Stellar granulation as seen in disk-integrated intensity

Abstract

Context. Solar granulation has been known for a long time to be a surface manifestation of convection. The space-borne missions CoRoT and Kepler enable us to observe the signature of this phenomena in disk-integrated intensity on a large number of stars. Aims. The space-based photometric measurements show that the global brightness fluctuations and the lifetime associated with granulation obeys characteristic scaling relations. We thus aimed at providing simple theoretical modeling to reproduce these scaling relations, and subsequently at inferring the physical properties of granulation across the Hertzsprung-Russell diagram. Methods. We developed a simple 1D theoretical model. The input parameters were extracted from 3D hydrodynamical models of the surface layers of stars, and the free parameters involved in the model were calibrated with solar observations. Two different prescriptions for representing the Fourier transform of the time-correlation of the eddy velocity were compared: a Lorentzian and an exponential form. Finally, we compared our theoretical prediction with 3D radiative hydrodynamical (RHD) numerical modeling of stellar granulation (hereafter ab initio approach). Results. Provided that the free parameters are appropriately adjusted, our theoretical model reproduces the observed solar granulation spectrum quite satisfactorily; the best agreement is obtained for an exponential form. Furthermore, our model results in granulation spectra that agree well with the ab initio approach using two 3D RHD models that are representative of the surface layers of an F-dwarf and a red-giant star. Conclusions. We have developed a theoretical model that satisfactory reproduces the solar granulation spectrum and gives results consistent with the ab initio approach. The model is used in a companion paper as theoretical framework for interpretating the observed scaling relations.