, Black holes and gravitational waves. III. The resonant frequencies of rotating holes, Astrophys. J. 239, 292 (1980).
  3. E. W. Leaver, An Analytic representation for the quasi normal modes of Kerr black holes, Proc. R. Soc. A 402, 285 (1985).
  4. S. R. Dolan and A. C. Ottewill, On an expansion method for black hole quasinormal modes and Regge poles, Classical Quantum Gravity 26, 225003 (2009).
  5. A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59, 084006 (1999).
  6. A. Albertini, A. Nagar, P. Rettegno, S. Albanesi, and R. Gamba, Waveforms and fluxes: Towards a self-consistent effective one body waveform model for nonprecessing, coalescing black-hole binaries for third generation detectors, Phys. Rev. D 105, 084025 (2022).
  7. S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. Jiménez Forteza, and A. 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).
  8. L. London, S. Khan, E. Fauchon-Jones, C. García, M. Hannam, S. Husa, X. Jiménez-Forteza, C. Kalaghatgi, F. Ohme, and F. Pannarale, First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries, Phys. Rev. Lett. 120, 161102 (2018).
  9. S. Khan, K. Chatziioannou, M. Hannam, and F. Ohme, Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects, Phys. Rev. D 100, 024059 (2019).
  10. M. Pürrer and C.-J. Haster, Gravitational waveform accuracy requirements for future ground-based detectors, Phys. Rev. Res. 2, 023151 (2020).
  11. H. Estellés et al., A detailed analysis of GW190521 with phenomenological waveform models, Astrophys. J. 924, 79 (2022).
  12. L. T. London, Modeling ringdown. II. Aligned-spin binary black holes, implications for data analysis and fundamental theory, Phys. Rev. D 102, 084052 (2020).
  13. X. J. Forteza, S. Bhagwat, S. Kumar, and P. Pani, Novel ringdown amplitude-phase consistency test, Phys. Rev. Lett. 130, 021001 (2023).
  14. M. H.-Y. Cheung, E. Berti, V. Baibhav, and R. Cotesta, Extracting linear and nonlinear quasinormal modes from black hole merger simulations, Phys. Rev. D 109, 044069 (2024); 110, 049902(E) (2024).
  15. S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, and M. Tiglio, Fast prediction and evaluation of gravitational waveforms using surrogate models, Phys. Rev. X 4, 031006 (2014).
  16. V. Varma, D. Gerosa, L. C. Stein, F. Hébert, and H. Zhang, High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants, Phys. Rev. Lett. 122, 011101 (2019).
  17. T. Islam, S. E. Field, S. A. Hughes, G. Khanna, V. Varma, M. Giesler, M. A. Scheel, L. E. Kidder, and H. P. Pfeiffer, Surrogate model for gravitational wave signals from nonspinning, comparable-to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity, Phys. Rev. D 106, 104025 (2022).
  18. M. Walker, V. Varma, G. Lovelace, and M. A. Scheel, Numerical-relativity surrogate modeling with nearly extremal black-hole spins, Classical Quantum Gravity 40, 055003 (2023).
  19. V. Varma, S. E. Field, M. A. Scheel, J. Blackman, L. E. Kidder, and H. P. Pfeiffer, Surrogate model of hybridized numerical relativity binary black hole waveforms, Phys. Rev. D 99, 064045 (2019).
  20. I. Kamaretsos, M. Hannam, and B. Sathyaprakash, Is black-hole ringdown a memory of its progenitor?, Phys. Rev. Lett. 109, 141102 (2012).
  21. L. Magaña Zertuche et al., High precision ringdown modeling: Multimode fits and BMS frames, Phys. Rev. D 105, 104015 (2022).
  22. L. Magaña Zertuche and E. Finch, qnmfits (2025), 10.5281/zenodo.14806974.
  23. L. Magaña Zertuche, L. Gao, E. Finch, and G. B. Cook, Multimode ringdown modelling with qnmfits and KerrRingdown, arXiv:2502.03155.
  24. H. Bondi, M. G. J. Van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system, Proc. R. Soc. A 269, 21 (1962).
  25. R. K. Sachs and H. Bondi, Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time, Proc. R. Soc. A 270, 103 (1962).
  26. M. Boyle, Transformations of asymptotic gravitational-wave data, Phys. Rev. D 93, 084031 (2016).
  27. K. Mitman et al., Fixing the BMS frame of numerical relativity waveforms, Phys. Rev. D 104, 024051 (2021).
  28. J. Yoo et al., Numerical relativity surrogate model with memory effects and post-Newtonian hybridization, Phys. Rev. D 108, 064027 (2023).
  29. 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).
  30. B. Sathyaprakash et al., Scientific objectives of Einstein telescope, Classical Quantum Gravity 29, 124013 (2012); 30, 079501(E) (2013).
  31. B. P. Abbott et al. (LIGO Scientific Collaboration), Exploring the sensitivity of next generation gravitational wave detectors, Classical Quantum Gravity 34, 044001 (2017).
  32. J. Bellovary et al. (NASA LISA Study Team), Getting ready for LISA: The data, support and preparation needed to maximize us participation in space-based gravitational wave science, arXiv:2012.02650.
  33. V. Kalogera et al., The next generation global gravitational wave observatory: The science book, arXiv:2111.06990.
  34. V. Baibhav, E. Berti, D. Gerosa, M. Mapelli, N. Giacobbo, Y. Bouffanais, and U. N. Di Carlo, Gravitational-wave detection rates for compact binaries formed in isolation: LIGO/Virgo O3 and beyond, Phys. Rev. D 100, 064060 (2019).
  35. V. Varma, L. C. Stein, and D. Gerosa, vijayvarma392/surfinbh: Surrogate Final BH properties (2018), 10.5281/zenodo.1435832.
  36. W. H. Press and S. A. Teukolsky, Perturbations of a rotating black hole. II. Dynamical stability of the Kerr metric, Astrophys. J. 185, 649 (1973).
  37. L. London and E. Fauchon-Jones, On modeling for Kerr black holes: Basis learning, QNM frequencies, and spherical-spheroidal mixing coefficients, Classical Quantum Gravity 36, 235015 (2019).
  38. H. Lim, G. Khanna, A. Apte, and S. A. Hughes, Exciting black hole modes via misaligned coalescences: II. The mode content of late-time coalescence waveforms, Phys. Rev. D 100, 084032 (2019).
  39. M. Isi and W. M. Farr, Analyzing black-hole ringdowns, arXiv:2107.05609.
  40. X. Li, L. Sun, R. K. L. Lo, E. Payne, and Y. Chen, Angular emission patterns of remnant black holes, Phys. Rev. D 105, 024016 (2022).
  41. G. B. Cook and M. Zalutskiy, Gravitational perturbations of the Kerr geometry: High-accuracy study, Phys. Rev. D 90, 124021 (2014).
  42. L. C. Stein, qnm: A python package for calculating Kerr quasinormal modes, separation constants, and spherical-spheroidal mixing coefficients, J. Open Source Software 4, 1683 (2019).
  43. M. Giesler, M. Isi, M. A. Scheel, and S. Teukolsky, Black hole ringdown: The importance of overtones, Phys. Rev. X 9, 041060 (2019).
  44. S. Bhagwat, X. J. Forteza, P. Pani, and V. Ferrari, Ringdown overtones, black hole spectroscopy, and no-hair theorem tests, Phys. Rev. D 101, 044033 (2020).
  45. C. Rasmussen and C. Williams, Gaussian Processes for Machine Learning (MIT Press, Cambridge, MA, 2006).
  46. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. VanderPlas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, scikit-learn: Machine learning in python, J. Mach. Learn. Res. 12, 2825 (2011), https://www.jmlr.org/papers/volume12/pedregosa11a/pedregosa11a.pdf.
  47. SpECCode, https://www.black-holes.org/code/SpEC.html.
  48. J. Moxon, M. A. Scheel, and S. A. Teukolsky, Improved Cauchy-characteristic evolution system for high-precision numerical relativity waveforms, Phys. Rev. D 102, 044052 (2020).
  49. J. Moxon, M. A. Scheel, S. A. Teukolsky, N. Deppe, N. Fischer, F. Hébert, L. E. Kidder, and W. Throwe, The SpECTRE Cauchy-characteristic evolution system for rapid, precise waveform extraction, Phys. Rev. D 107, 064013 (2023).
  50. N. Deppe et al., SpECTRE (2024), 10.5281/zenodo.12098412.
  51. K. Mitman, J. Moxon, M. A. Scheel, S. A. Teukolsky, M. Boyle, N. Deppe, L. E. Kidder, and W. Throwe, Computation of displacement and spin gravitational memory in numerical relativity, Phys. Rev. D 102, 104007 (2020).
  52. K. Mitman et al., Adding gravitational memory to waveform catalogs using BMS balance laws, Phys. Rev. D 103, 024031 (2021).
  53. M. Boyle et al., The SXS Collaboration catalog of binary black hole simulations, Classical Quantum Gravity 36, 195006 (2019).
  54. P. Ajith, Addressing the spin question in gravitational-wave searches: Waveform templates for inspiralling compact binaries with nonprecessing spins, Phys. Rev. D 84, 084037 (2011).
  55. C. Cutler and E. E. Flanagan, Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral wave form?, Phys. Rev. D 49, 2658 (1994).
  56. E. Poisson and C. M. Will, Gravitational waves from inspiraling compact binaries: Parameter estimation using second postNewtonian wave forms, Phys. Rev. D 52, 848 (1995).
  57. D. A. B. Iozzo et al., Comparing remnant properties from horizon data and asymptotic data in numerical relativity, Phys. Rev. D 103, 124029 (2021).
  58. M. Boyle, D. Iozzo, and L. C. Stein, moble/scri: v1.2 (2020), 10.5281/zenodo.4041972.
  59. X. Jiménez Forteza, S. Bhagwat, P. Pani, and V. Ferrari, Spectroscopy of binary black hole ringdown using overtones and angular modes, Phys. Rev. D 102, 044053 (2020).
  60. G. B. Cook, Aspects of multimode Kerr ringdown fitting, Phys. Rev. D 102, 024027 (2020).
  61. L. London, D. Shoemaker, and J. Healy, Modeling ringdown: Beyond the fundamental quasinormal modes, Phys. Rev. D 90, 124032 (2014); 94, 069902(E) (2016).
  62. V. Baibhav and E. Berti, Multimode black hole spectroscopy, Phys. Rev. D 99, 024005 (2019).
  63. E. Berti and A. Klein, Mixing of spherical and spheroidal modes in perturbed Kerr black holes, Phys. Rev. D 90, 064012 (2014).
  64. A. Dhani and B. S. Sathyaprakash, Overtones, mirror modes, and mode-mixing in binary black hole mergers, arXiv:2107.14195.
  65. E. Finch and C. J. Moore, Modeling the ringdown from precessing black hole binaries, Phys. Rev. D 103, 084048 (2021).
  66. A. Dhani, Importance of mirror modes in binary black hole ringdown waveform, Phys. Rev. D 103, 104048 (2021).
  67. K. Mitman et al., Nonlinearities in black hole ringdowns, Phys. Rev. Lett. 130, 081402 (2023).
  68. M. H.-Y. Cheung et al., Nonlinear effects in black hole ringdown, Phys. Rev. Lett. 130, 081401 (2023).
  69. C. Pacilio, S. Bhagwat, F. Nobili, and D. Gerosa, Flexible mapping of ringdown amplitudes for nonprecessing binary black holes, Phys. Rev. D 110, 103037 (2024).
  70. J. Blackman et al., Binary black-hole surrogate waveform catalog [Data set] (Zenodo, 2025), 10.5281/zenodo.14919209.

Outline

Information

Phys. Rev. D 112, 024077– Published 30 July, 2025
  • Received 6 February 2025
  • Accepted 22 June 2025
Article part of CHORUS
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation