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

TL;DR

This paper introduces a new analytic $T( au)$ relation for stellar models, fitted to simulation data, improving the accuracy of modeling stellar outer layers.

Contribution

It presents a novel analytic function for the $T( au)$ relation based on simulation data, enhancing the modeling of stellar atmospheres.

Findings

The fit achieves 0.82% accuracy for the solar simulation.

The fit is within 13% accuracy across a range of simulations.

Provides a more precise $T( au)$ relation for stellar modeling.

Abstract

Stellar models often use relations between the temperature $T$ and optical depth $\tau$ to evaluate the structure of their optically-thin outer layers. We fit a novel analytic function to the Hopf function $q(\tau)$ of a radiation-coupled hydrodynamics simulation of near-surface convection with solar parameters by Trampedach et al. (2014). The fit is accurate to within 0.82 per cent for the solar simulation and to within 13 per cent for all the simulations that are not on either the low-temperature or low-gravity edges of the grid of simulations.