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

Context. Type Ia supernovae (SN Ia) have become an invaluable cosmological tool because their exceptional brightness makes them observable even at very large distances (up to redshifts around z ≈ 1). To investigate possible systematic differences between local and distant SN Ia requires detailed models whose synthetic spectra can be compared to observations and in which the solution of the radiative transfer is a key ingredient. One commonly employed method is the Feautrier scheme, which is generally very robust but can lead to wrong results under certain conditions that frequently occur when modeling supernova ejecta or even the radiatively driven expanding atmospheres of hot stars. Aims. We attempt to improve the procedure we have developed for simulating the radiative transfer of metal-rich, intermediate- and low-density, line-dominated atmospheres to allow the method to be applied successfully even under conditions of high expansion velocities. Methods. We use a sophisticated model atmosphere code that considers the non-LTE effects and large velocity gradients that strongly affect the physics of SN Ia atmospheres at all wavelengths to simulate the formation of SN Ia spectra by the thousands of strong spectral lines that intricately interact with the “pseudo-continuum” formed entirely by these Doppler-shifted lines themselves. We focus on investigating the behavior of the Feautrier scheme under these conditions. Results. Synthetic spectra of SN Ia, a complex product of computer models replicating numerous physical processes that determine the conditions of matter and radiation in the ejecta, are affected by large spatial jumps of the line-dominated opacities and source functions for which the application of even well established methods may harbor certain pitfalls. We analyse the conditions that can lead to a breakdown of conventional procedures and we derive a modified description that yields more accurate results in the given circumstances for the Feautrier radiative transfer solver.