Collective plasma effects in scattering of radiation in astrophysical plasmas

The contribution to the radiative transport due to collective scattering in astrophysical plasmas and a generalization of the Kompaneets equation is obtained. Both the stimulated and spontaneous scattering and the contribution of scattering on electrons and ions are taken into account and shown to be important over a broad range of frequencies ωpe<ω<ωpec/vTe (ωpe is the plasma frequency, c is the light velocity and vTe is the electron thermal velocity). A new expression for the Eddington luminosity including collective effects is derived. In the transport cross section the scattering on ions starts to contribute for ω⩽3ωpec/vTe while in the generalized Kompaneets equation the scattering on ions dominate for ω⩽ωpe(c/vTe)(me/mi)1/4. It is shown that the contribution related to the change of frequency during the stimulated and spontaneous scattering modifies the structure of the transport equation. A new transport equation is derived which contains a derivative of the intensity with respect to the frequency and in general such an equation does not allow the use of the concept of opacity as normally defined.