Activity of Stars with Planets in the Habitable Zone

Based on data on stars with planets located in the habitable zone, a study is made of manifestations of their activity. Light curves obtained during observations in the Q3 set with the Kepler Space Telescope for them were studied and the amplitudes of the brightness variability were studied in order to determine the presence and properties of spots on their surface. Estimates of the rotation periods of the objects were also obtained. Diagrams of the dependence of the area of the spots A on the surface of stars with exoplanets according to published data (including in those in the Habitable Zone) on the effective temperature and rotation period are examined. Indications are obtained that the distributions of the stars with exoplanets located in the habitability zone are shifted toward the region of lower spot areas and rotation periods compared to the data for all the stars with exoplanets. Data from the archive of the Kepler Space Telescope for a star with pronounced rotational modulation, KOI-3497 (Kepler-1512, KIC 8424002) are analyzed. It is noted that it should be characterized by a a star of spectral class K, rather than M. KOI-3497 has flare activity (47 flashes with energy E in the range from 2·10³¹ to 2·10³² erg have been recorded for it.)