  We test approximate approaches to solving a neutrino transport problem that
presents itself in the analysis of some accretion-disk models. Approximation #1
consists of replacing the full, angular- dependent, distribution function by a
two-stream simulation, where the streams are respectively outwardly and
inwardly directed, with angles $\cos \theta=\pm 1/\sqrt{3}$ to the vertical. In
this approximation the full energy dependence of the distribution function is
retained, as are the energy and temperature dependences of the scattering
rates. Approximation #2, used in recent works on the subject, replaces the
distribution function by an intensity function and the scattering rates by
temperature-energy-averaged quantities. We compare the approximations to the
results of solving the full Boltzmann equation. Under some interesting
conditions, approximation #1 passes the test; approximation #2 does not. We
utilize the results of our analysis to construct a toy model of a disc at a
temperature and density such that relativistic particles are more abundant than
nucleons, and dominate both the opacity and pressure. The nucleons will still
provide most of the energy density. In the toy model we take the rate of heat
generation (which drives the radiative transfer problem) to be proportional to
the nucleon density. The model allows the simultaneous solution of the neutrino
transport and hydrostatic equilibrium problems in a disk in which the nucleon
density decreases approximately linearly as one moves from the median plane of
the disk upwards, reaching zero on the upper boundary.

Astrophysics