Hydrogen Recombination with Multilevel atoms

Hydrogen recombination is one of the most important atomic processes in many astrophysical objects such as Type II supernova (SN~II) atmospheres, the high redshift universe during the cosmological recombination era, and H II regions in the interstellar medium. Accurate predictions of the ionization fraction can be quite different from those given by a simple solution if one takes into account many angular momentum sub-states, non-resonant processes, and calculates the rates of all atomic processes from the solution of the radiative transfer equation instead of using a Planck function under the assumption of thermal equilibrium. We use the general purpose model atmosphere code PHOENIX 1D to compare how the fundamental probabilities such as the photo-ionization probability, the escape probability, and the collisional de-excitation probability are affected by the presence of other metals in the environment, multiple angular momentum sub-states, and non-resonant processes. Our comparisons are based on a model of SN 1999em, a SNe Type II, 20 days after its explosion.