Examining the Effects of Magnetic Field Extrapolation on MHD Flare Simulations

Abstract

Solar flare simulations are commonly initialised using non-linear force free field (NLFF) extrapolations derived from photospheric vector magnetograms. However, the force free assumption neglects plasma forces and may limit the available free magnetic energy. In this work, we perform a controlled comparison of two three-dimensional resistive magnetohydrodynamic simulations of the X2.1-class flare that occurred on 2011 September 06 in NOAA Active Region 11283. The simulations differ only in their initial magnetic configuration: one is based on a conventional NLFF extrapolation, while the other employs a non-force free extrapolation that self-consistently incorporates plasma pressure and gravity. Both models are evolved in an identical stratified atmosphere using the same numerical framework, enabling direct assessment of how the initial magnetic assumptions influence flare dynamics and energetics. We find that the non-force free model undergoes more extensive magnetic restructuring and releases approximately twice as much magnetic energy ($\approx4.4 \times 10^{31}$ erg) as the NLFF case ($\approx2.3 \times 10^{31}$ erg), bringing the energy budget into closer agreement with expectations for X-class flares. Synthetic extreme ultraviolet emission in the 94A channel is computed for both simulations and compared with observations from the Solar Dynamics Observatory. The non-force free model produces a brighter and more spatially extended emission structure that more closely resembles the observed flare morphology and light curve. These results demonstrate that assumptions made in constructing the pre-flare coronal magnetic field can significantly affect flare energetics and observable signatures, and suggest that non-force free extrapolations provide a promising pathway toward more realistic data-constrained flare modelling.

Figures (7)

• Figure 1: In the left column, the NLFF extrapolation is shown and in the right, the non-force free. The magnetic field lines shown are seeded at the same locations in both, with the field line density proportional to magnetic field strength at the lower boundary. The lower surface in the top row is coloured according to $B_{z}$ at the lower boundary. The second row shows the value of slogQ calculated at the lower boundary for the NLFF and non-force free field extrapolations respectively. Blue corresponds to open field lines, and red to closed lines. The black contour shows an absolute value of vertical magnetic field of $0.2$ kG. The lower panel shows the vertical magnetic field at the lower boundary, the initial surface magnetogram of AR11283, taken on 2011 September 06 at 20:48 UTC from SDO/HMI. This has been saturated at $\pm1$ kG for ease of comparison.
• Figure 2: In the first panel, the Lorentz force summed in each layer of the extrapolations is shown on a log scale as a function of height. The solid line represents the NLFF model and the dashed line represents the non-force free model. In the second panel, this is recast as average acceleration per layer using force and density. Both dependent variables are presented in normalised units.
• Figure 3: The left column shows the results of the simulation initialised with the NLFF extrapolation, and the right shows the non-force free simulation. The rows show the following viewpoints: isometric, $x$, $y$, $z$. The red lines show field lines which are initially closed at $t=0$, which become open at $t=100t_{A}$ and are shown in purple. The blue lines show field lines at $t=0$ whose end points move by more than $5$ Mm across the solar surface to the green field lines shown at $t=100t_{A}$.
• Figure 4: In the top row, results of the simulation initialised with the NLFF extrapolation is shown and in the middle row, the non-force free. The left column shows the initial configuration, the next two columns show the simulation at $t=20,40$$t_{A}$. The magnetic field lines shown are seeded at the same locations in both, with the field line density proportional to magnetic field strength at the lower boundary. The red volume corresponds to the location where anomalous resistivity is active during that stage of the simulation. The bottom panel shows the mean height of the anomalous resistivity region in both simulations over time, with the NLFF and non-force free models being represented by the dashed and solid lines respectively.
• Figure 5: Energy over time for both the NLFF (dashed lines) and non-force free (solid lines) simulations. The first plot (cyan) shows magnetic energy, the second (purple) shows kinetic energy, the third (green) shows thermal energy, and the fourth shows all of them together with a log-scale for comparison.