- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Differentially rotating neutron stars with dark matter cores

Lorenzo Cipriani1,2,*, Violetta Sagun3,†, Kalin V. Staykov4,‡, Daniela D. Doneva5,6,§, and Stoytcho S. Yazadjiev4,7,∥

  • *Contact author: lorenzo.cipriani@graduate.univaq.it
  • †Contact author: v.sagun@soton.ac.uk
  • ‡Contact author: kstaykov@phys.uni-sofia.bg
  • §Contact author: daniela.doneva@uni-tuebingen.de
  • ∥Contact author: yazad@phys.uni-sofia.bg
PDF

Phys. Rev. D 114, 023039 – Published 22 July, 2026

DOI: https://doi.org/10.1103/4rs2-973y

Abstract

Dark matter is expected to accumulate inside neutron stars, modifying the structure of isolated stars and influencing both the dynamics of binary mergers and the evolution of the resulting hypermassive remnants. Since differential rotation is the primary mechanism delaying the collapse of these remnants, understanding its behavior is crucial when assessing the impact of an embedded dark component. In this work, we extend the numerical code rns to describe two gravitationally coupled fluids in differential rotation, with baryonic matter modeled by a realistic nuclear equation of state and dark matter represented as a self-interacting bosonic condensate. Restricting the models to the zero-temperature approximation, we focus on the internal equilibrium structure. Within this framework, we construct equilibrium sequences for a representative differential rotation law, providing a basis to explore how dark matter may influence the global properties and rotational dynamics of binary neutron star remnants.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (79)

  1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  2. A. Bauswein, O. Just, H.-T. Janka, and N. Stergioulas, Neutron-star radius constraints from GW170817 and future detections, Astrophys. J. Lett. 850, L34 (2017).
  3. D. Radice, A. Perego, F. Zappa, and S. Bernuzzi, GW170817: Joint constraint on the neutron star equation of state from multimessenger observations, Astrophys. J. Lett. 852, L29 (2018).
  4. M. Shibata and K. Uryu, Simulation of merging binary neutron stars in full general relativity: Gamma=two case, Phys. Rev. D 61, 064001 (2000).
  5. L. Baiotti and L. Rezzolla, Binary neutron star mergers: A review of Einstein’s richest laboratory, Rep. Prog. Phys. 80, 096901 (2017).
  6. V. Paschalidis and N. Stergioulas, Rotating stars in relativity, Living Rev. Relativity 20, 7 (2017).
  7. T. W. Baumgarte, S. L. Shapiro, and M. Shibata, On the maximum mass of differentially rotating neutron stars, Astrophys. J. Lett. 528, L29 (2000).
  8. H. Komatsu, Y. Eriguchi, and I. Hachisu, Rapidly rotating general relativistic stars—ii. differentially rotating polytropes, Mon. Not. R. Astron. Soc. 239, 153 (1989).
  9. W. Kastaun and F. Galeazzi, Properties of hypermassive neutron stars formed in mergers of spinning binaries, Phys. Rev. D 91, 064027 (2015).
  10. M. Hanauske, K. Takami, L. Bovard, L. Rezzolla, J. A. Font, F. Galeazzi, and H. Stöcker, Rotational properties of hypermassive neutron stars from binary mergers, Phys. Rev. D 96, 043004 (2017).
  11. R. Ciolfi, W. Kastaun, B. Giacomazzo, A. Endrizzi, D. M. Siegel, and R. Perna, General relativistic magnetohydrodynamic simulations of binary neutron star mergers forming a long-lived neutron star, Phys. Rev. D 95, 063016 (2017).
  12. R. De Pietri, A. Feo, J. A. Font, F. Löffler, F. Maione, M. Pasquali, and N. Stergioulas, Convective excitation of inertial modes in binary neutron star mergers, Phys. Rev. Lett. 120, 221101 (2018).
  13. W. E. East, V. Paschalidis, F. Pretorius, and A. Tsokaros, Binary neutron star mergers: Effects of spin and post-merger dynamics, Phys. Rev. D 100, 124042 (2019).
  14. K. Takami, L. Rezzolla, and L. Baiotti, Spectral properties of the post-merger gravitational-wave signal from binary neutron stars, Phys. Rev. D 91, 064001 (2015).
  15. K. Uryū, A. Tsokaros, L. Baiotti, F. Galeazzi, K. Taniguchi, and S. Yoshida, Modeling differential rotations of compact stars in equilibriums, Phys. Rev. D 96, 103011 (2017).
  16. A. Passamonti and N. Andersson, Merger-inspired rotation laws and the low-t/w instability in neutron stars, Mon. Not. R. Astron. Soc. 498, 5904 (2020).
  17. L. R. Weih, M. Hanauske, and L. Rezzolla, Postmerger gravitational-wave signatures of phase transitions in binary mergers, Phys. Rev. Lett. 124, 171103 (2020).
  18. M. Cassing and L. Rezzolla, Realistic models of general-relativistic differentially rotating stars, Mon. Not. R. Astron. Soc. 532, 945 (2024).
  19. G. Camelio, T. Dietrich, S. Rosswog, and B. Haskell, Axisymmetric models for neutron star merger remnants with realistic thermal and rotational profiles, Phys. Rev. D 103, 063014 (2021).
  20. P. Iosif and N. Stergioulas, Equilibrium sequences of differentially rotating stars with post-merger-like rotational profiles, Mon. Not. R. Astron. Soc. 503, 850 (2021).
  21. P. Iosif and N. Stergioulas, Models of binary neutron star remnants with tabulated equations of state, Mon. Not. R. Astron. Soc. 510, 2948 (2021).
  22. J. Bramante, K. Fukushima, J. Kumar, and E. Stopnitzky, Bounds on self-interacting fermion dark matter from observations of old neutron stars, Phys. Rev. D 89, 015010 (2014).
  23. N. F. Bell, G. Busoni, T. F. Motta, S. Robles, A. W. Thomas, and M. Virgato, Nucleon structure and strong interactions in dark matter capture in neutron stars, Phys. Rev. Lett. 127, 111803 (2021).
  24. N. F. Bell, G. Busoni, S. Robles, and M. Virgato, Improved treatment of dark matter capture in neutron stars, J. Cosmol. Astropart. Phys. 09 (2020) 028.
  25. M. Stref and J. Lavalle, Modeling dark matter subhalos in a constrained galaxy: Global mass and boosted annihilation profiles, Phys. Rev. D 95, 063003 (2017).
  26. T. Lacroix, Dynamical constraints on a dark matter spike at the galactic centre from stellar orbits, Astron. Astrophys. 619, A46 (2018).
  27. A. E. Nelson, S. Reddy, and D. Zhou, Dark halos around neutron stars and gravitational waves, J. Cosmol. Astropart. Phys. 07 (2019) 012.
  28. J. Ellis, G. Hütsi, K. Kannike, L. Marzola, M. Raidal, and V. Vaskonen, Dark matter effects on neutron star properties, Phys. Rev. D 97, 123007 (2018).
  29. A. Del Popolo and M. Le Delliou, Review of solutions to the cusp-core problem of the ΛCDM model, Galaxies 9, 123 (2021).
  30. A. Suárez, V. H. Robles, and T. Matos, A review on the scalar field/Bose-Einstein condensate dark matter model, Astrophys. Space Sci. Proc. 38, 107 (2014).
  31. M. Hippert, E. Dillingham, H. Tan, D. Curtin, J. Noronha-Hostler, and N. Yunes, Dark matter or regular matter in neutron stars? how to tell the difference from the coalescence of compact objects, Phys. Rev. D 107, 115028 (2023).
  32. H.-M. Liu, J.-B. Wei, Z.-H. Li, G. F. Burgio, H. C. Das, and H. J. Schulze, Dark matter effects on the properties of neutron stars: Compactness and tidal deformability, Phys. Rev. D 110, 023024 (2024).
  33. H. Koehn, E. Giangrandi, N. Kunert, R. Somasundaram, V. Sagun, and T. Dietrich, Impact of dark matter on tidal signatures in neutron star mergers with the Einstein telescope, Phys. Rev. D 110, 103033 (2024).
  34. M. Bezares, D. Viganò, and C. Palenzuela, Gravitational wave signatures of dark matter cores in binary neutron star mergers by using numerical simulations, Phys. Rev. D 100, 044049 (2019).
  35. F. Di Giovanni, N. Sanchis-Gual, D. Guerra, M. Miravet-Tenés, P. Cerdá-Durán, and J. A. Font, Impact of ultralight bosonic dark matter on the dynamical bar-mode instability of rotating neutron stars, Phys. Rev. D 106, 044008 (2022).
  36. H. R. Rüter, V. Sagun, W. Tichy, and T. Dietrich, Quasiequilibrium configurations of binary systems of dark matter admixed neutron stars, Phys. Rev. D 108, 124080 (2023).
  37. A. Bauswein, G. Guo, J.-H. Lien, Y.-H. Lin, and M.-R. Wu, Compact dark objects in neutron star mergers, Phys. Rev. D 107, 083002 (2023).
  38. M. Emma, F. Schianchi, F. Pannarale, V. Sagun, and T. Dietrich, Numerical simulations of dark matter admixed neutron star binaries, Particles 5, 273 (2022).
  39. P. Routaray, A. Chakrawarty, N. K. Patra, and B. Kumar, Decoding dark matter admixed neutron stars: From static structure to rotational deformation, Phys. Dark Universe 50, 102093 (2025).
  40. J. Cronin, X. Zhang, and B. Kain, Rotating dark matter admixed neutron stars, Phys. Rev. D 108, 103016 (2023).
  41. A. Konstantinou, The effect of a dark matter core on the structure of a rotating neutron star, Astrophys. J. 968, 83 (2024).
  42. J. C. Mourelle, C. Adam, J. Calderón Bustillo, and N. Sanchis-Gual, Rotating fermion-boson stars, Phys. Rev. D 110, 123019 (2024).
  43. L. Cipriani, E. Giangrandi, V. Sagun, D. D. Doneva, and S. S. Yazadjiev, Rapidly spinning dark matter-admixed neutron stars, Phys. Rev. D 111, 123005 (2025).
  44. E. Giangrandi, H. Rueter, N. Kunert, M. Emma, A. Abac, A. Adhikari, T. Dietrich, V. Sagun, W. Tichy, and C. Providencia, Numerical relativity simulations of dark matter admixed binary neutron stars, arXiv:2504.20825.
  45. A. Issifu, A. Konstantinou, P. Thakur, and T. Frederico, Rotating protoneutron star admixed with mirror dark matter: A two-fluid approach, Phys. Rev. D 112, 103026 (2025).
  46. A. Abac et al. (ET Collaboration), The science of the Einstein telescope, arXiv:2503.12263.
  47. G. Bozzola, N. Stergioulas, and A. Bauswein, Universal relations for differentially rotating relativistic stars at the threshold to collapse, Mon. Not. R. Astron. Soc. 474, 3557 (2018).
  48. L. R. Weih, E. R. Most, and L. Rezzolla, On the stability and maximum mass of differentially rotating relativistic stars, Mon. Not. R. Astron. Soc. 473, L126 (2018).
  49. R. Ciolfi, G. Stratta, M. Branchesi, and B. Gendre, Multi-messenger astrophysics with theseus in the 2030s, Exp. Astron. 52, 245 (2021).
  50. P. Rosati, S. Basa, A. W. Blain, E. Bozzo, and M. Branchesi, Synergies of theseus with the large facilities of the 2030s and guest observer opportunities, Exp. Astron. 52, 407 (2021).
  51. N. Stergioulas and J. L. Friedman, Comparing models of rapidly rotating relativistic stars constructed by two numerical methods, Astrophys. J. 444, 306 (1995).
  52. N. Stergioulas, T. A. Apostolatos, and J. A. Font, Nonlinear pulsations in differentially rotating neutron stars: Mass—shedding—induced damping and splitting of the fundamental mode, Mon. Not. R. Astron. Soc. 352, 1089 (2004).
  53. A. Del Popolo, M. Le Delliou, and M. Deliyergiyev, Neutron stars and dark matter, Universe 6, 222 (2020).
  54. D. Farrell, F. Weber, and R. Negreiros, Differential rotation in neutron stars at finite temperatures, Front. Phys. 12, 1474615 (2024).
  55. A. B. Henriques, A. R. Liddle, and R. G. Moorhouse, Combined boson-fermion stars: Configurations and stability, Nucl. Phys. B337, 737 (1990).
  56. J. C. Mourelle, N. Sanchis-Gual, and J. A. Font, Differentially rotating fermion-boson stars (to be published).
  57. H. Komatsu, Y. Eriguchi, and I. Hachisu, Rapidly rotating general relativistic stars. I—numerical method and its application to uniformly rotating polytropes, Mon. Not. R. Astron. Soc. 237, 355 (1989).
  58. G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Spin-up of a rapidly rotating star by angular momentum loss: Effects of general relativity, Astrophys. J. 398, 203 (1992).
  59. L. Villain, J. A. Pons, P. Cerda-Duran, and E. Gourgoulhon, Evolutionary sequences of rotating protoneutron stars, Astron. Astrophys. 418, 283 (2004).
  60. P. Iosif and N. Stergioulas, Differentially rotating relativistic stars beyond the j-constant law, Phys. Sci. Forum 2, 62 (2021).
  61. M. Ansorg, D. Gondek-Rosińska, and L. Villain, On the solution space of differentially rotating neutron stars in general relativity, Mon. Not. R. Astron. Soc. 396, 2359 (2009).
  62. D. Gondek-Rosińska, I. Kowalska, L. Villain, M. Ansorg, and M. Kucaba, A new view on the maximum mass of differentially rotating neutron stars, Astrophys. J. 837, 58 (2017).
  63. S. Typel, G. Röpke, T. Klähn, D. Blaschke, and H. H. Wolter, Composition and thermodynamics of nuclear matter with light clusters, Phys. Rev. C 81, 015803 (2010).
  64. J. Antoniadis et al., A massive pulsar in a compact relativistic binary, Science 340, 6131 (2013).
  65. R. W. Romani, D. Kandel, A. V. Filippenko, T. G. Brink, and W. Zheng, PSR J1810+1744: Companion darkening and a precise high neutron star mass, Astrophys. J. Lett. 908, L46 (2021).
  66. R. W. Romani, D. Kandel, A. V. Filippenko, T. G. Brink, and W. Zheng, PSR J0952−0607: The fastest and heaviest known galactic neutron star, Astrophys. J. Lett. 934, L17 (2022).
  67. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121, 161101 (2018).
  68. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW190425: Observation of a compact binary coalescence with total mass ∼3.4M⊙, Astrophys. J. Lett. 892, L3 (2020).
  69. M. C. Miller et al., PSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter, Astrophys. J. Lett. 887, L24 (2019).
  70. T. E. Riley et al., A NICER view of PSR J0030+0451: Millisecond pulsar parameter estimation, Astrophys. J. Lett. 887, L21 (2019).
  71. M. C. Miller et al., The radius of PSR J0740+6620 from NICER and XMM-Newton data, Astrophys. J. Lett. 918, L28 (2021).
  72. T. E. Riley et al., A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy, Astrophys. J. Lett. 918, L27 (2021).
  73. D. Choudhury et al., A NICER view of the nearest and brightest millisecond pulsar: PSR J0437-4715, Astrophys. J. Lett. 971, L20 (2024).
  74. S. Typel, Equations of state for astrophysical simulations from generalized relativistic density functionals, J. Phys. G 45, 114001 (2018).
  75. M. Colpi, S. L. Shapiro, and I. Wasserman, Boson stars: Gravitational equilibria of selfinteracting scalar fields, Phys. Rev. Lett. 57, 2485 (1986).
  76. D. R. Karkevandi, S. Shakeri, V. Sagun, and O. Ivanytskyi, Bosonic dark matter in neutron stars and its effect on gravitational wave signal, Phys. Rev. D 105, 023001 (2022).
  77. D. R. Karkevandi, S. Shakeri, V. Sagun, and O. Ivanytskyi, Tidal deformability as a probe of dark matter in neutron stars, in 16th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (2021), arXiv:2112.14231.
  78. J. L. Friedman and N. Stergioulas, Rotating Relativistic Stars, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2013).
  79. R. De Pietri, A. Feo, J. A. Font, F. Löffler, M. Pasquali, and N. Stergioulas, Numerical-relativity simulations of long-lived remnants of binary neutron star mergers, Phys. Rev. D 101, 064052 (2020).

Outline

Information

Phys. Rev. D 114, 023039– Published 22 July, 2026
  • Received 17 December 2025
  • Accepted 1 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation