Non-Linear Force-Free Modeling of AR NOAA 10930 Based on Vector Magnetogram Observation with Hinode/SOT

Since the detection of three-dimensional (3D) magnetic field in active regions is crucially important to understand the trigger mechanism of solar flares, the methodologies to reconstruct the 3D magnetic field from magnetgram observation is quickly developed recently. In this study, we have developed a new Non-linear Force-Free (NLFF) field extrapolation method, based on the extended magnetofrictional model and the divergence field cleaning technique, and applied it onto the magnetograms of Active Region NOAA10930, which were observed by Hinode/SOT. The data covers the time span before and after the X-class flare arising on December 13, 2006 in this active region, and Hinode satellite clearly observed the typical features of flare; two ribbon and post flare loop structures by SOT, and sigmoidal structure before the onset and the cusp loop structures after that by XRT. As a result of the NLFF extrapolation, we found that, before the onset of flare, strong sheared structures were formed on the neutral line, whereas the field overlying magnetic neutral line was potential-like. Furthermore, we revealed that a sigmoid structure was not formed of a single sheared loop, but was composed of strong multiple sheared fields. It is also detected that, after the flare, elongated magnetic flux is partially formed but a part of magnetic shear was released. The results indicate that the NLFF relaxes towards the potential field on average during the flaring phase, although some sigmoidal structure remains. Also, the long term evolution of the active region and the storage process of magnetic energy and helicity in the active region are investigated.