A fast and reliable method to measure stellar differential rotation from photometric data

Co-rotating spots at different latitudes on the stellar surface generate periodic photometric variability and can be useful proxies to detect Differential Rotation (DR). DR is a major ingredient of the solar dynamo but observations of stellar DR are rather sparse. In view of the Kepler space telescope we are interested in the detection of DR using photometric information of the star, and to develop a fast method to determine stellar DR from photometric data. We ran a large 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 are prewhitened using Lomb-Scargle periodograms to derive parameters for a global sine fit to detect periodicities. We show under what 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} could be detected in 96.2% of all light curves. Detection of a second period close to P1_{out} is the signature of DR in our model. For the noise-free case, in 64.2% of all stars such a period was found. Calculating the measured latitudinal shear of two distinct spots α_{out}, and comparing it to the known original spot rotation rates shows that the real value is on average 3.2% lower. Comparing the total equator-to-pole shear $α$ to $α_{out}$ we find that $α$ is underestimated by 8.8%, esp. the detection of DR for stars with $α$ < 6% is challenging. Finally, we apply our method to four differentially rotating Kepler stars and find close agreement with results from detailed modeling. Our method is capable of measuring stellar rotation periods and detecting DR with relatively high accuracy and is suitable for large data sets.