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Context. Type Ia supernovae (SN Ia) have become an invaluable cosmologicaltool as their exceptional brightness makes them observable even at very largedistances (up to redshifts around z~1). To investigate possible systematicdifferences between local and distant SN Ia requires detailed models whosesynthetic spectra can be compared to observations, and in which the solution ofthe radiative transfer is a key ingredient. One commonly employed method is theFeautrier scheme, which is generally very robust, but which can yield wrongresults under certain conditions that frequently occur in the modelling ofsupernova ejecta or even in the radiatively driven expanding atmospheres of hotstars.  Methods. We use a sophisticated model atmosphere code which takes intoaccount the non-LTE effects and high velocity gradients that strongly affectthe physics of SN Ia atmospheres at all wavelengths to simulate the formationof SN Ia spectra by the thousands of strong spectral lines which intricatelyinteract with the "pseudo-continuum" formed entirely by these Doppler-shiftedlines themselves. We focus to an investigation of the behavior of the Feautrierscheme under these conditions.  Results. Synthetic spectra of SN Ia, a complex product of computer modelsreplicating numerous physical processes that determine the conditions of matterand radiation in the ejecta, are affected by large spatial jumps of theline-dominated opacities and source functions for which the application of evenwell-established methods may harbor certain pitfalls. We analyze the conditionsthat can lead to a breakdown of conventional procedures and we derive for theFeautrier radiative transfer solver a modified description which yields moreaccurate results in the given circumstances.

astronomy and astrophysics

Non-LTE models for synthetic spectra of type Ia supernovae. IV. A  modified Feautrier scheme for opacity-sampled pseudo-continua at high  expansion velocities and application to synthetic SN Ia spectra