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.

中文翻译：

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耀斑星耀斑频率的周期性

来自开普勒轨道天文台的数据用于对 76 颗耀斑星耀斑频率的周期性/周期性变化进行统计研究。获得了相应的耀斑频率周期函数，并测试了周期等于恒星自转周期的耀斑频率的可能周期性。结果表明，耀斑频率函数的周期性接近恒星的轴向自转周期。构建了相对于相位的耀斑理论分布，并与给定时期内类似的观察到的耀斑分布进行了比较。对于所有恒星，无一例外，这种比较（使用 χ2 标准）支持耀斑频率的周期性。这些结果表明（a）耀斑频率受恒星轴向旋转的调节，（b）这些恒星活动区域的结构和物理变化进行得相对缓慢。其中一些恒星具有行星系统。怀疑行星的轨道自转会影响恒星 KIC 5791720 的耀斑频率。