Formation and Eruption of Filament Channel in Solar Active Region 12975: Insights from Observations and Simulations of Magnetic Field Evolution

Technical Summary: Formation and Eruption of Filament Channel in Solar Active Region 12975

Problem Statement
Solar flares and coronal mass ejections (CMEs) are driven by the accumulation of magnetic energy and helicity in the solar corona, often stored in magnetic flux ropes (FRs). While the three-dimensional coronal magnetic field cannot be directly measured, numerical modeling is essential for reconstructing these fields and understanding the transition from stable configurations to eruptions. A central challenge in solar physics is identifying universal thresholds—specifically regarding magnetic helicity ratios—that distinguish eruptive from stable active regions (ARs). Previous studies based on idealized simulations suggested a critical ratio of current-carrying helicity to total relative helicity ($|H_J|/|H_V|$) of approximately 0.29 for the onset of torus instability. However, the applicability of this threshold to real, data-driven ARs with complex evolutionary pathways remains an open question. This study investigates the magnetic evolution of Active Region (AR) 12975, which produced two consecutive M-class flares and CMEs on March 28, 2022, to test these thresholds and model the filament formation process.

Methodology
The authors employed a time-dependent magnetofrictional (TMF) model, a data-driven approach that evolves coronal magnetic fields through a sequence of force-free states.

• Observational Data: The study utilized vector magnetograms from the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) to derive photospheric electric fields. These served as the lower boundary driver for the simulation. Multi-wavelength observations from SDO/AIA, Solar Orbiter/EUI, and STEREO-A/SECCHI provided context for the filament structure and CME morphology.
• Simulation Setup: The simulation was initialized at 12:00 UT on March 26, 2022, with a potential magnetic field extrapolated from HMI data. The coronal volume was discretized on a $224 \times 224 \times 120$ grid. The evolution was driven by photospheric electric fields derived from a time series of magnetograms, incorporating a non-inductive component parameterized by an emergence speed ($U$) to control magnetic twist injection.
• Parameter Tuning: A series of simulations were run with emergence speeds ($U$) ranging from 120 to 180 m s$^{-1}$. While $U=120$ m s$^{-1}$ matched the observed energy injection rate most closely, the authors selected $U=180$ m s$^{-1}$ because it better reproduced the morphological evolution and timing of the observed filament formation and pre-eruptive rise, acknowledging that higher energy injection is often required in TMF models to overcome methodological limitations in capturing horizontal fields.
• Analysis: The study analyzed the temporal evolution of magnetic energy, free energy, relative helicity, and the ratio $|H_J|/|H_V|$. Additionally, a decay-index analysis was performed to assess the onset of torus instability.

Key Results

• Magnetic Evolution and Filament Formation: The AR exhibited a simple bipolar configuration with new flux emerging from March 27. The simulation successfully reproduced the gradual formation of a sigmoidal, twisted flux rope over approximately 50 hours, consistent with EUV observations. The modeled flux rope formed adjacent to pre-existing magnetic fields, with a significant portion of the coronal structure not belonging to the FR system.
• Energy and Helicity Injection: The photospheric driving injected a total magnetic helicity of $\approx 2.3 \times 10^{42}$ Mx$^2$ and magnetic energy of $\approx 2.5 \times 10^{32}$ erg prior to the eruption. The simulation showed a free energy fraction of approximately 35% of the total magnetic energy at the time of eruption, consistent with previous TMF studies.
• Helicity Thresholds: At the time of the observed eruption (March 28, 12:00 UT), the simulated helicity ratio $|H_J|/|H_V|$ reached 0.23. This is lower than the proposed universal threshold of 0.29. The ratio continued to rise, reaching 0.32 approximately 7 hours after the observed eruption, at which point the flux rope entered the torus-unstable regime (decay index $n > 1.5$).
• Eruption Mechanism: The analysis ruled out kink instability as the primary trigger due to the lack of helical deformation or apex rotation. Instead, the decay-index analysis indicated that the flux rope entered the torus-unstable regime when its apex height exceeded the critical height ($h_{crit}$) where $n > 1.5$. This occurred at approximately 55 hours of simulation time, coinciding with the helicity ratio reaching 0.32.
• Morphological Accuracy: The simulation reproduced the large-scale configuration and gradual rise of the erupting structure with high morphological accuracy when compared to multi-viewpoint observations (Earth, Solar Orbiter, and STEREO-A), despite the model's quasi-static nature not capturing the fully dynamic eruption phase.

Significance and Claims
The paper concludes that while TMF models can reproduce filament formation with high morphological fidelity, quantitative evaluation of eruptive thresholds remains challenging.

• Context-Dependent Thresholds: The study highlights that the derived helicity ratio thresholds vary and deviate from the proposed universal value of 0.29. This deviation is attributed to the specific magnetic configuration of AR 12975, where the flux rope formed within emerging weak-field regions adjacent to pre-existing strong fields, and a substantial portion of the coronal structure was not part of the erupting system.
• Model Limitations: The authors note that reproducing the observed twisted structures required an energy injection parameter roughly twice the value inferred from photospheric velocity fields. This suggests that horizontal magnetic fields in such regions may be less sensitive in observations, requiring enhanced injection in models to accurately capture the electric currents necessary for filament formation.
• Eruptivity Criteria: The results suggest that the onset of eruption in this event is associated with a helicity ratio range of 0.23–0.35 and the simultaneous increase in flux rope height entering the torus-unstable regime. The study underscores that while helicity ratios are useful indicators, they are not universal constants and depend heavily on the evolutionary history and magnetic topology of the specific active region.