Fig. 3
Stability of the magnetic fields before and after the tether-cutting reconnection. a Photospheric magnetic field (B z ) of AR11158 taken by SDO/HMI observed at 16:00 UT on February 13, corresponding to 90 min approximately before the M6.6-class flare. The NLFFF and twist are calculated only from the region surrounded by the dashed-square in the range of 0.38 L* ≥ x ≥ 0.65 L* and 0.38 L* ≥ y ≥ 0.65 L*, where the outside of the boundary is fixed by the potential field. b Three-dimensional field lines of the NLFFF, which are represented with the current density |J|. c The field lines of the NLFFF, which focuses on the twisted lines enhanced with |J| in b. The color of the field lines and vertical cross section corresponds to the decay index. The small inset shows the side view with green isosurface of |J| = 30. d The field lines after the tether-cutting reconnection. e, f Twist (Tw) distribution of the NLFFF and a state after the tether-cutting reconnection, depending on |B z | measured at each footpoint of the field lines. g The decay index depending on the height measured along the vertical dashed line in d, where the horizontal dashed line marks n = 1.5. Red and blue regions indicate the unstable and stable those to the torus instability, i.e., a flux tube loses the equilibrium in a region marked in red. The arrow points out the height which is same one marked by the arrow in d
