Measuring stellar differential rotation with high-precision space-borne photometry

Context. Stellar differential rotation is important for understanding hydromagnetic stellar dynamos, instabilities, and transport processes in stellar interiors, as well as for a better treatment of tides in close binary and star-planet systems. Aims. We introduce a method of measuring a lower limit to the amplitude of surface differential rotation from high-precision, evenly sampled photometric time series, such as those obtained by space-borne telescopes. It is designed to be applied to main-sequence late-type stars whose optical flux modulation is dominated by starspots. Methods. An autocorrelation of the time series was used to select stars that allow an accurate determination of starspot rotation periods. A simple two-spot model was applied together with a Bayesian information criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty were obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov chain approach. We applied our method to the Sun and eight other stars for which previous spot modelling had been performed to compare our results with previous ones. Results. We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite for successfully measuring differential rotation through spot modelling. For a proper Monte Carlo Markov chain analysis, it is necessary to take the strong correlations among different parameters that exist in spot modelling into account. For the planet-hosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation of Delta P/P = 0.0523 +/- 0.0016. We confirm that the Sun as a star in the optical passband is not suitable for measuring differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison to more sophisticated and time-consuming approaches.