TWIST AND CONNECTIVITY OF MAGNETIC FIELD LINES IN THE SOLAR ACTIVE REGION NOAA 10930

Twist and connectivity of magnetic field lines in the flare-productive active region NOAA 10930 are investigated in terms of the vector magnetograms observed by the Solar Optical Telescope on board the Hinode satellite and the nonlinear force-free field (NLFFF) extrapolation. First, we show that the footpoints of magnetic field lines reconstructed by the NLFFF correspond well to the conjugate pair of highly sheared flare ribbons on the Ca II images, which were observed by Hinode as an X3.4 class flare on 2006 December 13. This demonstrates that the NLFFF extrapolation may be used to analyze the magnetic field connectivity. Second, we find that the twist of magnetic field lines anchored on the flare ribbons increased as the ribbons moved away from the magnetic polarity inversion line in the early phase of the flare. This suggests that magnetic reconnection might commence from a region located below the most strongly twisted field. Third, we reveal that the magnetic flux twisted more than a half turn and gradually increased during the last one day prior to the onset of the flare, and that it quickly decreased for two hours after the flare. This is consistent with the store-and-release scenario of magnetic helicity. However, within this active region, only a small fraction of the flux was twisted by more than one full turn and the field lines that reconnected first were twisted less than one turn. These results imply that the kink mode instability could hardly occur, at least before the onset of flare. Based on our results, we discuss the trigger process of solar flares.