Maximum-Entropy Distribution And Closure For Bose-Einstein And Fermi-Dirac Radiation Transport

We derive and study the variable Eddington factors following without approximation from the maximum entropy distribution. A unified formalism is developed for classical Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac radiation. In the classical and high occupancy limits the maximum entropy closure is bounded by previously known variable Eddington factors that depend only on the flux: the Levermore-Pomraning closure for Bose radiation at high occupation density and Minerbo's flux-limiter for the Boltzmann limit of either quantum statistics. For intermediate occupancy, the maximum entropy closure depends on both the occupation density and the flux. The Fermi-Dirac maximum entropy variable Eddington factor exhibits scale invariance, which leads to a simple analytic closure for fermion radiation. This Fermi-Dirac variable Eddington factor agrees well with Monte Carlo neutrino transport closures during early stages of neutron star formation.