The opacity of an expanding medium

Mathematics – Probability

Scientific paper

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Supernovae, Circumstellar Shells, Clouds, And Expanding Envelopes, Circumstellar Masers

Scientific paper

Shortly after the breakout of the initial shock wave generated by the collapsing core of a supernova, the expansion of the envelope becomes nearly isotropic. Hydrodynamic models of this phase can be quite simple. One complication is that standard opacity tables do not properly account for the way the radiation interacts with the expanding gas. Since a photon is continually Doppler shifted relative to the gas it is passing through, the probability that it interacts with a spectral line is greatly enhanced. It has been shown that the this enhancement can be as large as an order of magnitude in some circumstances. This paper is divided into four parts. After reviewing the expansion opacity for a homogeneous, isotropically expanding medium, we relax the assumptions. First, we consider the expansion opacity in a homogeneous, non-istropically expanding gas. Next, we drop the assumption of homogeneity, but restrict our attention to the case of an optically thick gas. Finally, we consider the general problem in which the photons are allowed to have an arbitrarily large mean free path.

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