Letter | Published:

Magnetic cage and rope as the key for solar eruptions

Nature volume 554, pages 211215 (08 February 2018) | Download Citation


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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from $8.99

All prices are NET prices.


  1. 1.

    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)

  2. 2.

    , & Flare-CME models: an observational perspective. Sol. Phys. 290, 3457–3486 (2015)

  3. 3.

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

  4. 4.

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

  5. 5.

    , & Quantifying the topology and evolution of a magnetic flux rope associated with multi-flare activities. Astrophys. J. 824, 148 (2016)

  6. 6.

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

  7. 7.

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

  8. 8.

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

  9. 9.

    , , & A new topological approach to the question of the trigger for solar flares. Sov. Astron. 32, 308–314 (1988)

  10. 10.

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

  11. 11.

    , , , & Observations of an X-shaped ribbon flare in the Sun and its three-dimensional magnetic reconnection. Astrophys. J. 823, L13 (2016)

  12. 12.

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

  13. 13.

    , , & Magnetic reconnection: a common origin for flares and AR interconnecting arcs. Astron. Astrophys. 363, 779–788 (2000)

  14. 14.

    , , & Observation of a 3D magnetic null point. Astrophys. J. 837, 173 (2017)

  15. 15.

    , , , & Topological analysis of emerging bipole clusters producing violent solar events. Sol. Phys. 289, 2041–2071 (2014)

  16. 16.

    , , & Can we explain atypical solar flares? Astron. Astrophys. 574, A37 (2015)

  17. 17.

    , , & 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)

  18. 18.

    & Helicity redistribution during relaxation of astrophysical plasmas. Phys. Rev. Lett. 84, 1196–1199 (2000)

  19. 19.

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

  20. 20.

    , & Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop. Astron. Astrophys. 413, L23–L26 (2004)

  21. 21.

    , , & Thermal and non-thermal emission from reconnecting twisted coronal loops. Astron. Astrophys. 585, A159 (2016)

  22. 22.

    & Helical kink instability in a confined eruption. Astrophys. J. 832, 106 (2016)

  23. 23.

    , , & Formation and eruption of a small flux rope in the chromosphere observed by NST, IRIS and SDO. Astrophys. J. 809, 83 (2015)

  24. 24.

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

  25. 25.

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

  26. 26.

    , , , & IRIS, HINODE, SDO, and RHESSI observations of a white light flare produced directly by non-thermal electrons. Astrophys. J. 836, 150 (2017)

  27. 27.

    et al. in ASP Conference Series (eds , , & ) Vol. 459, 189 (Astronomical Society of the Pacific, 2012)

  28. 28.

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

  29. 29.

    , & Characterizing and predicting the magnetic environment leading to solar eruptions. Nature 514, 465–469 (2014)

  30. 30.

    , & A preconditioned semi implicit scheme for magnetohydrodynamics equations. SIAM J. Sci. Comput. 21, 970–986 (1999)

  31. 31.

    & Transformation of vector magnetograms and the problem associated with the effects of perspective and the azimuthal ambiguity. Sol. Phys. 126, 21–36 (1990)

  32. 32.

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

  33. 33.

    , , , & 2010 August 1–2 sympathetic eruptions. I. Magnetic topology of the source-surface background field. Astrophys. J. 759, 70 (2012)

  34. 34.

    Magnetohydrodynamics of the Sun (Cambridge Univ. Press, 2014)

  35. 35.

    , , & Reconstruction of the solar coronal magnetic field in spherical geometry. Astron. Astrophys. 553, A43 (2013)

  36. 36.

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

  37. 37.

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

  38. 38.

    , , & 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations. J. Comput. Phys. 222, 592–623 (2007)

  39. 39.

    , , & Magneto-frictional modeling of coronal nonlinear force-free fields. I. Testing with analytic solutions. Astrophys. J. 828, 82 (2016)

  40. 40.

    , , , & Coronal mass ejection: initiation, helicity and flux ropes. II. Turbulent diffusion driven evolution. Astrophys. J. 595, 1231–1250 (2003)

  41. 41.

    , , , & Coronal mass ejection initiation by converging photospheric flows: toward a realistic model. Astrophys. J. 742, L27 (2011)

  42. 42.

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

Download references


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


  1. CPHT, Ecole Polytechnique, CNRS, Université Paris-Saclay, Route de Saclay, 91128 Palaiseau, France.

    • Tahar Amari
  2. Centre de Physique Théorique, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.

    • Aurélien Canou
  3. Université Paris Diderot, AIM, Sorbonne Paris Cité, CEA, CNRS, F-91191 Gif-sur-Yvette, France

    • Jean-Jacques Aly
  4. LPTMC, UMR 7600 of CNRS, Université Pierre et Marie Curie, Paris, France.

    • Francois Delyon
  5. INRIA Saclay Ile-de-France, Projet Gamma 3, 1 rue Honoré d’Estienne d’Orves, 91126 Palaiseau, France

    • Fréderic Alauzet


  1. Search for Tahar Amari in:

  2. Search for Aurélien Canou in:

  3. Search for Jean-Jacques Aly in:

  4. Search for Francois Delyon in:

  5. Search for Fréderic Alauzet in:


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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Tahar Amari.

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

Extended data

About this article

Publication history







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.