Twistness and Connectivity of Magnetic Field Line in the Solar Active Region NOAA 10930

Solar active regions are the primary driver of the solar active phenomena, and therefore the understanding of the three-dimensional (3D) magnetic structure on active regions is crucially important to reveal the mechanism of the solar active phenomena. The purpose of this study is to clarify the topological features in magnetic field such as the connectivity and the twistness of magnetic field lines on the solar active region NOAA 10930, which had produced an X3.4 class flare on Dec.13, 2006, and coronal mass ejection (CME) causing the substorm and ionospheric storm in our geo-space. 3D magnetic field was reconstructed in term of the Non-Linear Force-Free Field (NLFFF) approximation and the vector magnetic field data observed by the solar physics satellite Hinode. First, we reconstructed the typical field lines of the NLFFF corresponding to six hours prior to the flare onset, and compared them with the flare ribbons of Ca II images observed in the early phase of flare by Hinode/SOT. As a result, it was found that the location of the two foot-points of magnetic field lines well corresponds to the flare ribbons. This result indicates that the NLFFF well capture the 3D structure of magnetic field in the flaring region, even though the structure was very complicated. Second, we have performed the quantitative analysis of twistness of magnetic field, and found that the twist of magnetic field lines was less than one turn, although the twistness increased until the onset of the flare. This result implies that the active region might be stable to the kink mode instability at least six hours prior to the flare onset. Finally, it is also found that the twistness of field lines rootedon the regions where the ribbons had been strongly illuminated was drastically weakened after the flare. It can be explained well as a consequence of reconnection of twisted magnetic field. We will also report the relationship between the time evolution of the two-ribbon structure and Qusi-Separatrix Layer (QSL), to discuss reconnection dynamics in flare.