The Sobolev-P Method. III. The Sobolev-P Method Generalized for Three-dimensional Systems

The Sobolev-P method, a technique for the calculation of polarized line radiative transfer in atmospheres with large velocity gradients, was developed in an earlier paper by Jeffery for axisymmetric systems. In this paper, the Sobolev-P method is generalized for the treatment of three-dimensional systems. The Sobolev-P method expressions for axisymmetric and spherically symmetric systems are presented as special cases of the three-dimensional case expressions. The application of the Sobolev-P method to a simple spherically-symmetric system is described in order to give an example of how a Sobolev-P method calculation would proceed.