Nonlinear Force-free Field Research Articles

Investigating Energetic X-Shaped Flares on the Outskirts of A Solar Active Region.

Typical solar flares display two quasi-parallel, bright ribbons on the chromosphere. In between is the polarity inversion line (PIL) separating concentrated magnetic fluxes of opposite polarity in active regions (ARs). Intriguingly a series of flares exhibiting X-shaped ribbons occurred at the similar location on the outskirts of NOAA AR 11967, where magnetic fluxes were scattered, yet three of them were alarmingly energetic. The X shape, whose center coincided with hard X-ray emission, was similar in UV/EUV, which cannot be accommodated in the standard flare model. Mapping out magnetic connectivities in potential fields, we found that the X morphology was dictated by the intersection of two quasi-separatrix layers, i.e., a hyperbolic flux tube (HFT), within which a separator connecting a double null was embedded. This topology was not purely local but regulated by fluxes and flows over the whole AR. The nonlinear force-free field model suggested the formation of a current layer at the HFT, where the current dissipation can be mapped to the X-shaped ribbons via field-aligned heat conduction. These results highlight the critical role of HFTs in 3D magnetic reconnection and have important implications for astrophysical and laboratory plasmas.

SUNSPOT ROTATION AS A DRIVER OF MAJOR SOLAR ERUPTIONS IN THE NOAA ACTIVE REGION 12158

ABSTRACT We studied the development conditions of sigmoid structure under the influence of the magnetic non-potential characteristics of a rotating sunspot in the active region (AR) 12158. Vector magnetic field measurements from the Helioseismic Magnetic Imager and coronal EUV observations from the Atmospheric Imaging Assembly reveal that the erupting inverse-S sigmoid had roots at the location of the rotating sunspot. The sunspot rotates at a rate of 0°–5° h−1 with increasing trend in the first half followed by a decrease. The time evolution of many non-potential parameters had a good correspondence with the sunspot rotation. The evolution of the AR magnetic structure is approximated by a time series of force-free equilibria. The non-linear force-free field magnetic structure around the sunspot manifests the observed sigmoid structure. Field lines from the sunspot periphery constitute the body of the sigmoid and those from the interior overlie the sigmoid, similar to a flux rope structure. While the sunspot was rotating, two major coronal mass ejection eruptions occurred in the AR. During the first (second) event, the coronal current concentrations were enhanced (degraded), consistent with the photospheric net vertical current; however, magnetic energy was released during both cases. The analysis results suggest that the magnetic connections of the sigmoid are driven by the slow motion of sunspot rotation, which transforms to a highly twisted flux rope structure in a dynamical scenario. Exceeding the critical twist in the flux rope probably leads to the loss of equilibrium, thus triggering the onset of the two eruptions.

MAGNETO-FRICTIONAL MODELING OF CORONAL NONLINEAR FORCE-FREE FIELDS. II. APPLICATION TO OBSERVATIONS

ABSTRACT A magneto-frictional module has been implemented and tested in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) in the first paper of this series. Here, we apply the magneto-frictional method to observations to demonstrate its applicability in both Cartesian and spherical coordinates, and in uniform and block-adaptive octree grids. We first reconstruct a nonlinear force-free field (NLFFF) on a uniform grid of 1803 cells in Cartesian coordinates, with boundary conditions provided by the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) at 06:00 UT on 2010 November 11 in active region NOAA 11123. The reconstructed NLFFF successfully reproduces the sheared and twisted field lines and magnetic null points. Next, we adopt a three-level block-adaptive grid to model the same active region with a higher spatial resolution on the bottom boundary and a coarser treatment of regions higher up. The force-free and divergence-free metrics obtained are comparable to the run with a uniform grid, and the reconstructed field topology is also very similar. Finally, a group of active regions, including NOAA 11401, 11402, 11405, and 11407, observed at 03:00 UT on 2012 January 23 by SDO/HMI is modeled with a five-level block-adaptive grid in spherical coordinates, where we reach a local resolution of pixel−1 in an area of 790 Mm × 604 Mm. Local high spatial resolution and a large field of view in NLFFF modeling can be achieved simultaneously in parallel and block-adaptive magneto-frictional relaxations.

HIGH-RESOLUTION OBSERVATIONS OF A LARGE FAN-SHAPED SURGE

ABSTRACT We present high-resolution observations of a large fan-shaped surge, which was observed on 2013 June 5 with the current largest solar telescope, the 1.6 m New Solar Telescope (NST), at the Big Bear Solar Observatory. The observations are made at TiO, Hα, and 10830 Å wavebands with a spatial resolution better than 0 .″ 1 and a full-run cadence of ∼30 s. The fan-shaped surge consists of many small-scale threads with a typical width of 100 km and a length of up to 200 Mm at the maximum. The threads come from material ejections, which start with a velocity of several km s−1, and then accelerate up to 60–80 km s−1 over six to seven minutes with an acceleration of up to 0.2–0.3 km s−2. The threads can be observed in the Hα band and in SDO/AIA 171 Å images as absorbed objects, implying that they are cool material ejections. The surge is ejected along open magnetic field lines in the extrapolated non-linear force-free field, which might actually be a part of a large-scale magnetic loop stretching back to the solar surface. After 10–20 minutes, the ejections gradually decay and the surge eventually vanishes. The total lifetime is about 35 minutes. The Hα brightening at the root of the fan-shaped surge implies that there is heating in the chromosphere, which could be produced by low-atmosphere interchange magnetic reconnection. Our observation provides evidence of the reconnection model for the fan-shaped surges, which was proposed by Jiang et al.

TEMPORAL AND SPATIAL RELATIONSHIP OF FLARE SIGNATURES AND THE FORCE-FREE CORONAL MAGNETIC FIELD

ABSTRACT We investigate the plasma and magnetic environment of active region NOAA 11261 on 2011 August 2 around a GOES M1.4 flare/CME (SOL2011-08-02T06:19). We compare coronal emission at the (extreme) ultraviolet and X-ray wavelengths, using SDO AIA and RHESSI images, in order to identify the relative timing and locations of reconnection-related sources. We trace flare ribbon signatures at ultraviolet wavelengths in order to pin down the intersection of previously reconnected flaring loops in the lower solar atmosphere. These locations are used to calculate field lines from three-dimensional (3D) nonlinear force-free magnetic field models, established on the basis of SDO HMI photospheric vector magnetic field maps. Using this procedure, we analyze the quasi-static time evolution of the coronal model magnetic field previously involved in magnetic reconnection. This allows us, for the first time, to estimate the elevation speed of the current sheet’s lower tip during an on-disk observed flare as a few kilometers per second. A comparison to post-flare loops observed later above the limb in STEREO EUVI images supports this velocity estimate. Furthermore, we provide evidence for an implosion of parts of the flaring coronal model magnetic field, and identify the corresponding coronal sub-volumes associated with the loss of magnetic energy. Finally, we spatially relate the build up of magnetic energy in the 3D models to highly sheared fields, established due to the dynamic relative motions of polarity patches within the active region.

Properties of the prominence magnetic field and plasma distributions as obtained from 3D whole-prominence fine structure modeling

Aims. We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma β , and mass) using the 3D whole-prominence fine structure model.Methods. The model combines a 3D magnetic field configuration of an entire prominence, obtained from non-linear force-free field simulations, with a detailed semi-empirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model.Results. We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D whole-prominence fine structure model to reveal the distribution of the prominence plasma with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominence-corona transition region. We further demonstrate that the values of the plasma β are small throughout the majority of the modeled prominences when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma β may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed non-eruptive prominences.

TRACING THE CHROMOSPHERIC AND CORONAL MAGNETIC FIELD WITH AIA, IRIS, IBIS, AND ROSA DATA

ABSTRACT The aim of this study is to explore the suitability of chromospheric images for magnetic modeling of active regions. We use high-resolution images ( ), from the Interferometric Bidimensional Spectrometer in the Ca ii 8542 Å line, the Rapid Oscillations in the Solar Atmosphere instrument in the Hα 6563 Å line, the Interface Region Imaging Spectrograph in the 2796 Å line, and compare non-potential magnetic field models obtained from those chromospheric images with those obtained from images of the Atmospheric Imaging Assembly in coronal (171 Å, etc.) and in chromospheric (304 Å) wavelengths. Curvi-linear structures are automatically traced in those images with the OCCULT-2 code, to which we forward-fitted magnetic field lines computed with the Vertical-current Approximation Nonlinear Force Free Field code. We find that the chromospheric images: (1) reveal crisp curvi-linear structures (fibrils, loop segments, spicules) that are extremely well-suited for constraining magnetic modeling; (2) that these curvi-linear structures are field-aligned with the best-fit solution by a median misalignment angle of –7°; (3) the free energy computed from coronal data may underestimate that obtained from cromospheric data by a factor of –4, (4) the height range of chromospheric features is confined to km, while coronal features are detected up to h = 35,000 km; and (5) the plasma-β parameter is for all traced features. We conclude that chromospheric images reveal important magnetic structures that are complementary to coronal images and need to be included in comprehensive magnetic field models, something that is currently not accomodated in standard NLFFF codes.

FORCED FIELD EXTRAPOLATION OF THE MAGNETIC STRUCTURE OF THE Hα FIBRILS IN THE SOLAR CHROMOSPHERE

ABSTRACT We present a careful assessment of forced field extrapolation using the Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetogram. We use several metrics to check the convergence property. The extrapolated field lines below 3600 km appear to be aligned with most of the Hα fibrils observed by the New Vacuum Solar Telescope. In the region where magnetic energy is far larger than potential energy, the field lines computed by forced field extrapolation are still consistent with the patterns of Hα fibrils while the nonlinear force-free field results show a large misalignment. The horizontal average of the lorentz force ratio shows that the forced region where the force-free assumption fails can reach heights of 1400–1800 km. The non-force-free state of the chromosphere is also confirmed based on recent radiation magnetohydrodynamics simulations.

Magnetohydrodynamics modeling of coronal magnetic field and solar eruptions based on the photospheric magnetic field

In this paper, we summarize current progress on using the observed magnetic fields for magnetohydrodynamics (MHD) modeling of the coronal magnetic field and of solar eruptions, including solar flares and coronal mass ejections (CMEs). Unfortunately, even with the existing state-of-the-art solar physics satellites, only the photospheric magnetic field can be measured. We first review the 3D extrapolation of the coronal magnetic fields from measurements of the photospheric field. Specifically, we focus on the nonlinear force-free field (NLFFF) approximation extrapolated from the three components of the photospheric magnetic field. On the other hand, because in the force-free approximation the NLFFF is reconstructed for equilibrium states, the onset and dynamics of solar flares and CMEs cannot be obtained from these calculations. Recently, MHD simulations using the NLFFF as an initial condition have been proposed for understanding these dynamics in a more realistic scenario. These results have begun to reveal complex dynamics, some of which have not been inferred from previous simulations of hypothetical situations, and they have also successfully reproduced some observed phenomena. Although MHD simulations play a vital role in explaining a number of observed phenomena, there still remains much to be understood. Herein, we review the results obtained by state-of-the-art MHD modeling combined with the NLFFF.

Evolution of flare ribbons, electric currents, and quasi-separatrix layers during an X-class flare

The standard model for eruptive flares has in the past few years been extended to 3D. It predicts typical J-shaped photospheric footprints of the coronal current layer, forming at similar locations as the Quasi-Separatrix Layers (QSLs). Such a morphology is also found for flare ribbons observed in the EUV band, as well as in non-linear force-free field (NLFFF) magnetic field extrapolations and models. We study the evolution of the photospheric traces of the current density and flare ribbons, both obtained with the SDO instruments. We investigate the photospheric current evolution during the 6 September 2011 X-class flare (SOL2011-09-06T22:20) from observational data of the magnetic field obtained with HMI. This evolution is compared with that of the flare ribbons observed in the EUV filters of the AIA. We also compare the observed electric current density and the flare ribbon morphology with that of the QSLs computed from the flux rope insertion method/NLFFF model. The NLFFF model shows the presence of a fan-spine configuration of overlying field lines, due to the presence of a parasitic polarity, embedding an elongated flux rope that appears in the observations as two parts of a filament. The QSLs, evolved via a magnetofrictional method, also show similar morphology and evolution as both the current ribbons and the EUV flare ribbons obtained at several times during the flare. For the first time, we propose a combined analysis of the photospheric traces of an eruptive flare, in a complex topology, with direct measurements of electric currents and QSLs from observational data and a magnetic field model. The results, obtained by two different and independent approaches, 1) confirm previous results of current increase during the impulsive phase of the flare, 2) show how NLFFF models can capture the essential physical signatures of flares even in a complex magnetic field topology.

Deriving Potential Coronal Magnetic Fields from Vector Magnetograms

The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Ampere's law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this scalar potential obeys Laplace's equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, "least-squares" potential field, which minimizes the integrated square of the residual between the potential and actual fields. This has advantages in both not overfitting the radial field used for the Neumann BC, and maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of AR 11158, and find that residual discrepancies between the observed and potential fields are significant, and are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid potential fields have significantly less energy than the Neumann fields in every case --- by more than 10^(32) erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.

QUANTIFYING THE TOPOLOGY AND EVOLUTION OF A MAGNETIC FLUX ROPE ASSOCIATED WITH MULTI-FLARE ACTIVITIES

ABSTRACT Magnetic flux ropes (MFRs) play an important role in solar activities. The quantitative assessment of the topology of an MFR and its evolution is crucial for a better understanding of the relationship between the MFR and associated activities. In this paper, we investigate the magnetic field of active region (AR) 12017 from 2014 March 28–29, during which time 12 flares were triggered by intermittent eruptions of a filament (either successful or confined). Using vector magnetic field data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we calculate the magnetic energy and helicity injection in the AR, and extrapolate the 3D magnetic field with a nonlinear force-free field model. From the extrapolations, we find an MFR that is cospatial with the filament. We further determine the configuration of this MFR from the closed quasi-separatrix layer (QSL) around it. Then, we calculate the twist number and the magnetic helicity for the field lines composing the MFR. The results show that the closed QSL structure surrounding the MFR becomes smaller as a consequence of flare occurrence. We also find that the flares in our sample are mainly triggered by kink instability. Moreover, the twist number varies more sensitively than other parameters with the occurrence of flares.

Observing the release of twist by magnetic reconnection in a solar filament eruption.

Magnetic reconnection is a fundamental process of topology change and energy release, taking place in plasmas on the Sun, in space, in astrophysical objects and in the laboratory. However, observational evidence has been relatively rare and typically only partial. Here we present evidence of fast reconnection in a solar filament eruption using high-resolution H-alpha images from the New Vacuum Solar Telescope, supplemented by extreme ultraviolet observations. The reconnection is seen to occur between a set of ambient chromospheric fibrils and the filament itself. This allows for the relaxation of magnetic tension in the filament by an untwisting motion, demonstrating a flux rope structure. The topology change and untwisting are also found through nonlinear force-free field modelling of the active region in combination with magnetohydrodynamic simulation. These results demonstrate a new role for reconnection in solar eruptions: the release of magnetic twist.

THE VERTICAL-CURRENT APPROXIMATION NONLINEAR FORCE-FREE FIELD CODE—DESCRIPTION, PERFORMANCE TESTS, AND MEASUREMENTS OF MAGNETIC ENERGIES DISSIPATED IN SOLAR FLARES

ABSTRACT In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of , but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.

HOOKED FLARE RIBBONS AND FLUX-ROPE-RELATED QSL FOOTPRINTS

ABSTRACT We studied the magnetic topology of active region 12158 on 2014 September 10 and compared it with the observations before and early in the flare that begins at 17:21 UT (SOL2014-09-10T17:45:00). Our results show that the sigmoidal structure and flare ribbons of this active region observed by the Solar Dynamics Observatory/Atmospheric Imaging Assembly can be well reproduced from a Grad–Rubin nonlinear force-free field extrapolation method. Various inverse-S- and inverse-J-shaped magnetic field lines, which surround a coronal flux rope, coincide with the sigmoid as observed in different extreme-ultraviolet wavelengths, including its multithreaded curved ends. Also, the observed distribution of surface currents in the magnetic polarity where it was not prescribed is well reproduced. This validates our numerical implementation and setup of the Grad–Rubin method. The modeled double inverse-J-shaped quasi-separatrix layer (QSL) footprints match the observed flare ribbons during the rising phase of the flare, including their hooked parts. The spiral-like shape of the latter may be related to a complex pre-eruptive flux rope with more than one turn of twist, as obtained in the model. These ribbon-associated flux-rope QSL footprints are consistent with the new standard flare model in 3D, with the presence of a hyperbolic flux tube located below an inverse-teardrop-shaped coronal QSL. This is a new step forward forecasting the locations of reconnection and ribbons in solar flares and the geometrical properties of eruptive flux ropes.

Relationship Between Sunspot Rotation and a Major Solar Eruption on 12 July 2012

We present an analysis of Solar Dynamics Observatory (SDO) observations of an X1.4 class flare on 12 July 2012 (SOL2012-07-12T15:37L082C105), which was associated with a pronounced sunspot rotation in the associated active region. Based on the magnetograms taken with the Helioseismic and Magnetic Imager (HMI) on the SDO, we measured the rotational speed of the sunspot. We also used a technique, called the differential affine velocity estimator for vector magnetograms (DAVE4VM), to determine the horizontal velocities and the magnetic helicity flux transport. The helicity flux rate due to shearing motion changed sign after the onset of the eruption. A high correlation between the sunspot rotation speed and the change in the total accumulated helicity was found. We also calculated the net fluxes of the respective magnetic polarities and the net vertical currents. The net current in the region of interest showed a synchronous change with the sunspot rotation rate. The magnetic configurations of the sigmoid filament in the active region and the associated possible interaction between different structures were further investigated by means of a nonlinear force-free field extrapolation. We identified a possible magnetic reconnection region from the three-dimensional magnetic fields and its association with EUV structures. These results suggest that the major eruption of this active region was connected with the sunspot rotation.

CHAIN RECONNECTIONS OBSERVED IN SYMPATHETIC ERUPTIONS

ABSTRACT The nature of various plausible causal links between sympathetic events is still a controversial issue. In this work, we present multiwavelength observations of sympathetic eruptions, associated flares, and coronal mass ejections (CMEs) occurring on 2013 November 17 in two close active regions. Two filaments, i.e., F1 and F2, are observed in between the active regions. Successive magnetic reconnections, caused for different reasons (flux cancellation, shear, and expansion) have been identified during the whole event. The first reconnection occurred during the first eruption via flux cancellation between the sheared arcades overlying filament F2, creating a flux rope and leading to the first double-ribbon solar flare. During this phase, we observed the eruption of overlying arcades and coronal loops, which leads to the first CME. The second reconnection is believed to occur between the expanding flux rope of F2 and the overlying arcades of filament F1. We suggest that this reconnection destabilized the equilibrium of filament F1, which further facilitated its eruption. The third stage of reconnection occurred in the wake of the erupting filament F1 between the legs of the overlying arcades. This may create a flux rope and the second double-ribbon flare and a second CME. The fourth reconnection was between the expanding arcades of the erupting filament F1 and the nearby ambient field, which produced the bi-directional plasma flows both upward and downward. Observations and a nonlinear force-free field extrapolation confirm the possibility of reconnection and the causal link between the magnetic systems.

BIDIRECTIONAL OUTFLOWS AS EVIDENCE OF MAGNETIC RECONNECTION LEADING TO A SOLAR MICROFLARE

ABSTRACT Magnetic reconnection is a rapid energy release process that is believed to be responsible for flares on the Sun and stars. Nevertheless, such flare-related reconnection is mostly detected to occur in the corona, while there have been few studies concerning the reconnection in the chromosphere or photosphere. Here, we present both spectroscopic and imaging observations of magnetic reconnection in the chromosphere leading to a microflare. During the flare peak time, chromospheric line profiles show significant blueshifted/redshifted components on the two sides of the flaring site, corresponding to upflows and downflows with velocities of ±(70–80) km s−1, comparable with the local Alfvén speed as expected by the reconnection in the chromosphere. The three-dimensional nonlinear force-free field configuration further discloses twisted field lines (a flux rope) at a low altitude, cospatial with the dark threads in He i 10830 Å images. The instability of the flux rope may initiate the flare-related reconnection. These observations provide clear evidence of magnetic reconnection in the chromosphere and show the similar mechanisms of a microflare to those of major flares.

STRUCTURE AND STABILITY OF MAGNETIC FIELDS IN SOLAR ACTIVE REGION 12192 BASED ON NONLINEAR FORCE-FREE FIELD MODELING

ABSTRACT We analyze a three-dimensional (3D) magnetic structure and its stability in large solar active region (AR) 12192, using the 3D coronal magnetic field constructed under a nonlinear force-free field (NLFFF) approximation. In particular, we focus on the magnetic structure that produced an X3.1-class flare, which is one of the X-class flares observed in AR 12192. According to our analysis, the AR contains a multiple-flux-tube system, e.g., a large flux tube, with footpoints that are anchored to the large bipole field, under which other tubes exist close to a polarity inversion line (PIL). These various flux tubes of different sizes and shapes coexist there. In particular, the latter are embedded along the PIL, which produces a favorable shape for the tether-cutting reconnection and is related to the X-class solar flare. We further found that most of magnetic twists are not released even after the flare, which is consistent with the fact that no observational evidence for major eruptions was found. On the other hand, the upper part of the flux tube is beyond a critical decay index, essential for the excitation of torus instability before the flare, even though no coronal mass ejections were observed. We discuss the stability of the complicated flux tube system and suggest the reason for the existence of the stable flux tube. In addition, we further point out a possibility for tracing the shape of flare ribbons, on the basis of a detailed structural analysis of the NLFFF before a flare.

STRUCTURE, STABILITY, AND EVOLUTION OF MAGNETIC FLUX ROPES FROM THE PERSPECTIVE OF MAGNETIC TWIST

ABSTRACT We investigate the evolution of NOAA Active Region (AR) 11817 during 2013 August 10–12, when it developed a complex field configuration and produced four confined, followed by two eruptive, flares. These C-and-above flares are all associated with a magnetic flux rope (MFR) located along the major polarity inversion line, where shearing and converging photospheric flows are present. Aided by the nonlinear force-free field modeling, we identify the MFR through mapping magnetic connectivities and computing the twist number  w ?> for each individual field line. The MFR is moderately twisted ( ∣  w ∣ < 2 ?> ) and has a well-defined boundary of high squashing factor Q. We found that the field line with the extremum ∣  w ∣ ?> is a reliable proxy of the rope axis, and that the MFR's peak ∣  w ∣ ?> temporarily increases within half an hour before each flare while it decreases after the flare peak for both confined and eruptive flares. This pre-flare increase in ∣  w ∣ ?> has little effect on the AR's free magnetic energy or any other parameters derived for the whole region, due to its moderate amount and the MFR's relatively small volume, while its decrease after flares is clearly associated with the stepwise decrease in the whole region's free magnetic energy due to the flare. We suggest that  w ?> may serve as a useful parameter in forewarning the onset of eruption, and therefore, the consequent space weather effects. The helical kink instability is identified as the prime candidate onset mechanism for the considered flares.