  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.
