  Stellar rotation periods can be determined by observing brightness variations
caused by active magnetic regions transiting visible stellar disk as the star
rotates. The successful stellar photometric surveys stemming from the Kepler
and TESS observations led to the determination of rotation periods in tens of
thousands of young and active stars. However, there is still a lack of
information about 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, combine with the random emergence of active regions to make
period determination for such stars very difficult. We tested the performance
of the 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. We applied the GPS method to 1047 Sun-like stars
observed by the Kepler telescope. We show that the GPS method returns precise
values of 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 show that relative facular area decreases with stellar rotation
rate. Our results suggest that the GPS method can be successfully applied to
retrieve periods of stars with both regular and non-regular light curves.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics