A study of cold spots on the surfaces of stars with planetary systems from the Kepler space telescope data

Based on the photometric observations obtained with the Kepler telescope, we investigated the properties of the active regions (cold spots) on the surfaces of 737 stars with planetary systems (exoplanets). We used three methods for determining the spottedness (S) of stellar surfaces. A comparison of the results of the S determination through these three methods was performed for two stars (KOI 877 and KOI 896), taken as examples. We studied the dependences of the spottedness of the stars with exoplanets on the effective temperature and on the period of their axial rotation. There is no evidence that the magnetic activity of a star with exoplanets has any special features that distinguish it fromthe activity of the stars froma wider sample. The spottedness of stars with planetary systems in most cases does not exceed 5% of the area of their surface. The three objects for which it exceeds 5% were examined in detail. It was found that for the stars with effective temperatures less than 5750 K, there is a monotonic decrease of the spottedness with the increase of the rotation period of the star. We established the absence of stars with small values of S (less than 0.002) among the stars with effective temperatures less than 5750 K and rotation periods less than 10 days. Stars with effective temperatures of more than 5750 K have small spottedness in the case of rapid rotation, but S increases for objects with rotation periods of 20–25 days.