Mathematics – Logic
Scientific paper
May 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aas...200.1405g&link_type=abstract
American Astronomical Society, 200th AAS Meeting, #14.05; Bulletin of the American Astronomical Society, Vol. 34, p.664
Mathematics
Logic
Scientific paper
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.
Gayley Ken G.
Onifer Andrew J.
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