Non-LTE models for synthetic spectra of type Ia supernovae / hot stars with extremely extended atmospheres - II. Improved lower boundary conditions for the numerical solution of the radiative transfer

Context. Realistic atmospheric models that link the properties and the physical conditions of supernova ejecta to observable spectra are required for the quantitative interpretation of observational data of type Ia supernovae (SN Ia) and the assessment of the physical merits of theoretical supernova explosion models. The numerical treatment of the radiation transport – yielding the synthetic spectra – in models of SN Ia ejecta in early phases is usually carried out in analogy to atmospheric models of “normal” hot stars. Applying this analogy indiscriminately leads to inconsistencies in SN Ia models because a diffusive lower boundary, while justified for hot stars, is invalid for hydrogen and helium-deficient supernova ejecta. In type Ia supernovae the radiation field does not thermalize even at large depths, and large optical depths are not reached at all wavelengths. Aims. We aim to derive an improved description of the lower boundary that allows a more consistent solution of the radiation transfer in SN Ia and therefore yields more realistic synthetic spectra. Methods. We analyze the conditions that lead to a breakdown of the conventional diffusion approximation as the lower boundary in SN Ia. For the radiative transfer, we use a full non-LTE code originally developed for radiatively driven winds of hot stars, with adaptations for the physical conditions in SN Ia. In addition to a well-tested treatment of the underlying microphysical processes, this code allows a direct comparison of the results for SN Ia and hot stars. Results. We develop a semi-analytical description that allows us to overcome some of the limiting assumptions in the conventional treatment of the lower boundary in SN Ia radiative transfer models. We achieve good agreement in a comparison between the synthetic spectrum of our test model and an observed spectrum.