Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae

Nature volume 528, pages 376–379 (2015)Cite this article

Subjects

Abstract

Magnetohydrodynamic turbulence is important in many high-energy astrophysical systems, where instabilities can amplify the local magnetic field over very short timescales1,2. Specifically, the magnetorotational instability and dynamo action3,4,5,6 have been suggested as a mechanism for the growth of magnetar-strength magnetic fields (of 1015 gauss and above) and for powering the explosion7,8,9,10 of a rotating massive star11,12. Such stars are candidate progenitors of type Ic-bl hypernovae13,14, which make up all supernovae that are connected to long γ-ray bursts15,16. The magnetorotational instability has been studied with local high-resolution shearing-box simulations in three dimensions17,18,19, and with global two-dimensional simulations20, but it is not known whether turbulence driven by this instability can result in the creation of a large-scale, ordered and dynamically relevant field. Here we report results from global, three-dimensional, general-relativistic magnetohydrodynamic turbulence simulations. We show that hydromagnetic turbulence in rapidly rotating protoneutron stars produces an inverse cascade of energy. We find a large-scale, ordered toroidal field that is consistent with the formation of bipolar magnetorotationally driven outflows. Our results demonstrate that rapidly rotating massive stars are plausible progenitors for both type Ic-bl supernovae13,21,22 and long γ-ray bursts, and provide a viable mechanism for the formation of magnetars23,24. Moreover, our findings suggest that rapidly rotating massive stars might lie behind potentially magnetar-powered superluminous supernovae25,26.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Evolution of the maximum toroidal magnetic field.
Figure 2: Radial magnetic field strength.
Figure 3: Turbulent kinetic and electromagnetic energy spectra.
Figure 4: Three-dimensional volume renderings of the toroidal magnetic field, Bφ.

Similar content being viewed by others

References

  1. Fricke, K. Stability of rotating stars II. The influence of toroidal and poloidal magnetic fields. Astron. Astrophys. 1, 388–398 (1969)

    ADS  Google Scholar 

  2. Balbus, S. A. & Hawley, J. F. A powerful local shear instability in weakly magnetized disks. I—linear analysis. II—nonlinear evolution. Astrophys. J. 376, 214–233 (1991)

    Article  ADS  Google Scholar 

  3. Frisch, U., Pouquet, A., Leorat, J. & Mazure, A. Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. J. Fluid Mech. 68, 769–778 (1975)

    Article  ADS  Google Scholar 

  4. Moffatt, H. K. Magnetic Field Generation in Electrically Conducting Fluids. (Cambridge Univ. Press, 1978)

  5. Brandenburg, A. & Subramanian, K. Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  6. Brandenburg, A. The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550, 824–840 (2001)

    Article  ADS  Google Scholar 

  7. LeBlanc, J. M. & Wilson, J. R. A numerical example of the collapse of a rotating magnetized star. Astrophys. J. 161, 541–551 (1970)

    Article  ADS  Google Scholar 

  8. Burrows, A., Dessart, L., Livne, E., Ott, C. D. & Murphy, J. Simulations of magnetically driven supernova and hypernova explosions in the context of rapid rotation. Astrophys. J. 664, 416–434 (2007)

    Article  CAS  ADS  Google Scholar 

  9. Mösta, P. et al. Magnetorotational core-collapse supernovae in three dimensions. Astrophys. J. Lett. 785, L29 (2014)

    Article  ADS  Google Scholar 

  10. Takiwaki, T. & Kotake, K. Gravitational wave signatures of magnetohydrodynamically driven core-collapse supernova explosions. Astrophys. J. 743, 30 (2011)

    Article  ADS  Google Scholar 

  11. Akiyama, S., Wheeler, J. C., Meier, D. L. & Lichtenstadt, I. The magnetorotational instability in core-collapse supernova explosions. Astrophys. J. 584, 954–970 (2003)

    Article  ADS  Google Scholar 

  12. Thompson, T. A., Quataert, E. & Burrows, A. Viscosity and rotation in core-collapse supernovae. Astrophys. J. 620, 861–877 (2005)

    Article  CAS  ADS  Google Scholar 

  13. Drout, M. R. et al. The first systematic study of type Ibc supernova multi-band light curves. Astrophys. J. 741, 97 (2011)

    Article  ADS  Google Scholar 

  14. Soderberg, A. M. et al. Relativistic ejecta from X-ray flash XRF 060218 and the rate of cosmic explosions. Nature 442, 1014–1017 (2006)

    Article  CAS  ADS  Google Scholar 

  15. Hjorth, J. & Bloom, J. S. in Gamma-Ray Bursts (eds Wijers, R. A. M. J. & Woosley, S .) Ch. 9 (Cambridge Univ. Press, 2012)

  16. Modjaz, M. Stellar forensics with the supernova-GRB connection. Astron. Nachr. 332, 434–447 (2011)

    Article  CAS  ADS  Google Scholar 

  17. Obergaulinger, M., Cerdá-Durán, P., Müller, E. & Aloy, M. A. Semi-global simulations of the magneto-rotational instability in core collapse supernovae. Astron. Astrophys. 498, 241–271 (2009)

    Article  CAS  ADS  Google Scholar 

  18. Masada, Y., Takiwaki, T. & Kotake, K. Magnetohydrodynamic turbulence powered by magnetorotational instability in nascent protoneutron stars. Astrophys. J. Lett. 798, L22 (2015)

    Article  ADS  Google Scholar 

  19. Guilet, J., Müller, E. & Janka, H.-T. Neutrino viscosity and drag: impact on the magnetorotational instability in protoneutron stars. Mon. Not. R. Astron. Soc. 447, 3992–4003 (2015)

    Article  CAS  ADS  Google Scholar 

  20. Sawai, H., Yamada, S. & Suzuki, H. Global simulations of magnetorotational instability in the collapsed core of a massive star. Astrophys. J. Lett. 770, L19 (2013)

    Article  ADS  Google Scholar 

  21. Galama, T. J. et al. An unusual supernova in the error box of the γ-ray burst of 25 April 1998. Nature 395, 670–672 (1998)

    Article  CAS  ADS  Google Scholar 

  22. Woosley, S. E. & Heger, A. The progenitor stars of gamma-ray bursts. Astrophys. J. 637, 914–921 (2006)

    Article  CAS  ADS  Google Scholar 

  23. Thompson, C. & Duncan, R. C. Neutron star dynamos and the origins of pulsar magnetism. Astrophys. J. 408, 194–217 (1993)

    Article  ADS  Google Scholar 

  24. Duncan, R. C. & Thompson, C. Formation of very strongly magnetized neutron stars—implications for gamma-ray bursts. Astrophys. J. Lett. 392, L9–L13 (1992)

    Article  CAS  ADS  Google Scholar 

  25. Nicholl, M. et al. Slowly fading super-luminous supernovae that are not pair-instability explosions. Nature 502, 346–349 (2013)

    Article  CAS  ADS  Google Scholar 

  26. Greiner, J. et al. A very luminous magnetar-powered supernova associated with an ultra-long γ-ray burst. Nature 523, 189–192 (2015)

    Article  CAS  ADS  Google Scholar 

  27. Wheeler, J. C., Meier, D. L. & Wilson, J. R. Asymmetric supernovae from magnetocentrifugal jets. Astrophys. J. 568, 807–819 (2002)

    Article  CAS  ADS  Google Scholar 

  28. Pessah, M. E. & Goodman, J. On the saturation of the magnetorotational instability via parasitic modes. Astrophys. J. Lett. 698, L72–L76 (2009)

    Article  ADS  Google Scholar 

  29. Goodman, J. & Xu, G. Parasitic instabilities in magnetized, differentially rotating disks. Astrophys. J. 432, 213–223 (1994)

    Article  ADS  Google Scholar 

  30. Ott, C. D., Burrows, A., Thompson, T. A., Livne, E. & Walder, R. The spin periods and rotational profiles of neutron stars at birth. Astrophys. J. (Suppl.) 164, 130–155 (2006)

    Article  CAS  ADS  Google Scholar 

  31. Heger, A. & Langer, N. Presupernova evolution of rotating massive stars. II. Evolution of the surface properties. Astrophys. J. 544, 1016–1035 (2000)

    Article  CAS  ADS  Google Scholar 

  32. Wheeler, J. C., Kagan, D. & Chatzopoulos, E. The role of the magnetorotational instability in massive stars. Astrophys. J. 799, 85 (2015)

    Article  ADS  Google Scholar 

  33. Mösta, P. et al. GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit. Class. Quantum Gravity 31, 015005 (2014)

    Article  ADS  Google Scholar 

  34. Obergaulinger, M., Aloy, M. A. & Müller, E. Axisymmetric simulations of magneto-rotational core collapse: dynamics and gravitational wave signal. Astron. Astrophys. 450, 1107–1134 (2006)

    Article  ADS  Google Scholar 

  35. Winteler, C. et al. Magnetorotationally driven supernovae as the origin of early galaxy r-process elements? Astrophys. J. Lett. 750, L22 (2012)

    Article  ADS  Google Scholar 

  36. Nishimura, N., Takiwaki, T. & Thielemann, F.-K. The r-process nucleosynthesis in the various jet-like explosions of magnetorotational core-collapse supernovae. Astrophys. J. 810, 109 (2015)

    Article  ADS  Google Scholar 

  37. Balbus, S. A. & Hawley, J. F. Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1–53 (1998)

    Article  ADS  Google Scholar 

  38. Löffler, F. et al. The Einstein toolkit: a community computational infrastructure for relativistic astrophysics. Class. Quantum Gravity 29, 115001 (2012)

    Article  ADS  Google Scholar 

  39. Reisswig, C. et al. Three-dimensional general-relativistic hydrodynamic simulations of binary neutron star coalescence and stellar collapse with multipatch grids. Phys. Rev. D 87, 064023 (2013)

    Article  ADS  Google Scholar 

  40. Tchekhovskoy, A., McKinney, J. C. & Narayan, R. WHAM: a WENO-based general relativistic numerical scheme. I. Hydrodynamics. Mon. Not. R. Astron. Soc. 379, 469–497 (2007)

    Article  ADS  Google Scholar 

  41. Einfeldt, B. in Shock Tubes and Waves (ed. Groenig, H. ) 671–676 (VCH, 1988)

  42. Tóth, G. The ∇ ⋅ B = 0 constraint in shock-capturing magnetohydrodynamics codes. J. Comput. Phys. 161, 605–652 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  43. Lattimer, J. M. & Douglas Swesty, F. A generalized equation of state for hot, dense matter. Nucl. Phys. A 535, 331–376 (1991)

    Article  ADS  Google Scholar 

  44. O’Connor, E. & Ott, C. D. A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes. Class. Quantum Gravity 27, 4103 (2010)

    MathSciNet  MATH  Google Scholar 

  45. Ott, C. D. et al. Correlated gravitational wave and neutrino signals from general-relativistic rapidly rotating iron core collapse. Phys. Rev. D 86, 024026 (2012)

    Article  ADS  Google Scholar 

  46. Bogovalov, S. V. Boundary conditions and critical surfaces in astrophysical MHD winds. Astron. Astrophys. 323, 634–643 (1997)

    CAS  ADS  Google Scholar 

  47. Eswaran, V. & Pope, S. B. An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16, 257–278 (1988)

    Article  ADS  Google Scholar 

  48. Frisch, U. Turbulence. The Legacy of A. N. Kolmogorov (Cambridge Univ. Press, 1995)

  49. Zrake, J. & MacFadyen, A. I. Magnetic energy production by turbulence in binary neutron star mergers. Astrophys. J. Lett. 769, L29 (2013)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank S. Couch, J. Zrake, D. Tsang, C. Wheeler, E. Bentivegna and I. Hinder for discussions. This research was supported by National Science Foundation (NSF) grants AST-1212170, PHY-1151197 and OCI-0905046; by NASA through the Einstein Fellowship Program, grants PF5-160140 (to P.M.) and PF3-140114 (to L.F.R.); by a National Science and Engineering Research Council of Canada (NSERC) award to E.S.; and by the Sherman Fairchild Foundation. The simulations were carried out on the NSF/National Center for Supercomputing Applications (NCSA) BlueWaters supercomputer (PRAC ACI-1440083).

Author information

Authors and Affiliations

  1. TAPIR, Walter Burke Institute for Theoretical Physics, Mailcode 350-17, California Institute of Technology, Pasadena, 91125, California, USA

    Philipp Mösta, Christian D. Ott, David Radice & Luke F. Roberts

  2. Department of Astronomy, 501 Campbell Hall #3411, University of California at Berkeley, Berkeley, 94720, California, USA

    Philipp Mösta

  3. Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5, Ontario, Canada

    Erik Schnetter

  4. Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada

    Erik Schnetter

  5. Center for Computation & Technology, Louisiana State University, Baton Rouge, 70803, Louisiana, USA

    Erik Schnetter

  6. Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, Potsdam-Golm, 14476, Germany

    Roland Haas

Authors
  1. Philipp Mösta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian D. Ott
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Radice
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luke F. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Erik Schnetter
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Roland Haas
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P.M. contributed to project planning and leadership, simulation code development, simulations, simulation analysis, visualization, interpretation of results and manuscript preparation. C.D.O. led the group, conceived the idea for the project, and contributed to project planning and leadership, interpretation and manuscript preparation. D.R. contributed to simulation analysis, interpretation, simulation code development and manuscript preparation. L.F.R. interpreted the results and reviewed the manuscript. E.S. contributed to simulation code development and manuscript review. R.H. contributed to development of the simulation code and visualization software, and reviewed the manuscript.

Corresponding author

Correspondence to Philipp Mösta.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Evolution of the maximum poloidal magnetic field.

Both panels show the maximum poloidal magnetic field, Bp, as a function of time for the four resolutions: 500 m, 200 m, 100 m and 50 m. a, The global maximum field. b, The maximum field in a thin layer above and below the equatorial plane (−7.5 km ≤ z ≤ 7.5 km). The purple line indicates exponential growth with an exponential-folding time, τFGM, of 0.5 ms.

Extended Data Figure 2 Background flow stability analysis.

a, b, The stability criterion CMRI 20 ms after core bounce for the initial stellar collapse simulation. a, A two-dimensional x–y slice (z = 0) through the three-dimensional domain; b, an x–z slice (y = 0). Yellow and red indicate regions that are stable to shearing modes; dark blue and light blue indicate unstable regions. c, The wavelength, λFGM, of the FGM of the MRI. d, The growth time of the FGM, τFGM. Panels c and d are zoomed in on the shear layer around the protoneutron star.

Extended Data Figure 3 Angle-averaged poloidal magnetic current and magnetic flux.

All panels show r–z slices (cylindrical coordinates, angle-averaged in φ) of the poloidal magnetic current (Jpol, colour-coded) and superposed contours of magnetic flux (black lines) at t − tmap = 10.3 ms (final simulated time). a, The 500-m simulation; b, the 200-m simulation; c, the 100-m simulation; d, the 50-m simulation.

Extended Data Figure 4 Angle-averaged poloidal magnetic current and velocity vectors.

The figure shows r–z slices (cylindrical coordinates, angle-averaged in φ) of the poloidal magnetic current (Jpol, colour-coded) and superposed velocity vectors (red arrows) at t − tmap = 10.3 ms (final simulated time).

Extended Data Figure 5 AMR stellar collapse simulation.

All panels show profiles along the x direction of the initial stellar collapse simulation, 20 ms after core bounce. a, Density (ρ); b, entropy (s), kB is the Boltzmann constant; c, angular velocity (vang); d, fast magnetosonic speed (vfms).

Extended Data Figure 6 AMR stellar collapse simulation.

All panels show profiles along the z direction of the initial stellar collapse simulation, 20 ms after core bounce. a, Density; b, entropy; c, fast magnetosonic speed.

Extended Data Figure 7 Non-densitized turbulent kinetic and electromagnetic energy spectra.

a, A time series of non-densitized turbulent kinetic energy spectra, Ekin(k), compensated for Kolmogorov scaling (k−5/3), as a function of the dimensionless wavenumber k. b, A time series of non-densitized magnetic energy spectra, Emag(k), as a function of the dimensionless wavenumber k. In both panels, the initial spectrum at t − tmap = 0 ms (dashed black line) is shown for reference.

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mösta, P., Ott, C., Radice, D. et al. A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae. Nature 528, 376–379 (2015). https://doi.org/10.1038/nature15755

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature15755

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing