# A simple model of time-dependent ionization in Type IIP supernova envelopes

## TL;DR

This paper introduces a simple yet realistic model for time-dependent hydrogen ionization in Type IIP supernova envelopes, highlighting the persistent ionization freeze-out effect and providing criteria for non-equilibrium conditions.

## Contribution

It presents a minimal kinetic model for hydrogen ionization in supernova atmospheres and generalizes criteria for non-equilibrium states, enhancing understanding of ionization dynamics during supernova evolution.

## Key findings

- Ionization freeze-out occurs at large times in supernova envelopes.
- Non-equilibrium ionization effects are inevitable if early conditions are non-equilibrium.
- The model provides a simple criterion for assessing statistical equilibrium.

## Abstract

We propose a model kinetic system of the hydrogen atom (two levels plus continuum) under the conditions typical for atmospheres of Type IIP supernovae in the plateau stage. Despite the simplicity of this system, it describes realistically the basic properties of the complete system. Analysis shows that the ionization "freeze-out" effect is always manifest at large times. We give a simple criterion for checking the statistical equilibrium of a system under the given conditions at any time. It is shown that if the system is in non-equilibrium at early times, the time-dependent effect of ionization necessarily exists. We also generalize this criterion to the case of arbitrary multilevel systems. We discuss various factors that affect the strength of the time-dependent effect in the kinetics during the photospheric phase of a supernova explosion.