NLTE Modeling of SNe Ia Near Maximum Light

Modeling the atmospheres of SNe~Ia requires the solution of the NLTE radiative transfer equation. We discuss the formulation of the radiative transfer equation in the co-moving frame. For characteristic velocities larger than about 2000 km/s, the effects of advection on the synthetic spectra are non-negligible, and hence should be included in model calculations. We show that the time-independent or quasi-static approximation is adequate for SNe~Ia near maximum light, as well as for most other astrophysical problems; e.g., hot stars, novae, and other types of supernovae. We examine the use of the Sobolev approximation in modeling moving atmospheres and find that the number of overlapping lines in the co-moving frame make the approximation suspect in models that predict both lines and continua. We briefly discuss the form of the Rosseland mean opacity in the co-moving frame, and present a formula that is easy to implement in radiation hydrodynamics calculations.