Discriminating solar and antisolar differential rotation in high-precision light curves

Context. Surface differential rotation (DR) is one major ingredient of the magnetic field generation process in the Sun and likely in other stars. The term solar-like differential rotation describes the observation that solar equatorial regions rotate faster than polar ones. The opposite effect of polar regions rotating faster than equatorial ones (termed as antisolar DR) has only been observed in a few stars, although there is evidence from theoretical dynamo models. Aims. We present a new method of detecting the sign of DR (i.e., solar-like or antisolar DR) by analyzing long-term high-precision light curves with the Lomb-Scargle periodogram. Methods. We compute the Lomb-Scargle periodogram and identify a set of significant periods P-k, which we associate with active regions located at different latitudes on the stellar surface. If detectable, the first harmonics (P-k') of these periods were identified to compute their peak-height-ratios r(k) := h(P-k')/h(P-k). Spots rotating at lower latitudes generate less sine-shaped light curves, which requires additional power in the harmonics, and results in larger ratios r(k). Comparing different ratios r(k) and the associated periods P-k yields information about the spot latitudes, and reveals the sign of DR. Results. We tested our method on different sets of synthetic light curves all exhibiting solar-like DR. The number of cases where our method detects antisolar DR is the false-positive rate of our method. Depending on the set of light curves, the noise level, the required minimum peak separation, and the presence or absence of spot evolution, our method fails to detect the correct sign in at most 20%. We applied our method to 50 Kepler G stars and found 21-34 stars with solar-like DR and 5-10 stars with antisolar DR, depending on the minimum peak separation. Conclusions. The method is able to determine the sign of DR in a statistical way with a low false-positive rate. Applying our method to real data might suggest that - within the uncertainties - antisolar DR was detected in 5-10 Kepler stars.