- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

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
  • Access by Xinjiang University

Structure formation with dark magnetohydrodynamics

Pierce Giffin1,2,*, Andrew Liu3,†, Jeremias Boucsein1,4,‡, Akaxia Cruz5,3,6,§, Anirudh Prabhu3,7,∥, Stefano Profumo1,2,¶, and M. Grant Roberts1,2,**

  • 1Department of Physics, 1156 High Street, University of California Santa Cruz, Santa Cruz, California 95064, USA
  • 2Santa Cruz Institute for Particle Physics, 1156 High Street, Santa Cruz, California 95064, USA
  • 3Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 4Universität Heidelberg, Zentrum für Astronomie, Institut für theoretische Astrophysik, Albert-Ueberle-Strasse 3, 69120 Heidelberg, Germany
  • 5Center for Computational Astrophysics, Flatiron Institute, New York, New York 10010, USA
  • 6Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
  • 7Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA

  • *Contact author: pgiffin@ucsc.edu
  • †Contact author: al1279@alumni.princeton.edu
  • ‡Contact author: pv276@uni-heidelberg.de
  • §Contact author: akaxia@princeton.edu
  • ∥Contact author: prabhu@princeton.edu
  • Contact author: profumo@ucsc.edu
  • **Contact author: migrober@ucsc.edu
PDF

Phys. Rev. D 113, 063063 – Published 31 March, 2026

DOI: https://doi.org/10.1103/4fkn-vx39

Abstract

Long-range interactions in the dark sector can give rise to collective plasma phenomena that are capable of modifying the evolution of dark matter halos. We present the first study of gravitational collapse in a secluded dark U(1)D model using a magnetohydrodynamic description of the dark matter. We show that dark magnetic fields generate an anisotropic pressure that alters the Jeans scale and suppresses small-scale power in a direction-dependent manner. For a range of primordial magnetic spectral indices, this effect produces distinctive modifications to the linear matter power spectrum. We find that current observations cannot yet constrain viable dark magnetic fields, as cosmic microwave background (CMB) tensor modes mostly provide more stringent constraints. Nevertheless, forthcoming high-resolution probes of the matter power spectrum (CMB-HD lensing, HERA, and EDGES) will be able to test these predictions and are sensitive to dark charge-to-mass ratios in the range 10−20  GeV−1≲qχ/mχ≲10−14  GeV−1.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (95)

  1. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  2. V. Springel, C. S. Frenk, and S. D. M. White, The large-scale structure of the Universe, Nature (London) 440, 1137 (2006).
  3. P. D. Group, Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  4. S. Profumo, An Introduction to Particle Dark Matter, Advanced Textbooks in Physics (World Scientific, Singapore, 2017).
  5. D. N. Spergel and P. J. Steinhardt, Observational evidence for selfinteracting cold dark matter, Phys. Rev. Lett. 84, 3760 (2000).
  6. W. J. G. de Blok, The core-cusp problem, Adv. Astron. 2010, 789293 (2009).
  7. K. A. Oman, J. F. Navarro, A. Fattahi, C. S. Frenk, T. Sawala, S. D. M. White, R. Bower, R. A. Crain, M. Furlong, M. Schaller et al., The unexpected diversity of dwarf galaxy rotation curves, Mon. Not. R. Astron. Soc. 452, 3650 (2015).
  8. M. Kaplinghat, T. Ren, and H.-B. Yu, Dark matter cores and cusps in spiral galaxies and their explanations, J. Cosmol. Astropart. Phys. 06 (2020) 027.
  9. T. Ren, A. Kwa, M. Kaplinghat, and H.-B. Yu, Reconciling the diversity and uniformity of galactic rotation curves with self-interacting dark matter, Phys. Rev. X 9, 031020 (2019).
  10. N. C. Relatores et al., The dark matter distributions in low-mass disk galaxies. II. The inner density profiles, Astrophys. J. 877, 94 (2019).
  11. A. Zentner, S. Dandavate, O. Slone, and M. Lisanti, A critical assessment of solutions to the galaxy diversity problem, J. Cosmol. Astropart. Phys. 07 (2022) 031.
  12. M. G. Roberts, M. Kaplinghat, M. Valli, and H.-B. Yu, Gravothermal collapse and the diversity of galactic rotation curves, Phys. Rev. D 111, 103041 (2025).
  13. M. Boylan-Kolchin, J. S. Bullock, and M. Kaplinghat, Too big to fail? The puzzling darkness of massive Milky Way subhaloes, Mon. Not. R. Astron. Soc. Lett.415, L40 (2011).
  14. S. Tulin and H.-B. Yu, Dark matter self-interactions and small scale structure, Phys. Rep. 730, 1 (2018).
  15. S. Adhikari et al., Astrophysical tests of dark matter self-interactions, Rev. Mod. Phys. 97, 045004 (2025).
  16. Z. Bogorad, P. W. Graham, and H. Ramani, Coherent self-interactions of dark matter in the bullet cluster, J. Cosmol. Astropart. Phys. 03 (2025) 067.
  17. L. Ackerman, M. R. Buckley, S. M. Carroll, and M. Kamionkowski, Dark matter and dark radiation, Phys. Rev. D 79, 023519 (2009).
  18. R. Lasenby, Long range dark matter self-interactions and plasma instabilities, J. Cosmol. Astropart. Phys. 11 (2020) 034.
  19. A. Cruz and M. McQuinn, Astrophysical plasma instabilities induced by long-range interacting dark matter, J. Cosmol. Astropart. Phys. 04 (2023) 028.
  20. W. DeRocco and P. Giffin, Dark plasmas in the nonlinear regime: Constraints from particle-in-cell simulations, Phys. Rev. D 111, 095031 (2025).
  21. M. V. Medvedev and A. Loeb, Plasma constraints on the millicharged dark matter, J. Cosmol. Astropart. Phys. 01 (2025) 113.
  22. S. I. Blinnikov and M. Y. Khlopov, On possible effects of ’mirror’ particles, Sov. J. Nucl. Phys. 36, 472 (1982).
  23. S. I. Blinnikov and M. Khlopov, Possible astronomical effects of mirror particles, Sov. Astron. 27, 371 (1983).
  24. M. Y. Khlopov, G. M. Beskin, N. E. Bochkarev, L. A. Pustylnik, and S. A. Pustylnik, Observational physics of mirror world, Sov. Astron. 35, 21 (1991).
  25. P. Agrawal, F.-Y. Cyr-Racine, L. Randall, and J. Scholtz, Make dark matter charged again, J. Cosmol. Astropart. Phys. 05 (2017) 022.
  26. F.-Y. Cyr-Racine and K. Sigurdson, Cosmology of atomic dark matter, Phys. Rev. D 87, 103515 (2013).
  27. D. A. Gurnett and A. Bhattacharjee, Introduction to Plasma Physics: With Space, Laboratory and Astrophysical Applications, 2nd ed. (Cambridge University Press, Cambridge, 2017).
  28. J.-T. Li and T. Lin, Dynamics of millicharged dark matter in supernova remnants, Phys. Rev. D 101, 103034 (2020).
  29. M. Heikinheimo, M. Raidal, C. Spethmann, and H. Veermäe, Dark matter self-interactions via collisionless shocks in cluster mergers, Phys. Lett. B 749, 236 (2015).
  30. C. Spethmann, H. Veermäe, T. Sepp, M. Heikinheimo, B. Deshev, A. Hektor, and M. Raidal, Simulations of galaxy cluster collisions with a dark plasma component, Astron. Astrophys. 608, A125 (2017).
  31. M. Heikinheimo, M. Raidal, C. Spethmann, and H. Veermäe, Collisionless shocks in self-interacting dark matter, Plasma Phys. Controlled Fusion 60, 014011 (2017).
  32. J. Binney and S. Tremaine, Galactic Dynamics, 2nd ed., Princeton Series in Astrophysics (Princeton University Press, Princeton, NJ, 2008).
  33. D. Matravers, Steven weinberg: Cosmology, Gen. Relativ. Gravit. 41, 1455 (2009).
  34. R. Barkana and A. Loeb, In the beginning: The first sources of light and the reionization of the universe, Phys. Rep. 349, 125 (2001).
  35. A. E. Evrard et al., Virial scaling of massive dark matter halos: Why clusters prefer a high normalization cosmology, Astrophys. J. 672, 122 (2008).
  36. E. Munari, A. Biviano, S. Borgani, G. Murante, and D. Fabjan, The relation between velocity dispersion and mass in simulated clusters of galaxies: Dependence on the tracer and the baryonic physics, Mon. Not. R. Astron. Soc. 430, 2638 (2013).
  37. J. S. Bullock and M. Boylan-Kolchin, Small-scale challenges to the ΛCDM paradigm, Annu. Rev. Astron. Astrophys. 55, 343 (2017).
  38. R. J. Ewart, M. L. Nastac, P. J. Bilbao, T. Silva, L. O. Silva, and A. A. Schekochihin, Relaxation to universal non-Maxwellian equilibria in a collisionless plasma, Proc. Natl. Acad. Sci. U.S.A. 122, e2417813122 (2025).
  39. G. F. Chew, M. L. Goldberger, and F. E. Low, The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions, Proc. R. Soc. A 236, 112 (1956).
  40. R. Banerjee and K. Jedamzik, The evolution of cosmic magnetic fields: From the very early universe, to recombination, to the present, Phys. Rev. D 70, 123003 (2004).
  41. P. Trivedi, J. Reppin, J. Chluba, and R. Banerjee, Magnetic heating across the cosmological recombination era: Results from 3D MHD simulations, Mon. Not. R. Astron. Soc. 481, 3401 (2018).
  42. K. Jedamzik and A. Saveliev, Stringent limit on primordial magnetic fields from the cosmic microwave background radiation, Phys. Rev. Lett. 123, 021301 (2019).
  43. E.-J. Kim, A. V. Olinto, and R. Rosner, Generation of density perturbations by primordial magnetic fields, Astrophys. J. 468, 28 (1996).
  44. K. Subramanian and J. D. Barrow, Magnetohydrodynamics in the early universe and the damping of nonlinear alfvén waves, Phys. Rev. D 58, 083502 (1998).
  45. R. Durrer and C. Caprini, Primordial magnetic fields and causality, J. Cosmol. Astropart. Phys. 11 (2003) 010.
  46. L. Mestel and I. W. Roxburgh, On the thermal generation of toroidal magnetic fields in rotating stars, Astrophys. J. 136, 615 (1962).
  47. A. Schlüter, Über den Ursprung der Magnetfelder auf Sternen und im interstellaren Raum, Z. Naturforsch. Teil A 5, 65 (1950).
  48. E. S. Weibel, Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution, Phys. Rev. Lett. 2, 83 (1959).
  49. B. D. Fried, Mechanism for instability of transverse plasma waves, Phys. Fluids 2, 337 (1959).
  50. M. V. Medvedev, L. O. Silva, and M. Kamionkowski, Cluster magnetic fields from large-scale structure and galaxy cluster shocks, Astrophys. J. 642, L1 (2006).
  51. M. Lazar, R. Schlickeiser, R. Wielebinski, and S. Poedts, Cosmological effects of Weibel-type instabilities, Astrophys. J. 693, 1133 (2009).
  52. M. S. Turner and L. M. Widrow, Inflation-produced, large-scale magnetic fields, Phys. Rev. D 37, 2743 (1988).
  53. B. Ratra, Cosmological “seed” magnetic field from inflation, Astrophys. J. Lett. 391, L1 (1992).
  54. A. D. Dolgov, Breaking of conformal invariance and electromagnetic field generation in the universe, Phys. Rev. D 48, 2499 (1993).
  55. M. Gasperini, M. Giovannini, and G. Veneziano, Primordial magnetic fields from string cosmology, Phys. Rev. Lett. 75, 3796 (1995).
  56. M. Giovannini, Homogeneous magnetic fields in fully anisotropic string cosmological backgrounds, Phys. Rev. D 62, 067301 (2000).
  57. K. Atmjeet, I. Pahwa, T. R. Seshadri, and K. Subramanian, Cosmological magnetogenesis from extra-dimensional gauss-bonnet gravity, Phys. Rev. D 89, 063002 (2014).
  58. T. Fujita, R. Namba, Y. Tada, N. Takeda, and H. Tashiro, Consistent generation of magnetic fields in axion inflation models, J. Cosmol. Astropart. Phys. 05 (2015) 054.
  59. A. Kandus, K. E. Kunze, and C. G. Tsagas, Primordial magnetogenesis, Phys. Rep. 505, 1 (2011).
  60. K. Subramanian, Magnetic fields in the early universe, Astron. Nachr. 331, 110 (2010).
  61. K. Subramanian, The origin, evolution and signatures of primordial magnetic fields, Rep. Prog. Phys. 79, 076901 (2016).
  62. J. Martin and J. Yokoyama, Generation of large scale magnetic fields in single-field inflation, J. Cosmol. Astropart. Phys. 01 (2008) 025.
  63. B. Himmetoglu, C. R. Contaldi, and M. Peloso, Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature, Phys. Rev. D 80, 123530 (2009).
  64. A. Brandenburg, K. Enqvist, and P. Olesen, Large-scale magnetic fields from hydromagnetic turbulence in the very early universe, Phys. Rev. D 54, 1291 (1996).
  65. R. Banerjee and K. Jedamzik, Evolution of cosmic magnetic fields: From the very early universe, to recombination, to the present, Phys. Rev. D 70, 123003 (2004).
  66. T. Vachaspati, Magnetic fields from cosmological phase transitions, Phys. Lett. B 265, 258 (1991).
  67. A. P. Kazantsev, Enhancement of a magnetic field by a conducting fluid, Sov. J. Exp. Theor. Phys. 26, 1031 (1968).
  68. N. I. Kleeorin, A. A. Ruzmaikin, and D. D. Sokoloff, Correlative properties of self-exciting fluctuative magnetic fields, in Plasma Astrophysics, ESA Special Publication Vol. 251, edited by T. D. Guyenne and L. M. Zeleny (1986), pp. 557–561.
  69. A. P. Kazantsev, A. A. Ruzmaikin, and D. D. Sokolov, Magnetic field transport by an acoustic turbulence-type flow, Zh. Eksp. Teor. Fiz. 88, 487 (1985).
  70. D. Grasso and H. R. Rubinstein, Revisiting nucleosynthesis constraints on primordial magnetic fields, Phys. Lett. B 379, 73 (1996).
  71. R. Durrer, P. G. Ferreira, and T. Kahniashvili, Tensor microwave anisotropies from a stochastic magnetic field, Phys. Rev. D 61, 043001 (2000).
  72. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. I. Overview and the cosmological legacy of Planck, Astron. Astrophys. 641, A1 (2020).
  73. S. Chabanier, M. Millea, and N. Palanque-Delabrouille, Matter power spectrum: From Lyα forest to CMB scales, Mon. Not. R. Astron. Soc. 489, 2247 (2019).
  74. Dark Energy Survey Collaboration, Dark energy survey year 1 results: Cosmological constraints from cosmic shear, Phys. Rev. D 98, 043528 (2018).
  75. B. A. Reid et al., Cosmological constraints from the clustering of the Sloan Digital Sky Survey DR7 luminous red galaxies, Mon. Not. R. Astron. Soc. 404, 60 (2010).
  76. B. Abolfathi et al., The fourteenth data release of the sloan digital sky survey: First spectroscopic data from the extended baryon oscillation spectroscopic survey and from the second phase of the apache point observatory galactic evolution experiment, Astrophys. J. Suppl. Ser. 235, 42 (2018).
  77. I. Esteban, A. H. G. Peter, and S. Y. Kim, Milky Way satellite velocities reveal the dark matter power spectrum at small scales, Phys. Rev. D 110, 123013 (2024).
  78. A. MacInnis and N. Sehgal, CMB-HD as a probe of dark matter on sub-galactic scales, J. Cosmol. Astropart. Phys. 02 (2025) 048.
  79. D. R. DeBoer et al., Hydrogen epoch of reionization array (HERA), Publ. Astron. Soc. Pac. 129, 045001 (2017).
  80. M. Leo, T. Theuns, C. M. Baugh, B. Li, and S. Pascoli, Constraining structure formation using EDGES, J. Cosmol. Astropart. Phys. 04 (2020) 004.
  81. J. B. Muñoz, C. Dvorkin, and F.-Y. Cyr-Racine, Probing the small-scale matter power spectrum with large-scale 21-cm data, Phys. Rev. D 101, 063526 (2020).
  82. P. Ralegankar, E. Garaldi, and M. Viel, Matter power spectrum induced by primordial magnetic fields: From the linear to the non-linear regime, J. Cosmol. Astropart. Phys. 08 (2025) 011.
  83. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The string landscape, black holes and gravity as the weakest force, J. High Energy Phys. 06 (2007) 060.
  84. M. K. Seidel, J. Falcón-Barroso, I. Martínez-Valpuesta, S. Díaz-García, E. Laurikainen, H. Salo, and J. H. Knapen, The balrog project—I. Quantifying the influence of bars on the kinematics of nearby galaxies, Mon. Not. R. Astron. Soc. 451, 936 (2015).
  85. S. Díaz-García, H. Salo, E. Laurikainen, and M. Herrera-Endoqui, Characterization of galactic bars from 3.6  μm s4g imaging, Astron. Astrophys. 587, A160 (2016).
  86. T. Kim, D. A. Gadotti, E. Athanassoula, A. Bosma, K. Sheth, and M. G. Lee, Evidence of bar-induced secular evolution in the inner regions of stellar discs in galaxies: What shapes disc galaxies?, Mon. Not. R. Astron. Soc. 462, 3430 (2016).
  87. A. Collier and A.-M. Madigan, The coupling of galactic dark matter halos with stellar bars, Astrophys. J. 915, 23 (2021).
  88. D. A. Marostica, R. E. G. Machado, E. Athanassoula, and T. Manos, The response of the inner dark matter halo to stellar bars, Galaxies 12, 27 (2024).
  89. M. Das, R. Ianjamasimanana, S. S. McGaugh, J. Schombert, and K. S. Dwarakanath, Estimating the oblateness of dark matter halos using neutral hydrogen velocity dispersion, Astrophys. J. Lett. 946, L8 (2023).
  90. M. Das, R. Ianjamasimanana, S. S. McGaugh, J. Schombert, and K. S. Dwarakanath, The oblateness of dark matter halos of nearby galaxies and its correlation with gas mass fractions, Proc. IAU 19, 353 (2023).
  91. M. D. A. Orkney, E. Taylor, J. I. Read, M. P. Rey, A. Pontzen, O. Agertz, S. Y. Kim, and M. Delorme, Edge: The shape of dark matter haloes in the faintest galaxies, Mon. Not. R. Astron. Soc. 525, 3516 (2023).
  92. B. Keith, F. Munshi, A. M. Brooks, J. Van Nest, A. Engelhardt, A. Cruz, B. Keller, T. R. Quinn, and J. Wadsley, A marvel-ous study of how well galaxy shapes reflect dark matter halo shapes in cold dark matter simulations, Astrophys. J. 986, 138 (2025).
  93. J. Zavala and C. S. Frenk, Dark matter haloes and subhaloes, Galaxies 7, 81 (2019).
  94. A. H. G. Peter, M. Rocha, J. S. Bullock, and M. Kaplinghat, Cosmological simulations with self-interacting dark matter—II. Halo shapes versus observations, Mon. Not. R. Astron. Soc. 430, 105 (2013).
  95. J. E. C. Gliddon, Gravitational instability of anisotropic plasma, Astrophys. J. 145, 583 (1966).

Outline

Information

Phys. Rev. D 113, 063063– Published 31 March, 2026
  • Received 16 December 2025
  • Accepted 13 February 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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation