Stability and Dynamics of a Magnetic Field Producing the M6.6 Class Solar Flare in NOAA Active Region 11158

In this paper, we study the stability and dynamics of a magnetic field producing the M6.6 class solar flare taking place in NOAA active region (AR) 11158 on 2011 February 13th. Toriumi et. al. (2013) recently suggest that a fine scale magnetic structure on the photosphere gives a major possibility to produce the M6.6 class flare. On the other hand, they don't discuss the torus instability as a plausible mechanism even though Zhao et. al. (2014) and Janvier et. al. (2014) suspect it as the trigger mechanism of X2.2 class flare taking place later in the same AR. We are the first to investigate the stability of a nonlinear force-free field (NLFFF) prior to the M6.6 class flare against the torus instability by using analytical and numerical approaches. Consequently, we found that our NLFFF is quite stable against small perturbation. This result supports that the flare is triggered by the photospheric motion suggested by Toriumi et. al. (2013). We further perform another MHD simulation with an anomalous resistivity using the NLFFF as an initial condition. As a result, we found the eruption of strongly twisted lines. We compare our simulation results with observations and discuss relevant dynamics in detail.