Theoretical gravity darkening as a function of optical depth

Abstract

Aims. Recent observations of very fast rotating stars show systematic deviations from the von Zeipel theorem and pose a challenge to the theory of gravity-darkening exponents (β1). In this paper, we present a new insight into the problem of temperature distribution over distorted stellar surfaces to try to reduce these discrepancies. Methods. We use a variant of the numerical method based on the triangles strategy, which we previously introduced, to evaluate the gravity-darkening exponents. The novelty of the present method is that the theoretical β1 is now computed as a function of the optical depth, that is, β1 ? β1(τ). The stellar evolutionary models, which are necessary to obtain the physical conditions of the stellar envelopes/atmospheres inherent to the numerical method, are computed via the code GRANADA. Results. When the resulting theoretical β1(τ) are compared with the best accurate data of very fast rotators, a good agreement for the six systems is simultaneously achieved. In addition, we derive an equation that relates the locus of constant convective efficiency in the Hertzsprung-Russell (HR) diagram with gravity-darkening exponents.