Constructing angular distributions of neutrinos in core-collapse supernovae from zeroth and first moments calibrated by full Boltzmann neutrino transport

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