- 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

Subpopulation of low-mass, spinning black holes: Signatures of dynamical assembly

Hui Tong1,2,*, Thomas A. Callister3, Maya Fishbach4,5,6, Eric Thrane1,2, Fabio Antonini7, Simon Stevenson8,9, Isobel M. Romero-Shaw7, and Fani Dosopoulou7

  • *Contact author: hui.tong@monash.edu
PDF

Phys. Rev. D 114, 083007 – Published 5 October, 2026

DOI: https://doi.org/10.1103/lnzm-d2k1

Abstract

Gravitational-wave observations of massive, rapidly spinning black holes provide increasing evidence for the dynamical origin of some mergers. Previous studies have interpreted the mergers with primary mass ≳45M⊙ as being dominated by hierarchical, second-generation mergers, with rapidly spinning primaries being the products of previous black hole mergers assembled in dense stellar clusters. In this work, we present evidence of another subpopulation with rapid and isotropic spins at low mass containing the two exceptional events GW241011 and GW241110. Though other interpretations are possible, the properties of this subpopulation are consistent with a hierarchical-merger hypothesis. Interpreted in the hierarchical-merger framework, our result suggests the mass distribution of the candidate second-generation black holes may peak at low primary masses of ∼16M⊙ rather than ≳45M⊙ in the pair-instability gap. Such low-mass second-generation black holes must be formed from the merger of even lighter first-generation black holes, implying that dense, metal-rich stellar environments contribute to the binary black hole population. By separating the contamination of the possible higher-generation black holes, our analysis provides an estimate of the primary-mass distribution of first-generation black holes formed from stellar collapse, which suggests a dip between ∼12M⊙ and ∼20M⊙. This may indicate a dearth of black holes due to variation in the core compactness of the progenitor.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (95)

  1. J. Aasi et al., Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  2. F. Acernese et al., Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  3. T. Akutsu et al., Overview of KAGRA: Detector design and construction history, Prog. Theor. Exp. Phys. 2021, 05A101 (2021).
  4. Michela Mapelli, Binary black hole mergers: Formation and populations, Front. Astron. Space Sci. 7, 38 (2020).
  5. 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).
  6. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Population properties of merging compact binaries, Astrophys. J. Lett. 1005, L51 (2026).
  7. Z. Doctor, D. Wysocki, R. O’Shaughnessy, D. E. Holz, and B. Farr, Black hole coagulation: Modeling hierarchical mergers in black hole populations, Astrophys. J. 893, 35 (2020).
  8. Chase Kimball, C. Talbot, Christopher P. L. Berry, Matthew Carney, Michael Zevin, Eric Thrane, and Vicky Kalogera, Black hole genealogy: Identifying hierarchical mergers with gravitational waves, Astrophys. J. 900, 177 (2020).
  9. Chase Kimball et al., Evidence for hierarchical black hole mergers in the second LIGO–Virgo gravitational wave catalog, Astrophys. J. Lett. 915, L35 (2021).
  10. Matthew Mould, Davide Gerosa, and Stephen R. Taylor, Deep learning and Bayesian inference of gravitational-wave populations: Hierarchical black-hole mergers, Phys. Rev. D 106, 103013 (2022).
  11. Yuan-Zhu Wang, Yin-Jie Li, Jorick S. Vink, Yi-Zhong Fan, Shao-Peng Tang, Ying Qin, and Da-Ming Wei, Potential subpopulations and assembling tendency of the merging black holes, Astrophys. J. Lett. 941, L39 (2022).
  12. Yin-Jie Li, Yuan-Zhu Wang, Shao-Peng Tang, and Yi-Zhong Fan, Resolving the stellar-collapse and hierarchical-merger origins of the coalescing black holes, Phys. Rev. Lett. 133, 051401 (2024).
  13. Fabio Antonini, Isobel M. Romero-Shaw, and Thomas Callister, Star cluster population of high mass black hole mergers in gravitational wave data, Phys. Rev. Lett. 134, 011401 (2025).
  14. Hui Tong et al., Evidence of the pair instability gap in the distribution of black hole masses, Nature (London) 652, 874 (2026).
  15. Fabio Antonini, Isobel Romero-Shaw, Thomas Callister, Fani Dosopoulou, Debatri Chattopadhyay, Mark Gieles, and Michela Mapelli, Gravitational waves reveal the pair-instability mass gap and constrain nuclear burning in massive stars, Nat. Astron. 10, 1049 (2026).
  16. Davide Gerosa and Maya Fishbach, Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures, Nature (London) 5, 749 (2021).
  17. Frans Pretorius, Evolution of binary black hole spacetimes, Phys. Rev. Lett. 95, 121101 (2005).
  18. Alessandra Buonanno, Lawrence E. Kidder, and Luis Lehner, Estimating the final spin of a binary black hole coalescence, Phys. Rev. D 77, 026004 (2008).
  19. Jose A. Gonzalez, Ulrich Sperhake, Bernd Bruegmann, Mark Hannam, and Sascha Husa, Total recoil: The Maximum kick from nonspinning black-hole binary inspiral, Phys. Rev. Lett. 98, 091101 (2007).
  20. Maya Fishbach, Daniel E. Holz, and Ben Farr, Are LIGO’s black holes made from smaller black holes?, Astrophys. J. Lett. 840, L24 (2017).
  21. G. Pierra, S. Mastrogiovanni, and S. Perriès, The spin magnitude of stellar-mass black holes evolves with the mass, Astron. Astrophys. 692, A80 (2024).
  22. Jam Sadiq, Thomas Dent, and Ana Lorenzo-Medina, Seeking spinning subpopulations of black hole binaries via iterative density estimation, Phys. Rev. D 112, 123054 (2025).
  23. Fabio Antonini, Thomas Callister, Fani Dosopoulou, Isobel Romero-Shaw, and Debatri Chattopadhyay, Inferring the pair-instability mass gap from gravitational wave data using flexible models, Phys. Rev. D 112, 063040 (2025).
  24. Yin-Jie Li, Yuan-Zhu Wang, Shao-Peng Tang, and Yi-Zhong Fan, Aligned hierarchical black hole mergers in AGN disks revealed by GWTC-4, Phys. Rev. Lett. 137, 021407 (2026).
  25. T Damour, Coalescence of two spinning black holes: An effective one-body approach, Phys. Rev. D 64, 124013 (2001).
  26. Maya Fishbach, Chase Kimball, and Vicky Kalogera, Limits on hierarchical black hole mergers from the most negative χeff systems, Astrophys. J. Lett. 935, L26 (2022).
  27. Ethan Payne, Kyle Kremer, and Michael Zevin, Spin doctors: How to diagnose a hierarchical merger origin, Astrophys. J. Lett. 966, L16 (2024).
  28. Vishal Baibhav, Davide Gerosa, Emanuele Berti, Kaze W. K. Wong, Thomas Helfer, and Matthew Mould, The mass gap, the spin gap, and the origin of merging binary black holes, Phys. Rev. D 102, 043002 (2020).
  29. Fabio Antonini and Frederic A. Rasio, Merging black hole binaries in galactic nuclei: Implications for Advanced-LIGO detections, Astrophys. J. 831, 187 (2016).
  30. Davide Gerosa and Emanuele Berti, Are merging black holes born from stellar collapse or previous mergers?, Phys. Rev. D 95, 124046 (2017).
  31. Carl L. Rodriguez, Michael Zevin, Pau Amaro-Seoane, Sourav Chatterjee, Kyle Kremer, Frederic A. Rasio, and Claire S. Ye, Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties, Phys. Rev. D 100, 043027 (2019).
  32. Simon Stevenson, Matthew Sampson, Jade Powell, Alejandro Vigna-Gómez, Coenraad J. Neijssel, Dorottya Szécsi, and Ilya Mandel, The impact of pair-instability mass loss on the binary black hole mass distribution, Astrophys. J. 882, 121 (2019).
  33. Christos Karathanasis, Suvodip Mukherjee, and Simone Mastrogiovanni, Binary black holes population and cosmology in new lights: Signature of PISN mass and formation channel in GWTC-3, Mon. Not. R. Astron. Soc. 523, 4539 (2023).
  34. Samsuzzaman Afroz and Suvodip Mukherjee, Binary black hole phase space discovers the signature of pair instability supernovae mass gap, arXiv:2509.09123.
  35. Anarya Ray and Vicky Kalogera, Reexamining evidence of a pair-instability mass gap in the binary black hole population, Astrophys. J. Lett. 998, L20 (2026).
  36. Sharan Banagiri, Eric Thrane, and Paul D. Lasky, Evidence for three subpopulations of merging binary black holes at different primary masses, Phys. Rev. Lett. 137, 021403 (2026).
  37. Vaibhav Tiwari and Stephen Fairhurst, The emergence of structure in the binary black hole mass distribution, Astrophys. J. Lett. 913, L19 (2021).
  38. Vaibhav Tiwari, Exploring features in the binary black hole population, Astrophys. J. 928, 155 (2022).
  39. Vaibhav Tiwari, What’s in a binary black hole’s mass parameter?, Mon. Not. R. Astron. Soc. 527, 298 (2023).
  40. Jaxen Godfrey, Bruce Edelman, and Ben Farr, Cosmic cousins: Identification of a subpopulation of binary black holes consistent with isolated binary evolution, arXiv:2304.01288.
  41. Alexandre Toubiana, Michael L. Katz, and Jonathan R. Gair, Is there an excess of black holes around 20M⊙? Optimizing the complexity of population models with the use of reversible jump MCMC. Mon. Not. R. Astron. Soc. 524, 5844–5853 (2023).
  42. Thomas A. Callister and Will M. Farr, Parameter-Free tour of the binary black hole population, Phys. Rev. X 14, 021005 (2024).
  43. Claire S. Ye, Maya Fishbach, Kyle Kremer, and Marta Reina-Campos, Mass distribution of binary black hole mergers from young and old dense star clusters, Astrophys. J. 997, 267 (2026).
  44. A. G. Abac, I. Abouelfettouh, F. Acernese, K. Ackley, C. Adamcewicz et al., GW241011 and GW241110: Exploring binary formation and fundamental physics with asymmetric, high-spin black hole coalescences, Astrophys. J. Lett. 993, L21 (2025).
  45. Reed Essick et al., Compact binary coalescence sensitivity estimates with injection campaigns during the LIGO-Virgo-KAGRA Collaborations’ fourth observing run, Phys. Rev. D 112, 102001 (2025).
  46. Reed Essick, Amanda Farah, S. Galaudage, Colm Talbot, Maya Fishbach, Eric Thrane, and Daniel E. Holz, Don’t just leave-one-out: Probing extremal gravitational-wave events with coarse-grained likelihoods, Astrophys. J. 926, 34 (2022).
  47. Maya Fishbach, Daniel E. Holz, and Will M. Farr, Does the black hole merger rate evolve with redshift?, Astrophys. J. Lett. 863, L41 (2018).
  48. R. Abbott, T. D. Abbott, S. Abraham, F. Acernese et al., Population properties of compact objects from the second LIGO–virgo gravitational-wave transient catalog, Astrophys. J. Lett. 913, L7 (2021).

  49. The uniform distribution of χeff for 2G + 1G can be understood as follows. We make several assumptions about 2G + 1G binaries: that the mass ratio is typically q≈0.5;

    the secondary spin is small so that χ2≈0 and the primary spin is always χ1≈0.7. It follows that χeff is linearly related to the cosine of the primary tilt angle z1. Since z1 is approximately uniformly distributed, χeff is approximately uniformly distributed [13].

  50. F. R. N. Schneider, Ph. Podsiadlowski, and B. Müller, Pre-supernova evolution, compact object masses and explosion properties of stripped binary stars, Astron. Astrophys. 645, A5 (2021).
  51. Salvatore Vitale and Matthew Mould (Society of Physicists Interested in Non-aligned Spins, SPINS, (Society of Physicists Interested in Non-aligned Spins, SPINS)† Collaborations), Long road to alignment: Measuring black hole spin orientation with expanding gravitational-wave datasets, Phys. Rev. D 112, 083015 (2025).
  52. Noah E. Wolfe, Matthew Mould, Jack Heinzel, and Salvatore Vitale, Studying the gravitational-wave population without looking that FAR out, arXiv:2510.06220.
  53. Matthew Mould, Jack Heinzel, Sofia Alvarez-Lopez, Cailin Plunkett, Noah E. Wolfe, and Salvatore Vitale, Measurement prospects for the pair-instability mass cutoff with gravitational waves, Phys. Rev. D 113, 103021 (2026).
  54. R Abbott et al., The population of merging compact binaries inferred using gravitational waves through GWTC-3, Phys. Rev. X 13, 011048 (2023).
  55. K. Belczynski et al., The effect of pair-instability mass loss on black hole mergers, Astron. Astrophys. 594, A97 (2016).
  56. Tomoya Kinugawa, Kohei Inayoshi, Kenta Hotokezaka, Daisuke Nakauchi, and Takashi Nakamura, Possible indirect confirmation of the existence of Pop III massive stars by gravitational wave, Mon. Not. R. Astron. Soc. 442, 2963 (2014).
  57. Fabian R. N. Schneider, Philipp Podsiadlowski, and Eva Laplace, Bimodal black hole mass distribution and chirp masses of binary black hole mergers, Astrophys. J. Lett. 950, L9 (2023).
  58. Sourav Chatterjee, Carl L. Rodriguez, Vicky Kalogera, and Frederic A. Rasio, Dynamical formation of low-mass merging black hole binaries like GW151226, Astrophys. J. Lett. 836, L26 (2017).
  59. Sambaran Banerjee, Merger rate density of stellar-mass binary black holes from young massive clusters, open clusters, and isolated binaries: Comparisons with LIGO-Virgo-KAGRA results, Phys. Rev. D 105, 023004 (2022).
  60. Alejandro Vigna-Gómez, Silvia Toonen, Enrico Ramirez-Ruiz, Nathan W. C. Leigh, Jeff Riley, and Carl-Johan Haster, Massive stellar triples leading to sequential binary black hole mergers in the field, Astrophys. J. Lett. 907, L19 (2021).
  61. Y. Yang, I. Bartos, V. Gayathri, K. E. S. Ford, Z. Haiman, S. Klimenko, B. Kocsis, S. Márka, Z. Márka, B. McKernan, and R. O’Shaughnessy, Hierarchical black hole mergers in active galactic nuclei, Phys. Rev. Lett. 123, 181101 (2019).
  62. Cailin Plunkett, Thomas Callister, Michael Zevin, and Salvatore Vitale, Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset, Phys. Rev. Lett. 137, 021404 (2026).
  63. Evan O’Connor and Christian D. Ott, Black hole formation in failing core-collapse supernovae, Astrophys. J. 730, 70 (2011).
  64. Marcella Ugliano, Hans-Thomas Janka, Andreas Marek, and Almudena Arcones, Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors, Astrophys. J. 757, 69 (2012).
  65. Tuguldur Sukhbold and Stan Woosley, The compactness of presupernova stellar cores, Astrophys. J. 783, 10 (2014).
  66. T. Ertl, H. Th. Janka, S. E. Woosley, T. Sukhbold, and M. Ugliano, A two-parameter criterion for classifying the explodability of massive stars by the neutrino-driven mechanism, Astrophys. J. 818, 124 (2016).
  67. Bernhard Müller, A. Heger, D. Liptai, and J. B. Cameron, A simple approach to the supernova progenitor–explosion connection, Mon. Not. R. Astron. Soc. 460, 742 (2016).
  68. Shanika Galaudage and Astrid Lamberts, Compactness peaks: An astrophysical interpretation of the mass distribution of merging binary black holes, Astron. Astrophys. 694, A186 (2025).
  69. Vasco Gennari, Simone Mastrogiovanni, Nicola Tamanini, Sylvain Marsat, and Grégoire Pierra, Searching for additional structure and redshift evolution in the observed binary black hole population with a parametric time-dependent mass distribution, Phys. Rev. D 111, 123046 (2025).
  70. Vaibhav Tiwari, Examining the gap in the chirp mass distribution of binary black holes, Astrophys. J. 995, 177 (2025).
  71. R. Willcox, F. R. N. Schneider, E. Laplace, Ph. Podsiadlowski, K. Maltsev, I. Mandel, P. Marchant, H. Sana, T. Li, and T. Hertog, New gravitational-wave data support a bimodal black-hole mass distribution, arXiv:2508.20787.
  72. Reinhold Willcox, Fabian R. N. Schneider, Eva Laplace, Philipp Podsiadlowski, Kiril Maltsev, Ilya Mandel, Pablo Marchant, Hugues Sana, Tjonnie G. F. Li, and Thomas Hertog, Good things always come in 3s: Trimodality in the binary black-hole chirp-mass distribution supports bimodal black-hole formation, arXiv:2510.07573.
  73. Christian Adamcewicz, Paul D. Lasky, Eric Thrane, and Ilya Mandel, No evidence for a dip in the binary black hole mass spectrum, Astrophys. J. 975, 253 (2024).
  74. El-Badry et al., A sun-like star orbiting a black hole, Mon. Not. R. Astron. Soc. 518, 1057 (2022).
  75. El-Badry et al., A red giant orbiting a black hole, Mon. Not. R. Astron. Soc. 521, 4323 (2023).
  76. P. Panuzzo et al., Discovery of a dormant 33 solar-mass black hole in pre-release gaia astrometry, Astron. Astrophys. 686, L2 (2024).
  77. Hui Tong, Data release of Subpopulation of low-mass, spinning black holes: Signatures of dynamical assembly, v1, zenodo, 10.5281/zenodo.22745139.
  78. Colm Talbot, Amanda Farah, Shanika Galaudage, Jacob Golomb, and Hui Tong, gwpopulation: Hardware agnostic population inference for compact binaries and beyond, J. Open Source Softwaare 10, 7753 (2025).
  79. Eric Thrane and Colm Talbot, An introduction to bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models, Pub. Astron. Soc. Aust. 36 (2019).
  80. Ilya Mandel, Will M Farr, and Jonathan R Gair, Extracting distribution parameters from multiple uncertain observations with selection biases, Mon. Not. R. Astron. Soc. 486, 1086 (2019).
  81. Salvatore Vitale, Davide Gerosa, Will M. Farr, and Stephen R. Taylor, Inferring the properties of a population of compact binaries in presence of selection effects, in Handbook of Gravitational Wave Astronomy (Springer, Singapore, 2021).
  82. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Methods for identifying and characterizing gravitational-wave transients, Astrophys. J. Lett. 1004, L21 (2026).
  83. LIGO Scientific Collaboration and Virgo Collaboration, Gwtc-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run–parameter estimation data release (2022) 10.5281/zenodo.6513631.
  84. LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, Gwtc-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run—parameter estimation data release (2021) 10.5281/zenodo.5546663.
  85. LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, GWTC-4.0: Parameter estimation data release, 10.5281/zenodo.16053484 (2025).
  86. Gregory Ashton, Moritz Hübner, Paul D. Lasky et al., bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suupl. Ser. 241, 27 (2019).
  87. I M Romero-Shaw, C Talbot et al., Bayesian inference for compact binary coalescences with bilby: Validation and application to the first LIGO–Virgo gravitational-wave transient catalogue, Mon. Not. R. Astron. Soc. 499, 3295 (2020).
  88. Joshua S. Speagle, dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences, Mon. Not. R. Astron. Soc. 493, 3132 (2020).
  89. 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).
  90. 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).
  91. R Abbott et al., 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).
  92. LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, GW241011 and GW241110: Exploring binary formation and fundamental physics with asymmetric, high-spin black hole coalescences (2025) 10.5281/zenodo.17343574.
  93. Reed Essick and Will Farr, Precision Requirements for Monte Carlo Sums within Hierarchical Bayesian Inference, arXiv:2204.00461.
  94. Colm Talbot and Jacob Golomb, Growing pains: Understanding the impact of likelihood uncertainty on hierarchical Bayesian inference for gravitational-wave astronomy, Mon. Not. R. Astron. Soc. 526, 3495 (2023).
  95. Jack Heinzel and Salvatore Vitale, When (not) to trust Monte Carlo approximations for hierarchical Bayesian inference, arXiv:2509.07221.

Outline

Information

Phys. Rev. D 114, 083007– Published 5 October, 2026
  • Received 10 November 2025
  • Revised 12 June 2026
  • Accepted 31 August 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation