Measuring periods in aperiodic light curves -- Applying the GPS method to infer rotation periods of solar-like stars

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.