Determining the Frequency Function of Flares and Starspot Coverage in Active Flare Stars Discovered by the Kepler Mission

Based on data from the Kepler orbital observatory, this study investigates the most active flare stars, which exhibited 250 or more flares during the Kepler mission period. The main research objectives were: (a) analyzing light curves to identify unique physical characteristics of individual stars; (b) defining the periodic/cyclic flare frequency function (PFFF) of flare stars, associated with axial/orbital rotations; and (c) presenting a novel method for determining starspot coverage using the PFFF and applying this method. The study produced corresponding PFFF values with periodicities close to the star rotation periods. Expected phase distributions of flares were constructed and compared with observed flare distributions for the given rotation period. For all stars examined, this comparison (using the χ² criterion) supports the periodicity of flare frequency. It is hypothesized that the starspot distribution of flare stars can be represented by the von Mises circular distribution, with parameters derived from the respective flare frequency function. Estimates of the starspot coverage for the stars studied were obtained.