Infrared sources in molecular clouds

Abstract

As a model for infrared sources in molecular regions, we calculate the radiative transfer in a dust cloud surrounding a central star. The grain temperature at each radius r is determined from radiative equilibrium in the radiation of both the star and the other circumstellar dust. In most clouds which are optically thick to the stellar photons, heating by the dust reradiation is dominant. However, even with moderate opacity (τ_(100µ) ≾ 1), the temperature distribution with radius stays qualitatively similar to that of an optically thin envelope. Different portions of the infrared spectrum may help pinpoint the parameters characterizing the source. We find that (1) the spatial variation of the flux at λ ≳ 350 µ provides an excellent measure of the dust density distribution, (2) the falloff in intensity longward of the spectral peak is always slower than λ^(-(2+n)) for an λ^(-n) emissivity law, (3) the optical depth at the peak will always be less than or about unity, (4) a power-law form for S_v in the near-infrared quite generally indicates that the emission is optically thin, and (5) an exponential decrease in S_v in the near-infrared implies either that τ ≈ 1 at the peak or that there is a deficiency of grains at small r. Viewing the observational data for the Kleinmann-Low nebula in light of the models, we infer that the dust density distribution is n_d ∝ r^(-1.5), the long wavelength emissivity between 30 µ and 1 mm varies approximately as λ^(-1-5), and τ_(70µ) ≈ 1.