Radiation Energy-Balance Method for Calculating the Time Evolution of Type Ia Supernovae During the Post-Explosion Phase

Abstract

A new method is presented for calculating the time evolution of spherically symmetric Type Ia Supernova in the post-explosion phase, enabling light curves and spectra to be simulated in a physically self-consistent way. The commonly exploited radiative equilibrium, that is in essence a /gas energy balance/ condition, is unsuitable for this purpose for important physical and numerical reasons. Firstly, the RE depends on the heating and cooling rates of the gas by the radiation field, two quantities that almost completely cancel and are very difficult to calculate accurately. Secondly, the internal energy of the gas is only a tiny fraction of the total energy in the system (the vast majority of the energy resides in the radiation field), so that the vast majority of the energy is neglected in solving for the energy balance. The method presented in this paper, based on the /radiation energy balance/, addresses the bulk of the energy, does not depend on the heating/cooling rates, guarantees an accurate run of the bolometric luminosity over time while bringing the gas temperatures into consistence with the radiation field. We have implemented the method in the stellar atmosphere code PHOENIX and applied it to the classical W7 model. The results illustrate the importance of each of the four physical contributions to the energy balance as a function of time. The simulated spectra and light curves for W7 show good resemblance to the observations, which demonstrates what can be done using PHOENIX with the REB method.