Improved Monte Carlo techniques for the spectral synthesis of supernovae

Improvements in Monte Carlo techniques for computing synthetic spectra of supernovae (SNe) are described and tested using a simplified model for the atmosphere of a Type Ia SN. In the first innovation, a procedure is implemented that replaces the previously-assumed line formation by resonance scattering with a branching model using Sobolev escape probabilities, and the resulting improvement is demonstrated by comparison with exact calculations for Fe ii. In a second innovation, greatly accelerated convergence is achieved in the computation of emergent spectra by replacing the crude procedure of binning escaping Monte Carlo quanta with one based on the formal integral for emergent intensity. This is made possible by extracting lineand continuum source functions from a Monte Carlo simulation. Because of accelerated convergence, the required size of the Monte Carlo simulations is reduced by a factor ∼ 300, thus greatly speeding up the calculation of model spectra and thereby allowing interactive diagnostic analyses of the spectra of newly-discovered SNe.