Survey of Magnetic Field Parameters Associated with Large Solar Flares

Until now, how the magnetic fields in M/X-class flaring active regions (ARs) differ from C-class flaring ARs remains unclear. Here, we calculate the key magnetic field parameters within the area of high photospheric free energy density (HED region) for 323 ARs (217 C- and 106 M/X-flaring ARs), including total photospheric free magnetic energy density E _free , total unsigned magnetic flux Φ _HED , mean unsigned current helicity h _c , length of the polarity inversion lines L _PIL with a steep horizontal magnetic gradient, etc., and compare these with flare/coronal mass ejection (CME) properties. We first show the quantitative relations among the flare intensity, the eruptive character, and Φ _HED . We reveal that Φ _HED is a measure for the GOES flux upper limit of the flares in a given region. For a given Φ _HED , there exists the lower limit of F _SXR for eruptive flares. This means that only the relatively strong flares with the large fraction of energy release compared to the total free energy are likely to generate a CME. We also find that the combinations of E _free – L _PIL and E _free – h _c present a good ability to distinguish between C-class and M/X-class flaring ARs. Using determined critical values of E _free and L _PIL , one predicts correctly 93 out of 106 M/X-class flaring ARs and 159 out of 217 C-class flaring ARs. The large L _PIL or h _c for M/X-class flaring ARs probably implies the presence of a compact current with twisted magnetic fields winding about it.