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Two-moment neutrino transport methods have been widely used for developingtheoretical models of core-collapse supernova (CCSN), since they substantiallyreduce the computational burden inherent in the multi-dimensionalneutrino-radiation hydrodynamical simulations. The approximation, however,comes at a price; the detailed structure of angular distribution of neutrinosis sacrificed, that is the main drawback of this approach. In this paper, wedevelop a novel method by which to construct angular distributions of neutrinosfrom the zero-th and first angular moments. In our method, the angulardistribution is expressed with two quadratic functions of the neutrino angle ina piecewise fashion. We determine the best parameters in the fitting functionby comparing to the neutrino data in a spherically symmetric CCSN model withfull Boltzmann neutrino transport. We demonstrate the capability of our methodby using our recent 2D CCSN model. We find that the essential features of theangular distributions can be well reconstructed, whereas the angulardistributions of incoming neutrinos tend to have large errors that increasewith flux factor ($\kappa$). This issue originates from the insensitiveness ofincoming neutrinos to $\kappa$, that is an intrinsic limitation in momentmethods. Based on the results of the demonstration, we assess the reliabilityof ELN-crossing searches with two-moment neutrino transport. This analysis iscomplementary to our another paper that scrutinizes the limitation of crossingsearches with a few moments. We find that the systematic errors of angulardistributions for incoming neutrinos lead to misjudgements of the crossing at$\kappa \gtrsim 0.5$. This casts doubt on the results of ELN-crossing searchesbased on two-moment methods in some previous studies.

physical review. d/physical review. d.

Constructing angular distributions of neutrinos in core collapse  supernova from zero-th and first moments calibrated by full Boltzmann  neutrino transport