Stellar models often use relations between the temperature T and optical depth τ to evaluate the structure of their optically thin outer layers. We fit a novel analytic function to the Hopf function q(τ) of a radiation-coupled hydrodynamics simulation of near-surface convection with solar parameters by Trampedach et al. The fit is accurate to within 0.82% for the solar simulation and to within 13% for all the simulations that are not on either the low-temperature or low-gravity edges of the grid of simulations.

中文翻译：

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恒星模型的一种新的解析大气 T(τ) 关系

恒星模型通常使用温度T和光学深度τ之间的关系来评估其光学薄外层的结构。我们将新的解析函数拟合到 Trampedach 等人的具有太阳参数的近地表对流的辐射耦合流体动力学模拟的Hopf 函数q ( τ )。对于太阳模拟，拟合精度在 0.82% 以内，对于不在模拟网格的低温或低重力边缘的所有模拟，拟合精度在 13% 以内。