A Study of Magnetic Field Characteristics of Flaring Active Region Based on Nonlinear Force-free Field Extrapolation

Coronal magnetic fields are responsible for the onset of solar flares and solar eruptions. However, the type of magnetic field parameters that can be used to measure the critical condition for a solar eruption is still unclear. As an effort to understand the possible condition for a solar flare, we have examined the non-dimensional parameter $\kappa$ introduced by Ishiguro & Kusano (2017), which contains information about magnetic twist distribution and magnetic flux in an active region (AR). We introduce a new parameter $\kappa^\ast$, as a proxy for $\kappa$, and we have analyzed the evolution of $\kappa^\ast$ during the flaring period of an AR using the nonlinear force-free field (NLFFF) extrapolated from the photospheric vector magnetic field data. Using data from the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI), we have calculated $\kappa^\ast$ for the AR NOAA 11158 during its three-day flaring period. We found that $\kappa^\ast$ increased to a certain level before two large flares and decreased significantly after their onset. The results suggest that $\kappa^\ast$ may be used as an indicator of the necessary condition for the onset of a solar eruption in the AR. Based on this result, we propose a new method to assess the possibility of a large solar eruption from an AR by combining the parameter $\kappa^\ast$ and information about the magnetic energy of the AR.