Transfer of Radiation in Circumstellar Dust Envelopes. II. Intermediate Case

Abstract

view Abstract Citations (20) References (2) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Transfer of Radiation in Circumstellar Dust Envelopes. II. Intermediate Case Huang, Su-Shu Abstract In this paper the gradual conversion of optical radiation to infrared radiation in the circumstellar dust envelope with spherical symmetry is discussed on the basis that the dust particles not only absorb optical radiation but also scatter it. Scattering is treated as isotropic and coherent, while the tempera- ture at any point in the dust envelope is assumed to be in equilibrium with the combined infrared radia- tion and the absorbed portion of optical radiation at the point. If the opacity is due to the geometrical cross-sections of dust grains, it has been shown that the problem can be expressed by two independent Integro-differential equations. If the usual Eddington approximation is applied to these equations and if the opacity obeys some exponential law, as is generally assumed in the study of radiative transfer in spherical atmospheres, the main problem reduces itself to the solving of a Bessel equation with a pure imaginary argument. Con- sequently, the solution can be expressed analytically, and the optical thickness of the envelope may be derived in terms of the emergent infrared flux relative to the emergent optical flux. Also, the tempera- ture variation in the cloud has been derived. Two cases-one of uniform distribution of dust in the en- velope and the other of decreasing distribution outward-have been numerically carried out. Finally, the formal solution is given for the radiation field in the spherical shell of a finite thickness Publication: The Astrophysical Journal Pub Date: August 1969 DOI: 10.1086/150117 Bibcode: 1969ApJ...157..843H full text sources ADS | Related Materials (3) Erratum: 1969ApJ...158.1247H Part 1: 1969ApJ...157..835H Part 3: 1971ApJ...164...91H