Analytic model for photometric variation due to starspots on a differentially rotating star

We present an analytic model of the lightcurve variation for stars with non-evolving starspots on a differentially rotating surface. The Fourier coefficients of the harmonics of the rotation period are expressed in terms of the latitude of the spot, $\ell_{s}$, and the observer's line-of-sight direction, $\ell_{o}$, including the limb darkening effect. We generate different realizations of multi-spots according to the model, and perform mock observations of the resulting lightcurve modulations. We discuss to what extent one can recover the properties of the spots and the parameters for the differential rotation law from the periodogram analysis. Although our analytical model neglects the evolution of spots on the stellar surface (dynamical motion, creation and annihilation), it provides a basic framework to interpret the photometric variation of stars, in particular from the existing Kepler data and the future space-born mission. It is also applicable to photometric modulations induced by rotation of various astronomical objects.