  Light curves of solar-like stars are known to show highly irregular
variability. As a consequence, standard frequency analysis methods often fail
to detect the correct rotation period. Recently, Shapiro et al. (2020) showed
that the periods of such stars could still be measured by considering the
Gradient of the Power Spectrum (GPS) instead of the power spectrum itself. In
this study, the GPS method is applied to model light curves of solar-like stars
covering all possible inclination angles and a large range of metallicities and
observational noise levels. The model parameters are chosen such that they
resemble those of many stars in the Kepler field. We show that the GPS method
is able to detect the correct rotation period in 40% of all considered cases,
which is more than ten times higher than the detection rate of standard
techniques. Thus, we conclude that the GPS method is ideally suited to measure
periods of those Kepler stars lacking such a measurement so far. We also show
that the GPS method is significantly superior to auto-correlation methods when
starspot lifetimes are shorter than a few rotation periods. GPS begins to yield
rotation periods that are too short when dominant spot lifetimes are shorter
than one rotation period. We conclude that new methods are generally needed to
reliably detect rotation periods from sufficiently aperiodic time series --
these periods will otherwise remain undetected.
