Chirality and magnetic configuration associated with two-ribbon solar flares: AR 10930 versus AR 11158

The structural property of the magnetic field in flare-bearing solar active regions (ARs) is one of the key aspects for understanding and forecasting solar flares. In this paper, we make a comparative analysis on the chirality and magnetic configurations associated with two X-class two-ribbon flares happening in AR 10930 and AR 11158. The photospheric magnetic fields of the two ARs were observed by space-based instruments, and the corresponding coronal magnetic fields were calculated based on the nonlinear force-free field model. The analysis shows that the electric current in the two ARs was distributed mostly around the main polarity inversion lines (PILs) where the flares happened, and the magnetic chirality (indicated by the signs of force-free factor $\alpha$) along the main PILs is opposite for the two ARs, i.e., left-handed ($\alpha<0$) for AR 10930 and right-handed ($\alpha>0$) for AR 11158. It is found that, for both the flare events, a prominent magnetic connectivity (featured by co-localized strong $\alpha$ and strong current density distributions) was formed along the main PIL before flare and was totally broken after flare eruption. The two branches of the broken magnetic connectivity, combined with the prominent magnetic connectivity before flare, compose the opposite magnetic configurations in the two ARs owing to their opposite chirality, i.e., Z-shaped configuration in AR 10930 with left-handed chirality and inverse Z-shaped configuration in AR 11158 with right-handed chirality. It is speculated that two-ribbon flares can be generally classified to these two magnetic configurations by chirality in the flare source regions of ARs.