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:

Magnetic cage and rope as the key for solar eruptions

Abstract

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.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: Building magnetic input for the model.
Figure 2: Magnetic field evolution before the major flare.
Figure 3: TFR in the magnetic cage before the major confined eruption.
Figure 4: Evolution and confined instability of the TFR.

Similar content being viewed by others

References

  1. Schrijver, J. C. et al. Understanding space weather to shield society: a global road map for 2015–2025 commissioned by COSPAR and ILWS. Adv. Space Res. 55, 2745–2807 (2015)

    Article  ADS  Google Scholar 

  2. Schmieder, B., Aulanier, G. & Vrsnak, B. Flare-CME models: an observational perspective. Sol. Phys. 290, 3457–3486 (2015)

    Article  ADS  Google Scholar 

  3. Jiang, C. et al. How did a major confined flare occur in super solar active region 12192? Astrophys. J. 828, 62 (2016)

    Article  ADS  Google Scholar 

  4. Liu, R. et al. Structure, stability, and evolution of magnetic flux ropes from the perspective of magnetic twist. Astrophys. J. 818, 148 (2016)

    Article  ADS  Google Scholar 

  5. Yang, K., Guo, Y. & Ding, M. D. Quantifying the topology and evolution of a magnetic flux rope associated with multi-flare activities. Astrophys. J. 824, 148 (2016)

    Article  ADS  Google Scholar 

  6. Wang, H. et al. Witnessing magnetic twist with high-resolution observation from the 1.6-m new solar telescope. Nat. Commun. 6, 7008 (2015)

    Article  CAS  ADS  Google Scholar 

  7. Sun, X. et al. Why is the great solar active region 12192 flare-rich but CME-poor? Astrophys. J. 804, L28 (2015)

    Article  ADS  Google Scholar 

  8. Inoue, S., Hayashi, K. & Kusano, K. Structure and stability of magnetic fields in solar active region 12192 based on nonlinear force-free field modeling. Astrophys. J. 818, 168 (2016)

    Article  ADS  Google Scholar 

  9. Gorbachev, V. S., Kelner, S. R., Somov, B. V. & Shvarts, A. S. A new topological approach to the question of the trigger for solar flares. Sov. Astron. 32, 308–314 (1988)

    ADS  Google Scholar 

  10. Démoulin, P. et al. Quasi-separatrix layers in solar flares. I. Method. Astron. Astrophys. 308, 643–655 (1996)

    ADS  Google Scholar 

  11. Li, Y., Qiu, J., Longcope, D. W., Ding, M. D. & Yang, K. Observations of an X-shaped ribbon flare in the Sun and its three-dimensional magnetic reconnection. Astrophys. J. 823, L13 (2016)

    Article  ADS  Google Scholar 

  12. Mandrini, C. H. et al. Evidence of magnetic reconnection from H-alpha, soft X-ray and photospheric magnetic field observations. Sol. Phys. 174, 229–240 (1997)

    Article  ADS  Google Scholar 

  13. Bagalá, L. G., Mandrini, C. H., Rovira, M. G. & Démoulin, P. Magnetic reconnection: a common origin for flares and AR interconnecting arcs. Astron. Astrophys. 363, 779–788 (2000)

    ADS  Google Scholar 

  14. Romano, P., Falco, M., Guglielmino, S. L. & Mirabito, M. Observation of a 3D magnetic null point. Astrophys. J. 837, 173 (2017)

    Article  ADS  Google Scholar 

  15. Mandrini, C. H., Schmieder, B., Démoulin, P., Guo, Y. & Cristiani, G. D. Topological analysis of emerging bipole clusters producing violent solar events. Sol. Phys. 289, 2041–2071 (2014)

    Article  ADS  Google Scholar 

  16. Dalmasse, K., Chandra, R., Schmieder, B. & Aulanier, G. Can we explain atypical solar flares? Astron. Astrophys. 574, A37 (2015)

    Article  ADS  Google Scholar 

  17. Jiang, C., Feng, X., Wu, S. T. & Hu, Q. Study of the three-dimensional coronal magnetic field of active region 11117 around the time of a confined flare using a data driven CESE-MHD model. Astrophys. J. 759, 85 (2012)

    Article  ADS  Google Scholar 

  18. Amari, T. & Luciani, J. F. Helicity redistribution during relaxation of astrophysical plasmas. Phys. Rev. Lett. 84, 1196–1199 (2000)

    Article  CAS  ADS  Google Scholar 

  19. Török, T. & Kliem, B. Confined and ejective eruptions of kink-unstable flux ropes. Astrophys. J. 630, L97–L100 (2005)

    Article  ADS  Google Scholar 

  20. Kliem, B., Titov, V. S. & Torök, T. Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop. Astron. Astrophys. 413, L23–L26 (2004)

    Article  ADS  Google Scholar 

  21. Pinto, R., Gordovskyy, M., Browning, P. K. & Vilmer, N. Thermal and non-thermal emission from reconnecting twisted coronal loops. Astron. Astrophys. 585, A159 (2016)

    Article  ADS  Google Scholar 

  22. Hassanin, A. & Kliem, B. Helical kink instability in a confined eruption. Astrophys. J. 832, 106 (2016)

    Article  ADS  Google Scholar 

  23. Kumar, P., Yurchyshyn, V., Wang, H. & Cho, K. S. Formation and eruption of a small flux rope in the chromosphere observed by NST, IRIS and SDO. Astrophys. J. 809, 83 (2015)

    Article  ADS  Google Scholar 

  24. Chen, H. et al. Confined flare in solar active region 12192 from October 18 to 29. Astrophys. J. 808, L24 (2015)

    Article  ADS  Google Scholar 

  25. Myers, C. E. et al. A dynamic magnetic tension force as the cause of failed solar eruptions. Nature 528, 526–529 (2015)

    Article  CAS  ADS  Google Scholar 

  26. Lee, K.-S., Imada, S., Watanabe, K., Bamba, Y. & Brooks, D. H. IRIS, HINODE, SDO, and RHESSI observations of a white light flare produced directly by non-thermal electrons. Astrophys. J. 836, 150 (2017)

    Article  ADS  Google Scholar 

  27. Amari, T. et al. in ASP Conference Series (eds Pogorelov, N. V., Font, J. A., Audit, E. & Zank, G. P. ) Vol. 459, 189 (Astronomical Society of the Pacific, 2012)

    Google Scholar 

  28. DeRosa, M. L. et al. The influence of spatial resolution on nonlinear force-free modeling. Astrophys. J. 811, 107 (2015)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  30. Amari, T., Luciani, J. F. & Joly, P. A preconditioned semi implicit scheme for magnetohydrodynamics equations. SIAM J. Sci. Comput. 21, 970–986 (1999)

    Article  MathSciNet  Google Scholar 

  31. Allen Gary, G. & Hagyard, M. J. Transformation of vector magnetograms and the problem associated with the effects of perspective and the azimuthal ambiguity. Sol. Phys. 126, 21–36 (1990)

    Article  ADS  Google Scholar 

  32. Thompson, W. T. Coordinate systems for solar image data. Astron. Astrophys. 449, 791–803 (2006)

    Article  ADS  Google Scholar 

  33. Titov, V. S., Mikic, Z., Török, T., Linker, J. A. & Panasenco, O. 2010 August 1–2 sympathetic eruptions. I. Magnetic topology of the source-surface background field. Astrophys. J. 759, 70 (2012)

    Article  ADS  Google Scholar 

  34. Priest, E. R. Magnetohydrodynamics of the Sun (Cambridge Univ. Press, 2014)

  35. Amari, T., Aly, J.-J., Canou, A. & Mikic, Z. Reconstruction of the solar coronal magnetic field in spherical geometry. Astron. Astrophys. 553, A43 (2013)

    Article  Google Scholar 

  36. Amari, T. & Aly, J.-J. Observational constraints on well-posed reconstruction methods and the optimization-Grad-Rubin method. Astron. Astrophys. 522, A52 (2010)

    Article  ADS  Google Scholar 

  37. Wheatland, M. S. & Régnier, S. A Self-consistent nonlinear force-free solution for a solar active region magnetic field. Astrophys. J. 700, L88–L91 (2009)

    Article  ADS  Google Scholar 

  38. Alauzet, F., Frey, P. J., George, P. L. & Mohammadi, B. 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations. J. Comput. Phys. 222, 592–623 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  39. Guo, Y., Xia, C., Keppens, R. & Valori, G. Magneto-frictional modeling of coronal nonlinear force-free fields. I. Testing with analytic solutions. Astrophys. J. 828, 82 (2016)

    Article  ADS  Google Scholar 

  40. Amari, T., Luciani, J.-F., Aly, J.-J., Mikic, Z. & Linker, J. Coronal mass ejection: initiation, helicity and flux ropes. II. Turbulent diffusion driven evolution. Astrophys. J. 595, 1231–1250 (2003)

    Google Scholar 

  41. Amari, T., Aly, J.-J., Luciani, J.-F., Mikic, Z. & Linker, J. Coronal mass ejection initiation by converging photospheric flows: toward a realistic model. Astrophys. J. 742, L27 (2011)

    Article  ADS  Google Scholar 

  42. Taylor, J. B. Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33, 1139–1141 (1974)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Contributions

T.A. and A.C. planned and performed the various calculations and analysis discussed with J.-J.A. T.A. and F.A. worked on the mesh adaptation strategy while F.D. worked with T.A. on MESHMHD. The manuscript was written by T.A. and J.-J.A. with feedback from A.C.

Corresponding author

Correspondence to Tahar Amari.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Evolution of magnetic energies and twist.

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).

Extended Data Figure 2 Electric current structure of the magnetic environment.

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.

Extended Data Figure 3 Index of torus instability.

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.

Extended Data Figure 4 Role of volumetric current.

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.

Extended Data Figure 5 Quality of the reconstruction method.

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.

Extended Data Figure 6 Comparison with AIA data.

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.

Extended Data Figure 7 Comparison with AIA-1,600 Å wavelength.

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.

Extended Data Figure 8 Extreme-ultraviolet emission and magnetic structure.

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.

Extended Data Figure 9 Major eruption and role of the magnetic environment.

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.

Extended Data Figure 10 Post-eruptive state.

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).

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amari, T., Canou, A., Aly, JJ. et al. Magnetic cage and rope as the key for solar eruptions. Nature 554, 211–215 (2018). https://doi.org/10.1038/nature24671

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature24671

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

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