Gravity darkening in late-type stars. The Coriolis effect

TL;DR

This study uses 3D numerical simulations to explore how rotation influences surface heat flux distribution in stars with convective envelopes, revealing the role of the Rossby number and stratification in gravity darkening.

Contribution

It provides the first systematic analysis of heat flux distribution in rotating stellar convective envelopes, linking surface brightness variations to the local Rossby number and stratification effects.

Findings

Surface brightness varies with latitude, from brighter poles to darker equator.

The local Rossby number controls the surface heat flux distribution.

Stronger stratification leads to more uniform heat flux profiles.

Abstract

Recent interferometric data have been used to constrain the brightness distribution at the surface of nearby stars, in particular the so-called gravity darkening that makes fast rotating stars brighter at their poles than at their equator. However, good models of gravity darkening are missing for stars that posses a convective envelope. In order to better understand how rotation affects the heat transfer in stellar convective envelopes, we focus on the heat flux distribution in latitude at the outer surface of numerical models. We carry out a systematic parameter study of three-dimensional, direct numerical simulations of anelastic convection in rotating spherical shells. Restricting our investigations to hydrodynamical models with a thermal Prandtl number fixed to unity, we consider both thick and thin (solar-like) shells, and vary the stratification over three orders of magnitude. We measure the heat transfer efficiency in terms of the Nusselt number, defined as the output luminosity normalised by the conductive state luminosity. We report diverse Nusselt number profiles in latitude, ranging from brighter (usually at the onset of convection) to darker equator and uniform profiles. We find that the variations of the surface brightness are mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the dynamics, the heat flux is weakened in the equatorial region by the zonal wind and enhanced at the poles by convective motions inside the tangent cylinder. In the presence of a strong background density stratification however, as expected in real stars, the increase of the local Rossby number in the outer layers leads to uniformisation of the surface heat flux distribution.