Gravity darkening in rotating stars

Abstract

Context. Interpretation of interferometric observations of rapidly rotating stars requires a good model of their surface effective temperature. Until now, laws of the form Teffgeffβ have been used, but they are only valid for slowly rotating stars. Aims. We propose a simple model that can describe the latitudinal variations in the flux of rotating stars at any rotation rate. Methods. This model assumes that the energy flux is a divergence-free vector that is antiparallel to the effective gravity. Results. When mass distribution can be described by a Roche model, the latitudinal variations in the effective temperature only depend on a single parameter, namely the ratio of the equatorial velocity to the Keplerian velocity. We validate this model by comparing its predictions to those of the most realistic two-dimensional models of rotating stars issued from the ESTER code. The agreement is very good, as it is with the observations of two rapidly rotating stars, α Aql and α Leo. Conclusions. We suggest that as long as a gray atmosphere can be accepted, the inversion of data on flux distribution coming from interferometric observations of rotating stars uses such a model, which has just one free parameter. © 2011 ESO.