Nonlinear Force-free Field Extrapolation Research Articles

A Data-driven Magnetohydrodynamic Simulation of the 2011 February 15 Coronal Mass Ejection from Active Region NOAA 11158

We present a boundary data-driven magnetohydrodynamic (MHD) simulation of the 2011 February 15 coronal mass ejection (CME) event of Active Region NOAA 11158. The simulation is driven at the lower boundary with an electric field derived from the normal magnetic field and the vertical electric current measured from the Solar Dynamics Observatory (SDO) Helioseismic Magnetic Imager vector magnetograms. The simulation shows the buildup of a pre-eruption coronal magnetic field that is close to the nonlinear force-free field extrapolation, and it subsequently develops multiple eruptions. The sheared/twisted field lines of the pre-eruption magnetic field show qualitative agreement with the brightening loops in the SDO Atmospheric Imaging Assembly (AIA) hot passband images. We find that the eruption is initiated by the tether-cutting reconnection in a highly sheared field above the central polarity inversion line and a magnetic flux rope with dipped field lines forms during the eruption. The modeled erupting magnetic field evolves to develop a complex structure containing two distinct flux ropes and produces an outgoing double-shell feature consistent with the Solar Terrestrial Relations Observatory B/Extreme UltraViolet Imager observation of the CME. The foot points of the erupting field lines are found to correspond well with the dimming regions seen in the SDO/AIA observation of the event. These agreements suggest that the derived electric field is a promising way to drive MHD simulations to establish the realistic pre-eruption coronal field based on the observed vertical electric current and model its subsequent dynamic eruption.

Why Could a Newborn Active Region Produce Coronal Mass Ejections?

Solar active regions (ARs) are the main sources of flares and coronal mass ejections (CMEs). NOAA AR 12089, which emerged on 2014 June 10, produced two C-class flares accompanied by CMEs within 5 hr after its emergence. When producing the two eruptive flares, the total unsigned magnetic flux (ΦAR) and magnetic free energy (E f ) of the AR are much smaller than the common CME-producing ARs. Why can this extremely small AR produce eruptive flares so early? We compare the AR magnetic environment for the eruptive flares to that for the largest confined flare from the AR. In addition to the ΦAR and E f , we calculate the ratio between the mean characteristic twist parameter (α FPIL) within the flaring polarity inversion line (FPIL) region and ΦAR, a parameter considering both background magnetic field constraint and nonpotentiality of the core region, for the three flares. We find higher α FPIL/ΦAR values during the eruptive flares than during the confined flare. Furthermore, we compute the decay index along the polarity inversion line, revealing values of 1.69, 3.45, and 0.98 before the two eruptive and the confined flares, respectively. Finally, nonlinear force-free field extrapolation indicates that a flux rope was repeatedly formed along the FPIL before eruptive flares, which ejected out and produced CMEs. No flux rope was found before the confined flare. Our research suggests that even a newly emerged, extremely small AR can produce eruptive flares if it has sufficiently weak background field constraint and strong nonpotentiality in the core region.

Magnetic Eruption from a Three-ribbon Flare

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.

Multipoint study of the rapid filament evolution during a confined C2 flare on 28 March 2022, leading to eruption

This study focuses on the rapid evolution of the solar filament in active region 12975 during a confined C2 flare on 28 March 2022, which finally led to an eruptive M4 flare 1.5 h later. The event is characterized by the apparent breakup of the filament, the disappearance of its southern half, and the flow of the remaining filament plasma into a new, longer channel with a topology very similar to an extreme ultraviolet (EUV) hot channel observed during the flare. In addition, we outline the emergence of the original filament from a sheared arcade and discuss possible drivers for its rise and eruption. We took advantage of Solar Orbiter's favorable position, 0.33 AU from the Sun, and $83. 5^ west of the Sun-Earth line, to perform a multi-point study using the Spectrometer Telescope for Imaging X-rays (STIX) and the Extreme Ultraviolet Imager (EUI) in combination with the Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) and Halpha images from the Earth-based Kanzelhöhe Observatory for Solar and Environmental Research (KSO) and the Global Oscillation Network Group (GONG). While STIX and EUI observed the flare and the filament's rise from close up and at the limb, AIA and HMI observations provided highly complementary on-disk observations from which we derived differential emission measure (DEM) maps and nonlinear force-free (NLFF) magnetic field extrapolations. According to our pre-flare NLFF extrapolation, field lines corresponding to both filament channels existed in close proximity before the flare. We propose a loop-loop reconnection scenario based on field structures associated with the AIA 1600 Å flare ribbons and kernels. It involves field lines surrounding and passing beneath the shorter filament channel, and field lines closely following the southern part of the longer channel. Reconnection occurs in an essentially vertical current sheet at a polarity inversion line (PIL) below the breakup region, which enables the formation of the flare loop arcade and EUV hot channel. This scenario is supported by concentrated currents and free magnetic energy built up by antiparallel flows along the PIL before the flare, and by non-thermal X-ray emission observed from the reconnection region. The reconnection probably propagated to involve the original filament itself, leading to its breakup and new geometry. This reconnection geometry also provides a general mechanism for the formation of the long filament channel and realizes the concept of tether cutting. It was probably active throughout the filament's continuous rise phase, which lasted from at least 30 min before the C2 flare until the filament eruption. The C2 flare represents a period of fast reconnection during this otherwise more steady period, during which most of the original filament was reconnected and joined the longer channel. These results demonstrate how rapid changes in solar filament topology can be driven by loop-loop reconnection with nearby field structures, and how this can be part of a long-lasting tether-cutting reconnection process. They also illustrate how a confined precursor flare due to loop-loop reconnection (Type I) can contribute to the evolution towards a full eruption, and that they can produce a flare loop arcade when the contact region between interacting loop systems has a sheet-like geometry similar to a flare current sheet.

Unveiling the True Nature of Plasma Dynamics from the Reference Frame of a Superpenumbral Fibril

The magnetic geometry of the solar atmosphere, combined with projection effects, makes it difficult to accurately map the propagation of ubiquitous waves in fibrillar structures. These waves are of interest due to their ability to carry energy into the chromosphere and deposit it through damping and dissipation mechanisms. To this end, the Interferometric Bidimensional Spectrometer at the Dunn Solar Telescope was employed to capture high-resolution Hα spectral scans of a sunspot, with the transverse oscillations of a prominent superpenumbral fibril examined in depth. The oscillations are reprojected from the helioprojective Cartesian frame to a new frame of reference oriented along the average fibril axis through nonlinear force-free field extrapolations. The fibril was found to be carrying an elliptically polarized, propagating kink oscillation with a period of 430 s and a phase velocity of 69 ± 4 km s−1. The oscillation is damped as it propagates away from the sunspot with a damping length of approximately 9.2 Mm, resulting in the energy flux decreasing at a rate on the order of 460 W m−2/Mm. The Hα line width is examined and found to increase with distance from the sunspot, a potential sign of a temperature increase. Different linear and nonlinear mechanisms are investigated for the damping of the wave energy flux, but a first-order approximation of their combined effects is insufficient to recreate the observed damping length by a factor of at least 3. It is anticipated that the reprojection methodology demonstrated in this study will aid with future studies of transverse waves within fibrillar structures.

Evidence for Plasmoid-mediated Magnetic Reconnection during a Small-scale Flare in the Partially Ionized Low Solar Atmosphere

Magnetic reconnection plays a crucial role in the energy release process for different kinds of solar eruptions and activities. The rapid solar eruption requires a fast reconnection model. Plasmoid instability in the reconnecting current sheets is one of the most acceptable fast reconnection mechanisms for explaining the explosive events in the magnetohydrodynamics (MHD) scale, which is also a potential bridge between the macroscopic MHD reconnection process and microscale dissipations. Plenty of high-resolution observations indicate that the plasmoid-like structures exist in the high-temperature solar corona, but such evidences are very rare in the lower solar atmosphere with partially ionized plasmas. Utilizing joint observations from the Goode Solar Telescope and the Solar Dynamics Observatory, we discovered a small-scale eruptive phenomenon in NOAA Active Region 13085, characterized by clear reconnection cusp structures, supported by nonlinear force-free field extrapolation results. The plasmoid-like structures with a size of about 150 km were observed to be ejected downward from the current sheet at a maximum velocity of 24 km s−1 in the Hα line wing images, followed by enhanced emissions at around the postflare loop region in multiple wavelengths. Our 2.5D high-resolution MHD simulations further reproduced such a phenomenon and revealed reconnection fine structures. These results provide comprehensive evidences for the plasmoid-mediated reconnection in partially ionized plasmas, and suggest a unified reconnection model for solar flares with different length scales from the lower chromosphere to the corona.

3D Magnetic Free Energy and Flaring Activity Using 83 Major Solar Flares

In this Letter, we examine the relationship between 3D magnetic free energy (MFE) and flaring activity using 83 major solar flares (M-class and X-class) in nine solar active regions (ARs). For this, we use 998 nonlinear force-free field extrapolations compiled by the “Institute for Space-Earth Environmental Research Database” at Nagoya University. These ARs produced at least three major flares with distinct rising and peak phases of 3D MFE. For each phase, the solar flare occurrence rate (FOR) is calculated as a ratio of the number of flares to the duration. The major results from this study are summarized as follows. First, there is no clear linear correlation (CC = 0.15) between 3D MFE and flare peak flux. Second, the FOR (3.4 day−1) of the rising phase is a little higher than that (3.1 day−1) of the peak phase, depending on AR. Third, for several flares, there are noticeable decreases in 3D MFE, which correspond to the typical energy of a major flare (about 1032 erg). Fourth, it is interesting to note that there are noticeable enhancements in FORs at several local maxima of 3D MFE, which may be associated with flux emergence and/or shearing motions. Fifth, the flare index rates, which are defined as the summation of flaring activity divided by the duration, of rising and peak phases are 151 day−1 and 314 day−1, respectively. Our results imply that the traditional and simple “storage and release” model does not apply to flare activities, and the random perturbation may be important for triggering flares.

Rotation and Confined Eruption of a Double Flux-rope System

We perform a data-constrained simulation with the zero-β assumption to study the mechanisms of strong rotation and failed eruption of a filament in active region 11474 on 2012 May 5 observed by Solar Dynamics Observatory and Solar Terrestrial Relations Observatory. The initial magnetic field is provided by nonlinear force-free field extrapolation, which is reconstructed by the regularized Biot–Savart laws and magnetofrictional method. Our simulation reproduces most observational features very well, e.g., the filament large-angle rotation of about 130°, the confined eruption, and the flare ribbons, allowing us to analyze the underlying physical processes behind observations. We discover two flux ropes in the sigmoid system, an upper flux rope (MFR1) and a lower flux rope (MFR2), which correspond to the filament and hot channel in observations, respectively. Both flux ropes undergo confined eruptions. MFR2 grows by tether-cutting reconnection during the eruption. The rotation of MFR1 is related to the shear-field component along the axis. The toroidal field tension force and the nonaxisymmetry forces confine the eruption of MFR1. We also suggest that the mutual interaction between MFR1 and MFR2 contributes to the large-angle rotation and the eruption failure. In addition, we calculate the temporal evolution of the twist and writhe of MFR1, which is a hint of probable reversal rotation.

The Link between Nonthermal Velocity and Free Magnetic Energy in Solar Flares

The cause of excess spectral line broadening (nonthermal velocity) is not definitively known, but given its rise before and during flaring, the causal processes hold clues to understanding the triggers for the onset of reconnection and the release of free magnetic energy from the coronal magnetic field. A comparison of data during a 9 hr period from the extreme ultraviolet Imaging Spectrometer on the Hinode spacecraft—at a 3 minute cadence—and nonlinear force-free field extrapolations performed on Helioseismic and Magnetic Imager magnetograms—at a 12 minute cadence—shows an inverse relationship between nonthermal velocity and free magnetic energy on short timescales during two X-class solar flares on 2017 September 6. Analysis of these results supports suggestions that unresolved Doppler flows do not solely cause nonthermal broadening, and instead other mechanisms like Alfvén wave propagation and isotropic turbulence have a greater influence.

Are Electric-field-driven Magnetohydrodynamic Simulations of the Solar Corona Sensitive to the Initial Condition?

Magnetohydrodynamic (MHD) simulations of the solar corona are often started from a potential field initial condition, which may be far from the true state of the coronal magnetic field. To test the sensitivity of the simulations to the initial condition, an electric-field-driven MHD code was initiated from three different initial conditions: the commonly used potential field, a nonlinear force-free field (NLFFF) extrapolation, which is believed to be a better representation of the true coronal magnetic field, and a purely vertical field. After relaxation, the magnetic field in the MHD simulations was compared. It was found that there is a tendency for all of the initial conditions to converge to a similar connectivity, particularly in areas of strong fields that are not close to the boundary, suggesting that the final state of the simulation is not particularly sensitive to the initial condition. The relaxed solution more closely resembles the NLFFF initial condition than the other initial conditions, but still exhibits substantial differences from it.

Coronal Magnetic Field Extrapolation and Topological Analysis of Fine-scale Structures during Solar Flare Precursors

Magnetic field plays an important role in various solar eruption phenomena. The formation and evolution of the characteristic magnetic field topology in solar eruptions are critical problems that will ultimately help us understand the origin of these eruptions in the solar source regions. With the development of advanced techniques and instruments, observations with higher resolutions in different wavelengths and fields of view have provided more quantitative information for finer structures. It is therefore essential to improve the method with which we study the magnetic field topology in the solar source regions by taking advantage of high-resolution observations. In this study, we employ a nonlinear force-free field extrapolation method based on a nonuniform grid setting for an M-class flare eruption event (SOL2015-06-22T17:39) with embedded vector magnetograms from the Solar Dynamics Observatory (SDO) and the Goode Solar Telescope (GST). The extrapolation results for which the nonuniform embedded magnetogram for the bottom boundary was employed are obtained by maintaining the native resolutions of the corresponding GST and SDO magnetograms. We compare the field line connectivity with the simultaneous GST/Hα and SDO/Atmospheric Imaging Assembly observations for these fine-scale structures, which are associated with precursor brightenings. Then we perform a topological analysis of the field line connectivity corresponding to fine-scale magnetic field structures based on the extrapolation results. The analysis results indicate that when we combine the high-resolution GST magnetogram with a larger magnetogram from the SDO, the derived magnetic field topology is consistent with a scenario of magnetic reconnection among sheared field lines across the main polarity inversion line during solar flare precursors.

Photospheric and Chromospheric Magnetic Field Evolution during the X1.6 Flare in Active Region NOAA 12192

We report on observations acquired by the Interferometric Bidimensional Spectropolarimeter (IBIS) during SOL2014-10-22T14:02, an X1.6 flare that occurred in active region NOAA 12192, taken in the Fe i 617.30 nm and Ca ii 854.2 nm line profiles. We analyze polarization signatures in the Stokes profiles of the two lines across one of the flare ribbons. Focusing our attention on the chromospheric signals and using the weak-field approximation (WFA), we study the temporal variation of the line-of-sight (LOS) magnetic field. We find variations of the magnetic field or the opacity along the flare ribbon, in most cases within the first 3 minutes of the observation just after the flare peak, during the tail of the flare impulsive phase. This result was validated by the STiC inversion of the pixels used for the WFA analysis. The analysis of the photospheric magnetic field shows that in this layer, the LOS magnetic field does not show the same changes observed in the chromosphere in the selected pixels, nor clear evidence of changes along the polarity inversion line around a magnetic polarity intrusion. In this respect, we also find that the temporal observing window is not suitable for assessing the presence of stepwise changes. The nonlinear force-free field extrapolations, together with the analysis of the ribbons’ isophotes obtained from Interface Region Imaging Spectrograph data, suggest that the region corresponding to the magnetic intrusion observed by IBIS is characterized by a complex magnetic connectivity and is almost cospatial with the area affected by the initial energy release.

The Formation of a U-shaped Filament Due to the Successive Magnetic Reconnection between a Filament and Its Nearby Chromospheric Fibrils

Although magnetic reconnection plays a key role in the formation of a solar filament, the detailed formation process is still ambiguous. Combining the observational data from the New Vacuum Solar Telescope and the Solar Dynamics Observatory, we analyzed the formation of a U-shaped filament via successive magnetic reconnection in the AR NOAA 11598 on 2012 October 25. The successive reconnection occurred between a filament (F) and its nearby chromospheric fibrils (CF). The associated brightening and magnetic cancellation were observed. The changes in appearance of the CF at the reconnection site were accompanied by the formation and accumulation of some new magnetic loops, as well as plasmas propagated along the formed magnetic loops from the reconnection site, indicating the changes in the topology of the F and CF. These can provide comprehensive observational evidence for successive reconnection. After the reconnection, a longer U-shaped filament was formed. During the formation of the U-shaped filament, two major magnetic energy releases took place. While in the two energy release processes, the injected plasma from the reconnection site can provide part of the material for the formation of the U-shaped filament. Therefore, we conclude that the successive reconnection results in both the dynamical evolution and the subsequent formation associated with the U-shaped filament. And the results of nonlinear force-free field extrapolation demonstrated that the magnetic topology of the F was changed significantly; this is consistent with the observational results and further confirms the formation of the U-shaped filament.

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

A comparative study of data-driven MHD simulations of solar coronal evolution with photospheric flows derived from two different approaches

Data-driven simulation proves to be a powerful tool in revealing the dynamic process of the solar corona, but it remains challenging to implement the driving boundary conditions in a self-consistent way and match the observables at the photosphere. Here, we test two different photospheric velocity-driven MHD simulations in studying the quasi-static evolution of solar active region NOAA 11158. The two simulations were identically initialized with an MHD equilibrium as relaxed from a non-linear force-free field extrapolation from a vector magnetogram. Then, we energized the MHD system by applying the time series of photospheric velocity at the bottom boundary as derived by two different codes, the DAVE4VM and PDFI, from the observed vector magnetograms. To mimic the small-scale flux cancellation on the photosphere, the magnetic diffusion at the bottom boundary was set to be inversely proportional to the local scale length of the magnetic field. The result shows the evolution curves of the total magnetic energy and unsigned magnetic flux generated by the PDFI velocity match the corresponding curves from the observations much better than those by the DAVE4VM one. The structure of the current layer and synthetic image in PDFI simulation also has a more reasonable consistency with SDO/AIA 131 Å observation. The only shortage of the PDFI velocity is its capability in reproducing the morphology of sunspots, as characterized by a slightly lower correlation coefficient for the bottom magnetic field in simulations and magnetograms. Overall, this study suggests the superiority of each method in the models driven by the bottom velocity, which represents a further step toward the goal of reproducing more realistically the evolution of coronal magnetic fields using data-driven modeling.

A Large-Scale Dataset of Three-Dimensional Solar Magnetic Fields Extrapolated by Nonlinear Force-Free Method

It has been widely accepted that solar magnetic field manipulates all solar activities, especially violent solar bursts in solar corona. Thus, it is extremely important to reconstruct three-dimentional (3D) magnetic field of solar corona from really observed photospheric magnetogram. In this paper, a large-scale dataset of 3D solar magnetic fields of active regions is built by using the nonlinear force-free magnetic field (NLFFF) extrapolation from vector magnetograms of Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO). In this dataset, all space-weather HMI active region patches (SHARPs) with the corresponding serial numbers of national oceanic and atmospheric administration (NOAA) are included. They are downloaded from the SHARP 720 s series of JSOC every 96 minutes. In addition, each sample is labelled with a finer grained label for solar flare forecast. This paper is with the purpose of open availability of data resource and source code to the peers for refraining from repeated labor of data preparation. Meanwhile, with such a large-scale, high spatio-temporal resolution and high quality scientific data, we anticipate a wide attention and interest from artificial intelligence (AI) and computer vision communities, for exploring AI for astronomy over such a large-scale dataset.

Evolution of coronal magnetic field parameters during X5.4 solar flare

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz|≥ 300 G, areas of flare brightening seen in SDO Atmospheric Imaging Assembly imagery, and areas with surface |B| ≥ 1000 G and high twist. Time series of the magnetic field parameters were analyzed to investigate the evolution of the coronal field during the solar flare event and discern pre-eruptive signatures. The data shows that areas with |B| ≥ 1000 G and |Tw|≥ 1.5 align well with areas of initial flare brightening during the pre-flare phase and at the beginning of the eruptive phase of the flare, suggesting that measurements of the photospheric magnetic field strength and twist can be used to predict the flare location within an active region if triggered. Additionally, the evolution of seven investigated magnetic field parameters indicated a destabilizing magnetic field structure that could likely erupt.

Data-constrained MHD Simulation of a Multi-ribbon Flare Corresponding to a Successful and a Confined Eruption

The formation and eruption mechanisms of multi-ribbon flares are extremely complicated, especially when the flare is associated with homologous eruptions in the same region. In this paper, we investigate such an event, corresponding to a successful eruption and a confined eruption. This is an M7.1 flare, starting at 12:33 UT on 2011 September 24 in active region NOAA 11302. We obtain the coronal magnetic configuration for this region, using a nonlinear force-free field extrapolation based on the photospheric magnetogram at 12:00 UT. Taking this as the initial condition, we perform a data-constrained MHD simulation to study the evolution of the magnetic topology for this region. We analyze the magnetic null points and the 3D squashing degree for this region, indicating the existence of three flux ropes and two spine–fan structures. The model reproduces the rising processes of the two flux ropes, which form two homologous eruptions consistent with the observations as shown in 94 Å: a large-scale successful eruption that is followed by a small-scale confined eruption. By analyzing the magnetic configuration, the Lorentz force, and the decay index, we find that the torus instability plays an important role in driving the successful eruption of the large flux rope. The magnetic reconnection above the medium flux rope changes the direction of the overlying magnetic field, which provides a downward component of the Lorentz force to confine the eruption of the medium flux rope.

Sympathetic Partial Filament Eruptions Caused by the Interaction between Two Nearby Filaments

To better understand the physical connections in sympathetic solar eruptions, we investigated the interaction between two nearby filaments and their successive partial eruptions in the active region (AR) NOAA 12866 on 2021 September 9 by using data from the Solar Dynamics Observatory and the New Vacuum Solar Telescope. Based on Hα and extreme ultraviolet observations, we found that the right part of one filament (F1) became active first and experienced an obvious rolling motion. Then the whole body of the filament became wider and expanded toward another filament (F2). They collided with each other, and the interaction between them was accompanied by the brightening and bidirectional flows that appeared between them. This implies that magnetic reconnection occurred between the threads of two filaments. The interaction resulted in a rightward motion of F2 at first, and then its activation, and finally part of it erupted. Furthermore, when the erupted F2 deflected rapidly toward the middle part of F1, the left part of F1 erupted with its overlying magnetic fields pushed by F2. These observational results imply that these successive eruptions within a short time are physically linked, and this was caused by the interaction of the filaments. Nonlinear force-free field extrapolation reveals that the magnetic structure of the filament F1 was composed of several magnetic flux ropes with different twists. These results further advance our understanding of partial filament eruptions and sympathetic solar eruptions.

Changes of Magnetic Energy and Helicity in Solar Active Regions from Major Flares

Magnetic free energy powers solar flares and coronal mass ejections, and the buildup of magnetic helicity might play a role in the development of unstable structures that subsequently erupt. To better understand the roles of energy and helicity in large flares and eruptions, we have characterized the evolution of magnetic energy and helicity associated with 21 X-class flares from 2010 to 2017. Our sample includes both confined and eruptive events, with 6 and 15 in each category, respectively. Using the Helioseismic and Magnetic Imager vector magnetic field observations from several hours before to several hours after each event, we employ (a) the Differential Affine Velocity Estimator for Vector Magnetograms to determine the photospheric fluxes of energy and helicity, and (b) nonlinear force-free field extrapolations to estimate the coronal content of energy and helicity in source-region fields. Using superposed epoch analysis, we find, on average, the following: (1) decreases in both magnetic energy and helicity, in both photospheric fluxes and coronal content, that persist for a few hours after eruptions, but no clear changes, notably in relative helicity, for confined events; (2) significant increases in the twist of photospheric fields in eruptive events, with twist uncertainties too large in confined events to constrain twist changes (and lower overall twist in confined events); and (3) on longer timescales (event time +12 hr), replenishment of free magnetic energy and helicity content to near preevent levels for eruptive events. For eruptive events, magnetic helicity and free energy in coronal models clearly decrease after flares, with the amounts of decrease proportional to each region’s pre-flare content.