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

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Magnetically supramassive and hypermassive compact stars

Kōji Uryū1,*, Shijun Yoshida2,†, Eric Gourgoulhon3,4,‡, Charalampos Markakis5,6,§, Kotaro Fujisawa7,∥, Antonios Tsokaros8,6,9,¶, Keisuke Taniguchi1,**, Mina Zamani10,††, and Lambros Boukas11,‡‡

  • *Contact author: koji.uryu@gmail.com
  • †Contact author: yoshida@astr.tohoku.ac.jp
  • ‡Contact author: eric.gourgoulhon@obspm.fr
  • §Contact author: markakis@illinois.edu
  • ∥Contact author: kotaro.fujisawa@gmail.com
  • Contact author: tsokaros@illinois.edu
  • **Contact author: ktngc@cs.u-ryukyu.ac.jp
  • ††Contact author: m_zamani@znu.ac.ir
  • ‡‡Contact author: lboukas@gmail.com
PDF

Phys. Rev. D 114, 103002 – Published 3 November, 2026

DOI: https://doi.org/10.1103/4qvp-4l55

Abstract

It is known that the mass of a magnetized relativistic compact star is larger than that of a nonmagnetized one for the same equation of state and central density, albeit the excess of mass is sizable only if the magnetic fields are strong enough, B∼1017–1018  G. Using our recently developed numerical code cocal, we systematically compute such compact star solutions in equilibrium associated with mixed poloidal and toroidal magnetic fields, and show the magnetically supramassive solutions whose masses exceed by more than 10% the maximum mass of the static and spherically symmetric solutions. For some extremely strong magnetic field configurations, we also obtain solutions more massive than the maximum mass of the uniformly rotating solutions at the Kepler (mass-shedding) limit, namely magnetically hypermassive solutions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (36)

  1. J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55, 374 (1939); R. C. Tolman, Relativity, Thermodynamics and Cosmology (Clarendon Press, Oxford, 1934).
  2. S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (Wiley Interscience, New York, 1983).
  3. J. M. Lattimer, Annu. Rev. Nucl. Part. Sci. 62, 485 (2012); F. Özel and P. Freire, Annu. Rev. Astron. Astrophys. 54, 401 (2016); J. M. Lattimer, Annu. Rev. Nucl. Part. Sci. 71, 433 (2021).
  4. G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Astrophys. J. 398, 203 (1992).
  5. G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Astrophys. J. 422, 227 (1994); 424, 823 (1994).
  6. T. W. Baumgarte, S. L. Shapiro, and M. Shibata, Astrophys. J. 528, L29 (2000); I. A. Morrison, T. W. Baumgarte, and S. L. Shapiro, 610, 941 (2004); M. Ansorg, D. Gondek-Rosinska, L. Villain, and M. Bejger, EAS Publ. Ser. 30, 373 (2008).
  7. F. Galeazzi, S. Yoshida, and Y. Eriguchi, Astron. Astrophys. 541, A156 (2012); J. D. Kaplan, C. D. Ott, E. P. O’Connor, K. Kiuchi, L. Roberts, and M. Duez, Astrophys. J. 790, 19 (2014); K. Uryu, A. Tsokaros, F. Galeazzi, H. Hotta, M. Sugimura, K. Taniguchi, and S. Yoshida, Phys. Rev. D 93, 044056 (2016); D. Gondek-Rosinska, I. Kowalska, L. Villain, M. Ansorg, and M. Kucaba, Astrophys. J. 837, 58 (2017); A. M. Studzinska, M. Kucaba, D. Gondek-Rosinska, L. Villain, and M. Ansorg, Mon. Not. R. Astron. Soc. 463, 2667 (2016); K. Uryu, A. Tsokaros, L. Baiotti, F. Galeazzi, K. Taniguchi, and S. Yoshida, Phys. Rev. D 96, 103011 (2017); A. Bauswein and N. Stergioulas, Mon. Not. R. Astron. Soc. 471, 4956 (2017); G. Bozzola, N. Stergioulas, and A. Bauswein, 474, 3557 (2018); E. Zhou, A. Tsokaros, K. Uryu, R. Xu, and M. Shibata, Phys. Rev. D 100, 043015 (2019); A. Passamonti and N. Andersson, Mon. Not. R. Astron. Soc. 498, 5904 (2020); X. Xie, I. Hawke, A. Passamonti, and N. Andersson, Phys. Rev. D 102, 044040 (2020); P. Iosif and N. Stergioulas, Mon. Not. R. Astron. Soc. 503, 850 (2021); G. Camelio, T. Dietrich, S. Rosswog, and B. Haskell, Phys. Rev. D 103, 063014 (2021); P. Iosif and N. Stergioulas, Mon. Not. R. Astron. Soc. 510, 2948 (2022); K. Franceschetti, L. Del Zanna, J. Soldateschi, and N. Bucciantini, Universe 8, 172 (2022); M. Cassing and L. Rezzolla, Mon. Not. R. Astron. Soc. 532, 945 (2024); N. Muhammed, M. D. Duez, P. Chawhan, N. Ghadiri, L. T. Buchman, F. Foucart, P. C. K. Cheong, L. E. Kidder, H. P. Pfeiffer, and M. A. Scheel, Phys. Rev. D 110, 124063 (2024).
  8. A. G. Suvorov and K. Glampedakis, Phys. Rev. D 105, L061302 (2022).
  9. M. Bocquet, S. Bonazzola, E. Gourgoulhon, and J. Novak, Astron. Astrophys. 301, 757 (1995).
  10. C. Y. Cardall, M. Prakash, and J. M. Lattimer, Astrophys. J. 554, 322 (2001).
  11. A. Tsokaros and K. Uryū, Gen. Relativ. Gravit. 54, 52 (2022).
  12. K. Uryu, E. Gourgoulhon, C. M. Markakis, K. Fujisawa, A. Tsokaros, and Y. Eriguchi, Phys. Rev. D 90, 101501(R) (2014).
  13. K. Uryu, S. Yoshida, E. Gourgoulhon, C. Markakis, K. Fujisawa, A. Tsokaros, K. Taniguchi, and Y. Eriguchi, Phys. Rev. D 100, 123019 (2019), (Paper I).
  14. K. Uryu, S. Yoshida, E. Gourgoulhon, C. Markakis, K. Fujisawa, A. Tsokaros, K. Taniguchi, and M. Zamani, Phys. Rev. D 107, 103016 (2023), (Paper II).
  15. S. Chandrasekhar and E. Fermi, Astrophys. J. 118, 116 (1953); 122, 208(E) (1955).
  16. A. Rowlinson, P. T. O’Brien, B. D. Metzger, N. R. Tanvir, and A. J. Levan, Mon. Not. R. Astron. Soc. 430, 1061 (2013).
  17. A. Tsokaros, M. Ruiz, S. L. Shapiro, and K. Uryū, Phys. Rev. Lett. 128, 061101 (2022); P. C. K. Cheong, A. Tsokaros, M. Ruiz, F. Venturi, J. C. L. Chan, A. K. L. Yip, and K. Uryu, Phys. Rev. D 111, 063030 (2025).
  18. K. Kiuchi, K. Kyutoku, Y. Sekiguchi, and M. Shibata, Phys. Rev. D 97, 124039 (2018); R. Ciolfi, W. Kastaun, J. V. Kalinani, and B. Giacomazzo, 100, 023005 (2019); M. Ruiz, A. Tsokaros, V. Paschalidis, and S. L. Shapiro, 99, 084032 (2019). K. Kiuchi, K. Kyutoku, and M. Shibata, 86, 064008 (2012); P. Mösta, S. Richers, C. D. Ott, R. Haas, A. L. Piro, K. Boydstun, E. Abdikamalov, C. Reisswig, and E. Schnetter, Astrophys. J. 785, L29 (2014); P. Mösta, C. D. Ott, D. Radice, L. F. Roberts, E. Schnetter, and R. Haas, Nature (London) 528, 376 (2015).
  19. B. Giacomazzo, J. Zrake, P. Duffell, A. I. MacFadyen, and R. Perna, Astrophys. J. 809, 39 (2015); K. Kiuchi, K. Kyutoku, Y. Sekiguchi, and M. Shibata, Phys. Rev. D 97, 124039 (2018); C. Palenzuela, R. Aguilera-Miret, F. Carrasco, R. Ciolfi, J. V. Kalinani, W. Kastaun, B. Miñano, and D. Viganò, 106, 023013 (2022); E. M. Gutiérrez, D. Radice, J. Fields, and J. M. Stone, arXiv:2601.20953.
  20. E. Gourgoulhon, C. Markakis, K. Uryu, and Y. Eriguchi, Phys. Rev. D 83, 104007 (2011).
  21. X. Huang, C. Markakis, N. Sugiyama, and K. Uryu, Phys. Rev. D 78, 124023 (2008); K. Uryu and A. Tsokaros, 85, 064014 (2012); K. Uryu, A. Tsokaros, and P. Grandclement, 86, 104001 (2012); A. Tsokaros, K. Uryu, and L. Rezzolla, 91, 104030 (2015).
  22. L. Boukas, A. Tsokaros, and K. Uryu, Universe 10, 229 (2024).
  23. E. Gourgoulhon and S. Bonazzola, Classical Quantum Gravity 11, 443 (1994); R. Beig, Phys. Lett. 69A, 153 (1978); M. Shibata, K. Uryu, and J. L. Friedman, Phys. Rev. D 70, 044044 (2004); 70, 129901(E) (2004).
  24. T. E. Riley et al., Astrophys. J. Lett. 887, L21 (2019); G. Raaijmakers et al., 887, L22 (2019); A. V. Bilous et al., 887, L23 (2019); M. C. Miller et al., 887, L24 (2019); S. Bogdanov et al., 887, L25 (2019); 887, L26 (2019).
  25. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Astrophys. J. 983, 99 (2025).
  26. K. Makishima, T. Enoto, J. S. Hiraga, T. Nakano, K. Nakazawa, S. Sakurai, M. Sasano, and H. Murakami, Phys. Rev. Lett. 112, 171102 (2014).
  27. S. L. Shapiro, Astrophys. J. 544, 397 (2000).
  28. R. J. Tayler, Mon. Not. R. Astron. Soc. 161, 365 (1973); P. Markey and R. J. Tayler, 163, 77 (1973); G. A. E. Wright, 162, 339 (1973).
  29. L. Suleiman, M. Fortin, J. L. Zdunik, and C. Providencia, Phys. Rev. C 106, 035805 (2022).
  30. K. Kiuchi, M. Shibata, and S. Yoshida, Phys. Rev. D 78, 024029 (2008).
  31. For the stability of relativistic rotating stars, see e.g., J. L. Friedman and N. Stergioulas, Rotating Relativistic Stars (Cambridge University Press, Cambridge, England, 2013).
  32. J. L. Friedman, J. R. Ipser, and R. D. Sorkin, Astrophys. J. 325, 722 (1988).
  33. L. R. Weih, E. R. Most, and L. Rezzolla, Mon. Not. R. Astron. Soc. 473, L126 (2018).
  34. B. Carter, in Black Holes—Les Houches 1972, edited by C. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1973), p. 57.
  35. K. Uryu, E. Gourgoulhon, and C. Markakis, Phys. Rev. D 82, 104054 (2010).
  36. J. L. Friedman, K. Uryu and M. Shibata, Phys. Rev. D 65, 064035 (2002); 70, 129904(E) (2004).

Outline

Information

Phys. Rev. D 114, 103002– Published 3 November, 2026
  • Received 23 December 2025
  • Accepted 29 September 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation