ALI in Rapidly Expanding Envelopes

We discuss the current implementation of the ALI method into our HYDrodynamical RAdiation (Hydra) code for rapidly expanding, low density envelopes commonly found in core collapse and thermonuclear supernovae, novae and WR stars. Due to the low densities, non-thermal excitation by high energy photons (e.g. from radioactive decays) and the time dependence of the problem, significant departures from LTE are common throughout the envelope even at large optical depths. ALI is instrumental for both the coupling of the statistical equations and the hydrodynamical equations with the radiation transport (RT). We employ several concepts to improve the stability, and convergence rate/ control including the concept of leading elements, the use of net rates, level locking, reconstruction of global photon redistribution functions, equivalent-2-level approach, and predictive corrector methods. For appropriate conditions, the solution of the time-dependent rate equations can be reduced to the time-independent problem plus the (analytic) solution of an ODE For the 3-D problem, we solve the radiation transport via the moment equations. To construct the Eddington tensor elements, we use a Monte Carlo scheme to determine the deviation of the solution for the RT equation from the diffusion approximation (ALI of second kind). At the example of a subluminous, thermonuclear supernova (SN99by), we show an analysis of the light curves, flux and polarization spectra and discuss the limitations of our approach. 1. Physical and Numerical Environment For supernovae, novae and Wolf Rayet stars, detailed hydrodynamical radiation calculations are required to provide a link between the observables such as light curves and spectra, and the underlying physics of the objects. These applications go well beyond classical atmospheres. Density structures require detailed hydrodynamics, the low densities cause strong NLTE effects throughout the envelopes, chemical profiles are depth dependent, the energy source and sink terms due to hydrodynamical effects and radioactive decays may dominate throughout the photon decoupling region, i.e. location of the photosphere and the physical properties are time dependent (see Fig. 1). Typically, velocity fields are of the order of 500 to 30,000 km/sec. Thus, as a major simplification, we can neglect the intrinsic line widths due to pressure broadening, magnetic fields, etc.