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

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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.

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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.

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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

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.

Correspondence to Philipp Mösta.

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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.

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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) doi:10.1038/nature15755

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