On the Hydrogen Recombination Time in Type II Supernova Atmospheres

TL;DR

This paper investigates hydrogen recombination times in Type II supernova atmospheres using NLTE radiative transfer calculations, highlighting the importance of time dependence in early supernova epochs and the effects of multi-level hydrogen models.

Contribution

It demonstrates that time-dependent rate equations are crucial for accurate modeling of early supernova spectra and clarifies the impact of multi-level hydrogen atoms on recombination times.

Findings

Recombination time is increased over classical values in early supernova conditions.

Multi-level hydrogen models recover classical recombination times and show smaller recombination times at most optical depths.

Time dependence significantly affects early supernova spectra, especially the H-alpha profile.

Abstract

NLTE radiative transfer calculations of differentially expanding supernovae atmospheres are computationally intensive and are almost universally performed in time-independent snapshot mode. The validity of the steady-state approximation in the rate equations has recently been questioned. We calculate the effective recombination time of hydrogen in SN II using our general purpose model atmosphere code PHOENIX. While we find that the recombination time for the conditions of SNe II at early times is increased over the classical value for the case of a simple hydrogen model atom with energy levels corresponding to just the first 2 principle quantum numbers, the classical value of the recombination time is recovered in the case of a multi-level hydrogen atom. We also find that the recombination time at most optical depths is smaller in the case of a multi-level atom than for a simple two-level hydrogen atom. We find that time dependence in the rate equations is important in the early epochs of a supernova's lifetime. The changes due to the time dependent rate equation (at constant input luminosity) are manifested in physical parameters such as the level populations which directly affects the spectra. The H-alpha profile is affected by the time dependent rate equations at early times. At later times time dependence does not significantly modify the level populations and therefore the H-alpha profile is roughly independent of whether the steady-state or time-dependent approach is used.