Context. Quasi-periodic modulations of the stellar light curve may result from dark spots crossing the visible stellar disc. Owing to differential rotation, spots at different latitudes generally have different rotation periods. Hence, by studying spot-induced modulations, it is possible to learn about stellar surface (differential) rotation and magnetic activity. Recently, a method based on the Lomb-Scargle periodogram of light curves has been proposed to identify the sign of the differential rotation at the stellar surface.

Aims. Our goal is to understand how the modulation of the stellar light curve due to the presence of spots and the corresponding periodogram are affected by both the stellar and spot properties.

Methods. We generate synthetic light curves of stars with different properties (inclination angle, limb darkening, and rotation rate) and spot configurations (number of spots, latitude, intensity contrast, and size). By analysing their Lomb-Scargle periodograms, we compute the ratio between the heights of the second and first harmonics of the rotation period (peak-height ratio).

Results. We find that the peak-height ratios are essentially a function of a single parameter, the fraction of time the spot is visible, which is related to the sinusoidality of the spot modulation. We identify the conditions under which the periodogram analysis can actually provide an estimate of the spot latitudes and/or the stellar inclination angle. We also identify possible sources of error in the identification of the sign of the differential rotation.