Magnetic twist and writhe of δ active regions

We have selected 104 active regions with a d magnetic configuration from 1996 to 2002 to study how important a role the kink instability plays in such active regions. In this study, we employ the systematic tilt angle of each active region as a proxy for the writhe of a flux tube and the force-free parameter, a(best), as a proxy for the magnetic field twist in the flux tube. It is found that 65-67% of the active regions have the same sign of twist and writhe. About 34% (32%) of the active regions violate (follow) the Hale-Nicholson and Joy's Laws (HNJL) but follow (violate) the hemispheric helicity rule (HHR). Sixty-one (61) of the 104 active regions studied each produced more than five large flares. Active regions violating HNJL, but following HHR, have a much stronger tendency to produce X-class flares and/or strong proton events. Comparing with previous studies for active regions with well-defined (simpler) bipolar magnetic configuration, it is found that the numbers following both HNJL and HHR are significantly lower in the d-configuration case, while numbers violating one of the laws and the rule significantly increase with the increase of the magnetic complexity of the active regions. These results support the prediction for the presence of a kink instability, that the twist and writhe of the magnetic fields exhibit the same sign for d active regions (Linton et al., Astrophys. J. 507, 40, 1998, Astrophys. J. 522, 1205, 1999; Fan et al., Astrophys. J. 521, 460, 1999). Finally, we analyze possible origins of the twist and writhe of the magnetic fields for the active regions studied.