Changes of magnetic structure in three dimensions associated with the X3.4 flare of 2006 December 13

Recent observations demonstrated that sunspot structure can change rapidly and irreversibly after flares. One of the most puzzling results is the increase in magnetic shear around the flaring magnetic polarity inversion line after flares. However, all these observations were made at the photosphere level. In this Letter, we study the altitude variation of the nonpotentiality of the magnetic fields associated with the 4B/X3.4 flare of 2006 December 13. The vector magnetograms with unprecedented quality from Hinode before and after the flare are used as the boundary conditions to extrapolate the three-dimensional nonlinear force-free magnetic fields and the potential fields. The former are computed with the optimization algorithm and the latter with the Green's function method. At the photosphere boundary, magnetic shear increases after the flare in a local area close to the flaring magnetic polarity inversion line. Two measures of the magnetic nonpotentiality, the weighted mean shear theta(w) and the total magnetic shear theta B-w, are calculated in this area at progressively higher altitude. By comparing their altitude variation profiles before and after the flare, we find that the nonpotentiality of the local area increases after the flare below similar to 8 Mm and decreases from that height to similar to 70 Mm. Beyond 70 Mm, the magnetic fields approach potential for both times.