Non-equilibrium Equation of State in stellar atmospheres

TL;DR

This paper introduces a numerical method for solving the time-dependent atomic population equations in stellar atmospheres, enabling accurate modeling of non-LTE conditions where equilibrium assumptions fail.

Contribution

It develops a time-implicit numerical approach that efficiently handles large time steps for non-LTE population evolution in stellar chromospheres.

Findings

Successfully reproduces benchmark solutions for non-LTE kinetic equilibrium.

Demonstrates large time step handling without accuracy loss.

Aligns with established ionization and recombination time-scales.

Abstract

In the stellar chromospheres, radiative energy transport is dominated by only the strongest spectral lines. For these lines, the approximation of local thermodynamic equilibrium (LTE) is known to be very inaccurate, and a state of equilibrium cannot be assumed in general. To calculate the radiative energy transport under these conditions, the population evolution equation must be evaluated explicitly, including all time-dependent terms. We develop a numerical method to solve the evolution equation for the atomic-level populations in a time-implicit way, keeping all time-dependent terms to first order. We show that the linear approximation of the time dependence of the populations can handle very large time steps without losing the accuracy. We reproduce the benchmark solutions from earlier, well-established works in terms of non-LTE kinetic equilibrium solution and typical ionization/recombination time-scales in the solar chromosphere.