Magnetic Configuration Associated with Two-Ribbon Solar Flares

The magnetic configuration of flare-bearing active regions (ARs) is one key aspect for understanding the initiation of solar flares. In this paper, we perform a comparative analysis between the magnetic configurations of two X-class two-ribbon flares happening in AR 10930 and AR 11158, whose photospheric magnetic fields were observed by the Hinode and SDO satellites, respectively. The corresponding coronal magnetic fields were calculated based on the nonlinear force-free field model. The analysis shows that both the flares were initiated in local areas with extremely strong current density, and the magnetic chirality (indicated by the sign of force-free factor $\alpha$) along the main polarity inversion line (PIL) is opposite for the two ARs, that is, left-handed ($\alpha<0$) for AR 10930 and right-handed ($\alpha>0$) for AR 11158. Our previous study (He et al. 2014) showed that, for the flare of AR 10930, prominent magnetic connectivity (indicated by concentrated $\alpha$ and current distributions) was formed above the main PIL before the flare and was totally broken after the flare eruption. The two branches of broken magnetic connectivity, combined with the isolated electric current at the magnetic connectivity breaking site, compose a Z-shaped configuration. In this work, we find similar results for the flare of AR 11158 except that its magnetic configuration is inverse Z-shaped, which corresponds to the right-handed chirality of AR 11158 in contrast to the left-handed chirality of AR 10930. We speculate that two-ribbon flares can be generally classified to these two magnetic configurations by chirality ($\alpha$ sign) of ARs.