The Soboloev-P Method: A Generalization of the Sobolev Method for the Treatment of the Polarization State of Radiation and the Polarizing Effect of Resonance Line Scattering

The Sobolev-P method, a generalization of the Sobolev method, is developed for the treatment of the polarization state of radiation and the polarizing effect of resonance line scattering. The polarization state of the radiation is described by the Stokes parameters. The photon angular redistribution is described by a linear combination of the Rayleigh and isotropic phase matrices. Using this form of photon redistribution the Sobolev-P method formulas are derived for the case of axisymmetric systems. For continuum radiative transfer it is shown that quantitatively accurate calculations can be done using the Sobolev-P method and a discretized continuous opacity approximation. Sample synthetic flux and polarization spectra for model axisymmetric supernova systems calculated using Sobolev-P method are reported. A comparison of these sample results with spectropolarimetric data for SN 1987A shows some qualitative agreement of the features and indicates that it is pausible that SN 1987A has a length-width asymmetry of order 20 percent.