Panels a–c: Effective temperature T_eff(θ,η,α) / ⟨ T ⟩ given by Eq. (34) as a function of the co-latitude θ when Υ(θ) = cos^kθ, for η = 0.8, k = 0.5, 2.0 and 6.0, and α = − 0.5, 0.0 and +0.5. Panels d–f: Same for Υ(θ) = sin^kθ and the same values of k as before, but for α′ = − α/ (1 + α) where α is the same as in (a) to (c). The black-dashed lines correspond to the classic von Zeipel approximation normalized in θ = 0 at the curve corresponding to α = 0.0.