Viktor V. Sobolev and radiative transfer theory

Invited review A detailed review of V.V. Sobolev's contributions to the theory of radiative transfer is presented. First, the basic problems of the theory of monochromatic scattering are formulated, which were introduced and solved approximately by the founders of the theory (E. Milne, A. Eddington, and others). Then the fundamental contribution by academician V.A. Ambartsumian, Sobolev's scientific adviser, to the analytical radiative transfer theory is summarized. Academician V.V. Sobolev continued and profoundly developed this theory. He pioneered new areas of the theory of multiple light scattering: the scattering of polarized radiation; the theory of a time-dependent radiation field; and the scattering in inhomogeneous media, in plane–parallel media with reflecting boundaries, and in media expanding with a velocity gradient. He proposed new approximate methods for solving the problems of anisotropic monochromatic scattering as well as scattering in spectral lines in stationary and expanding media which are still in use today. The most important Sobolev's contribution was to the exact analytical theory of radiative transfer. He proposed the probability method to solve radiative transfer problems and the probabilistic treatment of scattering processes; he introduced and justified the approximation of CFR in spectral lines; he developed the resolvent method for the exact solution to the basic integral equation describing monochromatic scattering and scattering in spectral lines; and he developed the theory of anisotropic scattering to analytic perfection. V.V. Sobolev applied these solutions to the interpretation of observation data for many astrophysical objects: photometric, polarimetric, and spectral characteristics of planetary atmospheres; spectra of stationary and non-stationary stars; and polarization of X-ray sources and quasars. V.V. Sobolev coauthored several papers with his students. The publications by Sobolev's disciples that continued his research are also briefly described.