A critical evaluation of semianalytic methods in the study of centrally heated, unresolved, infrared sources

We critically evaluate current methods of analysis in infrared (IR) astronomy and investigate the conditions under which these semianalytic methods are reliable. Specifically we examine the usual assumptions of homogeneities in dust density and temperature, and neglect of opacity effects when applied to internally heated, unresolved IR sources. To accomplish this, a series of radiation transport models for these sources have been constructed. The model results are treated as observed quantities and analyzed to derive the source parameters, using simple semianalytic methods. The discrepancies between the derived and actual model parameters can then be attributed to the limitations of the analysis methods and provide a measure of their reliability. Applying this approach to centrally heated, unresolved IR sources, we have studied in detail the following diagnostic problems: (1) determination of dust mass from monochromatic and integrated luminosities; (2) estimation of dust temperature distribution from color temperatures derived from the flux spectrum; and (3) determination of the empirical grain emissivity law (opacity function) for both continuum and spectral features.