Minimal Analytical Model of Neutrino Distribution Function in Supernova

The possibility of an analytical approximation of nonequilibrium neutrino distribution under core-collapse supernova conditions is considered. In minimal model, an analytical approximation depends on four parameters at each point of the supernova. Within this model, three approximations of the energy neutrino distribution and three variants of angular neutrino distribution are analyzed, and their accuracy is estimated. Based on this analysis, two variants of total four-parametric approximation for inner and outer part of supernova are constructed. In case of outer part of supernova, the approximation parameters are presented as function of the radial coordinate. The time dependence of the approximation parameters is determined from their correlation with the radius of the core of the protoneutron star and the spatial scale of neutrinosphere for electron neutrinos. This approach allows to apply obtained results for wide range of supernova models.