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Abstract Despite decades of research, the fundamental processes involved in the initiation and acceleration of solar eruptions remain not fully understood, making them long-standing and challenging problems in solar physics. Recent high-resolution observations by the Goode Solar Telescope have revealed small-scale magnetic flux emergence in localized regions of solar active areas prior to eruptions. Although much smaller in size than the entire active region, these emerging fluxes reached strengths of up to 2000 G. To investigate their impact, we performed data-constrained magnetohydrodynamic simulations. We find that while the small-scale emerging flux does not significantly alter the preeruption evolution, it dramatically accelerates the eruption during the main phase by enhancing the growth of torus instability, which emerges in the nonlinear stage. This enhancement occurs independently of the decay index profile. Our analysis indicates that even subtle differences in the preeruption evolution can strongly influence the subsequent dynamics, suggesting that small-scale emerging flux can play a critical role in accelerating solar eruptions. 

Abstract We investigated the initiation and the evolution of an X7.1-class solar flare observed in NOAA Active Region 13842 on 2024 October 1, based on a data-constrained magnetohydrodynamic (MHD) simulation. The nonlinear force-free field (NLFFF) extrapolated from the photospheric magnetic field about 1 hr before the flare was used as the initial condition for the MHD simulations. The NLFFF reproduces highly sheared field lines that undergo tether-cutting reconnection in the MHD simulation, leading to the formation of a highly twisted magnetic flux rope (MFR), which then erupts rapidly, driven by both torus instability and magnetic reconnection. This paper focuses on the dynamics of the MFR and its role in eruptions. We find that magnetic reconnection in the preeruption phase is crucial in the subsequent eruption driven by the torus instability. Furthermore, our simulation indicates that magnetic reconnection also directly enhances the torus instability. These results suggest that magnetic reconnection is not just a by-product of the eruption due to reconnecting of postflare arcade, but also plays a significant role in accelerating the MFR during the eruption. 

Abstract We conducted data-constrained magnetohydrodynamic (MHD) simulations for solar active region (AR) NOAA AR 11429, which produced two X-class flares within a span of 63 minutes. The simulations were performed using the zero-βMHD approximation, with the initial condition derived from the nonlinear force-free field extrapolated from the photospheric magnetograms taken 2 hr before the first X5.4 flare. During the simulation, we enhanced magnetic reconnection locally by applying anomalous resistivity in the induction equation within the regions of interest. As a result, the simulations successfully reproduced the expansion of two magnetic flux ropes (MFRs) corresponding to the two observed eruptions. The result shows that the difference in stability between the two MFRs is related to the location of the magnetic reconnection that triggers the solar eruptions. Furthermore, comparison with the analysis of failed MFR eruptions indicates that both the initiation reconnection and the subsequent driving mechanism, torus instability, are equally important for a successful eruption. This simulation reveals a new mechanism in which long loops, formed via tether-cutting reconnection, push up the overlying twisted field lines, leading to their destabilization by torus instability. 

Abstract We present observations and analysis of an eruptive M1.5 flare (SOL2014-08-01T18:13) in NOAA active region (AR) 12127, characterized by three flare ribbons, a confined filament between ribbons, and rotating sunspot motions as observed by the Solar Dynamics Observatory. The potential field extrapolation model shows a magnetic topology involving two intersecting quasi-separatrix layers (QSLs) forming a hyperbolic flux tube (HFT), which constitutes the fishbone structure for the three-ribbon flare. Two of the three ribbons show separation from each other, and the third ribbon is rather stationary at the QSL footpoints. The nonlinear force-free field extrapolation model implies the presence of a magnetic flux rope (MFR) structure between the two separating ribbons, which was unclear in the observation. This suggests that the standard reconnection scenario for eruptive flares applies to the two ribbons, and the QSL reconnection for the third ribbon. We find rotational flows around the sunspot, which may have caused the eruption by weakening the downward magnetic tension of the MFR. The confined filament is located in the region of relatively strong strapping field. The HFT topology and the accumulation of reconnected magnetic flux in the HFT may play a role in holding it from eruption. This eruption scenario differs from the one typically known for circular ribbon flares, which is mainly driven by a successful inside-out eruption of filaments. Our results demonstrate the diversity of solar magnetic eruption paths that arises from the complexity of the magnetic configuration. 

Abstract We performed two data-based magnetohydrodynamic (MHD) simulations for solar active region 12371, which produced an M6.5 flare. The first simulation is a full data-driven simulation where the initial condition is given by a nonlinear force-free field (NLFFF). This NLFFF was extrapolated from photospheric magnetograms approximately 1 hr prior to the flare, and then a time-varying photospheric magnetic field is imposed at the bottom surface. The second simulation is also a data-driven simulation, but it stops driving at the bottom before the time of flare onset and then switches to the data-constrained simulation, where the horizontal component of the magnetic field varies according to an induction equation, while the normal component is fixed with time. Both simulations lead to an eruption, with both simulations producing highly twisted field lines before the eruption, which were not found in the NLFFF alone. After the eruption, the first simulation based on the time-varying photospheric magnetic field continues to produce sheared field lines after the flare without reproducing phenomena such as postflare loops. The second simulation reproduces the phenomena associated with flares well. However, in this case, the evolution of the bottom magnetic field is inconsistent with the evolution of the observed magnetic field. In this Letter, we report potential advantages and disadvantages in data-constrained and data-driven MHD simulations that need to be taken into consideration in future studies. 

Abstract The solar active region NOAA 12887 produced a strong X1.0 flare on 2021 October 28, which exhibits X-shaped flare ribbons and a circle-shaped erupting filament. To understand the eruption process with these characteristics, we conducted a data-constrained magnetohydrodynamics simulation using a nonlinear force-free field of the active region about an hour before the flare as the initial condition. Our simulation reproduces the filament eruption observed in the H α images of GONG and the 304 Å images of SDO/AIA, and suggests that two mechanisms can possibly contribute to the magnetic eruption. One is the torus instability of the preexisting magnetic flux rope (MFR) and the other is upward pushing by magnetic loops newly formed below the MFR via continuous magnetic reconnection between two sheared magnetic arcades. The presence of this reconnection is evidenced by the SDO/AIA observations of the 1600 Å brightening in the footpoints of the sheared arcades at the flare onset. To clarify which process is more essential for the eruption, we performed an experimental simulation in which the reconnection between the sheared field lines is suppressed. In this case too, the MFR could erupt, but at a much reduced rising speed. We interpret this result as indicating that the eruption is not only driven by the torus instability, but additionally accelerated by newly formed and rising magnetic loops under continuous reconnection. 

Abstract In this paper, we study the evolution of the X5.4 flare (SOL2012-03-07T00:02) in NOAA Active Region 11429, focusing on its initiation mechanisms and back-reaction effects. To help our study, three-dimensional (3D) coronal magnetic field models are extrapolated from the photospheric magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory under the assumptions of nonlinear force-free field (NLFFF) and non-force-free field (non-FFF). We investigate the 3D magnetic structure and MHD kink instability, torus instability, and double-arc instability (DAI), and find that this flare is most likely triggered by the tether-cutting reconnection and the subsequent DAI. For the back-reactions of the flare, both NLFFF and non-FFF models clearly show an increase in horizontal magnetic field (B_h) and a decrease in inclination angle (ϕ) of the magnetic field near the polarity inversion line, from the photosphere up to a certain height (5 Mm and 8 Mm for non-FFF and NLFFF, respectively). In addition, the non-FFF model shows an enhancement of the downward Lorentz force acting on the photosphere, and the location of the enhancement spatially coincides with the location of the flare onset. The observed back-reaction is likely a consequence of magnetic reconnection. 

Using multi-wavelength observations, we analysed magnetic field variations associated with a gradual X1.2 flare that erupted on January 7, 2014 in active region (AR) NOAA 11944 located near the disk center. A fast coronal mass ejection (CME) was observed following the flare, which was noticeably deflected in the south-west direction. A chromospheric filament was observed at the eruption site prior to and after the flare. We used SDO/HMI data to perform non-linear force-free field extrapolation of coronal magnetic fields above the AR and to study the evolution of AR magnetic fields prior to the eruption. The extrapolated data allowed us to detect signatures of several magnetic flux ropes present at the eruption site several hours before the event. The eruption site was located under slanted sunspot fields with a varying decay index of 1.0-1.5. That might have caused the erupting fields to slide along this slanted magnetic boundary rather than vertically erupt, thus explaining the slow rise of the flare as well as the observed direction of the resulting CME. We employed sign-singularity tools to quantify the evolutionary changes in the model twist and observed current helicity data, and found rapid and coordinated variations of current systems in both data sets prior to the event as well as their rapid exhaustion after the event onset. 

Abstract We present both the observation and the magnetohydrodynamics (MHD) simulation of the M2.4 flare (SOL2017-07-14T02:09) of NOAA active region (AR) 12665 with a goal to identify its initiation mechanism. The observation by the Atmospheric Image Assembly (AIA) on board the Solar Dynamics Observatory (SDO) shows that the major topology of the AR is a sigmoidal configuration associated with a filament/flux rope. A persistent emerging magnetic flux and the rotation of the sunspot in the core region were observed with Magnetic Imager (HMI) on board the SDO on the timescale of hours before and during the flare, which may provide free magnetic energy needed for the flare/coronal mass ejection (CME). A high-lying coronal loop is seen moving outward in AIA EUV passbands, which is immediately followed by the impulsive phase of the flare. We perform an MHD simulation using the potential magnetic field extrapolated from the measured pre-flare photospheric magnetic field as initial conditions and adopting the observed sunspot rotation and flux emergence as the driving boundary conditions. In our simulation, a sigmoidal magnetic structure and an overlying magnetic flux rope (MFR) form as a response to the imposed sunspot rotation, and the MFR rises to erupt like a CME. These simulation results in good agreement with the observation suggest that the formation of the MFR due to the sunspot rotation and the resulting torus and kink instabilities were essential to the initiation of this flare and the associated coronal mass ejection.