On the hydrogen recombination time in Type II supernova atmospheres

Abstract

Non-local thermodynamic equilibrium radiative transfer calculations of differentially expanding supernovae atmospheres are computationally intensive and are almost universally performed in a time-independent snapshot mode, where both the radiative transfer problem and the rate equations are solved assuming the steady-state approximation. The validity of the steady-state approximation in the rate equations has recently been questioned for Type II supernova (SN II) atmospheres after maximum light on to the plateau. 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 two principal quantum numbers, the classical value of the recombination time is recovered in the case of a multilevel hydrogen atom. We also find that the recombination time at most optical depths is smaller in the case of a multilevel 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 affect the spectra. The Hα 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 Hα profile is roughly independent of whether the steady-state or time-dependent approach is used.