Periodicity of Flare Frequency of Active Flare Stars Detected by Tess

Data from the TESS orbital observatory are used to study the most active flare stars indicating 100 or more flares during the period from July 2018 through October 2020. The main objectives of this study were: (a) analysis of the light curves, determination of the axial rotation periods, and identification of physical features in individual stars, (b) determination of the parameters of the periodic/cyclical variability of the flare frequencies of flare stars owing to axial/orbital rotations. The corresponding periods of the flare frequency functions were obtained and compared with the axial rotation periods of the stars. The periods of the frequency functions of the flares turned out to be close to the axial rotation periods of the stars. Theoretical phase distributions of the flares are constructed and compared with analogous observations of the flares for the given period. For all the stars without exception, a comparison with the aid of the χ² criterion confirms the periodicity of the flare frequency. It is proposed that the distribution of spots over the longitude of flare stars can be represented by an angular von Mises distribution, for which the parameters are determined by the corresponding parameters of the flare frequency function. The binarity of the star CD-56 1032 is discussed in detail.