Inflection point in the power spectrum of stellar brightness variations

Abstract

Context. Stellar rotation periods can be determined by observing brightness variations caused by active magnetic regions transiting visible stellar disk as the star rotates. Successful stellar photometric surveys stemming from the Kepler and TESS observations have led to the determination of rotation periods in tens of thousands of young and active stars. However, there is still a lack of information on the rotation periods of older and less active stars like the Sun. The irregular temporal profiles of light curves caused by the decay times of active regions, which are comparable to, or even shorter than, stellar rotation periods, in combination with the random emergence of active regions make period determination for such stars very difficult. Aims. We tested the performance of a new method for the determination of stellar rotation periods against stars with previously determined rotation periods. The method is based on calculating the gradient of the power spectrum (GPS) and identifying the position of the inflection point (i.e. point with the highest gradient). The GPS method is specifically aimed at determining rotation periods of low-activity stars like the Sun. Methods. We applied the GPS method to 1047 Sun-like stars observed by the Kepler telescope. We considered two stellar samples individually: one with near-solar rotation periods (24–27.4 d) and a broad range of effective temperatures (5000–6000 K) and the other with near-solar effective temperatures (5700–5900 K) and a broad range of rotation periods (15–40 d). Results. We show that the GPS method returns precise values for stellar rotation periods. Furthermore, it allows us to constrain the ratio between facular and spot areas of active regions at the moment of their emergence. We also show that the relative facular area decreases with the stellar rotation rate. Conclusions. Our results suggest that the GPS method can be successfully applied to retrieve the periods of stars with both regular and non-regular light curves.