Monte Carlo transition probabilities. II

Abstract

The macroscopic quantizations of matter into macro-atoms and radiant and thermal energies into r- and k-energy packets initiated in Paper I is completed with the definition of transition probabilities governing energy flows to and from the thermal pool. The resulting Monte Carlo method is then applied to the problem of computing the hydrogen spectrum of a type II supernova. This test problem is used to demonstrate the scheme's consistency as the number of energy packets N → ∞, to investigate the accuracy of Monte Carlo estimators for radiative rates, and to illustrate the convergence characteristics of the geometry-independent, constrained Λ-iteration method employed to obtain the NLTE stratifications of temperature and level populations. In addition, the method's potential, when combined with analytic ionization and excitation formulae, for obtaining useful approximate NLTE solutions is emphasized.