Torus Instability Research Articles

Helicity shedding by flux rope ejection

Context. We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. Aims. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. Methods. The helicity shed is found to vary over a broad range from a minor to a major part of the initial helicity, with self helicity being largely or completely shed and mutual helicity, which makes up the larger part of the initial helicity, being shed only partly. Torus-unstable configurations with subcritical twist and without a guide field shed up to about two-thirds of the initial helicity, while a highly twisted, kink-unstable configuration sheds only about one-quarter. The parametric study also yields stable force-free flux rope equilibria up to a total flux-normalized helicity of 0.25, with a ratio of self- to total helicity of 0.32 and a ratio of flux rope to external poloidal flux of 0.94. Results. These results numerically demonstrate the conjecture of helicity shedding by coronal mass ejections and provide a first account of its parametric dependence. Both self- and mutual helicity are shed significantly; this reduces the total initial helicity by a fraction of ∼0.4 − 0.65 for typical source region parameters.

Prominence instability and CMEs triggered by massive coronal rain in the solar atmosphere

Context. The triggering process for prominence instability and consequent coronal mass ejections (CMEs) is not fully understood. Prominences are maintained by the Lorentz force against the gravity; therefore, reduction of the prominence mass due to the coronal rain may cause the change of the force balance and hence destabilisation of the structures. Aims. We aim to study the observational evidence of the influence of coronal rain on the stability of prominence and subsequent eruption of CMEs. Methods. We used the simultaneous observations from the Atmospheric Imaging Assembly (AIA) of Solar Dynamics Observatory (SDO) and Sun Earth Connection Coronal and Heliospheric Investigation (SECHHI) of Solar Terrestrial Relations Observatory (STEREO) spacecrafts from different angles to follow the dynamics of prominence and to study the role of coronal rain in their destabilisation. Results. Three different prominences observed during the years 2011–2012 were analysed using observations acquired by SDO and STEREO. In all three cases, massive coronal rain from the prominence body led to the destabilisation of prominence and subsequently to the eruption of CMEs. The upward rising of prominences consisted of the slow and fast rise phases. The coronal rain triggered the initial slow rise of prominences, which led to the final instability (the fast rise phase) after 18–28 h in all cases. The estimated mass flux carried by coronal rain blobs showed that the prominences became unstable after 40% of mass loss. Conclusions. We suggest that the initial slow rise phase was triggered by the mass loss of prominence due to massive coronal rain, while the fast rise phase (the consequent instability of prominences) was caused by the torus instability and/or magnetic reconnection with the overlying coronal field. Therefore, the coronal rain triggered the instability of prominences and consequent CMEs. If this is the case, then the coronal rain can be used to predict the CMEs and hence to improve the space weather predictions.

Partial Eruption, Confinement, and Twist Buildup and Release of a Double-decker Filament

Abstract We investigate the failed partial eruption of a filament system in NOAA AR 12104 on 2014 July 5, using multiwavelength EUV, magnetogram, and Hα observations, as well as magnetic field modeling. The filament system consists of two almost co-spatial segments with different end points, both resembling a C shape. Following an ejection and a precursor flare related to flux cancellation, only the upper segment rises and then displays a prominent twisted structure, while rolling over toward its footpoints. The lower segment remains undisturbed, indicating that the system possesses a double-decker structure. The erupted segment ends up with a reverse-C shape, with material draining toward its footpoints, while losing its twist. Using the flux rope insertion method, we construct a model of the source region that qualitatively reproduces key elements of the observed evolution. At the eruption onset, the model consists of a flux rope atop a flux bundle with negligible twist, which is consistent with the observational interpretation that the filament possesses a double-decker structure. The flux rope reaches the critical height of the torus instability during its initial relaxation, while the lower flux bundle remains in stable equilibrium. The eruption terminates when the flux rope reaches a dome-shaped quasi-separatrix layer that is reminiscent of a magnetic fan surface, although no magnetic null is found. The flux rope is destroyed by reconnection with the confining overlying flux above the dome, transferring its twist in the process.

Understanding the Initiation of the M2.4 Flare on 2017 July 14

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.

Torus-stable zone above starspots

ABSTRACT Whilst intense solar flares are almost always accompanied by a coronal mass ejection (CME), reports on stellar CMEs are rare, despite the frequent detection of stellar ‘super flares’. The torus instability of magnetic flux ropes is believed to be one of the main driving mechanisms of solar CMEs. Suppression of the torus instability, due to a confining background coronal magnetic field that decreases sufficiently slowly with height, may contribute to the lack of stellar CME detection. Here, we use the solar magnetic field as a template to estimate the vertical extent of this ‘torus-stable zone’ (TSZ) above a stellar active region. For an idealized potential field model comprising the fields of a local bipole (mimicking a pair of starspots) and a global dipole, we show that the upper bound of the TSZ increases with the bipole size, the dipole strength, and the source surface radius where the coronal field becomes radial. The boundaries of the TSZ depend on the interplay between the spots’ and the dipole’s magnetic fields, which provide the local- and global-scale confinement, respectively. They range from about half the bipole size to a significant fraction of the stellar radius. For smaller spots and an intermediate dipole field, a secondary TSZ arises at a higher altitude, which may increase the likelihood of ‘failed eruptions’. Our results suggest that the low apparent CME occurrence rate on cool stars is, at least partially, due to the presence of extended TSZs.

Tether-cutting and Overlying Magnetic Reconnections in an MHD Simulation of Prominence-cavity System

Abstract We investigate the magnetic reconnection in an MHD simulation of a coronal magnetic flux rope (MFR) confined by a helmet streamer, where a prominence-cavity system forms. This system includes a hot cavity surrounding a prominence with prominence horns and a central hot core above the prominence. The evolution of the system from quasi-equilibrium to eruption can be divided into four phases: quasi-static, slow-rise, fast-rise, and propagation phases. The emerged MFR initially stays quasi-static and magnetic reconnection occurs at the overlying high-Q (squashing factor) apex region, which gradually evolves into a hyperbolic flux tube (HFT). The decrease of the integrated magnetic tension force (above the location of the overlying reconnection) is due to the removal of overlying confinement by the enhanced overlying reconnection between the MFR and the overlying fields at the apex HFT, thus engines the slow rise of the MFR with a nearly constant velocity. Once the MFR reaches the regime of torus instability, another HFT immediately forms at the dip region under the MFR, followed by the explosive flare reconnection. The integrated resultant force (above the location of the flare reconnection) exponentially increases, which drives the exponential fast rise of the MFR. The system enters the propagation phase, once its apex reaches the height of about one solar radius above the photosphere. The simulation reproduces the main processes of one group of prominence eruptions especially those occurring on the quiet Sun.

An MHD Modeling of the Successive X2.2 and X9.3 Solar Flares of 2017 September 6

Abstract The solar active region 12673 produced two successive X-class flares (X2.2 and X9.3) approximately 3 hr apart in 2017 September. The X9.3 flare was the largest recorded solar flare in Solar Cycle 24. In this study we perform a data-constrained magnetohydrodynamic simulation taking into account the observed photospheric magnetic field to reveal the initiation and dynamics of the X2.2 and X9.3 flares. According to our simulation, the X2.2 flare is first triggered by magnetic reconnection at a local site where at the photosphere the negative polarity intrudes into the opposite-polarity region. This magnetic reconnection expels the innermost field lines upward, beneath which the magnetic flux rope is formed through continuous reconnection with external twisted field lines. Continuous magnetic reconnection after the X2.2 flare enhances the magnetic flux rope, which is lifted up and eventually erupts via the torus instability. This gives rise to the X9.3 flare.

Nonequilibrium Flux Rope Formation by Confined Flares Preceding a Solar Coronal Mass Ejection

Abstract We present evidence that a magnetic flux rope was formed before a coronal mass ejection (CME) and its associated long-duration flare during a pair of preceding confined eruptions and associated impulsive flares in a compound event in NOAA Active Region 12371. Extreme-ultraviolet images and the extrapolated nonlinear force-free field show that the first two (impulsive) flares, SOL2015-06-21T01:42, result from the confined eruption of highly sheared low-lying flux, presumably a seed flux rope. The eruption spawns a vertical current sheet, where magnetic reconnection creates flare ribbons and loops, a nonthermal microwave source, and a sigmoidal hot channel that can only be interpreted as a magnetic flux rope. Until the subsequent long-duration flare, SOL2015-06-21T02:36, the sigmoid’s elbows expand, while its center remains stationary, suggesting nonequilibrium but not yet instability. The “flare reconnection” during the confined eruptions acts like “tether-cutting reconnection” whose flux feeding of the rope leads to instability. The subsequent full eruption is seen as an accelerated rise of the entire hot channel, seamlessly evolving into the fast halo CME. Both the confined and ejective eruptions are consistent with the onset of the torus instability in the dipped decay index profile that results from the region’s two-scale magnetic structure. We suggest that the formation or enhancement of a nonequilibrium but stable flux rope by confined eruptions is a generic process occurring prior to many CMEs.

Laboratory Study of the Torus Instability Threshold in Solar-relevant, Line-tied Magnetic Flux Ropes

Abstract Coronal mass ejections (CMEs) occur when long-lived magnetic flux ropes (MFRs) anchored to the solar surface destabilize and erupt away from the Sun. This destabilization is often described in terms of an ideal magnetohydrodynamic instability called the torus instability. It occurs when the external magnetic field decreases sufficiently fast such that its decay index, , is larger than a critical value, , where for a full, large aspect ratio torus. However, when this is applied to solar MFRs, a range of conflicting values for is found in the literature. To investigate this discrepancy, we have conducted laboratory experiments on arched, line-tied flux ropes and applied a theoretical model of the torus instability. Our model describes an MFR as a partial torus with foot points anchored in a conducting surface and numerically calculates various magnetic forces on it. This calculation yields better predictions of that take into account the specific parameters of the MFR. We describe a systematic methodology to properly translate laboratory results to their solar counterparts, provided that the MFRs have a sufficiently small edge safety factor or, equivalently, a large enough twist. After this translation, our model predicts that in solar conditions falls near and within a larger range of , depending on the parameters. The methodology of translating laboratory MFRs to their solar counterparts enables quantitative investigations of CME initiation through laboratory experiments. These experiments allow for new physics insights that are required for better predictions of space weather events but are difficult to obtain otherwise.

Evolution of the Nonpotential Magnetic Field in the Solar Active Region 12673 Based on a Nonlinear Force-free Modeling

Abstract Active region (AR) 12673 has produced many M-class and several X-class flares, one of which being an X9.3 flare, which is recorded as the largest solar flare in solar cycle 24. We studied the evolution of the three-dimensional flare-productive magnetic field within AR 12673, using a time series of nonlinear force-free field extrapolations of every 12 hr from 2017 September 4 00:00 UT to 6 00:00 UT. Our analysis found that three magnetic flux ropes (MFRs) formed by September 4, one of which produced the X9.3 flare on September 6. One MFR has positive magnetic twist, which is a different sign from the other two MFRs. Since the temporal evolution of the magnetic flux of the MFR accumulating the positive twist is consistent with the profile of the GOES X-ray flux well observed from September 4 to 6, we suggest that the formation of the MFR having the positive twist is closely related to the occurrence of the M-class flares, including an M5.5 flare. We further found a magnetic null in the magnetic field surrounding the MFRs, in particular above the MFR having positive twist before the M5.5 flare, which is the largest M-flare observed during this period. By comparing with Atmospheric Imaging Assembly 1600 Å images, we found that the footpoints of the overlying field lines are anchored to the area where the brightening was initially observed. Therefore, we suggest that reconnection induced by the torus instability of the positively twisted MFR at the null possibly drove the M5.5 flare.

Successive occurrences of quasi-circular ribbon flares in a fan-spine-like configuration involving hyperbolic flux tube

ABSTRACT We present a comprehensive analysis of the formation and the evolution of a fan-spine-like configuration that developed over a complex photospheric configuration where dispersed negative polarity regions were surrounded by positive polarity regions. This unique photospheric configuration, analogous to the geological ‘atoll’ shape, hosted four homologous flares within its boundary. Computation of the degree of squashing factor (Q) maps clearly revealed an elongated region of high Q-values between the inner and outer spine-like lines, implying the presence of an hyperbolic flux tube (HFT). The coronal region associated with the photospheric atoll configuration was distinctly identified in the form of a diffused dome-shaped bright structure directly observed in Extreme Ultraviolet (EUV) images. A filament channel resided near the boundary of the atoll region. The activation and eruption of flux ropes from the filament channel led to the onset of four eruptive homologous quasi-circular ribbon flares within an interval of ≈11 h. During the interval of the four flares, we observed continuous decay and cancellation of negative polarity flux within the atoll region. Accordingly, the apparent length of the HFT gradually reduced to a null-point-like configuration before the fourth flare. Prior to each flare, we observed localized brightening beneath the filaments which, together with flux cancellation, provided support for the tether-cutting model of solar eruption. The analysis of magnetic decay index revealed favourable conditions for the eruption, once the pre-activated flux ropes attained the critical heights for torus instability.

Evolutionary stages and triggering process of a complex eruptive flare with circular and parallel ribbons

ABSTRACT We report multiwavelength study of a complex M-class solar eruptive flare that consists of three different sets of flare ribbons, viz. circular, parallel, and remote ribbons. Magnetic field modelling of source active region NOAA 12242 exhibits the presence of 3D null-point magnetic topology that encompasses an inner bipolar region. The event initiates with the faint signatures of the circular ribbon along with remote brightening right from the pre-flare phase that points toward the ongoing slow yet persistent null-point reconnection. We first detected flux cancellation and an associated brightening, which are likely signatures of tether-cutting reconnection that builds the flux rope near the polarity inversion line (PIL) of the inner bipolar region. In the next stage, with the onset of M8.7 flare, there is a substantial enhancement in the brightening of circular ribbon, which essentially suggests an increase in the rate of ongoing null-point reconnection. Finally, the eruption of underlying flux rope triggers ‘standard flare reconnection’ beneath it producing an abrupt rise in the intensity of the parallel ribbons as well as enhancing the rate of null-point reconnection by external forcing. We show that within the the fan dome, the region with magnetic decay index n > 1.5 borders the null-point QSL. Our analysis suggests that both the torus instability and the breakout model have played role toward the triggering mechanism for the eruptive flare. This event is a nice example of the dynamical evolution of a flux rope initially confined in a null-point topology that subsequently activates and erupts with the progression of the circular-cum-parallel ribbon flare.

Variation of Magnetic Flux Ropes through Major Solar Flares

Abstract It remains unclear how solar flares are triggered and in what conditions they can be eruptive with coronal mass ejections. Magnetic flux ropes (MFRs) has been suggested as the central magnetic structure of solar eruptions, and their ideal instabilities, including the kink instability (KI) and torus instability (TI), are important candidates for triggering mechanisms. Here, using magnetic field extrapolations from observed photospheric magnetograms, we systematically studied the variation of coronal magnetic fields, focusing on MFRs, through major flares including 29 eruptive and 16 confined events. We found that nearly 90% of events possess MFRs before flares, and 70% have MFRs even after flares. We calculated the controlling parameters of KI and TI, including the MFR’s maximum twist number and the decay index of its strapping field. Using the KI and TI thresholds empirically derived solely from the pre-flare MFRs, two distinctly different regimes are shown in the variation of the MFR controlling parameters through flares. For the events with both parameters below their thresholds before flares, we found no systematic change of the parameters after the flares, in either the eruptive or confined events. In contrast, for the events with any of the two parameters exceeding their threshold before flares (most of them are eruptive), there is systematic decrease in the parameters to below their thresholds after flares. These results provide a strong constraint for the values of the instability thresholds and also stress the necessity of exploring other eruption mechanisms in addition to the ideal instabilities.

Exploring the coronal evolution of AR 12473 using time-dependent, data-driven magnetofrictional modelling

Aims. We present a detailed examination of the magnetic evolution of AR 12473 using time-dependent, data-driven magnetofrictional modelling. Methods. We used maps of the photospheric electric field inverted from vector magnetogram observations, obtained by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO), to drive our fully time-dependent, data-driven magnetofrictional model. Our modelled field was directly compared to extreme ultraviolet observations from the Atmospheric Imaging Assembly, also onboard SDO. Metrics were also computed to provide a quantitative analysis of the evolution of the magnetic field. Results. The flux rope associated with the eruption on 28 December 2015 from AR 12473 was reproduced by the simulation and found to have erupted due to a torus instability.

On the partial eruption of a bifurcated solar filament structure

ABSTRACT The partial eruption of a filament channel with bifurcated substructures is investigated using data sets obtained from both ground-based and space-borne facilities. Small-scale flux reconnection/cancellation events in the region triggered the pile-up of ambient magnetic field, observed as bright extreme ultraviolet (EUV) loops in close proximity to the filament channel. This led to the formation of a V-shaped cusp structure at the site of interaction between the coalesced EUV loops and the filament channel, with the presence of distinct plasmoid structures and associated bidirectional flows. Analysis of imaging data from SDO/AIA further suggests vertical splitting of the filament structure into two substructures. The perturbed upper branch of the filament structure rose up and erupted with the onset of an energetic GOES M1.4 flare at 04:30 ut on 2015 January 28. The estimated twist number and squashing factor obtained from non-linear force free-field extrapolation of the magnetic field data support the vertical split in the filament structure with high twist in the upper substructure. The loss in equilibrium of the upper branch due to torus instability implies that this is a potential triggering mechanism for the observed partial eruption.

Eruptive–Impulsive Homologous M-class Flares Associated with Double-decker Flux Rope Configuration in Minisigmoid of NOAA 12673

Abstract We present a multiwavelength analysis of two homologous, short-lived, impulsive flares of GOES class M1.4 and M7.3 that occurred from a very localized minisigmoid region within the active region NOAA 12673 on 2017 September 7. Both flares were associated with initial jetlike plasma ejection that for a brief amount of time moved toward the east in a collimated manner before drastically changing direction toward the southwest. Nonlinear force-free field extrapolation reveals the presence of a compact double-decker flux rope configuration in the minisigmoid region prior to the flares. A set of open field lines originating near the active region that were most likely responsible for the anomalous dynamics of the erupted plasma gave the earliest indication of an emerging coronal hole near the active region. The horizontal field distribution suggests a rapid decay of the field above the active region, implying high proneness of the flux rope system toward eruption. In view of the low coronal double-decker flux ropes and compact extreme ultraviolet brightening beneath the filament, along with associated photospheric magnetic field changes, our analysis supports the combination of initial tether-cutting reconnection and subsequent torus instability for driving the eruption.

Caltech Lab Experiments and the Insights They Provide Into Solar Corona Phenomena

AbstractA comprehensive overview of two decades of Caltech experiments relevant to solar corona physics is presented. The extent to which the experiments scale to the solar corona, the basic configurations and operation, and the importance of the magnetic force J × B common to all the experiments is discussed. Summaries are given of the various configurations used, the main observations, and interpretations of these observations, including new models developed to provide these interpretations. Topics include observations and explanations for flux rope self‐collimation, axial flows along flux ropes, eruption of arched flux ropes, strapping magnetic fields that inhibit eruption, the torus instability, and effects such as X‐ray emission of a kink‐driven secondary Rayleigh‐Taylor instability.

An Eruptive Circular-ribbon Flare with Extended Remote Brightenings

Abstract We study an eruptive X1.1 circular-ribbon flare on 2013 November 10, combining multiwavelength observations with a coronal field reconstruction using a non-force-free field method. In the first stage, a filament forms via magnetic reconnection between two mildly twisted sheared arcades, which are embedded under the fan dome associated with a null point (NP). This reconnection seems to be driven by photospheric shearing and converging flows around the inner two arcade footpoints, consistent with the flare-related changes of the transverse field. The southern portion of the filament rises upward due to torus instability and pushes against the NP. The induced NP reconnection then generates the circular ribbon and the initial remote brightening in the west, as accelerated electrons precipitate along the fan and propagate outward along quasi-separatix surfaces with high values of the squashing factor (Q) in the envelope fields, which have a curtain-like shape here. In the second stage, the southern end of the flux rope breaks away from the surface, sequentially disrupts the dome and overlying fields, and erupts in a whipping-like fashion to become a partial halo coronal mass ejection. This leads to an enhanced flare emission and fast-moving remote brightenings at the footpoints of the magnetic curtain, which span a remarkably broad region and are also associated with coronal dimmings. This is a rare example of eruptive circular-ribbon flares, in which the evolution of a flux rope from its formation to successful eruption out of the dome and the resulting unusually extended remote brightenings are completely observed.

2D and 3D Analysis of a Torus-unstable Quiet-Sun Prominence Eruption

Abstract The role of ideal-MHD instabilities in a prominence eruption is explored through 2D and 3D kinematic analysis of an event observed with the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory between 22:06 UT on 2013 February 26 and 04:06 UT on 2013 February 27. A series of 3D radial slits are used to extract height–time profiles ranging from the midpoint of the prominence leading edge to the southeastern footpoint. These height–time profiles are fit with a kinematic model combining linear and nonlinear rise phases, returning the nonlinear onset time (t nl) as a free parameter. A range (1.5–4.0) of temporal power indices (i.e., β in the nonlinear term ) are considered to prevent prescribing any particular form of nonlinear kinematics. The decay index experienced by the leading edge is explored using a radial profile of the transverse magnetic field from a PFSS extrapolation above the prominence region. Critical decay indices are extracted for each slit at their own specific values of height at the nonlinear phase onset (h(t nl)) and filtered to focus on instances resulting from kinematic fits with (restricting β to 1.9–3.9). Based on this measure of the critical decay index along the prominence structure, we find strong evidence that the torus instability is the mechanism driving this prominence eruption. Defining any single decay index as being “critical” is not that critical because there is no single canonical or critical value of decay index through which all eruptions must succeed.

Initiation and Early Kinematic Evolution of Solar Eruptions

Abstract We investigate the initiation and early evolution of 12 solar eruptions, including six active-region hot channel and six quiescent filament eruptions, which were well observed by the Solar Dynamics Observatory, as well as by the Solar Terrestrial Relations Observatory for the latter. The sample includes one failed eruption and 11 coronal mass ejections, with velocities ranging from 493 to 2140 km s−1. A detailed analysis of the eruption kinematics yields the following main results. (1) The early evolution of all events consists of a slow-rise phase followed by a main-acceleration phase, the height–time profiles of which differ markedly and can be best fit, respectively, by a linear and an exponential function. This indicates that different physical processes dominate in these phases, which is at variance with models that involve a single process. (2) The kinematic evolution of the eruptions tends to be synchronized with the flare light curve in both phases. The synchronization is often but not always close. A delayed onset of the impulsive flare phase is found in the majority of the filament eruptions (five out of six). This delay and its trend to be larger for slower eruptions favor ideal MHD instability models. (3) The average decay index at the onset heights of the main acceleration is close to the threshold of the torus instability for both groups of events (although, it is based on a tentative coronal field model for the hot channels), suggesting that this instability initiates and possibly drives the main acceleration.