Quantifying the Complexity of Flaring Active Regions

While solar physicists have a better understanding of the importance magnetic fields play in the solar heating mechanism, it is still not possible to predict whether or when an active region will flare. In recent decades, qualitative studies of the changes in active region morphology have shown that there is generally an increase in the complexity of the spatial configuration of a solar active region leading up to a flare event. In this study, we quantify the spatial structure of the region using the differential Box-Counting Method (DBC) of fractal analysis. We analyze data from NASA/Marshall Space Flight Centr's vector magnetograph from two flaring active regions: AR 6089 from June 10, 1990, which produced one M1.7 flare, and AR 6659 from June 8, 9 and 10, 1991, this data set including one C5.7 and two M(6.4 and 3.2) flare. (AR 6659 produced several other flares). Several magnetic parameters are studied, including the transverse and longitudinal magnetic field components (Bt and B1), the total field (Bmag), and the magnetic shear, which describes the non-potentiality of the field. Results are presented for the time series of magnetograms in relation to the timing of flare events.