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K. G. Gayley, A. J. Onifer (University of Iowa)
When dealing with highly optically thick atmospheres, even in the presence of considerable scattering, it is customary and convenient to assume that the zeroth-order moment of the radiation field completely thermalizes. This in turn implies that the frequency-dependent flux is inversely proportional to the local frequency-dependent opacity, resulting in the well-known Rosseland mean as the flux-weighted average. The necessary logic is that the energy density determines the energy flux, but this is actually only true on scales large compared to the thermalization length. On smaller scales, the reverse is true: conserving flux determines the energy density, and thus the energy density will not be locally thermalized whenever the mean-free-path varies on scales smaller than the thermalization length. This has important ramifications for the Rosseland mean in the presence of opacity inhomogeneities, such as from ionization gradients in static atmospheres, line distributions in supersonic flows, and clumping.
We wish to acknowledge NSF grant AST-0098155.
The author(s) of this abstract have provided an email address for comments about the abstract: kenneth-gayley@uiowa.edu
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Bulletin of the American Astronomical Society, 34
© 2002. The American Astronomical Soceity.