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. In general, we find that the range of applicability of current techniques is smaller than expected. However, the range can be extended with relatively little effort, and where appropriate we suggest alternative methods of analysis. While determining the absolute dust mass is difficult, obtaining an accurate ratio of dust masses for similar sources is possible. We find the dust temperature distribution to be the most important source parameter for the emergent spectrum and hence in determining other source parameters. For internally heated sources, the temperature distribution is well approximated by a power law. Although the power-law index is strongly dependent on the source opacity, it can be determined fairly accurately from the distribution of color temperatures based on the flux spectrum. The continuum opacity function can be determined either from the slope of the IR excess or by fitting the flux spectrum. In the latter case the temperature distribution greatly influences the shape of the spectrum. For both methods, the derived values are consistently too low by 5%-100%. We have also investigated the effects of radiation transport in determining the source opacity from spectral features. We find that the optical depth derived from absorption features are always underestimates, leading to errors which may be greater than a factor of 10.