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Since solar cycle 16, the { heliospheric} current sheet (HCS) has been found to be shifted southward during the late declining to minimum phase. However, this trend is broken at the end of solar cycle 24. In this paper, we analyze the shift of the HCS by using information obtained from coronal model and insitu data provide by the near-Earth OMNI database and the Parker Solar Probe (PSP). Coronal potential field source surface (PFSS) modeling results show that the northward shift is established at the beginning of 2018 and remains stable for about two years. Interplanetary magnetic field data obtained from and within 1 au also support the northward shift, as the southern polarity T appears more frequently than the northern polarity A between 2018-2020. Both model results and insitu observation obtained by PSP imply that the HCS shift is established in the corona, and then propagates into the heliosphere. The quadrupole term still has a significant influence on the formation of the HCS shift., Comment: Accepted by MNRAS

There is a heated debate regarding the specific roles played by ideal magnetohydrodynamic (MHD) instability and magnetic reconnection in the causes of solar eruptions. In the context with a pre-existing magnetic flux rope (MFR) before an eruption, it is widely believed that an ideal MHD instability, in particular, the torus instability, is responsible for triggering and driving the eruption, while reconnection, as invoked in the wake of the erupting MFR, plays a secondary role. Here we present a new numerical MHD model in which the eruption of a pre-existing MFR is primarily triggered and driven by reconnection. In this model, a stable MFR embedded in a strapping field is set as the initial condition. A surface converging flow is then applied at the lower boundary, pushing magnetic flux towards to the main polarity inversion line. It drives a quasi-static evolution of the system, during which a current layer is built up below the MFR with decreasing thickness. Once reconnection starts in the current sheet, the eruption commences, which indicates that the reconnection plays a determining role in triggers the eruption. By further analyzing the works done by in the magnetic flux of the pre-existing MFR and the newly reconnected flux during the acceleration stage of the eruption, we find that the latter plays a major role in driving the eruption. Such a model may explain observed eruptions in which the pre-eruption MFR has not reached the conditions for ideal instability., Comment: 12 pages, 7 figures, accepted by MNRAS

The rotation of sunspots around their umbral center has long been considered as an important process in leading to solar eruptions, but the underlying mechanism remains unclear. A prevailing physical picture on how sunspot rotation leads to eruption is that, by twisting the coronal magnetic field lines from their footpoints, the rotation can build up a magnetic flux rope and drive it into some kinds of ideal magnetohydrodynamics (MHD) instabilities which initiate eruptions. Here with a data-inspired MHD simulation we studied the rotation of a large sunspot in solar active region NOAA 12158 leading to a major eruption, and found that it is distinct from prevailing theories based on ideal instabilities of twisted flux rope. The simulation suggests that, through successive rotation of the sunspot, the coronal magnetic field is sheared with a central current sheet created progressively within the sheared arcade before the eruption, but without forming a flux rope. Then the eruption is instantly triggered once fast reconnection sets in at the current sheet, while a highly twisted flux rope is created during the eruption. Furthermore, the simulation reveals an intermediate evolution stage between the quasi-static energy-storage phase and the impulsive eruption-acceleration phase. This stage may correspond to the slow-rise phase in observation and it enhances building up of the current sheet., Comment: Updated from the initial version and text overlap with arXiv:2308.06977 is removed

Solar eruptions are the leading driver of space weather, and it is vital for space weather forecast to understand in what conditions the solar eruptions can be produced and how they are initiated. The rotation of sunspots around their umbral center has long been considered as an important condition in causing solar eruptions. To unveil the underlying mechanisms, here we carried out a data-driven magnetohydrodynamics simulation for the event of a large sunspot with rotation for days in solar active region NOAA 12158 leading to a major eruption. The photospheric velocity as recovered from the time sequence of vector magnetograms are inputted directly at the bottom boundary of the numerical model as the driving flow. Our simulation successfully follows the long-term quasi-static evolution of the active region until the fast eruption, with magnetic field structure consistent with the observed coronal emission and onset time of simulated eruption matches rather well with the observations. Analysis of the process suggests that through the successive rotation of the sunspot the coronal magnetic field is sheared with a vertical current sheet created progressively, and once fast reconnection sets in at the current sheet, the eruption is instantly triggered, with a highly twisted flux rope originating from the eruption. This data-driven simulation stresses magnetic reconnection as the key mechanism in sunspot rotation leading to eruption., Comment: Accept by A&A

Recently we established a fundamental mechanism of solar eruption initiation, in which an eruption can be initiated from a bipolar field through magnetic reconnection in the current sheet (CS) that is formed slowly in the core field as driven by photospheric shearing motion. Here using a series of fully 3D MHD simulations with a range of different photospheric magnetic flux distributions, we extended this fundamental mechanism to the quadrupolar magnetic field containing a null point above the core field, which is the basic configuration of the classical breakout model. As is commonly believed, in such multipolar configuration, the reconnection triggered in the CS originated at the null point (namely, the breakout reconnection) plays the key role in eruption initiation by establishing a positive feedback-loop between the breakout reconnection and the expansion of the core field. However, our simulation showed that the key of eruption initiation in such multipolar configuration remains to be the slow formation of the CS in the sheared core rather than the onset of fast breakout reconnection. The breakout reconnection only helps the formation of the core CS by letting the core field expand faster, but the eruption cannot occur when the bottom surface driving is stopped well before the core CS is formed, even though the fast reconnection has already been triggered in the breakout CS. This study clarified the role of breakout reconnection and confirmed formation of the core CS as the key to the eruption initiation in a multipolar magnetic field., Comment: 21 pages, 12 figures, 4 animations

Solar eruptions are explosive disruption of coronal magnetic fields, and often launch coronal mass ejections into the interplanetary space. Intriguingly, many solar eruptions fail to escape from the Sun, and the prevailing theory for such failed eruption is based on ideal MHD instabilities of magnetic flux rope (MFR); that is, a MFR runs into kink instability and erupts but cannot reach the height for torus instability. Here, based on numerical MHD simulation, we present a new model of failed eruption in which magnetic reconnection plays a leading role in the initiation and failure of the eruption. Initially, a core bipolar potential field is embedded in a background bipolar field, and by applying shearing and converging motions to the core field, a current sheet is formed within the core field. Then, tether-cutting reconnection is triggered at the current sheet, first slow for a while and becoming fast, driving an erupting MFR. Eventually, the rise of MFR is halted by the downward magnetic tension force of the overlying field, although the MFR apex has well exceeded the critical height of torus instability. More importantly, during the rise of the MFR, it experiences a significant rotation around the vertical axis (with a direction contrary to that predicted by kink instability), rendering the field direction at the rope apex almost inverse to the overlying field. As a result, a strong current sheet is formed between the MFR and the overlying flux, and reconnection occurring in this current sheet ruins completely the MFR., Comment: Submitted to MNRAS

In this paper we study the initiation mechanism of the first on-disk X-class eruptive flare in solar cycle 25. Coronal magnetic field reconstructions reveal a magnetic flux rope (MFR) with configuration highly consistent with a filament existing for a long period before the flare, and the eruption of the whole filament indicates that the MFR erupted during the flare. However, quantitative analysis shows that the pre-flare MFR resides in a height too low to trigger a torus instability (TI). The filament experienced a slow rise before the flare onset, for which we estimate evolution of the filament height using a triangulation method by combining the SDO and STEREO observations, and find it is also much lower than the critical height for triggering TI. On the other hand, the pre-flare evolution of the current density shows progressive thinning of a vertical current layer on top of the flare PIL, which suggests that a vertical current sheet forms before the eruption. Meanwhile, there is continuously shearing motion along the PIL under the main branch of the filament, which can drive the coronal field to form such a current sheet. As such, we suggest that the event follows a reconnection-based initiation mechanism as recently established using a high-accuracy MHD simulation, in which an eruption is initiated by reconnection in a current sheet that forms gradually within continuously-sheared magnetic arcade. The eruption should be further driven by TI as the filament quickly rises into the TI domain during the eruption.

Solar flares fall into two types with eruptive ones associated with coronal mass ejection (CME) and confined ones without CME. To explore whether there are pre-flare conditions in terms of magnetic energy and helicity that can effectively determine the types of flares, here we analyzed a suite of related parameters of the reconstructed pre-flare coronal magnetic field of major solar flares, either eruptive or confined, from 2011 to 2017 near the solar disk center. The investigated parameters include the extensive-type quantities such as the total magnetic energy $E_T$, the potential energy $E_P$, the free energy $E_F$, the relative helicity $H_R$, and the non-potential helicity $H_J$, as well as the intensive-type indices $E_F/E_P$, $|H_J/H_R|$, $|H_R/\phi^{\prime2}|$ and $|H_J/\phi^{\prime2}|$, where $\phi^{\prime}$ is half of the total unsigned magnetic flux. We have the following key findings: (1) None of the extensive parameters can effectively distinguish the eruptive and confined potential of the pre-flare coronal fields, though the confined events have averagely larger values; (2) All the intensive parameters have significantly larger average and median values for eruptive flares than the confined events, which indicates that the field for eruptive flares have overall higher degree of non-potentiality and complexity than that of the confined flares; (3) The energy ratio $E_F/E_P$ and the normalized non-potential helicity $|H_J/\phi^{\prime2}|$, which are strongly correlated with each other, have among the highest capability of distinguishing the fields that possibly produce a major eruptive or confined flare, as over 75\% of all the events are successfully discriminated between eruptive and confined flares by using critical values of $E_F/E_P\ge0.27$ and $|H_J/\phi^{\prime2}|\ge0.009$., Comment: accepted by ApJ

Data-driven simulation is becoming an important approach for realistically characterizing the configuration and evolution of solar active regions, revealing the onset mechanism of solar eruption events and hopefully achieving the goal of accurate space weather forecast, which is beyond the scope of any existing theoretical modelling. Here we performed a full 3D MHD simulation using the data-driven approach and followed the whole evolution process from quasi-static phase to eruption successfully for solar active region NOAA 11429. The MHD system was driven at the bottom boundary by photospheric velocity field, which is derived by the DAVE4VM method from the observed vector magnetograms. The simulation shows that a magnetic flux rope was generated by persistent photospheric flow before the flare onset and then triggered to erupt by torus instability. Our simulation demonstrates a high degree of consistency with observations in the pre-eruption magnetic structure, the time scale of quasi-static stage, the pattern of flare ribbons as well as the time evolution of magnetic energy injection and total unsigned magnetic flux. We further found that an eruption can also be initiated in the simulation as driven by only the horizontal components of photospheric flow, but a comparison of the different simulations indicates that the vertical flow at the bottom boundary is necessary in reproducing more realistically these observed features, emphasizing the importance of flux emergence during the development of this AR., Comment: 12 pages, 5 figures

Magnetic flux emergence from the solar interior to the atmosphere is believed to be a key process of formation of solar active regions and driving solar eruptions. Due to the limited capability of observation, the flux emergence process is commonly studied using numerical simulations. In this paper, we developed a numerical model to simulate the emergence of a twisted magnetic flux tube from the convection zone to the corona using the AMR--CESE--MHD code, which is based on the conservation-element solution-element method with adaptive mesh refinement. The result of our simulation agrees with that of many previous ones with similar initial conditions but using different numerical codes. In the early stage, the flux tube rises from the convection zone as driven by the magnetic buoyancy until it reaches close to the photosphere. The emergence is decelerated there and with piling-up of the magnetic flux, the magnetic buoyancy instability is triggered, which allows the magnetic field to partially enter into the atmosphere. Meanwhile, two gradually separated polarity concentration zones appear in the photospheric layer, transporting the magnetic field and energy into the atmosphere through their vortical and shearing motions. Correspondingly, the coronal magnetic field has also been reshaped to a sigmoid configuration containing a thin current layer, which resembles the typical pre-eruptive magnetic configuration of an active region. Such a numerical framework of magnetic flux emergence as established will be applied in future investigations of how solar eruptions are initiated in flux emergence active regions.

It is well known that major solar eruptions are often produced by active regions with continual photospheric shearing and converging motions. Here, through high accuracy magnetohydrodynamics simulation, we show how solar eruption is initiated in a single bipolar configuration as driven by first shearing and then converging motions at the bottom surface. Different from many previous simulations, we applied the converging motion without magnetic diffusion, thus it only increases the magnetic gradient across the polarity inversion line but without magnetic flux cancellation. The converging motion at the footpoints of the sheared arcade creates a current sheet in a quasi-static way, and the eruption is triggered by magnetic reconnection of the current sheet, which supports the same scenario as shown in our previous simulation with only shearing motion. With the converging motion, the current sheet is formed at a lower height and has a higher current density than with shearing motion alone, which makes reconnection more effective and eruption stronger. Moreover, the converging motion renders a fast decay rate of the overlying field with height and thus favorable for an eruption. This demonstrate that the converging flow is more efficient to create the current sheet and more favorable for eruption than by solely the shearing flow.

The relationship between solar eruption and sunspot rotation has been widely reported, and the underlying mechanism requires to be studied. Here we performed a full 3D MHD simulation of data-constrained approach to study the mechanism of flare eruptions in active region (AR) NOAA 10930, which is characterized by continuous sunspot rotation and homologous eruptions. We reconstructed the potential magnetic field from the magnetogram of Hinode/SOT as the initial condition and drove the MHD system by applying continuous sunspot rotation at the bottom boundary. The key magnetic structure before the major eruptions and the pre-formed current sheet were derived, which is responsible for the complex MHD evolution with multiple stages. The major eruptions were triggered directly by fast reconnection in the pre-formed current sheet above the main polarity inversion line between the two major magnetic polarities of the AR. Furthermore, our simulation shows the homologous eruption successfully. It has reasonable consistence with observations in relative strength, energy release, X-ray and H{\alpha} features and time interval of eruptions. In addition, the rotation angle of the sunspot before the first eruption in the simulation is also close to the observed value. Our simulation offers a scenario different from many previous studies based on ideal instabilities of twisted magnetic flux rope, and shows the importance of sunspot rotation and magnetic reconnection in efficiently producing homologous eruptions by continuous energy injection and impulsive energy release in a recurrent way.

The Sun often produces coronal mass ejections with similar structure repeatedly from the same source region, and how these homologous eruptions are initiated remains an open question. Here, by using a new magnetohydrodynamic simulation, we show that homologous solar eruptions can be efficiently produced by recurring formation and disruption of coronal current sheet as driven by continuously shearing of the same polarity inversion line within a single bipolar configuration. These eruptions are initiated by the same mechanism, in which an internal current sheet forms slowly in a gradually sheared bipolar field and reconnection of the current sheet triggers and drives the eruption. Each of the eruptions does not release all the free energy but with a large amount left in the post-flare arcade below the erupting flux rope. Thus, a new current sheet can be more easily formed by further shearing of the post-flare arcade than by shearing a potential field arcade, and this is favorable for producing the next eruption. Furthermore, it is found that the new eruption is stronger since the newly formed current sheet has a larger current density and a lower height. In addition, our results also indicate the existence of a magnetic energy threshold for a given flux distribution, and eruption occurs once this threshold is approached.

Solar eruptions are explosive release of coronal magnetic field energy as manifested in solar flares and coronal mass ejection. Observations have shown that the core of eruption-productive regions are often a sheared magnetic arcade, i.e., a single bipolar configuration, and, particularly, the corresponding magnetic polarities at the photosphere are elongated along a strong-gradient polarity inversion line (PIL). It remains unclear what mechanism triggers the eruption in a single bipolar field and why the one with a strong PIL is eruption-productive. Recently, using high accuracy simulations, we have established a fundamental mechanism of solar eruption initiation that a bipolar field as driven by quasi-static shearing motion at the photosphere can form an internal current sheet, and then fast magnetic reconnection triggers and drives the eruption. Here we investigate the behavior of the fundamental mechanism with different photospheric magnetic flux distributions, i.e., magnetograms, by combining theoretical analysis and numerical simulation. Our study shows that the bipolar fields of different magnetograms, as sheared continually, all exhibit similar evolutions from the slow storage to fast release of magnetic energy in accordance with the fundamental mechanism, which demonstrates the robustness of the mechanism. We further found that the magnetograms with stronger PIL produce larger eruptions, and the key reason is that the sheared bipolar fields with stronger PIL can achieve more non-potentiality, and their internal current sheet can form at a lower height and with a larger current density, by which the reconnection can be more efficient. This also provides a viable trigger mechanism for the observed eruptions in active region with strong PIL.

Magnetic flux ropes (MFRs) constitute the core structure of coronal mass ejections (CMEs), but hot debates remain on whether the MFR forms before or during solar eruptions. Furthermore, how flare reconnection shapes the erupting MFR is still elusive in three dimensions. Here we studied a new MHD simulation of CME initiation by tether-cutting magnetic reconnection in a single magnetic arcade. The simulation follows the whole life, including the birth and subsequent evolution, of an MFR during eruption. In the early phase, the MFR is partially separated from its ambient field by a magnetic quasi-separatrix layer (QSL) that has a double-J shaped footprint on the bottom surface. With the ongoing of the reconnection, the arms of the two J-shaped footprints continually separate from each other, and the hooks of the J shaped footprints expand and eventually become closed almost at the eruption peak time, and thereafter the MFR is fully separated from the un-reconnected field by the QSL. We further studied the evolution of the toroidal flux in the MFR and compared it with that of the reconnected flux. Our simulation reproduced an evolution pattern of increase-to-decrease of the toroidal flux, which is reported recently in observations of variations in flare ribbons and transient coronal dimming. The increase of toroidal flux is owing to the flare reconnection in the early phase that transforms the sheared arcade to twisted field lines, while its decrease is a result of reconnection between field lines in the interior of the MFR in the later phase., Comment: 10 pages, 5 figures, accepted by Frontiers in Physics

Solar eruptions are spectacular magnetic explosions in the Sun's corona, and how they are initiated remains unclear. Prevailing theories often rely on special magnetic topologies that may not generally exist in the pre-eruption source region of corona. Here, using fully three-dimensional magnetohydrodynamic simulations with high accuracy, we show that solar eruptions can be initiated in a single bipolar configuration with no additional special topology. Through photospheric shearing motion alone, an electric current sheet forms in the highly sheared core field of the magnetic arcade during its quasi-static evolution. Once magnetic reconnection sets in, the whole arcade is expelled impulsively, forming a fast-expanding twisted flux rope with a highly turbulent reconnecting region underneath. The simplicity and efficacy of this scenario argue strongly for its fundamental importance in the initiation of solar eruptions., Comment: Published in Nature Astronomy (2021)

The solar minimum 23/24 is considered to be unusual because it exhibits features that differ notably from those commonly seen in pervious minima. In this letter, we analyze the solar polar magnetic field, the potential-field solution of the solar corona, and the in-situ solar wind measurements to see whether the recent solar minimum 24/25 is another unusual one. While the dipolar configuration that are commonly seen during minimum 22/23 and earlier minima persist for about half a year after the absolute minimum of solar cycle 24, the corona has a morphology more complex than a simple dipole before the absolute minimum. The fast solar wind streams are less dominant than minimum 23/24. The IMF strength, density and mass flux that are historically low in the minimum 23/24 are regained during minimum 24/25, but still do not reach the minimum 22/23 level. From the analysis of this Letter, it seems that the minimum 24/25 is only partially unusual, and the recovery of the commonly minimum features may result from the enhancement of the polar field., Comment: Accepted by APJL

It is well known that magnetic fields dominate the dynamics in the solar corona, and new generation of numerical modelling of the evolution of coronal magnetic fields, as featured with boundary conditions driven directly by observation data, are being developed. This paper describes a new approach of data-driven magnetohydrodynamic (MHD) simulation of solar active region (AR) magnetic field evolution, which is for the first time that a data-driven full-MHD model utilizes directly the photospheric velocity field from DAVE4VM. We constructed a well-established MHD equilibrium based on a single vector magnetogram by employing an MHD-relaxation approach with sufficiently small kinetic viscosity, and used this MHD equilibrium as the initial conditions for subsequent data-driven evolution. Then we derived the photospheric surface flows from a time series of observed magentograms based on the DAVE4VM method. The surface flows are finally inputted in time sequence to the bottom boundary of the MHD model to self-consistently update the magnetic field at every time step by solving directly the magnetic induction equation at the bottom boundary. We applied this data-driven model to study the magnetic field evolution of AR 12158 with SDO/HMI vector magnetograms. Our model reproduced a quasi-static stress of the field lines through mainly the rotational flow of the AR's leading sunspot, which makes the core field lines to form a coherent S shape consistent with the sigmoid structure as seen in the SDO/AIA images. The total magnetic energy obtained in the simulation matches closely the accumulated magnetic energy as calculated directly from the original vector magnetogram with the DAVE4VM derived flow field. Such a data-driven model will be used to study how the coronal field, as driven by the slow photospheric motions, reaches a unstable state and runs into eruptions., Comment: 11 pages, 8 figures, accepted by Frontiers in Physics

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 mainly the kink instability (KI) and torus instability (TI) provide 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\% events possess MFR before flare and 70\% have MFR even after flare. 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 from solely the pre-flare MFRs, two distinct different regimes are shown in the variation of the MFR controlling parameters through flares. For the events with both parameters below their thresholds before flare, 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 flare (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., Comment: 8 pages, 4 figures, accepted by ApJL

This review article summarizes the advancement in the studies of Earth-affecting solar transients in the last decade that encompasses most of solar cycle 24. The Sun Earth is an integrated physical system in which the space environment of the Earth sustains continuous influence from mass, magnetic field and radiation energy output of the Sun in varying time scales from minutes to millennium. This article addresses short time scale events, from minutes to days that directly cause transient disturbances in the Earth space environment and generate intense adverse effects on advanced technological systems of human society. Such transient events largely fall into the following four types: (1) solar flares, (2) coronal mass ejections (CMEs) including their interplanetary counterparts ICMEs, (3) solar energetic particle (SEP) events, and (4) stream interaction regions (SIRs) including corotating interaction regions (CIRs). In the last decade, the unprecedented multi viewpoint observations of the Sun from space, enabled by STEREO Ahead/Behind spacecraft in combination with a suite of observatories along the Sun-Earth lines, have provided much more accurate and global measurements of the size, speed, propagation direction and morphology of CMEs in both 3-D and over a large volume in the heliosphere. Several advanced MHD models have been developed to simulate realistic CME events from the initiation on the Sun until their arrival at 1 AU. Much progress has been made on detailed kinematic and dynamic behaviors of CMEs, including non-radial motion, rotation and deformation of CMEs, CME-CME interaction, and stealth CMEs and problematic ICMEs. The knowledge about SEPs has also been significantly improved., Comment: Review article, 184 pages

Solar eruptions are the most powerful drivers of space weather. To understand their cause and nature, it is crucial to know how the coronal magnetic field evolves before eruption. Here we study the formation process of a relatively large-scale magnetic flux rope (MFR) in active region NOAA~12371 that erupts with a major flare and coronal mass ejection on 2015 June 21. A data-driven numerical magnetohydrodynamic model is employed to simulate three-dimensional coronal magnetic field evolution of one-day duration before the eruption. Comparison between the observed features and our modeled magnetic field discloses how the pre-eruption MFR forms. Initially, the magnetic field lines were weakly twisted as being simple sheared arcades. Then a long MFR was formed along the polarity inversion line due to the complex photospheric motion, which is mainly shearing rather than twisting. The presence of the MFR is evidenced by a coherent set of magnetic field lines with twist number above unity. Below the MFR a current sheet is shown in the model, suggesting that tether-cutting reconnection plays a key role in the MFR formation. The MFR's flux grows as more and more field lines are twisted due to continuous injection of magnetic helicity by the photospheric motions. Meanwhile, the height of the MFR's axis increases monotonely from its formation. By an analysis of the decay index of its overlying field, we suggest that it is because the MFR runs into the torus instability regime and becomes unstable that finally triggers the eruption., Comment: 10 pages, 6 figures, accept by ApJ

Two X-class solar flares occurred on 2017 September 6 from active region NOAA 12673: the first one is a confined X2.2 flare, and it is followed only $\sim 3$ hours later by the second one, which is the strongest flare in solar cycle 24, reaching X9.3 class and accompanied with a coronal mass ejection. Why these two X-class flares occurred in the same position with similar magnetic configurations, but one is eruptive while the other is not? Here we track the coronal magnetic field evolution via nonlinear force-free field extrapolations from a time sequence of vector magnetograms with high cadence. A detailed analysis of the magnetic field shows that a magnetic flux rope (MFR) forms and grows gradually before the first flare, and shortly afterwards, the MFR's growth is significantly enhanced with a much faster rise in height, from far below the threshold of torus instability to above it, while the magnetic twist only increases mildly. Combining EUV observations and the magnetic field extrapolation, we found that overlying the MFR is a null-point magnetic topology, where recurrent brightening is seen after the first flare. We thus suggest a scenario to interpret the occurrence of the two flares. The first flare occurred since the MFR reached a high enough height to activate the null point, and its continuous expansion forces the null-point reconnection recurrently. Such reconnection weakens the overlying field, allowing the MFR to rise faster, which eventually crosses the threshold of torus instability and triggers the second, eruptive flare., Comment: 11 pages, 5 figures, accepted by ApJ

The Kelvin-Helmholtz (KH) instability is commonly found in many astrophysical, laboratory, and space plasmas. It could mix plasma components of different properties and convert dynamic fluid energy from large scale structure to smaller ones. In this study, we combined the ground-based New Vacuum Solar Telescope (NVST) and the Solar Dynamic Observatories (SDO) / Atmospheric Imaging Assembly (AIA) to observe the plasma dynamics associated with active region 12673 on 09 September 2017. In this multi-temperature view, we identified three adjacent layers of plasma flowing at different speeds, and detected KH instabilities at their interfaces. We could unambiguously track a typical KH vortex and measure its motion. We found that the speed of this vortex suddenly tripled at a certain stage. This acceleration was synchronized with the enhancements in emission measure and average intensity of the 193 \AA{} data. We interpret this as evidence that KH instability triggers plasma heating. The intriguing feature in this event is that the KH instability observed in the NVST channel was nearly complementary to that in the AIA 193 \AA{}. Such a multi-thermal energy exchange process is easily overlooked in previous studies, as the cold plasma component is usually not visible in the extreme ultraviolet channels that are only sensitive to high temperature plasma emissions. Our finding indicates that embedded cold layers could interact with hot plasma as invisible matters. We speculate that this process could occur at a variety of length scales and could contribute to plasma heating., Comment: 3 figures

Magnetic flux ropes (MFRs) are thought to be the central structure of solar eruptions, and their ideal MHD instabilities can trigger the eruption. Here we performed a study of all the MFR configurations that lead to major solar flares, either eruptive or confined, from 2011 to 2017 near the solar disk center. The coronal magnetic field is reconstructed from observed magnetograms, and based on magnetic twist distribution, we identified the MFR, which is defined as a coherent group of magnetic field lines winding an axis with more than one turn. It is found that 90% of the events possess pre-flare MFRs, and their three-dimensional structures are much more complex in details than theoretical MFR models. We further constructed a diagram based on two parameters, the magnetic twist number which controls the kink instability (KI), and the decay index which controls the torus instability (TI). It clearly shows lower limits for TI and KI thresholds, which are $n_{\rm crit} = 1.3$ and $|T_w|_{\rm crit} = 2$, respectively, as all the events above $n_{\rm crit}$ and nearly 90% of the events above $|T_w|_{\rm crit}$ erupted. Furthermore, by such criterion, over 70% of the events can be discriminated between eruptive and confined flares, and KI seems to play a nearly equally important role as TI in discriminating between the two types of flare. There are more than half of events with both parameters below the lower limits, and 29% are eruptive. These events might be triggered by magnetic reconnection rather than MHD instabilities., Comment: 18 pages, 11 figures, accept by ApJ

Solar flares are often associated with coronal eruptions, but there are confined ones without eruption, even for some X-class flares. How such large flares occurred and why they are confined are still not well understood. Here we studied a confined X2.2 flare in NOAA 12673 on 2017 September 6. It exhibits two episodes of flare brightening with rather complex, atypical ribbons. Based on topology analysis of extrapolated coronal magnetic field, we revealed that there is a two-step magnetic reconnection process during the flare. Prior to the flare, there is a magnetic flux rope (MFR) with one leg rooted in a rotating sunspot. Neighboring to the leg is a magnetic null-point structure. The sunspot drives the MFR to expand, pushing magnetic flux to the null point, and reconnection is first triggered there. The disturbance from the null-point reconnection triggers the second reconnection, i.e., a tether-cutting reconnection below the rope. However, these two reconnections failed to produce an eruption, because the rope is firmly held by its strapping flux. Furthermore, we compared this flare with an eruptive X9.3 flare in the same region with 2 hours later, which has a similar MFR configuration. The key difference between them is that, for the confined flare, the MFR is fully below the threshold of torus instability, while for the eruptive one, the MFR reaches entirely above the threshold. This study provides a good evidence supporting that reconnection alone may not be able to trigger eruption, rather, MHD instability plays a more important role., Comment: accept by ApJ

Three-dimensional magnetic topology is crucial to understanding the explosive release of magnetic energy in the corona during solar flares. Much attention has been given to the pre-flare magnetic topology to identify candidate sites of magnetic reconnection, yet it is unclear how the magnetic reconnection and its attendant topological changes shape the eruptive structure and how the topology evolves during the eruption. Here we employed a realistic, data-constrained magnetohydrodynamic simulation to study the evolving magnetic topology for an X9.3 eruptive flare that occurred on 2017 September 6. The simulation successfully reproduces the eruptive features and processes in unprecedented detail. The numerical results reveal that the pre-flare corona contains multiple twisted flux systems with different connections, and during the eruption, these twisted fluxes form a coherent flux rope through tether-cutting-like magnetic reconnection below the rope. Topological analysis shows that the rising flux rope is wrapped by a quasi-separatrix layer, which intersects itself below the rope, forming a topological structure known as hyperbolic flux tube, where a current sheet develops, triggering the reconnection. By mapping footpoints of the newly-reconnected field lines, we are able to reproduce both the spatial location and, for the first time, the temporal separation of the observed flare ribbons, as well as the dynamic boundary of the flux rope's feet. Futhermore, the temporal profile of the total reconnection flux is comparable to the soft X-ray light curve. Such a sophisticated characterization of the evolving magnetic topology provides important insight into the eventual understanding and forecast of solar eruptions., Comment: Accepted by ApJ. arXiv admin note: substantial text overlap with arXiv:1802.02759

Accurate forecasting of the properties of coronal mass ejections as they approach Earth is now recognized as an important strategic objective for both NOAA and NASA. The time of arrival of such events is a key parameter, one that had been anticipated to be relatively straightforward to constrain. In this study, we analyze forecasts submitted to the Community Coordinated Modeling Center (CCMC) at NASA's Goddard Space Flight Center over the last six years to answer the following questions: (1) How well do these models forecast the arrival time of CME-driven shocks? (2) What are the uncertainties associated with these forecasts? (3) Which model(s) perform best? (4) Have the models become more accurate during the past six years? We analyze all forecasts made by 32 models from 2013 through mid 2018, and additionally focus on 28 events all of which were forecasted by six models. We find that the models are generally able to predict CME-shock arrival times -- in an average sense -- to within 10 hours, but with standard deviations often exceeding 20 hours. The best performers, on the other hand, maintained a mean error (bias) of -1 hour, a mean absolute error of 13 hours, and a precision (s.d.) of 15 hours. Finally, there is no evidence that the forecasts have become more accurate during this interval. We discuss the intrinsic simplifications of the various models analyzed, the limitations of this investigation, and suggest possible paths to improve these forecasts in the future.

Three-dimensional magnetic topology of solar flare plays a crucial role in understanding its explosive release of magnetic energy in the corona. However, such three-dimensional coronal magnetic field is still elusive in direct observation. Here we realistically simulate the magnetic evolution during the eruptive process of a great flare, using a numerical magnetohydrodynamic model constrained by observed solar vector magnetogram. The numerical results reveal that the pre-flare corona contains multi-set twisted magnetic flux, which forms a coherent rope during the eruption. The rising flux rope is wrapped by a quasi-separatrix layer, which intersects itself below the rope, forming a hyperbolic flux tube and magnetic reconnection is triggered there. By tracing the footprint of the newly-reconnected field lines, we reproduce both the spatial location and its temporal evolution of flare ribbons with an expected accuracy in comparison of observed images. This scenario strongly confirms the three-dimensional version of standard flare model., Comment: 20 pages, 9 figures, (and 5 supplementary movies which are available from the author upon request). Comments are welcome

Further studies on the corner singularity of GS reconstruction are are compiled in this paper. It's focused on solution of the Data Completion (DC) problem with the Extended Hilbert Transform (EHT) over plane rectangular region. Optimal selections of the regular parameters in{\it Tikhonov} solution of corresponding DC problem are developed in this study. The 6-parameter regular solutions and the {\it Jacobian} matrix and one {\it Hessian} tensor to the regular parameters are derived in this work. A concise formula for EHT in the near field of corners, which shows property for EHT near the corner, are also provided. It serves as the additional constraints for our parameter optimization problem (OP). Third, a nonlinear convex function defined by the regular solution and the corner constraints is introduced and is taken as the object function for the OP of the 6 regular parameters on half-space $(\mathbf{p}>0)$. Given an initial guess of $\mathbf{p}_0$, the optimal parameters are solved from the OP through a well known constrained nonlinear optimization method. Last, the benchmark tests to the proposed solution approach are carried out, and detailed results from totally 9 different bench-cases are tabulated. In contrast to solutions with given regular parameters, our bench results demonstrate that an objective way for selection of the optimal $\mathbf{p}$ is successfully laid out here. Robustness and efficiency of the suggested new approach are also highlighted in this study., Comment: 7 pages, 3 figures, and 2 tables