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Detecting intermediate-mass black holes using miniature pulsar timing arrays in globular clusters

Xian Chen1,2,*, Verónica Vázquez-Aceves2, Siyuan Chen3,4, Kejia Lee1,5,6,7, Yanjun Guo4,5, and Kuo Liu3,4

  • 1Department of Astronomy, School of Physics, Peking University, Beijing 100871, China
  • 2Kavli Institute for Astronomy and Astrophysics at Peking University, Beijing 100871, China
  • 3Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China
  • 4State Key Laboratory of Radio Astronomy and Technology, A20 Datun Road, Chaoyang District, Beijing 100101, China
  • 5National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100101, China
  • 6Yunnan Astronomical Observatories, Chinese Academy of Sciences, Kunming 650216, Yunnan, China
  • 7Beijing Laser Acceleration Innovation Center, Huairou, Beijing 101400, China

  • *Contact author: xian.chen@pku.edu.cn

Phys. Rev. Research 7, 033300 – Published 29 September, 2025

DOI: https://doi.org/10.1103/nb5d-qzm8

Abstract

Theoretical models predict that intermediate-mass black holes (IMBHs) exist in globular clusters (GCs), but observational evidence remains elusive. Millisecond pulsars (MSPs), which are abundant in GCs and have served as precise probes for gravitational waves, offer a unique opportunity to detect potential IMBH binaries in GCs. Here, we consider the possibility of using multiple MSPs in a GC to form a miniature pulsar timing array (PTA), so as to take advantage of their correlated timing residuals to search for potential IMBH binaries in the same cluster. Our semianalytical calculations reveal that nearby IMBH binaries around MSPs in GCs could induce microsecond-level timing residuals. In GCs like ω Centauri and M15, favorable configurations are found that could lead to the detection of binaries with mass ratios q≳0.1 and orbital periods of a few days. We estimate that future higher-precision timing programs could achieve 100-ns sensitivity, substantially expanding the searchable parameter space and establishing mini-PTAs as powerful detectors of IMBHs.

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References (59)

  1. M. V. Sazhin, Opportunities for detecting ultralong gravitational waves, Sov. Astron. 22, 36 (1978).
  2. S. Detweiler, Pulsar timing measurements and the search for gravitational waves, Astrophys. J. 234, 1100 (1979).
  3. R. W. Hellings and G. S. Downs, Upper limits on the isotropic gravitational radiation background from pulsar timing analysis, Astrophys. J. 265, L39 (1983).
  4. G. Agazie et al., The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  5. J. Antoniadis, P. Arumugam, S. Arumugam, S. Babak, M. Bagchi, A. S. Bak Nielsen, C. G. Bassa, A. Bathula, A. Berthereau, M. Bonetti, E. Bortolas, P. R. Brook, M. Burgay, R. N. Caballero, A. Chalumeau, D. J. Champion, S. Chanlaridis, S. Chen et al. (EPTA Collaboration, InPTA Collaboration), The second data release from the European pulsar timing array. III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023).
  6. D. J. Reardon et al., Search for an isotropic gravitational-wave background with the Parkes pulsar timing array, Astrophys. J. Lett. 951, L6 (2023).
  7. H. Xu et al., Searching for the nano-hertz stochastic gravitational wave background with the Chinese pulsar timing array data release I, Res. Astron. Astrophys. 23, 075024 (2023).
  8. M. T. Miles et al., The MeerKAT pulsar timing array: The first search for gravitational waves with the MeerKAT radio telescope, Mon. Not. R. Astron. Soc. 536, 1489 (2024).
  9. A. G. Lyne, A. Brinklow, J. Middleditch, S. R. Kulkarni, and D. C. Backer, The discovery of a millisecond pulsar in the globular cluster M28, Nature (London) 328, 399 (1987).
  10. Pulsars in GCs: https://www3.mpifr-bonn.mpg.de/staff/pfreire/GCpsr.html.
  11. D.-J. Yin, L.-Y. Zhang, B.-D. Li, M.-H. Li, L. Qian, and Z. Pan, The analyses of globular cluster pulsars and their detection efficiency, Res. Astron. Astrophys. 23, 055012 (2023).
  12. D. Yin, L.-Y. Zhang, L. Qian, R. P. Eatough, B. Li, D. R. Lorimer, Y. Dai, Y. Li, X. Zhang, M. Li, T. Su, Y. Wu, Y. Pan, Y. Lian, T. Liu, Z. Yan, and Z. Pan, FAST discovery of eight isolated millisecond pulsars in NGC 6517, Astrophys. J. Lett. 969, L7 (2024).
  13. Y. Wu, Z. Pan, L. Qian, S. M. Ransom, R. P. Eatough, B. Wang, P. C. C. Freire, K. Liu, Z. Yan, J. Luo, L. Zhang, M. Li, D. Yin, B. Li, Y. Li, Y. Dai, Y. Li, X. Zhang, T. Liu, and Y. Pan, The discovery of three pulsars in the globular cluster M15 with FAST, Astrophys. J. Lett. 974, L23 (2024).
  14. Z. Pan, L. Qian, X. Ma, K. Liu, L. Wang, J. Luo, Z. Yan, S. Ransom, D. Lorimer, D. Li, and P. Jiang, FAST globular cluster pulsar survey: Twenty-four pulsars discovered in 15 Globular clusters, Astrophys. J. Lett. 915, L28 (2021).
  15. S.-J. Gao, Y.-X. Shao, P. Wang, P. Zhou, X.-D. Li, L. Zhang, J. W. Kania, D. R. Lorimer, and D. Li, Discovery of a millisecond pulsar associated with Terzan 6, Astrophys. J. Lett. 974, L2 (2024).
  16. Y. Lian et al., The FAST globular cluster pulsar survey (GC FANS), Astrophys. J. Suppl. Ser. 279, 51 (2025).
  17. A. Ridolfi et al., Eight new millisecond pulsars from the first MeerKAT globular cluster census, Mon. Not. R. Astron. Soc. 504, 1407 (2021).
  18. J. Das, J. Roy, P. C. C. Freire, S. M. Ransom, B. Bhattacharyya, K. Adámek, W. Armour, S. Kudale, and M. V. Muley, Globular clusters GMRT pulsar search (GCGPS). I. Survey description, discovery and timing of the first pulsar in NGC6093 (M80), Astrophys. J. 988, 161 (2025).
  19. S. Dai, S. Johnston, M. Kerr, F. Camilo, A. Cameron, L. Toomey, and H. Kumamoto, Discovery of millisecond pulsars in the globular cluster omega centauri, Astrophys. J. Lett. 888, L18 (2020).
  20. S. Dai, S. Johnston, M. Kerr, J. Berteaud, B. Bhattacharyya, F. Camilo, and E. Keane, Timing of pulsars in the globular cluster Omega Centauri, Mon. Not. R. Astron. Soc. 521, 2616 (2023).
  21. J. Singleton, M. DeCesar, S. Dai, D. Bhakta, S. Ransom, J. Strader, L. Chomiuk, and J. Miller-Jones, Timing of seven isolated pulsars in the globular cluster Terzan 1, arXiv:2412.11271.
  22. J. Hessels, A. Possenti, M. Bailes, C. Bassa, P. C. C. Freire, D. R. Lorimer, R. Lynch, S. M. Ransom, and I. H. Stairs, Pulsars in globular clusters with the SKA, in Advancing Astrophysics with the Square Kilometre Array (AASKA14) (SISSA, Trieste, Italy, 2015), p. 47.
  23. A. Askar, V. F. Baldassare, and M. Mezcua, Intermediate-mass black holes in star clusters and dwarf galaxies, arXiv:2311.12118.
  24. M. Mezcua, Observational evidence for intermediate-mass black holes, Int. J. Mod. Phys. D 26, 1730021 (2017).
  25. J. E. Greene, J. Strader, and L. C. Ho, Intermediate-mass black holes, Annu. Rev. Astron. Astrophys. 58, 257 (2020).
  26. H. Baumgardt, J. Makino, and T. Ebisuzaki, Massive black holes in star clusters. II. Realistic cluster models, Astrophys. J. 613, 1143 (2004).
  27. S. Lee, H. M. Lee, J.-h. Kim, R. Spurzem, J. Hong, and E. Chung, Formation and evolution of compact binaries containing intermediate-mass black holes in dense star clusters, Astrophys. J. 988, 15 (2025).
  28. M. Giersz, N. Leigh, A. Hypki, N. Lützgendorf, and A. Askar, MOCCA code for star cluster simulations—IV. A new scenario for intermediate mass black hole formation in globular clusters, Mon. Not. R. Astron. Soc. 454, 3150 (2015).
  29. L. Blecha, N. Ivanova, V. Kalogera, K. Belczynski, J. Fregeau, and F. Rasio, Close binary interactions of intermediate-mass black holes: Possible ultraluminous X-ray sources? Astrophys. J. 642, 427 (2006).
  30. N. W. C. Leigh, N. Lützgendorf, A. M. Geller, T. J. Maccarone, C. Heinke, and A. Sesana, On the coexistence of stellar-mass and intermediate-mass black holes in globular clusters, Mon. Not. R. Astron. Soc. 444, 29 (2014).
  31. M. MacLeod, M. Trenti, and E. Ramirez-Ruiz, The close stellar companions to intermediate-mass black holes, Astrophys. J. 819, 70 (2016).
  32. M. Arca Sedda, P. Amaro Seoane, and X. Chen, Merging stellar and intermediate-mass black holes in dense clusters: Implications for LIGO, LISA, and the next generation of gravitational wave detectors, Astron. Astrophys. 652, A54 (2021).
  33. S. Konstantinidis, P. Amaro-Seoane, and K. D. Kokkotas, Investigating the retention of intermediate-mass black holes in star clusters using N-body simulations, Astron. Astrophys. 557, A135 (2013).
  34. C.-J. Haster, F. Antonini, V. Kalogera, and I. Mandel, N-body dynamics of intermediate mass-ratio inspirals in star clusters, Astrophys. J. 832, 192 (2016).
  35. M. A. Gürkan, J. M. Fregeau, and F. A. Rasio, Massive black hole binaries from collisional runaways, Astrophys. J. 640, L39 (2006).
  36. P. Amaro-Seoane and M. Freitag, Intermediate-mass black holes in colliding clusters: Implications for lower frequency gravitational-wave astronomy, Astrophys. J. 653, L53 (2006).
  37. A. Rasskazov, G. Fragione, and B. Kocsis, Binary intermediate-mass black hole mergers in globular clusters, Astrophys. J. 899, 149 (2020).
  38. L. Souvaitzis, A. Rantala, and T. Naab, The role of massive black holes in merging star clusters: Dynamical evolution, stellar and compact object ejections and gravitational waves, Mon. Not. R. Astron. Soc. 539, 45 (2025).
  39. M. V. Sazhin and M. V. Saphonova, Gravitational action of binaries on pulsar timing in globular clusters, Astrophys. Space Sci. 208, 93 (1993).
  40. R. Fakir, Detectable time delays from gravity waves? Phys. Rev. D 50, 3795 (1994).
  41. A. N. Lommen, J. Bilikova, F. A. Jenet, S. Portegies Zwart, and B. W. Stappers, Using pulsars to detect black hole binaries in globular clusters, in Binary Radio Pulsars, edited by F. A. Rasio and I. H. Stairs (Astronomical Society of the Pacific Conference Series, San Francisco, 2005), Vol. 328, pp. 225–230.
  42. T. Damour and G. Esposito-Farèse, Light deflection by gravitational waves from localized sources, Phys. Rev. D 58, 044003 (1998).
  43. S. M. Kopeikin, G. Schäfer, C. R. Gwinn, and T. M. Eubanks, Astrometric and timing effects of gravitational waves from localized sources, Phys. Rev. D 59, 084023 (1999).
  44. A. D. Helfer, Light rays, gravitational waves and pulse-time offsets, Mon. Not. R. Astron. Soc. 430, 305 (2013).
  45. F. A. Jenet, T. Creighton, and A. Lommen, Pulsar timing and the detection of black hole binary systems in globular clusters, Astrophys. J. 627, L125 (2005).
  46. D. R. Madison, D. F. Chernoff, and J. M. Cordes, Pulsar timing perturbations from galactic gravitational wave bursts with memory, Phys. Rev. D 96, 123016 (2017).
  47. B. B. P. Perera, B. W. Stappers, A. G. Lyne, C. G. Bassa, I. Cognard, L. Guillemot, M. Kramer, G. Theureau, and G. Desvignes, Evidence for an intermediate-mass black hole in the globular cluster NGC 6624, Mon. Not. R. Astron. Soc. 468, 2114 (2017).
  48. M. Häberle, N. Neumayer, A. Seth, A. Bellini, M. Libralato, H. Baumgardt, M. Whitaker, A. Dumont, M. Alfaro-Cuello, J. Anderson, C. Clontz, N. Kacharov, S. Kamann, A. Feldmeier-Krause, A. Milone, M. S. Nitschai, R. Pechetti, and G. van de Ven, Fast-moving stars around an intermediate-mass black hole in ω centauri, Nature (London) 631, 285 (2024).
  49. Y. Huang, Q. Li, J. Liu, X. Dong, H. Zhang, Y. Lu, and C. Du, A high-velocity star recently ejected by an intermediate-mass black hole in M15, Natl. Sci. Rev. 12, nwae347 (2025).
  50. M. Anholm, S. Ballmer, J. D. E. Creighton, L. R. Price, and X. Siemens, Optimal strategies for gravitational wave stochastic background searches in pulsar timing data, Phys. Rev. D 79, 084030 (2009).
  51. Notice here a sign difference between the definitions in Refs. [2, 45].
  52. B. J. Prager, S. M. Ransom, P. C. C. Freire, J. W. T. Hessels, I. H. Stairs, P. Arras, and M. Cadelano, Using long-term millisecond pulsar timing to obtain physical characteristics of the bulge globular cluster Terzan 5, Astrophys. J. 845, 148 (2017).
  53. P. C. C. Freire, A. Ridolfi, M. Kramer, C. Jordan, R. N. Manchester, P. Torne, J. Sarkissian, C. O. Heinke, N. D’Amico, F. Camilo, D. R. Lorimer, and A. G. Lyne, Long-term observations of the pulsars in 47 Tucanae—II. Proper motions, accelerations, and jerks, Mon. Not. R. Astron. Soc. 471, 857 (2017).
  54. P. V. Padmanabh et al., Discovery and timing of ten new millisecond pulsars in the globular cluster Terzan 5, Astron. Astrophys. 686, A166 (2024).
  55. M. Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford University Press, Oxford, 2007).
  56. P. C. Peters and J. Mathews, Gravitational radiation from point masses in a Keplerian orbit, Phys. Rev. 131, 435 (1963).
  57. A. Bañares-Hernández, F. Calore, J. Martin Camalich, and J. I. Read, New constraints on the central mass contents of Omega Centauri from combined stellar kinematics and pulsar timing, Astron. Astrophys. 693, A104 (2025).
  58. J. Gerssen, R. P. van der Marel, K. Gebhardt, P. Guhathakurta, R. C. Peterson, and C. Pryor, Hubble space telescope evidence for an intermediate-mass black hole in the globular cluster M15. II. Kinematic analysis and dynamical modeling, Astron. J. 124, 3270 (2002).
  59. H. Baumgardt, P. Hut, J. Makino, S. McMillan, and S. Portegies Zwart, On the central structure of M15, Astrophys. J. 582, L21 (2003).

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