Effects of Grain Size on the Spectral Energy Distribution of Dusty Circumstellar Envelopes

We study the effects of dust grain size on the spectral energy distribution(SED) of spherical circumstellar envelopes. Based on the self-similarityrelations of dusty SEDs derived by Ivezic & Elitzur (1997), we expect anapproximate invariance of the IR SED for models with different grain sizes.Approximate invariance follows from the fact that differently sized grains havesimilar optical properties at long wavelengths where the dust reprocesses thestarlight. In this paper, we discuss what are the physical requirements on themodel parameters to maintain the approximate invariance of the IR SED. Singlegrain size models are studied for a wide range of grain sizes in three opticaldepth regimes. In this study, we find limits for the cases where the IR SED isand is not capable of conveying information about grain sizes, and to whatextent it does so. We find that approximate invariance occurs for a much largerrange of grain sizes than previously believed, and, when approximate invarianceholds, the SED is controlled mainly by one parameter, the reprocessing opticaldepth, a quantity that measures the fraction of starlight that is absorbed bythe dust grains. Models with a grain size distribution are studied as well. Forthese models, we find that, in many instances, the concept of approximateinvariance may be extended from the IR SED to all wavelengths. This means that,for a wide range of optical depths, models with different grain sizedistributions will produce very similar SEDs and, hence, the reprocessingoptical depth is the only quantity that can be unambiguously obtained from theSED. The observational consequences of this result are discussed in detail