Gravity darkening coefficient β as a function of flattening. The values were calculated using a least-square fit to the profile of effective temperature. Solid line: model presented in this paper. Crosses: ESTER models of set 1 (X_c = X). Triangles: ESTER models of set 2 (X_c = 0.5X). The corresponding value of β for von Zeipel’s law is 0.25. The boxes represent the values of β, with their corresponding errors, obtained by interferometry for several rotating stars: Altair (Monnier et al. 2007), α Cephei (Zhao et al. 2009), β Cassiopeiae, and α Leonis (Che et al. 2011).