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Characterizing and predicting the magnetic environment leading to solar eruptions



The physical mechanism responsible for coronal mass ejections has been uncertain for many years, in large part because of the difficulty of knowing the three-dimensional magnetic field in the low corona1. Two possible models have emerged. In the first, a twisted flux rope moves out of equilibrium or becomes unstable, and the subsequent reconnection then powers the ejection2,3,4,5. In the second, a new flux rope forms as a result of the reconnection of the magnetic lines of an arcade (a group of arches of field lines) during the eruption itself6. Observational support for both mechanisms has been claimed7,8,9. Here we report modelling which demonstrates that twisted flux ropes lead to the ejection, in support of the first model. After seeing a coronal mass ejection, we use the observed photospheric magnetic field in that region from four days earlier as a boundary condition to determine the magnetic field configuration. The field evolves slowly before the eruption, such that it can be treated effectively as a static solution. We find that on the fourth day a flux rope forms and grows (increasing its free energy). This solution then becomes the initial condition as we let the model evolve dynamically under conditions driven by photospheric changes (such as flux cancellation). When the magnetic energy stored in the configuration is too high, no equilibrium is possible and the flux rope is ‘squeezed’ upwards. The subsequent reconnection drives a mass ejection.

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Figure 1: Magnetic field evolution during the days before major eruption day D.
Figure 2: Twisted flux rope before the major eruption.
Figure 3: Accumulation of magnetic energy.
Figure 4: Evolution and eruption of the twisted flux rope.

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The numerical simulations described in this paper were performed on the IBM x3750 of the IDRIS institute of the Centre National de la Recherche Scientifique (CNRS). We thank the Centre National d’Etudes Spatiales (CNES) for its financial support. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway). Hα data used in this study were provided by Paris-Meudon Observatory, X-ray data came from Hinode/XRT and extreme-ultraviolet data came from SOHO/EIT.

Author information

Authors and Affiliations



T.A. and A.C. planned and performed the various calculations, and discussed the analysis with J.-J.A. The manuscript was written by T.A. and J.-J.A. with feedback from A.C.

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Correspondence to Tahar Amari.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Another multiscale model.

Full-Sun magnetic configuration obtained using composite data set (Hinode/SOT and SOLIS synoptic map) and the state-of-the-art numerical code MESHMHD, which is a tetrahedral adaptive-mesh equilibrium code. Local and global scales are both accessible using very high-resolution data around the active region and lower resolution elsewhere. The twisted rope obtained with XTRAPOL is fully recovered. a, Global view showing the disk of tetrahedral-cell mesh and the spherical photosphere, where we have indicated the various resolutions for the northern hemisphere and, in transparency behind the disk, for the southern hemisphere. b, Zoom onto the active region showing the high resolution used around it. c, Closer look at the rope, with a cut showing how the adaptive scheme allows high mesh resolution in the regions where the coronal electric current and magnetic field are stronger. d, Another point of view, exhibiting the large extent of the rope, which is still confined by the overlying field lines (orange).

Extended Data Figure 2 Hyperbolic flux tube.

a, Breaking of the twisted rope into various components to exhibit its hyperbolic nature, using the same colour code as in Fig. 1. b, Core of the rope, which is highly twisted (by about 2.25π). c, Underlying highly sheared arcades below the core. d, Two J-shaped arcades whose central parts become tangential to each other. e, One of the J-shaped set of loops (green) above the sheared arcades (yellow), becoming tangential to each other near the neutral line.

Extended Data Figure 3 Signature of the pre-eruptive current density of the reconstructed magnetic configuration of 12 December, 20:30 ut.

We have plotted here two isosurfaces of the force-free function α measuring the ratio of the electric current density to the magnetic field: a, α = −0.23 Mm−1; b, α = −0.05 Mm−1. These isosurfaces are coloured according to the values of the modulus of the current density, |j|. The large-scale structure of the twisted rope (and of small parts above) is well exhibited by this quantity α in a, in agreement with Fig. 2b, whereas weaker electric currents (overlying) structures are shown in b.

Extended Data Figure 4 Extreme-ultraviolet emission and magnetic structure.

Selected field lines of the reconstructed magnetic configuration of 12 December, 20:30 ut, overlaid on an SOHO/EIT extreme-ultraviolet emission image taken at 23:49 ut. The emission is well correlated with the magnetic lines in the region of the twisted rope and in the regions of approximately current-free loops, such as that located on the right-hand side of the rope.

Supplementary information

Evolution of the photospheric magnetic field. Evolution of the ratio V/I measured by HINODE/SOT/NFI between 2006 December 09, at 17:01 UT and 2006 December 12, at 20:00 UT.

V is the circular polarization and I the total intensity. V/I is similar to the line of sight component of the magnetic field. The field of view is expressed in Mm. As the southern sunspot emerge, it takes an elongated shape characteristic of the emergence of a twisted flux rope from below the photosphere. (MOV 3163 kb)

Emergence and formation of the Twisted Flux Rope. Animation showing the successive magnetic configurations computed from an extended set of data taken between 2006 December 09, and December 13.

It can be seen that, during the pre-eruptive phase, flux emergence occurs and magnetic shear correlatively increases along the neutral line until the appearance and formation of the rope on December 12. This animation also includes solutions obtained from data taken during the post-eruptive phase (December 13). They show clearly the relaxation of the configuration to a lower energy state in which the rope has disappeared. (MOV 1331 kb)

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Amari, T., Canou, A. & Aly, JJ. Characterizing and predicting the magnetic environment leading to solar eruptions. Nature 514, 465–469 (2014).

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