The Sobolev approximation in a spherical shell expanding with constant radial velocity.

Abstract

A simple model of line radiative transfer in a circumstellar shell surrounding a supernova is presented. An examination of optical depth in an atmosphere with power-law expansion and a single source of opacity highlights certain difficulties arising as the power-law index approaches zero. The Sobolev approximation is shown, however, to be applicable to the case of a constant-radial-velocity wind so long as the intrinsic line profile of the opacity source is a Dirac delta function. Sample line profiles for various geometries are presented along with the source code used to generate the profiles. The simple model predicts the shape of spectral features with a characteristic size of about 10--100 km s-1 in the observed spectrum of a core-collapse supernova that shows evidence for circumstellar interaction.