2003ApJ...593..402J

To study the dependence of scattering-induced polarization on source properties in reflection nebulae and circumstellar envelopes, the transport of polarized radiation in a dusty medium is solved for spherical geometry with spherical dust grains. The Stokes parameters for linear polarization are calculated by iterating between a short characteristic solution of the linear ray equations that determines the angular distribution of the radiation field and a numerical integration of the scattering kernel. The combined moment equation is used to determine the mean intensities, which are used to improve the iteration process. The scattering phase matrix is calculated for non-Rayleigh (Mie) scattering in a model circumstellar dust shell using a sum over Fourier coefficients and general spherical functions. Specific intensity is calculated for a resolved source, from which polarization maps are constructed, and the variance of polarization with properties of the dust and of the circumstellar shell is studied. Polarization in the near-IR, visible, and UV is ubiquitous for all models in this study and should be observable in any marginally resolved source, even for a beam size as large as one-fourth the source size. The critical wavelength λ_c at which polarization remains significant in the infrared is related to the grain albedo ω and dust temperature T_d by logωλ_c∝λ_cT_d^–1. For models applicable to circumstellar shells of asymptotic giant branch stars, this wavelength ranges from 1 to 5 µm. In general, λ_c increases with the dust shell opacity, grain size, and albedo. Although λ_c is insensitive to the dust density distribution and the ambient interstellar radiation field, the polarization spectrum and peak polarization depend strongly on these parameters. To test the realism of our models, a model is constructed for a source similar to IRC +10216. The results are found to be consistent with available observations.