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:

A comprehensive three-dimensional radiative magnetohydrodynamic simulation of a solar flare

Nature Astronomy volume 3, pages 160–166 (2019)Cite this article

Subjects

Abstract

Solar and stellar flares are the most intense emitters of X-rays and extreme ultraviolet radiation in planetary systems1,2. On the Sun, strong flares are usually found in newly emerging sunspot regions3. The emergence of these magnetic sunspot groups leads to the accumulation of magnetic energy in the corona. When the magnetic field undergoes abrupt relaxation, the energy released powers coronal mass ejections as well as heating plasma to temperatures beyond tens of millions of kelvins. While recent work has shed light on how magnetic energy and twist accumulate in the corona4 and on how three-dimensional magnetic reconnection allows for rapid energy release5,6, a self-consistent model capturing how such magnetic changes translate into observable diagnostics has remained elusive. Here, we present a comprehensive radiative magnetohydrodynamics simulation of a solar flare capturing the process from emergence to eruption. The simulation has sufficient realism for the synthesis of remote sensing measurements to compare with observations at visible, ultraviolet and X-ray wavelengths. This unifying model allows us to explain a number of well-known features of solar flares7, including the time profile of the X-ray flux during flares, origin and temporal evolution of chromospheric evaporation and condensation, and sweeping of flare ribbons in the lower atmosphere. Furthermore, the model reproduces the apparent non-thermal shape of coronal X-ray spectra, which is the result of the superposition of multi-component super-hot plasmas8 up to and beyond 100 million K.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Fig. 1: Synthetic X-ray flux time profiles and associated hot plasma.
Fig. 2: Doppler velocity maps and velocity profiles for plasma at various temperatures.
Fig. 3: Synthetic X-ray spectrum and EUV/X-ray emission maps at t = −9 s.

Similar content being viewed by others

Data availability

We have opted not to make the MURaM code publicly available. The codebase is frequently updated, and running the code in an appropriate and efficient manner requires expert assistance. The numerical methods employed by the code are provided in detail in refs 17,50. Interested parties are invited to contact the authors for more detailed information. Simulation snapshots are available for download from the Stanford Digital Repository (https://purl.stanford.edu/dv883vb9686). The repository also provides Interactive Data Language and Python routines for analysing the simulation data.

References

  1. Priest, E. R. & Forbes, T. G. The magnetic nature of solar flares. Astron. Astrophys. Rev. 10, 313–377 (2002).

    Article  ADS  Google Scholar 

  2. Shibata, K. & Magara, T. Solar flares: magnetohydrodynamic processes. Living Rev. Solar Phys. 8, 6 (2011).

    Article  ADS  Google Scholar 

  3. Schrijver, C. J. Driving major solar flares and eruptions: a review. Adv. Space Res. 43, 739–755 (2009).

    Article  ADS  Google Scholar 

  4. Fisher, G. H. et al. The coronal global evolutionary model: using HMI vector magnetogram and Doppler data to model the buildup of free magnetic energy in the solar corona. Space Weather 13, 369–373 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Wyper, P. F., Antiochos, S. K. & DeVore, C. R. A universal model for solar eruptions. Nature 544, 452–455 (2017).

    Article  ADS  Google Scholar 

  7. Benz, A. O. Flare observations. Living Rev. Solar Phys. 5, 1 (2008).

    Article  ADS  Google Scholar 

  8. Caspi, A. & Lin, R. P. RHESSI line and continuum observations of super-hot flare plasma. Astrophys. J. Lett. 725, L161–L166 (2010).

    Article  ADS  Google Scholar 

  9. Fisher, G. H., Canfield, R. C. & McClymont, A. N. Flare loop radiative hydrodynamics. VI. Chromospheric evaporation due to heating by nonthermal electrons. Astrophys. J. 289, 425–433 (1985).

    Article  ADS  Google Scholar 

  10. Reeves, K. K., Warren, H. P. & Forbes, T. G. Theoretical predictions of X-ray and extreme-UV flare emissions using a loss-of-equilibrium model of solar eruptions. Astrophys. J. 668, 1210–1220 (2007).

    Article  ADS  Google Scholar 

  11. Longcope, D. W., Guidoni, S. E. & Linton, M. G. Gas-dynamic shock heating of post-flare loops due to retraction following localized, impulsive reconnection. Astrophys. J. Lett. 690, L18–L22 (2009).

    Article  ADS  Google Scholar 

  12. Takasao, S., Matsumoto, T., Nakamura, N. & Shibata, K. Magnetohydrodynamic shocks in and above post-flare loops: two-dimensional simulation and a simplified model. Astrophys. J. 805, 135 (2015).

    Article  ADS  Google Scholar 

  13. Kusano, K. et al. Magnetic field structures triggering solar flares and coronal mass ejections. Astrophys. J. 760, 31 (2012).

    Article  ADS  Google Scholar 

  14. Janvier, M., Aulanier, G. & Démoulin, P. From coronal observations to MHD simulations, the building blocks for 3D models of solar flares (invited review). Solar Phys. 290, 3425–3456 (2015).

    Article  ADS  Google Scholar 

  15. Kleint, L. et al. The fast filament eruption leading to the X-flare on 2014 March 29. Astrophys. J. 806, 9 (2015).

    Article  ADS  Google Scholar 

  16. Young, P. R., Tian, H. & Jaeggli, S. The 2014 March 29 X-flare: subarcsecond resolution observations of Fe XXI λ1354.1. Astrophys. J. 799, 218 (2015).

    Article  ADS  Google Scholar 

  17. Rempel, M. Extension of the MURaM radiative MHD code for coronal simulations. Astrophys. J. 834, 10 (2017).

    Article  ADS  Google Scholar 

  18. Archontis, V. & Török, T. Eruption of magnetic flux ropes during flux emergence. Astron. Astrophys. 492, L35–L38 (2008).

    Article  ADS  Google Scholar 

  19. Aulanier, G., Török, T., Démoulin, P. & DeLuca, E. E. Formation of torus-unstable flux ropes and electric currents in erupting sigmoids. Astrophys. J. 708, 314–333 (2010).

    Article  ADS  Google Scholar 

  20. Cheng, X., Zhang, J., Liu, Y. & Ding, M. D. Observing flux rope formation during the impulsive phase of a solar eruption. Astrophys. J. Lett. 732, L25 (2011).

    Article  ADS  Google Scholar 

  21. Nindos, A., Patsourakos, S., Vourlidas, A. & Tagikas, C. How common are hot magnetic flux ropes in the low solar corona? A statistical study of EUV observations. Astrophys. J. 808, 117 (2015).

    Article  ADS  Google Scholar 

  22. Yokoyama, T. & Shibata, K. Magnetohydrodynamic simulation of a solar flare with chromospheric evaporation effect based on the magnetic reconnection model. Astrophys. J. 549, 1160–1174 (2001).

    Article  ADS  Google Scholar 

  23. Reep, J. W., Bradshaw, S. J. & Alexander, D. Optimal electron energies for driving chromospheric evaporation in solar flares. Astrophys. J. 808, 177 (2015).

    Article  ADS  Google Scholar 

  24. Fletcher, L. & Hudson, H. S. Impulsive phase flare energy transport by large-scale Alfvén waves and the electron acceleration problem. Astrophys. J. 675, 1645–1655 (2008).

    Article  ADS  Google Scholar 

  25. Kowalski, A. F., Allred, J. C., Daw, A., Cauzzi, G. & Carlsson, M. The atmospheric response to high nonthermal electron beam fluxes in solar flares. I. Modeling the brightest NUV footpoints in the X1 solar flare of 2014 March 29. Astrophys. J. 836, 12 (2017).

    Article  ADS  Google Scholar 

  26. Del Zanna, G., Schmieder, B., Mason, H., Berlicki, A. & Bradshaw, S. The gradual phase of the X17 flare on October 28, 2003. Solar Phys. 239, 173–191 (2006).

    Article  ADS  Google Scholar 

  27. Milligan, R. O. & Dennis, B. R. Velocity characteristics of evaporated plasma using hinode/EUV imaging spectrometer. Astrophys. J. 699, 968–975 (2009).

    Article  ADS  Google Scholar 

  28. Jeffrey, N. L. S., Fletcher, L. & Labrosse, N. First evidence of non-Gaussian solar flare EUV spectral line profiles and accelerated non-thermal ion motion. Astron. Astrophys. 590, A99 (2016).

    Article  ADS  Google Scholar 

  29. Liu, W., Petrosian, V., Dennis, B. R. & Jiang, Y. W. Double coronal hard and soft X-ray source observed by RHESSI: evidence for magnetic reconnection and particle acceleration in solar flares. Astrophys. J. 676, 704–716 (2008).

    Article  ADS  Google Scholar 

  30. Krucker, S. & Battaglia, M. Particle densities within the acceleration region of a solar flare. Astrophys. J. 780, 107 (2014).

    Article  ADS  Google Scholar 

  31. Boris, J. P. A Physically Motivated Solution of the Alfvén Problem NRL Memorandum Report 2167 (Naval Research Laboratory, 1970).

  32. Gombosi, T. I. et al. Semirelativistic magnetohydrodynamics and physics-based convergence acceleration. J. Comput. Phys. 177, 176–205 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  33. Gombosi, T. I., Jokipii, J. R., Kota, J., Lorencz, K. & Williams, L. L. The telegraph equation in charged particle transport. Astrophys. J. 403, 377–384 (1993).

    Article  ADS  Google Scholar 

  34. Snodin, A. P., Brandenburg, A., Mee, A. J. & Shukurov, A. Simulating field-aligned diffusion of a cosmic ray gas. Mon. Not. R. Astron. Soc. 373, 643–652 (2006).

    Article  ADS  Google Scholar 

  35. Rempel, M. Numerical simulations of quiet Sun magnetism: on the contribution from a small-scale dynamo. Astrophys. J. 789, 132 (2014).

    Article  ADS  Google Scholar 

  36. Judge, P. G., Kleint, L., Donea, A., Sainz Dalda, A. & Fletcher, L. On the origin of a sunquake during the 2014 March 29X1 flare. Astrophys. J. 796, 85 (2014).

    Article  ADS  Google Scholar 

  37. 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 

  38. Li, Y., Ding, M. D., Qiu, J. & Cheng, J. X. Chromospheric evaporation in an X1.0 flare on 2014 March 29 observed with IRIS and EIS. Astrophys. J. 811, 7 (2015).

    Article  ADS  Google Scholar 

  39. Rubio da Costa, F., Kleint, L., Petrosian, V., Liu, W. & Allred, J. C. Data-driven radiative hydrodynamic modeling of the 2014 March 29 X1.0 solar flare. Astrophys. J. 827, 38 (2016).

    Article  ADS  Google Scholar 

  40. Liu, C. et al. A circular-ribbon solar flare following an asymmetric filament eruption. Astrophys. J. Lett. 812, L19 (2015).

    Article  ADS  Google Scholar 

  41. Fan, Y. The emergence of a twisted flux tube into the solar atmosphere: sunspot rotations and the formation of a coronal flux rope. Astrophys. J. 697, 1529–1542 (2009).

    Article  ADS  Google Scholar 

  42. Manchester, W. B. IV Solar atmospheric dynamic coupling due to shear motions driven by the Lorentz force. Astrophys. J. 666, 532–540 (2007).

    Article  ADS  Google Scholar 

  43. Antiochos, S. K., DeVore, C. R. & Klimchuk, J. A. A model for solar coronal mass ejections. Astrophys. J. 510, 485–493 (1999).

    Article  ADS  Google Scholar 

  44. Lynch, B. J., Antiochos, S. K., DeVore, C. R., Luhmann, J. G. & Zurbuchen, T. H. Topological evolution of a fast magnetic breakout CME in three dimensions. Astrophys. J. 683, 1192–1206 (2008).

    Article  ADS  Google Scholar 

  45. Manchester, W. B. IV, Gombosi, T., DeZeeuw, D. & Fan, Y. Eruption of a buoyantly emerging magnetic flux rope. Astrophys. J. 610, 588–596 (2004).

    Article  ADS  Google Scholar 

  46. Jiang, C. et al. Data-driven magnetohydrodynamic modelling of a flux-emerging active region leading to solar eruption. Nat. Commun. 7, 11522 (2016).

    Article  ADS  Google Scholar 

  47. Hansteen, V. H., Hara, H., De Pontieu, B. & Carlsson, M. On redshifts and blueshifts in the transition region and corona. Astrophys. J. 718, 1070–1078 (2010).

    Article  ADS  Google Scholar 

  48. Cheung, M. C. M. & DeRosa, M. L. A method for data-driven simulations of evolving solar active regions. Astrophys. J. 757, 147 (2012).

    Article  ADS  Google Scholar 

  49. Cheung, M. C. M. et al. Homologous helical jets: observations by IRIS, SDO, and Hinode and magnetic modeling with data-driven simulations. Astrophys. J. 801, 83 (2015).

    Article  ADS  Google Scholar 

  50. Vögler, A. et al. Simulations of magneto-convection in the solar photosphere. Equations, methods, and results of the MURaM code. Astron. Astrophys. 429, 335–351 (2005).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support from NASA's Heliophysics Grand Challenges Research grant 'Physics and Diagnostics of the Drivers of Solar Eruptions' (NNX14AI14G to the LMSAL). M.R. is supported by NASA grant NNX13AK54G. F.C. and A.M. are supported by the Advanced Study Program postdoctoral fellowship at NCAR. NCAR is sponsored by the National Science Foundation. We acknowledge high-performance computing support from Cheyenne (https://doi.org/10.5065/D6RX99HX), provided by NCAR's Computational and Information Systems Laboratory and sponsored by the National Science Foundation, as well as from the NASA High-End Computing programme through the NASA Advanced Supercomputing Division at Ames Research Center. Data are courtesy of the science teams of the SDO and IRIS. M.C.M.C., G.C., M.L.D. and B.D.P. acknowledge support from NASA's SDO/AIA (NNG04EA00C) contract to the LMSAL. P.T. acknowledges support from contracts 4101946323, 8100002705 and SP02H1701R from Lockheed Martin, and NASA contract NNM07AB07C, to the SAO. The AIA and Helioseismic and Magnetic Imager are instruments onboard the SDO—a mission for NASA's Living With a Star Program. IRIS is a NASA small explorer mission, developed and operated by the LMSAL, with mission operations executed at the NASA Ames Research Center, and major contributions to downlink communications funded by the Norwegian Space Center through an ESA PRODEX contract. This work is supported by NASA under contract NNG09FA40C (IRIS), European Research Council grant agreement number 291058 and contract 8100002705 from the LMSAL to the SAO. This research was also supported by the Research Council of Norway through grant 170935/V30.

Author information

Author notes

  1. These authors contributed equally: M. C. M. Cheung, M. Rempel.

Authors and Affiliations

  1. Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA, USA

    M. C. M. Cheung, G. Chintzoglou, J. Martínez-Sykora, A. Sainz Dalda, M. L. DeRosa, V. Hansteen & B. De Pontieu

  2. Stanford University, Stanford, CA, USA

    M. C. M. Cheung & A. Sainz Dalda

  3. High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO, USA

    M. Rempel, F. Chen, A. Malanushenko & S. W. McIntosh

  4. University Corporation for Atmospheric Research, Boulder, CO, USA

    G. Chintzoglou

  5. Smithsonian Astrophysical Observatory, Cambridge, MA, USA

    P. Testa

  6. Bay Area Environmental Research Institute, Petaluma, CA, USA

    J. Martínez-Sykora & A. Sainz Dalda

  7. Institute of Theoretical Astrophysics, University of Oslo, Oslo, Norway

    V. Hansteen, B. De Pontieu, M. Carlsson & B. Gudiksen

  8. Rosseland Centre for Solar Physics, University of Oslo, Oslo, Norway

    V. Hansteen, M. Carlsson & B. Gudiksen

Authors
  1. M. C. M. Cheung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Rempel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Chintzoglou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Testa
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. Martínez-Sykora
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. Sainz Dalda
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. M. L. DeRosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. A. Malanushenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. V. Hansteen
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. B. De Pontieu
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. M. Carlsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. B. Gudiksen
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. S. W. McIntosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.C.M.C. wrote code to synthesize and analyse remote sensing diagnostics from the numerical simulation, analysed SDO and IRIS data, managed the team of co-authors and contributed to writing the text. M.R. implemented the coronal extension of the MURaM radiative MHD code, conducted the MHD simulations, and contributed to data analysis and writing of the paper. G.C., M.L.D., V.H. and A.M. performed the analysis on the magnetic evolution of the simulated flare. F.C. performed the analysis on X-ray fluxes from the simulation. A.S.D. performed analysis on photospheric magnetic observables. P.T., B.D.P., M.C. and S.W.M. performed analysis on optically thin X-ray and EUV emission, and contributed to the text. J.M.-S. performed the analysis and wrote the text for the section on κ versus Gaussian distributions. M.C., B.G. and V.H. contributed to the extension of the numerical model to couple the convection zone with the atmosphere.

Corresponding author

Correspondence to M. C. M. Cheung.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figures 1–9, captions of Supplementary Videos 1–6

Supplementary Video 1

Animation of Fig. 2

Supplementary Video 2

Animation of Fig. 3

Supplementary Video 3

Animation of panel a of Supplementary Figure 1

Supplementary Video 4

Animation of Supplementary Figure 5

Supplementary Video 5

Animation of Supplementary Figure 7

Supplementary Video 6

Animation of Supplementary Figure 8

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheung, M.C.M., Rempel, M., Chintzoglou, G. et al. A comprehensive three-dimensional radiative magnetohydrodynamic simulation of a solar flare. Nat Astron 3, 160–166 (2019). https://doi.org/10.1038/s41550-018-0629-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-018-0629-3

This article is cited by

Search

Advanced 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