Relativistic radiative transfer: moment formalisms

Two moment formalisms are developed for radiative transfer in a relativistic, differentially moving medium in flat or curved spacetime. One formalism applies to systems with no special symmetries; its moments of the photon direction distribution are ‘projected, symmetric trace-free tensors’ ℳ^{α₁ α₂ …α_k}. The other formalism applies to systems with spherical, planar or pseudospherical symmetry; its moments are scalar functions analogous to the J, H and K of non-relativistic theory. Both formalisms come in three variants: a frequency-dependent variant (moments are functions of frequency ν and of location in spacetime x^α); a redshifted variant applicable only to spacetimes with a ‘universal redshift function’ R(x^α) (moments are functions of redshifted frequency f = Rv and of x^α); and a frequency-integrated variant (moments are functions of x^α only). The moment formalisms’ emission, absorption and scattering terms are evaluated explicitly for an unmagnetized, fully ionized medium whose electrons are non-degenerate and non-relativistic and are in thermal equilibrium with each other. It is shown that double Compton scattering (one photon in and two out) followed by Comptonization of the new photon (‘DC+C’)can be a far more effective source of photon energy than bremsstrahlung in hot, dilute plasmas [at $$T/10^7 \text K\gt(\rho_0/10^{-8}\text g\enspace\text {cm}^{-3})^{2/11}$$]. It is shown, further, that when the medium is sufficiently optically thick to Comptonization, DC + C can be described by a negative opacity (equation 6.43).