Comparison of the full τ-averaged temperature structure, 〈T〉_τ, from the solar simulation, with some often used solar T(τ) relations. (a) The difference in Rosseland T(τ) relations between the simulation and the semi-empirical model by Holweger & Müller (1974, solid line), and an atlas9 atmosphere model (Kurucz 1993; Castelli, Gratton & Kurucz 1997, dashed line). Here we also show the difference between the two τ-scales (dot–dashed line) as T(τ_Ross = x) − T(τ₅₀₀₀ = x), as well as comparisons with the averaging methods of Fig. 1 in grey: dotted for case (b) 〈T〉_L(〈τ_Ross〉_L) and dashed for case (c) 〈T〉_L(τ_Ross(〈ϱ〉_L, 〈T〉_L)). (b) Differences, on a τ₅₀₀₀-scale, between the simulation and an atlas9 model, and four semi-empirical atmosphere models: the model by Holweger & Müller (1974), the classical fit by Krishna Swamy (1966), the HSRA model (Gingerich, Noyes & Kalkofen 1971) and the average, quiet-Sun, VAL model (Vernazza et al. 1981, see the text).