Data-driven Radiative Magnetohydrodynamics Simulations with the MURaM Code: the Emergence of Active Region 11158 and the X2.2 Flare

TL;DR

This work demonstrates a data-driven radiative MHD simulation of AR 11158 using MURaM, spanning emergence to eruption and applying a refined three-stage hybrid strategy. By driving the system with observed magnetic-field data and a calibrated energy-injection parameter, the authors capture the buildup of free magnetic energy, the formation and eruption of a flux rope, and a flare that yields a synthetic X-class GOES flux along with a CME-like shock and a Moreton-wave counterpart. The simulated flare ribbons and chromospheric responses arise self-consistently from energy deposition via conduction and pressure-gradient forces, with ribbons extending along the PIL and toward outer sunspots in a manner consistent with observations. Overall, the study establishes the viability of data-driven radiative MHD for realistic solar eruptions and provides a framework for investigating pre-eruption evolution, large-scale coronal dynamics, and the coupling across atmospheric layers.

Abstract

We present the application of the data-driven branch of the MURaM code to the extensively studied flare-productive active region 11158. We refine the hybrid model strategy, which was described in the earlier paper of this series, to model the emergence of the active region during 4 solar days starting shortly before 2011 February 11 and the eruption of an X2.2 flare on February 15. After 4 days of evolution, a major eruption of a magnetic flux rope occurs in the simulation at approximately 3 hours (3\% difference) before the real flare. The eruption leads to magnetic reconnection that contributes to bulk heating in the chromosphere and corona. The deposition of flare energy in the chromosphere causes strong condensations and evaporations, which fill hot post-flare loops and bright flare ribbons that exhibit separation and extension similar to the observed ribbon evolution. The synthesized soft X-ray flux corresponds to X class, which is close to the real event. The upward eruption of the flux rope leads to a piston-driven shock and horizontal expansion that exerts a strong downward impact on the lower atmosphere and generate an apparently fast-propagating chromospheric Moreton wave. We conclude that the data-driven radiative simulation of this active region can reproduce the key observational results of the real flare and demonstrate the great potential of this method for studying solar eruptions in a realistic corona environment.

Figures (6)

• Figure 1: The upper panels display the evolution of the observed radial magnetic field of AR 11158. The second row illustrates the coronal magnetic field in the zero-$\beta$ run. Fieldlines are calculated from static seed points that are uniformly distributed in a rectangular area covering the sunspots in the active region. The points of view are chosen according to the location of the real active region on the solar disk. The bottom row shows the evolution of the magnetic energy in the 4 days covered by the zero-$\beta$ run and the rapid decay of the magnetic energy in the radiative MHD runs during the eruption, as indicated by the gray banner.
• Figure 2: Course of the eruption. Panel (a) shows the horizontally averaged density from the combined data of the evo. and flare runs, which illustrate the slow rise and eruption of a plasma-hosting magnetic flux rope. The overlay black line plots the synthesized GOES 1-8Å soft X-ray flux, which indicates a flare above X class. Panels (b)--(g) present 3D visualizations of the plasma and magnetic field structures of the eruption. The corresponding time stamps are marked by the white dashed lines in Panel (a). The opacity of the features is chosen on the basis of the the plasma density in the erupted flux rope, whereas lower and higher values are made transparent. The magnetic field lines are calculated from seed points that are randomly distributed in the coronal volume above the sunspots. The color of the density features and fieldlines reflects the plasma temperature on a logarithmic scale.
• Figure 3: The emission measured line-of-sight velocity from a top view. It represents the Doppler velocity from a spectroscopic observation of an active region near the solar disk center. The original outputs of the emission measures and line-of-sight velocities at an interval of $\log T=$0.1 are binned to three temperature ranges, as indicated at the top panel of each column, and the rows correspond to three snapshots as marked in the first panel of each row.
• Figure 4: Piston-driven shock in the corona and the Moreton waves in the chromosphere. In the left column, Panel (a) presents the vertical velocity $v_{z}$ at $t=356$ s in a $y-z$ plane placed at $x=130$ Mm; Panels (b) and (c) are time-distance diagrams of $v_{z}$ along the vertical and horizontal slits, which are placed at the dashed lines in Panel (a), respectively. In the right column, Panel (d) shows $v_{z}$ in a horizontal layer at 2 Mm height; Panels (e) and (f) are time-distance diagrams of $v_{z}$ along the $y$- and $x$-slits, as indicated by the dashed lines in Panel (d), respectively.
• Figure 5: The flare ribbons at $t=410$ s. Only the lowermost 12.8 Mm (200 grid points) are considered in this analysis to highlight the emission in the lowest part of the domain and to exclude the contribution from ejected chromospheric plasma with the erupted flux rope. The first row displays emission measures binned to three wide temperature ranges. The second row shows the vertical component of field-aligned velocities, i.e., the upward evaporation flows, at the surface of a certain temperature, as indicated above Panels (d)--(f). Panels (g)--(i) present the vertical acceleration driven by the pressure gradient force along the magnetic field. Panels (j)--(l) illustrate the thermal conduction flux at these three temperature surfaces.