Abstract—In the first part of our work, we present the results of a comparative analysis of photometric observations of stars using the Kepler mission and its continuation K2. The comparability of the data was estimated by an indirect method based on the values of the stellar surface spottedness parameter \(S\) calculated by us, which were determined by the amplitudes of the brightness variability of the objects \({{R}_{{{\text{var}}}}}\) from the observations of the main mission and K2. The main conclusion of our work is that the considered data form a single array that can be used in further research. Conclusions are drawn about changes in the activity of stars of different temperatures and how the activity is related to rotation. The conclusion that the data under consideration form a single array allowed us to conduct a generalized analysis of two independent samples of stars with planetary systems in the second part of the work. Using an estimate of the radii of stars (data from the Kepler telescope archive), we obtained the values \(A\) of the area of spots on the surface of stars in millionths of the visible hemisphere of the Sun. We found a good agreement between the estimates of the characteristics of spots on the surface of stars with exoplanets based on the observations of the main mission Kepler and its continuation K2. From our list of more than 700 objects with planetary systems, 76 stars with effective temperatures \({{T}_{{{\text{eff}}}}}\) differing from the solar temperature by 100 K were selected for further consideration. For them, conclusions were made about the decrease in the activity of objects with rotation periods of more than 10–12 days. From the consideration of the ratio of the spottedness of objects \(A\) and their age \(t\) (established by the gyrochronological ratio), it is concluded that stars with an age of less than 1 billion years are the most active. For one set of observations (Q3) of the Kepler mission, a preliminary analysis of photometric observations of 9 objects with the largest values of the spottedness parameter \(A\) (more than 10 000 in millionths of the solar hemisphere) has been performed. The variability of their light curves at times comparable to the periods of rotation and its noticeable amplitude, indicating an increased area of spots on the surface, are registered.

摘要——在我们工作的第一部分，我们展示了使用开普勒任务及其延续 K2 对恒星的光度观测进行比较分析的结果。数据的可比性是根据我们计算的恒星表面斑点度参数\(S\)的值，通过间接方法估计的，该值由物体亮度变化的幅度\({{R}_ {{{\text{var}}}}}\)从主要任务和K2的观察。我们工作的主要结论是所考虑的数据形成了一个可用于进一步研究的单一阵列。得出关于不同温度恒星活动的变化以及活动与自转的关系的结论。所考虑的数据形成单个阵列的结论使我们能够在工作的第二部分中对具有行星系统的两个独立恒星样本进行广义分析。使用恒星半径的估计（来自开普勒望远镜档案的数据），我们获得了值\(A\)以太阳可见半球的百万分之一为单位的恒星表面斑点面积。我们发现，基于主要任务开普勒及其延续 K2 的观测，对具有系外行星的恒星表面斑点特征的估计具有良好的一致性。从我们拥有行星系统的 700 多个物体的列表中，选择了 76 颗有效温度\({{T}_{{{\text{eff}}}}}\)与太阳温度相差 100 K 的恒星以进行进一步的研究。考虑。对他们来说，结论是自转周期超过 10-12 天的物体的活动减少。从物体的斑点度\(A\)与其年龄\(t\)的比值考虑（由陀螺年代比建立），结论是年龄小于10亿年的恒星最活跃。对于开普勒任务的一组观测（Q3），对 9 个具有最大斑点参数值\(A\)（太阳半球百万分之一以上的 10 000 个）的光度观测进行了初步分析. 记录了它们的光变曲线在与旋转周期相当的时间及其显着幅度的变化，表明表面上的斑点面积增加。