Gravity darkening in rotating stars

Context. Interpretation of interferometric observations of rapidly rotating stars requires a good model of their surface effective temperature. Until now, laws of the form T-eff proportional to g(eff)(beta) 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, alpha Aql and alpha 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.