A Simple Treatment of the Problem of Radiative Transfer in Supernova-Like Envelopes

Extract

Since the only direct information, on the physics of supernova explosions comes from spectrophotometry of their light curves, it is wortwhile to put considerable effort on understanding the properties of supernova atmospheres. Two problems appear, however, in doing so. First, the mean free path of a photon in the region where the Spectrum forms (the atmosphere) is an important fraction of the supernova size and the plane parallel approximation breaks down. Second, the roles of scattering and absorption in the formation of the continuum are not clearly determined.

The complications introduced by spherical geometry arise from the angular derivative terms in the transfer equation and from the high degree of anisotropy introduced by the geometry. The complications introduced by scattering arise from the presence of the mean intensity in the source term of the transfer equation. As an outcome, its numerical solution is time consuming, and classical simplifications are not possible due to the strong anisotropy of the radiation field. In hydrodynamical calculations it is better to calculate the moments of the radiation field, but the success of this method depends on the possibility of replacing the infinite set of differential equations by the equations of low order moments plus a closure relationship that keeps all the properties of the higher moments.