Comparing different approaches to model the rotational modulation of the Sun as a star

Context. The space missions MOST, COROT and Kepler are going to provide us with high-precision optical photometry of solar-like stars with time series extending from tens of days to several years. They can be modelled to obtain information on stellar magnetic activity by fitting the rotational modulation of the stellar flux produced by the brightness inhomogeneities associated with photospheric active regions. Aims. The variation of the total solar irradiance provides a good proxy for those photometric time series and can be used to test the performance of different spot modelling approaches. Methods. We test discrete spot models as well as maximum entropy and Tikhonov regularized spot models by comparing the reconstructed total sunspot area variation and longitudinal distributions of sunspot groups with those actually observed in the Sun along activity cycle 23. Appropriate statistical methods are introduced to measure model performance versus the timescale of variation. Results. The maximum entropy regularized spot models show the best agreement with solar observations reproducing the total sunspot area variation on time scales ranging from a few months to the activity cycle, although the model amplitudes are affected by systematic errors during the minimum and the maximum activity phases. The longitudinal distributions derived from the models compare well with the observed sunspot group distributions except during the minimum of activity, when faculae dominate the rotational modulation. The resolution in longitude attainable through the spot modelling is similar to 60 degrees, on average. Conclusions. The application of the maximum entropy modelling to solar analogues will provide us with a quite detailed picture of their photospheric magnetic activity that can be the base for comparative and evolutionary studies of solar-like magnetic activity and irradiance variations.