Nonlinear Force-free Modeling of a Three-dimensional Sigmoid Observed on the Sun

In this work, we analyze the characteristics of the three-dimensional magnetic structure of a sigmoid observed over an active region (AR 10930) and followed by X-class flares. This is accomplished by combining a nonlinear force-free field (NLFFF) model of a coronal magnetic field and the high-resolution vector-field measurement of a photospheric magnetic field by Hinode. The key findings of our analysis reveal that the value of the X-ray intensity associated with the sigmoid is more sensitive to the strength of the electric current rather than the twist of the field lines. The strong electric current flows along the magnetic field lines and composes the central part of the sigmoid, even though the twist of the field lines is weak in that region. On the other hand, the outer region (i.e., the elbow part) of the sigmoid is basically occupied by field lines of strong twist and weak current density. Consequently, weak X-ray emission is observed. As the initial Ca II illumination basically occurs from the central part of the sigmoid, this region plays an important role in determining the onset mechanism of the flare despite its weak twisted field-line configuration. We also compare our results with the magnetohydrodynamic simulation for the formation of a sigmoid. Although the estimated values of the twist from the simulation are found to be a little higher than the values obtained from the NLFFF, we find that the field-line configurations generated by the simulation and NLFFF are remarkably analogous as long as we deal with the lower coronal region.