Radiation hydrodynamics in a moving plasma with Compton scattering: Frequency-dependent solutions

Radiation hydrodynamical equations with Compton scattering are generally difficult to solve analytically, and usually examined numerically, even if in the subrelativistic regime. We examine the equations available in the subrelativistic regime of kBT$/$(mec2) ≲ 0.1, hν$/$(mec2) ≲ 0.1, and v$/$c ≲ 0.1, where T is the electron temperature, ν the photon frequency, and v the fluid bulk velocity. For simplicity, we ignore the induced scattering terms. We then seek and obtain analytical solutions of frequency-dependent radiative moment equations of a hot plasma with bulk motions for several situations in the subrelativistic regime. For example, in the static case of a plane-parallel atmosphere without bulk motions, where equations involve the generalized Kompaneets equation with subrelativistic corrections, we find the Wien-type solution, which reduces to the usual Milne–Eddington solution in the nonrelativistic limit, as well as the power-law-type one, which has a form of [hν$/$(kBT)]−4. In the moving case of an accelerating one-dimensional flow with bulk motions, we also find the Wien-type and the power-law-type solutions affected by the bulk Compton effect. Particularly, in the Wien-type solutions, due to the bulk Compton effect, the radiation fields gain momentum from the hot plasma in the low-frequency regime of hν < 3kBT, while they lose it in the high-frequency regime of hν > 3kBT.