Analytical approximation of neutrino distribution function in core-collapse supernova

Abstract

Results of the numerical simulations of the neutrino angular distribution in core-collapse supernova were analyzed. As analysis shown, the neutrino angular distribution function can be approximated by a one-parametric Gaussian function. The proposed approximation describes about 90% of all neutrinos in the core-collapse supernova at times t ≳ 0.2 sec after a core bounce and relatively large distances from proto-neutron-star center. Therefore, it could be a good analytical approximation of the numerical data. At small values of time and distance an accuracy of this approximation significantly decreases.