Photospheric Magnetic Field Properties of Flaring versus Flare-quiet Active Regions. III. Magnetic Charge Topology Models

A magnetic charge topology (MCT) model is applied to time series of photospheric vector magnetic field data for seven active regions divided into epochs classified as flare-quiet and flare-productive. In an approach that parallels an earlier study by the authors using quantities describing the photospheric properties of the vector magnetic field, we define quantities derived from the MCT analysis that quantify the complexity and topology of the active region coronal fields. With the goal of distinguishing between flare-quiet and flare-imminent magnetic topology, the time series are initially displayed for three active regions for visual inspection with few clear distinguishing characteristics resulting. However, an analysis of all 24 epochs using the discriminant analysis statistical approach indicates that coronal field topology, derived from the observed photospheric vertical field, may indeed hold relevant information for distinguishing these populations, although the small sample size precludes a definite conclusion. The variables derived from the characterization of coronal topology routinely result in higher probabilities of being able to distinguish between the two populations than the analogous variables derived for the photospheric field.