Solar flares are spectacular coronal events that release large amounts of energy. They are classified as either eruptive or confined1,2, depending on whether they are associated with a coronal mass ejection. Two types of model have been developed to identify the mechanism that triggers confined flares, although it has hitherto not been possible to decide between them because the magnetic field at the origin of the flares could not be determined with the required accuracy3,4,5,6,7,8. In the first type of model, the triggering is related to the topological complexity of the flaring structure, which implies the presence of magnetically singular surfaces9,10,11. This picture is observationally supported by the fact that radiative emission occurs near these features in many flaring regions12,13,14,15,16,17. The second type of model attributes a key role to the formation of a twisted flux rope, which becomes unstable. Its plausibility is supported by simulations18,19,20,21,22, by interpretations of some observations23,24 and by laboratory experiments25. Here we report modelling of a confined event that uses the measured photospheric magnetic field as input. We first use a static model to compute the slowly evolving magnetic state of the corona before the eruption, and then use a dynamical model to determine the evolution during the eruption itself. We find that a magnetic flux rope must be present throughout the entire event to match the field measurements. This rope evolves slowly before saturating and suddenly erupting. Its energy is insufficient to break through the overlying field, whose lines form a confining cage, but its twist is large enough to trigger a kink instability, leading to the confined flare, as previously suggested18,19. Topology is not the main cause of the flare, but it traces out the locations of the X-ray emission. We show that a weaker magnetic cage would have produced a more energetic eruption with a coronal mass ejection, associated with a predicted energy upper bound for a given region.
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We were granted access to the High Performance Computing resources of the Centre Informatique National de l’Enseignement Supérieur (CINES) and of the Institut du Développement et de Ressources en Informatique (IDRIS) under allocation 2016-16050438 made by Grand Equipement National de Calcul Intensif (GENCI) and also to the mesocentre Phymat of the Centre National de la Recherche Scientifique/École Polytechnique. We acknowledge support of the Centre National d’Etudes Spatiales (CNES) and of the Direction Générale de l’Armement (DGA). T.A. thanks R. Huart for discussions. The Solar Dynamics Observatory (SDO) data are courtesy of the National Aeronautics and Space Administration (NASA), and the SDO/HMI and AIA science teams.
The authors declare no competing financial interests.
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Extended data figures and tables
Evolution during the four hours preceding the eruption of the actual magnetic field energy (blue), the potential field energy (black), and the semi-open field energy (purple), expressed in physical units. The evolution of the twist is also plotted (red).
Set of selected flux ropes, including the central highly twisted flux rope and some ropes having a non-negligible twist of more than 0.5. These ropes are located around and above the major TFR and reveal a complex non-potential environment. Those in blue (red) are associated with a negative (positive) value of α.
a, Magnetogram at 21:00 ut with rectangles indicating the sample area in which the index n is computed. The yellow rectangle is located just below the TFR, while the black rectangle, used as a reference, is chosen outside it. b, Variation with altitude of the torus index computed above the sample areas shown in a (with the same colour coding) by using the horizontal component19 of the mean potential (current-free) magnetic field, 〈Bπ,h〉. The horizontal line indicates the critical value of the index often used for the torus instability, while the vertical one indicates the height of the TFR axis.
Variation of the magnetic intensity mean value above the rectangles shown in Extended Data Fig. 3a for the current-free solution (red curve), the force-free solution B′, computed by removing the photospheric electric current exterior to the base of the TFR (green curve), and the full force-free solution (B), computed by taking into account the total electric current (blue curve). The number ksi measures the degree of removal of those external currents, with ksi = 0 (ksi = 1) indicating total (no) removal. As in Extended Data Fig. 3, the vertical yellow line indicates the height of the TFR axis. a, The central rectangle; b, the reference rectangle outside the TFR area.
Evolution of the angle θi between the electric current vector and the magnetic field (a good measure of how force-free the solution is) during the iterations of the algorithm, as well as that of the diagnostic standard parameter 〈| fi|〉, measuring the divergence of the solution. i is the iteration number.
a, Selected field lines and set of different isosurfaces of the force-free scalar function α (red for positive values and blue for negative values) for the reconstructed pre-eruptive magnetic configuration of 24 October 2014 at 21:00 ut. b, Corresponding composite image from the AIA-131 Å and AIA-171 Å wavelength data. c, Synthetic emissivity computed by using the magnetic field and the electric current density of the reconstructed pre-eruptive magnetic configuration of 24 October 2014 at 21:00 ut.
a, AIA emission at 1,600 Å. b, Plot of the vertically integrated dissipation J2 (where J is the norm of the electric current density) above the regions with high values of the squashing factor33, as for the reconstructed pre-eruptive magnetic configuration of 24 October 2014 at 21:00 ut. This plot highlights the strong electric current regions, in which reconnection is expected to occur.
a, Selected field lines of the evolving magnetic configuration during the flare. b, AIA emission at 94 Å on 24 October 2014 at 22:00 ut. c, Synthetic emissivity computed by using the magnetic field and the electric current density of the evolving magnetic configuration during the flare.
Selected field lines of the configuration that evolved into a major coronal mass ejection from the pre-eruptive configuration of 24 October 2014 at 21:00 ut when flux cancellation was applied on a larger scale, including the magnetic cage, whose confinement effect has thus been weakened.
Comparison of the post-eruptive states obtained from the simulation after the full relaxation of the evolving unstable state (a) and using HMI vector magnetic data from 25 October 2014 (b).
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Amari, T., Canou, A., Aly, J. et al. Magnetic cage and rope as the key for solar eruptions. Nature 554, 211–215 (2018). https://doi.org/10.1038/nature24671
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