Large Magnetic Flux Rope Formation in an X2.1 Flare observed on September 6, 2011

TL;DR

The paper addresses how a large magnetic flux rope (MFR) can form during a prominent solar flare by linking observed 3D magnetic topology with eruption dynamics. It combines NLFFF extrapolation to reconstruct preflare fields with data-constrained MHD simulations to track reconnection and twist transfer, revealing that reconnection among the sigmoidal core, adjacent fan-dome fields, and neighboring loops builds a rising MFR. A key finding is that twist quantified by the twist number $T_w$ is redistributed along the system, with MFR footpoints aligning with the circular flare ribbon and remote brightenings, thereby explaining the observed morphology and dimming signatures. While the results reproduce several observed features, the authors note limitations from the finite computational domain and bottom-boundary treatment, suggesting that larger domains and improved boundary conditions are needed to capture the full eruption evolution and acceleration.

Abstract

Solar active region 11283 produced an X2.1 flare associated with a solar eruption on September 6, 2011. Observations revealed a preflare sigmoidal structure and a circular flare ribbon surrounding the typical two ribbon structure, along with remote brightenings located at a considerable distance from the main flare site. To interpret these observations in terms of the three dimensional (3D) coronal magnetic field dynamics, we conducted data constrained magnetohydrodynamic (MHD) simulations. Using a non linear force free field (NLFFF) as the initial condition, we reconstructed a realistic pre flare magnetic environment, capturing a sheared sigmoid above the polarity inversion line (PIL) surmounted by a fan spine structure. Our simulations revealed that reconnection between the sigmoidal field, the adjacent fan dome field lines, and the neighboring large loops facilitated the transfer of magnetic twist and led to the formation of a large magnetic flux rope (MFR). This transfer and propagation of twist are clearly visible throughout the MFR. As reconnection progresses, the entire fan spine structure expands along with the evolving MFR. A notable outcome of the simulation is that the footpoints of the newly formed MFR align closely with the observed circular flare ribbon and the remote brightening region. Our findings suggest that a large MFR formed during the X2.1 flare, providing a coherent explanation for the observed phenomena.

Figures (13)

• Figure 1: (a) Full-disk AIA 131 Å image of the Sun during the X2.1 flare onset (SOL2011-09-06T22:18), with AR11283 enclosed within a white box. (b) Time evolution of the GOES-15 satellite soft X-ray flux during the flare, recorded between 21:00 UT and 23:30 UT on September 6, 2011. The 0.5–4.0 Å and 1.0–8.0 Å passbands are plotted in blue and red, respectively. Vertical dashed black lines indicate the start and end times of the flare event.
• Figure 2: (a) Photospheric radial magnetic field ($B_z$) of AR 11283 at 20:36 UT on September 6, 2011, used as the bottom boundary for all simulations. Positive and negative magnetic fields are shown in white and black, respectively, with $B_z$ normalized by $B_0$ (= 0.24 T). The four major magnetic polarities are labeled as P0, P1, P2, and N. The region spans approximately 180 × 180 Mm$^2$. (b) AIA 171 Å snapshot of the same region near the flare onset time (22:00:49 UT). The blue arrow highlights an S-shaped brightening, the white arrow indicates circular loops above the S-shaped brightening, and the yellow arrows mark large neighboring coronal loops. (c) Top view of the extrapolated 3D coronal magnetic field lines illustrating the magnetic connectivity in the region. The red field lines represent the low-lying, sheared magnetic fields aligned along the polarity inversion line (PIL). The cyan field lines outline a dome-shaped structure connected remotely to P0, forming a fan-like topology. The yellow field lines trace the surrounding, large-scale coronal loops. The inset provides a zoomed-in view of the core magnetic structure, where the cyan fan-like field lines pass through a null point (NP) marked in purple. (d) 3D magnetic field lines overlaid on the AIA 171 Å image from panel (b).
• Figure 3: (a) Iso-surface of current density ($|\bm{J}|) = 40$ in cyan, corresponding to the critical current in the anomalous resistivity, overlaid on the radial magnetic field ($B_z$). The inset provides a view of the same isosurface from a different field of view (FOV). (b–d) Side views of the 3D magnetic field configuration: (b) NLFFF, (c) MHD simulation Run 2b at $t=1.2$, and (d) Run 2c at $t=1.2$, with footpoints (FPs) of the sigmoid marked in cyan. (e) Temporal evolution of kinetic energy for Runs 2a (green), 2b (blue), and 2c (red). The vertical dashed black line marks $t=1.2$, where the magnetic fields from Run 2c serve as the initial condition for Run 2d. (f, g) Magnetic twist maps corresponding to the field lines in (b) and (d), respectively, taken at approximately 720 km above the surface. In (f), the red arrow indicates a region with a twist number ranging from half a turn to one full turn. In (g), black circles mark regions where the twist exceeds one full turn. The inset panel presents field lines traced from these highlighted regions.
• Figure 4: Formation and temporal evolution of the MFR during the data-constrained MHD simulation (Run 2d). (a) and (b) show side and top views of the magnetic field lines, respectively, colored by the vertical velocity component ($V_z$). The vertical slice in (a) displays the $|\bm{J}|/|\bm{B}|$ distribution. In panel (a), at t = 7.2, the green arrow marks the presence of MHD waves ahead of the rising MFR. (c) Side view of the field lines, with $|\bm{J}|/|\bm{B}|$, illustrates the transfer of magnetic twist from the strongly twisted, low-lying structure to the large-loops during the MFR evolution. (An animation of this figure is available in the online journal. The composite animation shows the temporal evolution of the flux rope structure from $t = 0$ to $t = 14.4$, where $t = 1$ corresponds to 3 minutes in physical time. The realtime duration of the video is 6 s. It displays synchronized time evolution from panel (a) on the left, panel (b) in the center, and panel (c) on the right.)
• Figure 5: Temporal evolution of the magnetic-to-kinetic energy conversion rate (${\bm v}\cdot({\bm J}\times {\bm B})$), computed as the volume integral ($\int \bm{v} \cdot (\bm{J} \times \bm{B}) \, dV$), plotted as a function of normalized Alfvén time.