Stellar granulation as seen in disk-integrated intensity. I. Simplified theoretical modeling

TL;DR

This paper presents a simplified 1D theoretical model of stellar granulation that reproduces observed scaling relations and agrees with 3D hydrodynamical simulations, aiding the understanding of surface convection across stars.

Contribution

It introduces a simple, adjustable 1D model calibrated with solar data that successfully matches observations and complex 3D simulations of stellar granulation.

Findings

The exponential eddy time-correlation model fits solar data best.

The theoretical model reproduces the shape and amplitude of observed granulation spectra.

Good agreement with 3D RHD simulations confirms the model's validity.

Abstract

The solar granulation is known for a long time to be a surface manifestation of convection. Thanks to the current space-borne missions CoRoT and Kepler, it is now possible to observe in disk-integrated intensity the signature of this phenomena in a growing number of stars. The space-based photometric measurements show that the global brightness fluctuations and the lifetime associated with granulation obeys characteristic scaling relations. We thus aim at providing a simple theoretical modeling to reproduce these scaling relations and subsequently at inferring the physical properties of granulation properties across the HR diagram. We develop a simple 1D theoretical model that enable us to test any prescription concerning the time-correlation between granules. The input parameters of the model are extracted from 3D hydrodynamical models of the surface layers of stars, and the free parameters involved in the model are calibrated with solar observations. Two different prescriptions for representing the eddy time-correlation in the Fourier space are compared: a Lorentzian and an exponential form. Finally, we compare our theoretical prediction with a 3D radiative hydrodynamical (RHD) numerical modeling of stellar granulation (ab-initio approach). Provided that the free parameters are appropriately adjusted, our theoretical model satisfactorily reproduces the shape and the amplitude of the observed solar granulation spectrum. The best agreement is obtained with an exponential form. Furthermore, our theoretical model results in granulation spectra that consistently agree with the these calculated on the basis of the ab-initio approach with two 3D RHD models. Comparison between theoretical granulation spectra calculated with the present model and high precision photometry measurements of stellar granulation is undertaken in a companion paper.