Abstract
We obtain the angular distributions that maximize the entropy functional for Maxwell-Boltzmann (classical) Bose-Einstein, and Fermi-Dirac radiation. In the low and high occupancy limits, the maximum entropy closure is bounded by previously known variable Eddington factors that depend only on the flux. For intermediate occupancy, the maximum entropy closure depends on both the occupation density and the flux. The Fermi-Dirac maximum entropy variable Eddington factor shows a scale invariance, which leads to a simple, exact analytic closure for fermions. This two-dimensional variable Eddington factor gives results that agree well with exact (Monte Carlo) neutrino transport calculations out of a collapse residue during early phases of hydrostatic neutron star formation.
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