Determination of Starspot Coverage of Solar-Type Stars with Superflares

Abstract

The paper addresses the problem of determining the degree of starspot coverage of solar-type stars producing superflares, using a method previously developed by the author to estimate the spottedness of flaring stars based on the chronology of recorded flares. The method involves determining a periodic function of flare rate using statistical analysis of time series. The latter are interpreted as a Poisson process with a cyclic parameter associated with the stellar rotation period. Transformation of this function into the von Mises probability density function of circular distribution shifts the perspective from flare frequency to the angular distribution of starspots and determining the effective surface area covered by spots. Nine of the most active solar-type stars from the catalog of Okamoto et al. were investigated. For these stars, rotation periods were calculated using flare chronology, concentration parameters of the flare distribution were determined, and angular distributions of starspot coverage were obtained. The estimated degrees of spottedness range from 1–4% for minimally spotted hemispheres to up to 10% for maximally spotted hemispheres, which significantly exceeds the corresponding values for the Sun. Comparison with the results of Okamoto et al. demonstrates a high degree of agreement, with a correlation coefficient r = 0.896. The developed approach enables determining stellar spottedness based solely on time series of flare activity without the use of high-resolution photometric or spectroscopic data, making it a valuable tool for statistical studies of magnetic activity in solar-type stars exhibiting superflares.