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We present a magnetic analysis of the formation and eruption of an activeregion (AR) sigmoid in AR 11283 from 2011 September 4 to 6. To follow thequasi-static evolution of the coronal magnetic field, we reconstruct a timesequence of static fields using a recently developed nonlinear force-free fieldmodel constrained by the SDO/HMI vector magnetograms. A detailed analysis ofthe fields compared with the SDO/AIA observations suggests the followingscenario for the evolution of the region. Initially, a new bipole emerges intothe negative polarity of a pre-existing bipolar AR, forming a null pointtopology between the two flux systems. A weakly twisted flux rope (FR) is thenbuilt up slowly in the embedded core region, largely through flux-cancellationphotospheric reconnections, forming a bald patch separatrix surface (BPSS)separating the FR from its ambient field. The FR grows gradually until its axisruns into a torus instability (TI) domain near the end of the third day, andthe BPSS also develops a fully S-shape. Unlike in the case of standard TI, theFR does not erupt instantly since it is still attached at the photosphere alongthe bald patch (BP) portion of the polarity inversion line. The combinedeffects of the TI-driven expansion of the FR and the line-tying at the BP tearthe FR into two parts with the upper portion freely expelled and the lowerportion remaining behind the post-flare arcades. This process dynamicallyperturbs the BPSS and results in the transient enhanced brightening of thesigmoid. The accelerated expansion of the upper portion of the FR stronglypushes its envelope flux near the null point and triggers breakout reconnectionat the null, as evidenced by a remarkable circular flare ribbon, which furtherfacilitates the eruption. We discuss the important implications of theseresults for the formation and disruption of sigmoid region with FR.

Formation and Eruption of an Active Region Sigmoid: I. Study by Nonlinear Force-Free Field Modeling