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


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.

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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.

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 ( The repository also provides Interactive Data Language and Python routines for analysing the simulation data.


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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 (, 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.

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Authors and Affiliations



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.

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Correspondence to M. C. M. Cheung.

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Supplementary Information

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

Supplementary Video 1

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Supplementary Video 2

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Supplementary Video 3

Animation of panel a of Supplementary Figure 1

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Supplementary Video 5

Animation of Supplementary Figure 7

Supplementary Video 6

Animation of Supplementary Figure 8

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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).

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