Periodicity of the Flare Frequency of Flare Stars

Data from the Kepler Orbital Observatory are used in a statistical study of the periodic/cyclical variability of the flare frequency of 76 flare stars. Corresponding periodic functions of the flare frequency are obtained and a possible periodicity of the flare frequency with a period equal to the star’s rotation period is tested. The periodicities of the function of the flare frequency turned out to be close to the axial rotation periods of the stars. Theoretical distributions of the flares with respect to phase are constructed and compared with the analogous observed distribution of the flares for a given period. For all the stars, without exception, this comparison (using the χ² criterion) supports a periodicity of the flare frequency. These results indicate that (a) the flare frequency is modulated by the axial rotation of the stars and (b) structural and physical variations in the active regions of these stars proceeded relatively slowly. Some of these stars have planetary systems. It is suspected that the orbital rotation of a planet affects the flare frequency of the star KIC 5791720.