Magnetic Winding as an Indicator of Flare Activity in Solar Active Regions

Magnetic helicity is a measure of the entanglement of magnetic field lines used to characterize the complexity of solar active region (AR) magnetic fields. Previous attempts to use helicity-based indicators to predict solar eruptive/flaring events have shown promise but not been universally successful. Here we investigate the use of a quantity associated with the magnetic helicity, the magnetic winding, as a means to predict flaring activity. This quantity represents the fundamental entanglement of magnetic field lines and is independent of the magnetic field strength. We use vector magnetogram data derived from the Helioseismic Magnetic Imager (HMI) to calculate the evolution and distribution of the magnetic winding flux associated with five different ARs, three of them with little flaring activity/nonflaring (AR 11318, AR 12119, AR 12285) and two highly active with X-class flares (AR 11158, AR 12673). We decompose these quantities into "current-carrying"and "potential"parts. It is shown that the ARs that show flaring/eruptive activity have significant contributions to the winding input from the current-carrying part of the field. A significant and rapid input of current-carrying winding is found to be a precursor of flaring/eruptive activity, and, in conjunction with the helicity, sharp inputs of both quantities are found to precede individual flaring events by several hours. This suggests that the emergence/submergence of topologically complex current-carrying field is an important element for the ignition of AR flaring.