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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.