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
  • Access by Xinjiang University

Dynamics and gravitational radiation of stable and unstable boson-star mergers

Bo-Xuan Ge1,*, Eugene A. Lim1,†, Ulrich Sperhake2,3,4, Tamara Evstafyeva2,5,‡, Daniela Cors2,§, Eloy de Jong1,∥, Robin Croft6,¶, and Thomas Helfer7,**

  • *Contact author: bo-xuan.ge@kcl.ac.uk
  • Contact author: eugene.a.lim@gmail.com
  • Contact author: te307@cam.ac.uk
  • §Contact author: dc889@cam.ac.uk
  • Contact author: eloydejong93@gmail.com
  • Contact author: robin.croft@uniroma1.it
  • **Contact author: thomashelfer@live.de

Phys. Rev. D 112, 124080 – Published 26 December, 2025

DOI: https://doi.org/10.1103/2dhs-phl4

Abstract

We explore the gravitational-wave emission from head-on collisions of equal-mass solitonic boson-star binaries from simulations spanning a two-dimensional parameter space, consisting of the central scalar-field amplitude of the stars and the solitonic potential parameter. We report the gravitational-wave energies emitted by boson-star binaries which, due to their combination of moderately high compactness with significant deformability, we often find to be louder by up to an order of magnitude than analogous black-hole collisions. The dependence of the radiated energy on the boson-star parameters exhibits striking needle-sharp features and discontinuous jumps to the value emitted by black-hole binaries. We explain these features in terms of the solitonic potential and the stability properties of the respective individual stars.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (115)

  1. A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins, Nature (London) 217, 709 (1968).
  2. S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (John Wiley & Sons, Inc., New York, 1983).
  3. E. Berger, Annu. Rev. Astron. Astrophys. 52, 43 (2014).
  4. B. P. Abbott et al. (LIGO Scientific, Virgo, Fermi GBM, INTEGRAL, IceCube, AstroSat Cadmium Zinc Telluride Imager Team, IPN, Insight-Hxmt, ANTARES, Swift, AGILE Team, 1M2H Team, Dark Energy Camera GW-EM, DES, DLT40, GRAWITA, Fermi-LAT, ATCA, ASKAP, Las Cumbres Observatory Group, OzGrav, DWF (Deeper Wider Faster Program), AST3, CAASTRO, VINROUGE, MASTER, J-GEM, GROWTH, JAGWAR, CaltechNRAO, TTU-NRAO, NuSTAR, Pan-STARRS, MAXI Team, TZAC Consortium, KU, Nordic Optical Telescope, ePESSTO, GROND, Texas Tech University, SALT Group, TOROS, BOOTES, MWA, CALET, IKI-GW Follow-up, H.E.S.S., LOFAR, LWA, HAWC, Pierre Auger, ALMA, Euro VLBI Team, Pi of Sky, Chandra Team at McGill University, DFN, ATLAS Telescopes, High Time Resolution Universe Survey, RIMAS, RATIR, and SKA South Africa/MeerKAT Collaborations), Astrophys. J. Lett. 848, L12 (2017).
  5. A. Cattaneo et al., Nature (London) 460, 213 (2009).
  6. M. J. Rees, Annu. Rev. Astron. Astrophys. 22, 471 (1984).
  7. P. Reig, Astrophys. Space Sci. 332, 1 (2011).
  8. A. Escrivà, F. Kuhnel, and Y. Tada, Black Holes in the Era of Gravitational-Wave Astronomy (Elsevier, New York, 2024), pp. 261–377.
  9. F. Özel and P. Freire, Annu. Rev. Astron. Astrophys. 54, 401 (2016).
  10. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 121, 161101 (2018).
  11. J. M. Lattimer, Annu. Rev. Nucl. Part. Sci. 71, 433 (2021).
  12. V. Cardoso, L. Gualtieri, C. Herdeiro, and U. Sperhake, Living Rev. Relativity 18, 1 (2015).
  13. L. Barack et al., Classical Quantum Gravity 36, 143001 (2019).
  14. V. Cardoso, O. J. C. Dias, G. S. Hartnett, M. Middleton, P. Pani, and J. E. Santos, J. Cosmol. Astropart. Phys. 03 (2018) 043.
  15. E. Berti et al., Classical Quantum Gravity 32, 243001 (2015).
  16. R. Abbott et al. (LIGO Scientific Collaboration, VIRGO Collaboration, and KAGRA Collaboration), Phys. Rev. D 112, 084080 (2025).
  17. B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016).
  18. R. Abbott et al. (KAGRA Collaboration, VIRGO Collaboration, and LIGO Scientific Collaboration), Phys. Rev. X 13, 041039 (2023).
  19. J. L. Feng, Annu. Rev. Astron. Astrophys. 48, 495 (2010).
  20. F. Kahlhoefer, Int. J. Mod. Phys. A 32, 1730006 (2017).
  21. S. Cebrián, J. Phys. Conf. Ser. 2502, 012004 (2023).
  22. P. Jaranowski and A. Krolak, Living Rev. Relativity 8, 3 (2005).
  23. M. Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments, Oxford Master Series in Physics (Oxford University Press, New York, 2007).
  24. T. Evstafyeva, U. Sperhake, I. Romero-Shaw, and M. Agathos, Phys. Rev. Lett. 133, 131401 (2024).
  25. S. L. Liebling and C. Palenzuela, Living Rev. Relativity 15, 6 (2012).
  26. L. Visinelli, Int. J. Mod. Phys. D 30, 2130006 (2021).
  27. M. Bezares and N. Sanchis-Gual, arXiv:2406.04901.
  28. J. C. Aurrekoetxea, C. Hoy, and M. Hannam, Phys. Rev. Lett. 132, 181401 (2024).
  29. J. Calderón Bustillo, N. Sanchis-Gual, A. Torres-Forné, J. A. Font, A. Vajpeyi, R. Smith, C. Herdeiro, E. Radu, and S. H. W. Leong, Phys. Rev. Lett. 126, 081101 (2021).
  30. D. J. Kaup, Phys. Rev. 172, 1331 (1968).
  31. N. Siemonsen and W. E. East, Phys. Rev. D 103, 044022 (2021).
  32. N. Sanchis-Gual, F. Di Giovanni, M. Zilhão, C. Herdeiro, P. Cerdá-Durán, J. A. Font, and E. Radu, Phys. Rev. Lett. 123, 221101 (2019).
  33. S. Yoshida and Y. Eriguchi, Phys. Rev. D 56, 762 (1997).
  34. E. W. Mielke, Fundam. Theor. Phys. 183, 115 (2016).
  35. B. Kleihaus, J. Kunz, and M. List, Phys. Rev. D 72, 064002 (2005).
  36. F. Di Giovanni, N. Sanchis-Gual, P. Cerdá-Durán, M. Zilhão, C. Herdeiro, J. A. Font, and E. Radu, Phys. Rev. D 102, 124009 (2020).
  37. A. S. Dmitriev, D. G. Levkov, A. G. Panin, E. K. Pushnaya, and I. I. Tkachev, Phys. Rev. D 104, 023504 (2021).
  38. V. Cardoso, P. Pani, M. Cadoni, and M. Cavaglia, Phys. Rev. D 77, 124044 (2008).
  39. C.-W. Lai, A numerical study of boson stars, Other thesis, 2004.
  40. N. Siemonsen, Phys. Rev. Lett. 133, 031401 (2024).
  41. Pedro V. P. Cunha, E. Berti, and Carlos A. R. Herdeiro, Phys. Rev. Lett. 119, 251102 (2017).
  42. V. Cardoso, E. Franzin, and P. Pani, Phys. Rev. Lett. 116, 171101 (2016); 117, 089902(E) (2016).
  43. Pedro V. P. Cunha, C. Herdeiro, E. Radu, and N. Sanchis-Gual, Phys. Rev. Lett. 130, 061401 (2023).
  44. T. Helfer, U. Sperhake, R. Croft, M. Radia, B.-X. Ge, and E. A. Lim, Classical Quantum Gravity 39, 074001 (2022).
  45. R. Croft, T. Helfer, B.-X. Ge, M. Radia, T. Evstafyeva, E. A. Lim, U. Sperhake, and K. Clough, Classical Quantum Gravity 40, 065001 (2023).
  46. C. Palenzuela, P. Pani, M. Bezares, V. Cardoso, L. Lehner, and S. Liebling, Phys. Rev. D 96, 104058 (2017).
  47. F. Atteneder, H. R. Rüter, D. Cors, R. Rosca-Mead, D. Hilditch, and B. Brügmann, Phys. Rev. D 109, 044058 (2024).
  48. M. Bezares, C. Palenzuela, and C. Bona, Phys. Rev. D 95, 124005 (2017).
  49. N. Sanchis-Gual, M. Zilhão, C. Herdeiro, F. Di Giovanni, J. A. Font, and E. Radu, Phys. Rev. D 102, 101504(R) (2020).
  50. C. Palenzuela, L. Lehner, and S. L. Liebling, Phys. Rev. D 77, 044036 (2008).
  51. B. C. Mundim, A numerical study of boson star binaries, Ph.D. thesis, British Columbia University, 2010.
  52. T. Evstafyeva, U. Sperhake, T. Helfer, R. Croft, M. Radia, B.-X. Ge, and E. A. Lim, Classical Quantum Gravity 40, 085009 (2023).
  53. N. Siemonsen and W. E. East, Phys. Rev. D 108, 124015 (2023).
  54. M. Bezares, M. Bošković, S. Liebling, C. Palenzuela, P. Pani, and E. Barausse, Phys. Rev. D 105, 064067 (2022).
  55. T. Dietrich, S. Ossokine, and K. Clough, Classical Quantum Gravity 36, 025002 (2019).
  56. K. Clough, T. Dietrich, and J. C. Niemeyer, Phys. Rev. D 98, 083020 (2018).
  57. V. Cardoso, T. Ikeda, Z. Zhong, and M. Zilhão, Phys. Rev. D 106, 044030 (2022).
  58. M. Bezares and C. Palenzuela, Classical Quantum Gravity 35, 234002 (2018).
  59. M. Alcubierre, J. Barranco, A. Bernal, J. C. Degollado, A. Diez-Tejedor, M. Megevand, D. Nunez, and O. Sarbach, Classical Quantum Gravity 35, 19LT01 (2018).
  60. N. Sanchis-Gual, F. Di Giovanni, C. Herdeiro, E. Radu, and J. A. Font, Phys. Rev. Lett. 126, 241105 (2021).
  61. V. Jaramillo, N. Sanchis-Gual, J. Barranco, A. Bernal, J. C. Degollado, C. Herdeiro, and D. Núñez, Phys. Rev. D 101, 124020 (2020).
  62. A. Bernal, J. Barranco, D. Alic, and C. Palenzuela, Phys. Rev. D 81, 044031 (2010).
  63. S. H. Hawley and M. W. Choptuik, Phys. Rev. D 67, 024010 (2003).
  64. F. S. Guzmán and A. A. Avilez, Phys. Rev. D 97, 116003 (2018).
  65. T. Helfer, E. A. Lim, Marcos A. G. Garcia, and M. A. Amin, Phys. Rev. D 99, 044046 (2019).
  66. R. Brito, V. Cardoso, Caio F. B. Macedo, H. Okawa, and C. Palenzuela, Phys. Rev. D 93, 044045 (2016).
  67. J. Y. Widdicombe, T. Helfer, and E. A. Lim, J. Cosmol. Astropart. Phys. 01 (2020) 027.
  68. P. Grandclement, G. Fodor, and P. Forgacs, Phys. Rev. D 84, 065037 (2011).
  69. R. Brito, V. Cardoso, C. A. R. Herdeiro, and E. Radu, Phys. Lett. B 752, 291 (2016).
  70. N. Sanchis-Gual, C. Herdeiro, J. A. Font, E. Radu, and F. Di Giovanni, Phys. Rev. D 99, 024017 (2019).
  71. C. A. R. Herdeiro, E. Radu, N. Sanchis-Gual, N. M. Santos, and E. dos Santos Costa Filho, Phys. Lett. B 852, 138595 (2024).
  72. N. Siemonsen and W. E. East, Phys. Rev. D 107, 124018 (2023).
  73. J. Y. Widdicombe, T. Helfer, D. J. E. Marsh, and E. A. Lim, J. Cosmol. Astropart. Phys. 10 (2018) 005.
  74. R. Luna, M. Llorens-Monteagudo, A. Lorenzo-Medina, J. Calderón Bustillo, N. Sanchis-Gual, A. Torres-Forné, J. A. Font, C. A. R. Herdeiro, and E. Radu, Phys. Rev. D 110, 024004 (2024).
  75. C. Palenzuela, I. Olabarrieta, L. Lehner, and S. L. Liebling, Phys. Rev. D 75, 064005 (2007).
  76. D. I. Choi, K. C. W. Lai, M. W. Choptuik, E. W. Hirschmann, S. L. Liebling, and F. Pretorius (2009), https://laplace.physics.ubc.ca/Group/Papers/choi-etal-prd-05/choi-etal-prd-05.pdf.
  77. M. W. Choptuik and F. Pretorius, Phys. Rev. Lett. 104, 111101 (2010).
  78. K. Thorne, in Magic Without Magic, edited by J. Klauder (Freeman, San Francisco, 1972), p. 231.
  79. N. Sanchis-Gual, J. Calderón Bustillo, C. Herdeiro, E. Radu, J. A. Font, S. H. W. Leong, and A. Torres-Forné, Phys. Rev. D 106, 124011 (2022).
  80. U. Sperhake, W. Cook, and D. Wang, Phys. Rev. D 100, 104046 (2019).
  81. T. Evstafyeva, R. Rosca-Mead, U. Sperhake, and B. Brugmann, Phys. Rev. D 108, 104064 (2023).
  82. B.-X. Ge, Gravitational waves in boson star mergers, Doctoral thesis, King’s College London, 2024.
  83. K. Clough, P. Figueras, H. Finkel, M. Kunesch, E. A. Lim, and S. Tunyasuvunakool, Classical Quantum Gravity 32, 245011 (2015).
  84. M. Radia, U. Sperhake, A. Drew, K. Clough, P. Figueras, E. A. Lim, J. L. Ripley, J. C. Aurrekoetxea, T. França, and T. Helfer, Classical Quantum Gravity 39, 135006 (2022).
  85. T. Andrade et al., J. Open Source Software 6, 3703 (2021).
  86. D. Alic, C. Bona-Casas, C. Bona, L. Rezzolla, and C. Palenzuela, Phys. Rev. D 85, 064040 (2012).
  87. M. Adams et al., Tech. Report No. LBNL-6616E, 2019.
  88. W. G. Cook, P. Figueras, M. Kunesch, U. Sperhake, and S. Tunyasuvunakool, Int. J. Mod. Phys. D 25, 1641013 (2016).
  89. M. Alcubierre, S. Brandt, B. Bruegmann, D. Holz, E. Seidel, R. Takahashi, and J. Thornburg, Int. J. Mod. Phys. D 10, 273 (2001).
  90. F. Pretorius, Classical Quantum Gravity 22, 425 (2005).
  91. J. Balakrishna, E. Seidel, and W.-M. Suen, Phys. Rev. D 58, 104004 (1998).
  92. N. Sanchis-Gual, C. Herdeiro, and E. Radu, Classical Quantum Gravity 39, 064001 (2022).
  93. M. Brito, C. Herdeiro, E. Radu, N. Sanchis-Gual, and M. Zilhão, Phys. Rev. D 107, 084022 (2023).
  94. J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55, 374 (1939).
  95. R. C. Tolman, Phys. Rev. 55, 364 (1939).
  96. G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Astrophys. J. 424, 823 (1994).
  97. J. L. Friedman, J. R. Ipser, and R. D. Sorkin, Astrophys. J. 325, 722 (1988).
  98. B. K. Harrison, K. S. Thorne, M. Wakano, and J. A. Wheeler, Gravitation Theory and Gravitational Collapse (University Chicago Press, Chicago, 1965).
  99. N. Straumann, General Relativity and Relativistic Astrophysics (Springer, Berlin; New York, 1984).
  100. T. D. Lee and Y. Pang, Nucl. Phys. B315, 477 (1989).
  101. M. Gleiser, Phys. Rev. D 38, 2376 (1988); 39, 1257(E) (1989).
  102. M. Gleiser and R. Watkins, Nucl. Phys. B319, 733 (1989).
  103. P. Jetzer, Nucl. Phys. B316, 411 (1989).
  104. P. Jetzer, Nucl. Phys. B, Proc. Suppl. 14, 265 (1990).
  105. P. Jetzer, Phys. Lett. B 222, 447 (1989).
  106. E. Seidel and W.-M. Suen, Phys. Rev. D 42, 384 (1990).
  107. M. Alcubierre, R. Becerril, S. F. Guzman, T. Matos, D. Nunez, and L. A. Urena-Lopez, Classical Quantum Gravity 20, 2883 (2003).
  108. N. M. Santos, C. L. Benone, and C. A. R. Herdeiro, J. Cosmol. Astropart. Phys. 06 (2024) 068.
  109. N. Sennett, T. Hinderer, J. Steinhoff, A. Buonanno, and S. Ossokine, Phys. Rev. D 96, 024002 (2017).
  110. M. Okounkova, arXiv:2004.00671.
  111. U. Sperhake, Phys. Rev. D 76, 104015 (2007).
  112. T. Helfer, D. J. E. Marsh, K. Clough, M. Fairbairn, E. A. Lim, and R. Becerril, J. Cosmol. Astropart. Phys. 03 (2017) 055.
  113. A. Toubiana, S. Babak, E. Barausse, and L. Lehner, Phys. Rev. D 103, 064042 (2021).
  114. B.-X. Ge, Dynamics and gravitational radiation of stable and unstable boson stars, GitHub repository, https://github.com/boxuange/Dynamics-and-gravitational-radiation-of-stable-and-unstable-boson-star (2025).
  115. W. G. Cook and U. Sperhake, Classical Quantum Gravity 34, 035010 (2017).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation