2016A&A...588A..15C

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.