  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.
