- 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

Interplay of magnetic fields, turbulence, and vorticity in core-collapse supernovae

David Calvert1, Michael Redle2,3, Bibek Gautam1, Charles J. Stapleford4, Carla Fröhlich1,*, James P. Kneller1,†, and Matthias Liebendörfer5

  • *Contact author: cfrohli@ncsu.edu
  • †Contact author: jpknelle@ncsu.edu
PDF

Phys. Rev. D 114, 083043 – Published 23 October, 2026

DOI: https://doi.org/10.1103/lgc5-tn23

Abstract

The convective turbulent motion of the fluid below the shock in a core-collapse supernova stretches and amplifies the magnetic field of the progenitor star. The energy contained in the field is sourced from the work done by the fluid on the field which comes at the expense of the fluid’s kinetic and internal energy. In addition to the energy exchange with the fluid, the magnetic field also has a backreaction upon the fluid via a contribution to the baroclinic vector and thus affects the fluid vorticity. In this paper we explore the interaction of the magnetic field with the fluid in core-collapse supernovae using the elephant code with solar-metallicity stars of 15 and 20M⊙ zero-age main sequence mass and purely toroidal initial magnetic fields of B0=0,1010, and 1012  G. We find that the magnetic field in the gain region does not become so large that it alters the global dynamics above the 10% level in the early postbounce evolution. The turbulent kinetic energy of the fluid in the gain region is smaller in simulations with a strong initial magnetic field, but the exact amount of reduction is uncertain due to limitations of the methods for measuring turbulent kinetic energy. The structure of the field in the simulations quickly becomes a tangled mass of flux ropes as soon as convection begins, which leads to a large magnetic field contribution to the baroclinic vector that dominates over the hydrodynamic contribution. Although governed by very similar transport equations to the magnetic field, the fluid vorticity and magnetic field are always close to being randomly aligned at every stage of the evolution. The enstrophy, which is seen to be closely associated with the turbulent kinetic energy, is found to be reduced in simulations with a strong initial magnetic field supporting the inference that the magnetic field reduces the amount of turbulence in the fluid.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (93)

  1. H. A. Bethe and J. R. Wilson, Revival of a stalled supernova shock by neutrino heating, Astrophys. J. 295, 14 (1985).
  2. A. Burrows, J. Hayes, and B. A. Fryxell, On the nature of core-collapse supernova explosions, Astrophys. J. 450, 830 (1995).
  3. H. T. Janka, Long-term multidimensional models of core-collapse supernovae: Progress and challenges, Annu. Rev. Nucl. Part. Sci. 75, 425 (2025).
  4. T. Fischer, S. C. Whitehouse, A. Mezzacappa, F.-K. Thielemann, and M. Liebendörfer, Protoneutron star evolution and the neutrino-driven wind in general relativistic neutrino radiation hydrodynamics simulations, Astron. Astrophys. 517, A80 (2010).
  5. L. Hüdepohl, B. Müller, H. T. Janka, A. Marek, and G. G. Raffelt, Neutrino signal of electron-capture supernovae from core collapse to cooling, Phys. Rev. Lett. 104, 251101 (2010).
  6. A. Mezzacappa, M. Liebendörfer, O. E. Messer, W. R. Hix, F.-K. Thielemann, and S. W. Bruenn, Simulation of the spherically symmetric stellar core collapse, bounce, and postbounce evolution of a star of 13 solar masses with Boltzmann neutrino transport, and its implications for the supernova mechanism, Phys. Rev. Lett. 86, 1935 (2001).
  7. M. Rampp and H. T. Janka, Radiation hydrodynamics with neutrinos. Variable Eddington factor method for core-collapse supernova simulations, Astron. Astrophys. 396, 361 (2002).
  8. T. A. Thompson, A. Burrows, and P. A. Pinto, Shock breakout in core-collapse supernovae and its neutrino signature, Astrophys. J. 592, 434 (2003).
  9. M. Liebendörfer, O. E. B. Messer, A. Mezzacappa, S. W. Bruenn, C. Y. Cardall, and F. K. Thielemann, A finite difference representation of neutrino radiation hydrodynamics in spherically symmetric general relativistic spacetime, Astrophys. J. Suppl. Ser. 150, 263 (2004).
  10. K. Sumiyoshi, S. Yamada, H. Suzuki, H. Shen, S. Chiba, and H. Toki, Postbounce evolution of core-collapse supernovae: Long-term effects of the equation of state, Astrophys. J. 629, 922 (2005).
  11. H. T. Janka, K. Langanke, A. Marek, G. Martínez-Pinedo, and B. Müller, Theory of core-collapse supernovae, Phys. Rep. 442, 38 (2007).
  12. H.-T. Janka, Neutrino-driven explosions, in Handbook of Supernovae, edited by A. W. Alsabti and P. Murdin (Springer International Publishing AG, Cham, Switzerland, 2017), p. 1095.
  13. S. M. Couch, The mechanism(s) of core-collapse supernovae, Phil. Trans. R. Soc. A 375, 20160271 (2017).
  14. T. Kuroda, A. Arcones, T. Takiwaki, and K. Kotake, Magnetorotational explosion of a massive star supported by neutrino heating in general relativistic three-dimensional simulations, Astrophys. J. 896, 102 (2020).
  15. R. Bollig, N. Yadav, D. Kresse, H.-T. Janka, B. Müller, and A. Heger, Self-consistent 3D supernova models from −7 minutes to +7  s: A 1-bethe explosion of a 19M⊙ progenitor, Astrophys. J. 915, 28 (2021).
  16. K. Nakamura, T. Takiwaki, and K. Kotake, Three-dimensional simulation of a core-collapse supernova for a binary star progenitor of SN 1987A, Mon. Not. R. Astron. Soc. 514, 3941 (2022).
  17. D. Vartanyan, M. S. B. Coleman, and A. Burrows, The collapse and three-dimensional explosion of three-dimensional massive-star supernova progenitor models, Mon. Not. R. Astron. Soc. 510, 4689 (2022).
  18. B. Sykes and B. Müller, Long-time 3D supernova simulations of nonrotating progenitors with magnetic fields, Phys. Rev. D 111, 063042 (2025).
  19. S. Shibagaki, T. Kuroda, K. Kotake, T. Takiwaki, and T. Fischer, Three-dimensional GRMHD simulations of rapidly rotating stellar core collapse, Mon. Not. R. Astron. Soc. 531, 3732 (2024).
  20. T. Wang and A. Burrows, Nucleosynthetic analysis of three-dimensional core-collapse supernova simulations, Astrophys. J. 962, 71 (2024).
  21. J. W. Murphy and C. Meakin, A global turbulence model for neutrino-driven convection in core-collapse supernovae, Astrophys. J. 742, 74 (2011).
  22. R. Fernández, Hydrodynamics of core-collapse supernovae at the transition to explosion. I. Spherical symmetry, Astrophys. J. 749, 142 (2012).
  23. J. C. Dolence, A. Burrows, J. W. Murphy, and J. Nordhaus, Dimensional dependence of the hydrodynamics of core-collapse supernovae, Astrophys. J. 765, 110 (2013).
  24. E. Endeve, C. Y. Cardall, R. D. Budiardja, A. Mezzacappa, and J. M. Blondin, Turbulence and magnetic field amplification from spiral SASI modes in core-collapse supernovae, Phys. Scr. T 155, 014022 (2013).
  25. T. Handy, T. Plewa, and A. Odrzywołek, Toward connecting core-collapse supernova theory with observations. I. Shock revival in a 15M⊙ blue supergiant progenitor with SN 1987A energetics, Astrophys. J. 783, 125 (2014).
  26. E. Abdikamalov, C. D. Ott, D. Radice, L. F. Roberts, R. Haas, C. Reisswig, P. Mösta, H. Klion, and E. Schnetter, Neutrino-driven turbulent convection and standing accretion shock instability in three-dimensional core-collapse supernovae, Astrophys. J. 808, 70 (2015).
  27. S. M. Couch and C. D. Ott, The role of turbulence in neutrino-driven core-collapse supernova explosions, Astrophys. J. 799, 5 (2015).
  28. D. Radice, C. D. Ott, E. Abdikamalov, S. M. Couch, R. Haas, and E. Schnetter, Neutrino-driven convection in core-collapse supernovae: High-resolution simulations, Astrophys. J. 820, 76 (2016).
  29. D. Radice, E. Abdikamalov, C. D. Ott, P. Mösta, S. M. Couch, and L. F. Roberts, Turbulence in core-collapse supernovae, J. Phys. G Nucl. Phys. 45, 053003 (2018).
  30. J. Casanova, E. Endeve, E. J. Lentz, O. E. B. Messer, W. R. Hix, J. A. Harris, and S. W. Bruenn, On the character of turbulent-like flows in self-consistent models of core-collapse supernovae, Phys. Scr. 95, 064005 (2020).
  31. D. Calvert, M. Redle, B. Gautam, C. J. Stapleford, C. Fröhlich, J. P. Kneller, and M. Liebendorfer, Turbulence in core-collapse supernovae, Astrophys. J. 995, 109 (2025).
  32. T. Melson, H.-T. Janka, and A. Marek, Neutrino-driven supernova of a low-mass iron-core progenitor boosted by three-dimensional turbulent convection, Astrophys. J. Lett. 801, L24 (2015).
  33. B. Müller and H.-T. Janka, nonradial instabilities and progenitor asphericities in core-collapse supernovae, Mon. Not. R. Astron. Soc. 448, 2141 (2015).
  34. E. Abdikamalov, A. Zhaksylykov, D. Radice, and S. Berdibek, Shock-turbulence interaction in core-collapse supernovae, Mon. Not. R. Astron. Soc. 461, 3864 (2016).
  35. H.-T. Janka, T. Melson, and A. Summa, Physics of core-collapse supernovae in three dimensions: A sneak preview, Annu. Rev. Nucl. Part. Sci. 66, 341 (2016).
  36. B. Müller, T. Melson, A. Heger, and H.-T. Janka, Supernova simulations from a 3D progenitor model—Impact of perturbations and evolution of explosion properties, Mon. Not. R. Astron. Soc. 472, 491 (2017).
  37. Q. A. Mabanta and J. W. Murphy, How turbulence enables core-collapse supernova explosions, Astrophys. J. 856, 22 (2018).
  38. M. J. Raives, T. A. Thompson, and S. M. Couch, The antesonic condition for the explosion of core-collapse supernovae—II. Rotation and turbulence, Mon. Not. R. Astron. Soc. 502, 4125 (2021).
  39. J. S. Bloom, S. R. Kulkarni, S. G. Djorgovski, A. C. Eichelberger, P. Côté, J. P. Blakeslee, S. C. Odewahn, F. A. Harrison, D. A. Frail, A. V. Filippenko, D. C. Leonard, A. G. Riess, H. Spinrad, D. Stern, A. Bunker, A. Dey, B. Grossan, S. Perlmutter, R. A. Knop, I. M. Hook, and M. Feroci, The unusual afterglow of the γ-ray burst of 26 March 1998 as evidence for a supernova connection, Nature (London) 401, 453 (1999).
  40. S. E. Woosley and J. S. Bloom, The supernova gamma-ray burst connection, Annu. Rev. Astron. Astrophys. 44, 507 (2006).
  41. A. Burrows, L. Dessart, E. Livne, C. D. Ott, and J. Murphy, Simulations of magnetically driven supernova and hypernova explosions in the context of rapid rotation, Astrophys. J. 664, 416 (2007).
  42. C. Winteler, R. Käppeli, A. Perego, A. Arcones, N. Vasset, N. Nishimura, M. Liebendörfer, and F.-K. Thielemann, Magnetorotationally driven supernovae as the origin of early galaxy r-process elements?, Astrophys. J. Lett. 750, L22 (2012).
  43. B. Müller, Supernova simulations, 10.1007/978-981-97-8522-3_19 (2024).
  44. M. Obergaulinger and M. Á. Aloy, Magnetorotational core collapse of possible GRB progenitors—III. Three-dimensional models, Mon. Not. R. Astron. Soc. 503, 4942 (2021).
  45. B. Müller and V. Varma, A 3D simulation of a neutrino-driven supernova explosion aided by convection and magnetic fields, Mon. Not. R. Astron. Soc. 498, L109 (2020).
  46. J. Matsumoto, T. Takiwaki, and K. Kotake, Neutrino-driven massive stellar explosions in 3D fostered by magnetic fields via turbulent α-effect, Mon. Not. R. Astron. Soc. 528, L96 (2023).
  47. K. Nakamura, T. Takiwaki, J. Matsumoto, and K. Kotake, Three-dimensional magnetohydrodynamic simulations of core-collapse supernovae—I. Hydrodynamic evolution and protoneutron star properties, Mon. Not. R. Astron. Soc. 536, 280 (2024).
  48. J. Matsumoto, Y. Asahina, T. Takiwaki, K. Kotake, and H. R. Takahashi, Magnetic support for neutrino-driven explosion of 3D non-rotating core-collapse supernova models, Mon. Not. R. Astron. Soc. 516, 1752 (2022).
  49. V. Varma, B. Müller, and F. R. N. Schneider, 3D simulations of strongly magnetized non-rotating supernovae: Explosion dynamics and remnant properties, Mon. Not. R. Astron. Soc. 518, 3622 (2022).
  50. V. Varma and B. Müller, Resolution dependence in magnetohydrodynamic simulations of neutrino-driven core-collapse supernovae, Mon. Not. R. Astron. Soc. 548, stag626 (2026).
  51. G. Leidi, R. Andrassy, J. Higl, P. V. F. Edelmann, and F. K. Röpke, Turbulent dynamo action and its effects on the mixing at the convective boundary of an idealized oxygen-burning shell, Astron. Astrophys. 679, A132 (2023).
  52. S. Akiyama, J. C. Wheeler, D. L. Meier, and I. Lichtenstadt, The magnetorotational instability in core-collapse supernova explosions, Astrophys. J. 584, 954 (2003).
  53. A. Brandenburg, R. L. Jennings, Å. Nordlund, M. Rieutord, R. F. Stein, and I. Tuominen, Magnetic structures in a dynamo simulation, J. Fluid Mech. 306, 325 (1996).
  54. E. Endeve, C. Y. Cardall, R. D. Budiardja, and A. Mezzacappa, Generation of magnetic fields by the stationary accretion shock instability, Astrophys. J. 713, 1219 (2010).
  55. E. Endeve, C. Y. Cardall, R. D. Budiardja, S. W. Beck, A. Bejnood, R. J. Toedte, A. Mezzacappa, and J. M. Blondin, Turbulent magnetic field amplification from spiral SASI modes: Implications for core-collapse supernovae and proto-neutron star magnetization, Astrophys. J. 751, 26 (2012).
  56. E. N. Parker, The dynamical state of the interstellar gas and field, Astrophys. J. 145, 811 (1966).
  57. P. Bradshaw, An Introduction to Turbulence and Its Measurement (Pergamon Press, Oxford, UK, 1971).
  58. A. Tsinober, An Informal Introduction to Turbulence (Springer Dordrecht, Dordrecht, Netherlands, 2004), Vol. 63.
  59. R. M. Cabezón, K.-C. Pan, M. Liebendörfer, T. Kuroda, K. Ebinger, O. Heinimann, A. Perego, and F.-K. Thielemann, Core-collapse supernovae in the hall of mirrors. A three-dimensional code-comparison project, Astron. Astrophys. 619, A118 (2018).
  60. R. Käppeli, S. C. Whitehouse, S. Scheidegger, U.-L. Pen, and M. Liebendörfer, Fish: A three-dimensional parallel magnetohydrodynamics code for astrophysical applications, Astrophys. J. Suppl. Ser. 195, 20 (2011).
  61. M. Liebendörfer, S. C. Whitehouse, and T. Fischer, The isotropic diffusion source approximation for supernova neutrino transport, Astrophys. J. 698, 1174 (2009).
  62. S. Rosswog and M. Liebendörfer, High-resolution calculations of merging neutron stars—II. Neutrino emission, Mon. Not. R. Astron. Soc. 342, 673 (2003).
  63. J. M. Lattimer and F. D. Swesty, A generalized equation of state for hot, dense matter, Nucl. Phys. A535, 331 (1991).
  64. A. Marek, H. Dimmelmeier, H.-T. Janka, E. Müller, and R. Buras, Exploring the relativistic regime with newtonian hydrodynamics: An improved effective gravitational potential for supernova simulations, Astron. Astrophys. 445, 273 (2006).
  65. U.-L. Pen, P. Arras, and S. Wong, A free, fast, simple, and efficient total variation diminishing magnetohydrodynamic code, Astrophys. J. Suppl. Ser. 149, 447 (2003).
  66. S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Commun. Pure Appl. Math. 48, 235 (1995).
  67. S. E. Woosley and A. Heger, Nucleosynthesis and remnants in massive stars of solar metallicity, Phys. Rep. 442, 269 (2007).
  68. A. Heger, S. E. Woosley, and H. C. Spruit, Presupernova evolution of differentially rotating massive stars including magnetic fields, Astrophys. J. 626, 350 (2005).
  69. M. Obergaulinger and H.-T. Janka, Magnetic field amplification in collapsing, non-rotating stellar cores, arXiv:1101.1198.
  70. M. Obergaulinger, H.-T. Janka, and M. A. Aloy, Magnetic field amplification and magnetically supported explosions of collapsing, non-rotating stellar cores, Mon. Not. R. Astron. Soc. 445, 3169 (2014).
  71. J. Matsumoto, T. Takiwaki, K. Kotake, Y. Asahina, and H. R. Takahashi, 2d numerical study for magnetic field dependence of neutrino-driven core-collapse supernova models, Mon. Not. R. Astron. Soc. 499, 4174 (2020).
  72. A. Heger, S. E. Woosley, and H. C. Spruit, Presupernova evolution of differentially rotating massive stars including magnetic fields, Astrophys. J. 626, 350 (2005).
  73. S. E. de Mink, N. Langer, R. G. Izzard, H. Sana, and A. de Koter, The rotation rates of massive stars: The role of binary interaction through tides, mass transfer, and mergers, Astrophys. J. 764, 166 (2013).
  74. A. Oliva, F. D. Moyano, L. Sciarini, S. Ekström, P. Eggenberger, and G. Meynet, Modeling the origin of the rotation of massive stars, Astron. Astrophys. 710, 7 (2026).
  75. S. Shankar, P. Mösta, R. Haas, and E. Schnetter, 3D full-GR simulations of magnetorotational core-collapse supernovae on GPUs: A systematic study of rotation rates and magnetic fields, Mon. Not. R. Astron. Soc. 548, stag646 (2016).
  76. S. C. Schnauck, S. Shankar, P. Mösta, R. Haas, and E. Schnetter, Gravitational waves from magnetorotational core-collapse supernovae using 3D GRMHD simulations: Effect of rotation and magnetic fields, Mon. Not. R. Astron. Soc. 546, stag056 (2026).
  77. L. Kovalenko, E. O’Connor, H. Andresen, and S. M. Couch, A three-dimensional exploration of magnetic fields, rotation, and shock revival in a 39M⊙ core-collapse supernova progenitor, arXiv:2605.18347.
  78. J. M. Blondin, A. Mezzacappa, and C. DeMarino, Stability of standing accretion shocks, with an eye toward core-collapse supernovae, Astrophys. J. 584, 971 (2003).
  79. J. M. Blondin and A. Mezzacappa, Pulsar spins from an instability in the accretion shock of supernovae, Nature (London) 445, 58 (2007).
  80. A. Mezzacappa, A. C. Calder, S. W. Bruenn, J. M. Blondin, M. W. Guidry, M. R. Strayer, and A. S. Umar, An investigation of neutrino-driven convection and the core collapse supernova mechanism using multigroup neutrino transport, Astrophys. J. 495, 911 (1998).
  81. H. T. Janka and E. Mueller, The first second of a type II supernova: Convection, accretion, and shock propagation, Astrophys. J. Lett. 448, L109 (1995).
  82. L. Landau, J. Bell, M. Kearsley, L. Pitaevskii, E. Lifshitz, and J. Sykes, Electrodynamics of Continuous Media, Course of Theoretical Physics (Elsevier Science, Oxford, UK, 2013).
  83. A. Brandenburg and K. Subramanian, Astrophysical magnetic fields and nonlinear dynamo theory, Phys. Rep. 417, 1 (2005).
  84. M. V. Penston, Dynamics of self-gravitating gaseous spheres-II. Collapses of gas spheres with cooling and the behaviour of polytropic gas spheres, Mon. Not. R. Astron. Soc. 145, 457 (1969).
  85. M. V. Penston, Dynamics of self-gravitating gaseous spheres-III. Analytical results in the free-fall of isothermal cases, Mon. Not. R. Astron. Soc. 144, 425 (1969).
  86. M. L. Goossens, I. Arregui, and T. Van Doorsselaere, Mixed properties of MHD waves in non-uniform plasmas, Front. Astron. Space Sci. 6, 20 (2019).
  87. J. Cho, E. T. Vishniac, A. Beresnyak, A. Lazarian, and D. Ryu, Growth of magnetic fields induced by turbulent motions, Astrophys. J. 693, 1449 (2009).
  88. N. E. L. Haugen, A. Brandenburg, and W. Dobler, Is nonhelical hydromagnetic turbulence peaked at small scales?, Astrophys. J. Lett. 597, L141 (2003).
  89. H. Marmanis, Analogy between the Navier-Stokes equations and Maxwell’s equations: Application to turbulence, Phys. Fluids 10, 1428 (1998).
  90. T. Kambe, A new formulation of equations of compressible fluids by analogy with Maxwell’s equations, Fluid Dyn. Res. 42, 055502 (2010).
  91. R. J. Thompson and T. M. Moeller, A Maxwell formulation for the equations of a plasma, Phys. Plasmas 19, 010702 (2012).
  92. http://www.tacc.utexas.edu.
  93. C. Frohlich, J. Kneller, D. Calvert, M. Redle, B. Gautam, M. Liebendörfer, and C. Stapleford, The interplay of magnetic fields, turbulence and vorticity in core-collapse supernovae (Zenodo, 2026), 10.5281/zenodo.21900438.

Outline

Information

Phys. Rev. D 114, 083043– Published 23 October, 2026
  • Received 26 June 2026
  • Accepted 14 August 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