Variability of Sun-like stars: reproducing observed photometric trends

Context. The Sun and stars with low magnetic activity levels become photometrically brighter when their activity increases. Magnetically more active stars display the opposite behavior and become fainter when their activity increases. Aims. We reproduce the observed photometric trends in stellar variations with a model that treats stars as hypothetical suns with coverage by magnetic features different from that of the Sun. Methods. The model attributes the variability of stellar spectra to the imbalance between the contributions from different components of the solar atmosphere, such as dark starspots and bright faculae. A stellar spectrum is calculated from spectra of the individual components by weighting them with corresponding disk-area coverages. The latter are obtained by extrapolating the solar dependences of spot and facular disk-area coverages on chromospheric activity to stars with different levels of mean chromospheric activity. Results. We find that the contribution by starspots to the variability increases faster with chromospheric activity than the facular contribution. This causes the transition from faculae-dominated variability and direct activity-brightness correlation to spot-dominated variability and inverse activity-brightness correlation with increasing chromospheric activity level. We show that the regime of the variability also depends on the angle between the stellar rotation axis and the line-of-sight and on the latitudinal distribution of active regions on the stellar surface. Our model can be used as a tool for extrapolating the observed photometric variability of the Sun to Sun-like stars at different activity levels, which makes a direct comparison between solar and stellar irradiance data possible.