SPECTRUM FORMATION IN SUPERNOVAE - NUMERICAL TECHNIQUES

We have combined several novel techniques for spectrum simulation in t he computer program EDDINGTON which solves the comoving frame equation of transfer coupled with the statistical and radiative equilibrium eq uations. The first of these is a generalization of the accelerated lam bda iteration (ALI) scheme to include an approximate frequency-derivat ive operator. This greatly enhances the convergence rate of ALI in opt ically thick, high-velocity shear flows. The next is a partial lineari zation technique which is capable of efficiently solving a very large (approximately 10(4)) number of rate equations on a moderately sized c omputer; part of its efficiency derives from a '' fixed-excitation '' iteration which allows this technique to handle simulations with a lar ge number of (intrinsically) overlapping lines and continua. Finally, we derive an expansion opacity and emissivity approximation which allo ws us to determine the effect on the transfer and statistical equilibr ium of a very large number of lines not explicitly represented in the frequency grid and additionally to treat line-blanketing from species not explicitly included in the rate equations. We illustrate the utili ty of these techniques with models of two supernovae. The first is a t ypical Type II supernova 45 days past explosion which illustrates the power of the ALI scheme for optically thick problems in rapidly moving flows. The second is a Type la supernova 250 days past explosion whic h demonstrates the ability of partial linearization and the expansion opacity/emissivity approximation to treat a problem with 727 atomic en ergy levels coupled by all continua and 4447 lines. For each we discus s rates of convergence and the effect of various convergence-accelerat ing techniques. Detailed models of various supernovae and the microphy sics (e.g., energy deposition and atomic data) we employ will be discu ssed in future publications.