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 which, however, 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 eruption 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.

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Solar eruptions are well-recognized as major drivers of space weather but what causes them remains an open question. Here we show how an eruption is initiated in a non-potential magnetic flux-emerging region using magnetohydrodynamic modelling driven directly by solar magnetograms. Our model simulates the coronal magnetic field following a long-duration quasi-static evolution to its fast eruption. The field morphology resembles a set of extreme ultraviolet images for the whole process. Study of the magnetic field suggests that in this event, the key transition from the pre-eruptive to eruptive state is due to the establishment of a positive feedback between the upward expansion of internal stressed magnetic arcades of new emergence and an external magnetic reconnection which triggers the eruption. Such a nearly realistic simulation of a solar eruption from origin to onset can provide important insight into its cause, and also has the potential for improving space weather modelling.

Current magnetohydrodynamic (MHD) simulations of the initiation of solar eruptions are still commonly carried out with idealized magnetic field models, whereas the realistic coronal field prior to eruptions can possibly be reconstructed from the observable photospheric field. Using a nonlinear force-free field extrapolation prior to a sigmoid eruption in AR 11283 as the initial condition in a MHD model, we successfully simulate the realistic initiation process of the eruption event, as is confirmed by a remarkable resemblance to the SDO/AIA observations. Analysis of the pre-eruption field reveals that the envelope flux of the sigmoidal core contains a coronal null and furthermore the flux rope is prone to a torus instability. Observations suggest that reconnection at the null cuts overlying tethers and likely triggers the torus instability of the flux rope, which results in the eruption. This kind of simulation demonstrates the capability of modeling the realistic solar eruptions to provide the initiation process.

We present a magnetic analysis of the formation and eruption of an active region (AR) sigmoid in AR 11283 from 2011 September 4 to 6. To follow the quasi-static evolution of the coronal magnetic field, we reconstruct a time sequence of static fields using a recently developed nonlinear force-free field model constrained by the SDO/HMI vector magnetograms. A detailed analysis of the fields compared with the SDO/AIA observations suggests the following scenario for the evolution of the region. Initially, a new bipole emerges into the negative polarity of a pre-existing bipolar AR, forming a null point topology between the two flux systems. A weakly twisted flux rope (FR) is then built up slowly in the embedded core region, largely through flux-cancellation photospheric reconnections, forming a bald patch separatrix surface (BPSS) separating the FR from its ambient field. The FR grows gradually until its axis runs into a torus instability (TI) domain near the end of the third day, and the BPSS also develops a fully S-shape. Unlike in the case of standard TI, the FR does not erupt instantly since it is still attached at the photosphere along the bald patch (BP) portion of the polarity inversion line. The combined effects of the TI-driven expansion of the FR and the line-tying at the BP tear the FR into two parts with the upper portion freely expelled and the lower portion remaining behind the post-flare arcades. This process dynamically perturbs the BPSS and results in the transient enhanced brightening of the sigmoid. The accelerated expansion of the upper portion of the FR strongly pushes its envelope flux near the null point and triggers breakout reconnection at the null, as evidenced by a remarkable circular flare ribbon, which further facilitates the eruption. We discuss the important implications of these results for the formation and disruption of sigmoid region with FR.

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 crit = 1.3 and |T w | crit = 2, respectively, as all the events above n crit and nearly 90% of the events above |T w | 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.

The magnetic flux rope is among the most fundamental magnetic configurations in plasma. Although its presence after solar eruptions has been verified by spacecraft measurements near Earth, its formation on the Sun remains elusive, yet is critical to understanding a broad spectrum of phenomena. Here we study the dynamic formation of a magnetic flux rope during a classic two-ribbon flare. Its feet are identified unambiguously with conjugate coronal dimmings completely enclosed by irregular bright rings, which originate and expand outward from the far ends of flare ribbons. The expansion is associated with the rapid ribbon separation during the flare main phase. Counting magnetic flux through the feet and the ribbon-swept area reveals that the rope’s core is more twisted than its average of four turns. It propagates to the Earth as a typical magnetic cloud possessing a similar twist profile obtained by the Grad-Shafranov reconstruction of its three dimensional structure.

Due to the absence of direct measurement, the magnetic field in the solar corona is usually extrapolated from the photosphere in numerical way. At the moment, the nonlinear force-free field (NLFFF) model dominates the physical models for field extrapolation in the low corona. Recently we have developed a new NLFFF model with MHD relaxation to reconstruct the coronal magnetic field. This method is based on CESE-MHD model with the conservation-element/solution-element (CESE) spacetime scheme. In this paper, we report the application of the CESE-MHD-NLFFF code to SDO/HMI data with magnetograms sampled for two active regions (ARs), NOAA AR 11158 and 11283, both of which were very non-potential, producing X-class flares and eruptions. The raw magnetograms are preprocessed to remove the force and then inputted into the extrapolation code. Qualitative comparison of the results with the SDO/AIA images shows that our code can reconstruct magnetic field lines resembling the EUV-observed coronal loops. Most important structures of the active regions are reproduced excellently, like the highly-sheared field lines that suspend filaments in AR 11158 and twisted flux rope which corresponds to a sigmoid in AR 11283. Quantitative assess of the results shows that the force-free constraint is fulfilled very well in the strong-field regions but apparently not that well in the weak-field regions because of data noise and numerical errors in the small currents.