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Stellar models often use relations between the temperature $T$ and opticaldepth $\tau$ to evaluate the structure of their optically-thin outer layers. Wefit a novel analytic function to the Hopf function $q(\tau)$ of aradiation-coupled hydrodynamics simulation of near-surface convection withsolar parameters by Trampedach et al. (2014). The fit is accurate to within0.82 per cent for the solar simulation and to within 13 per cent for all thesimulations that are not on either the low-temperature or low-gravity edges ofthe grid of simulations.

A novel analytic atmospheric $T(\tau)$ relation for stellar models