Fast and reliable method for measuring stellar differential rotation from photometric data

Context. Co-rotating spots at different latitudes on the stellar surface generate periodic photometric variability and can be useful proxies for detecting differential rotation (DR). This is a major ingredient of the solar dynamo, but observations of stellar DR are very sparse. Because the Kepler space telescope steadily collects more data, we are interested in detecting DR using photometric information of a star. Aims. The main goal of this paper is to develop a fast method for determining stellar DR from photometric data. Methods. We ran an extensive Monte Carlo simulation of differentially rotating spotted stars with very different properties to investigate the detectability of DR. For different noise levels the resulting light curves were prewhitened using Lomb-Scargle periodograms to derive parameters for a global sine fit to detect periodicities. Results. We show under which conditions DR can successfully be detected from photometric data, and in which cases the light curve provides insufficient or even misleading information on the stellar rotation law. In our simulations, the most significant period P1(out) is on average 2.4% shorter than the actual spot rotation-rate. This period was detected in 96.2% of all light curves. The signature of DR is a second period close to P1(out) in our model. For the noise-free case, we found such a period in 64.2% of all stars. Calculating the measured latitudinal shear of two distinct spots alpha(out), and comparing this with the known original spot rotation-rates shows that the real value is on average 3.2% lower. Comparing the total equator-to-pole shear alpha to alpha(out), we find that alpha is underestimated by 8.8%, especially the detection of DR for stars with alpha < 6% is challenging. Finally, we applied our method to four differentially rotating Kepler stars and found close agreement with results from detailed modeling. Conclusions. The method we developed is capable of measuring stellar rotation periods and detecting DR with relatively high accuracy and is suitable for large data sets. We will apply our analysis to more Kepler data in a forthcoming paper.