Modelling the rotational modulation of the Sun as a star

We analyse the time variability of the total solar irradiance (TSI) as measured by VIRGO/SoHO in order to model the variability of the Sun as a star. Apart from the phases near the minimum at the beginning of activity cycle 23, the period of the rotational modulation is significantly different from the solar synodic period as a consequence of the growth and decay of active regions on time scales shorter than a solar rotation. In order to model the variability of the TSI, we have considered the contributions of discrete active regions and a uniformly distributed background emission. To reproduce the rotational modulation of the TSI, we used three active regions, the areas and coordinates of which were changed every seven days to account for their evolution. The simultaneous presence of dark spots and bright faculae was considered by means of appropriate contrast functions which took into account the observed center-to-limb dependence of their contrast with respect to the unperturbed photosphere. The method proved to be capable of modelling the variability of the TSI on time scales going from $7{-}10$ days up to the solar cycle. The relative amplitude of the residuals was of the order of $(1{-}2)\times 10^{-4}$ with the larger values observed during the phases of maximum solar activity of cycle 23. The application of a similar technique to solar-like stars, such as those that will be observed by the next generation of space-borne photometers, should allow us to minimize the effects of stellar magnetic activity on the detection of planetary transits. Moreover, the availability of long-term highly accurate light curves will allow us to measure stellar rotation period, detect stellar activity cycles, and derive information on the inclination of the stellar rotation axis. The location of the active regions and their irradiance properties can also be retrieved with moderate accuracy from single-band light curves. However, a combination of multi-band photometry and spectroscopy will allow us to constrain some of the free parameters of the model and improve the mapping of stellar surfaces.