# Flavor-dependent neutrino angular distribution in core-collapse supernovae

## TL;DR

This paper analyzes the energy and angular distributions of neutrinos in core-collapse supernovae, highlighting how flavor-dependent angular distributions influence collective neutrino flavor evolution.

## Contribution

It provides detailed energy and angle distributions of neutrinos from supernova simulations and explains how to extract this information for further research.

## Key findings

- Distributions become more forward peaked near the neutrino sphere.
- Angular spread varies among neutrino flavors, being largest for  and smallest for x.
- The  minus ar angle distribution has a dip but remains non-negative.

## Abstract

According to recent studies, the collective flavor evolution of neutrinos in core-collapse supernovae depends strongly on the flavor-dependent angular distribution of the local neutrino radiation field, notably on the angular intensity of the electron-lepton number carried by neutrinos. To facilitate further investigations of this subject, we study the energy and angle distributions of the neutrino radiation field computed with the Vertex neutrino-transport code for several spherically symmetric (1D) supernova simulations (of progenitor masses 11.2, 15 and 25 M_sun) and explain how to extract this information from additional models of the Garching group. Beginning in the decoupling region ("neutrino sphere"), the distributions are more and more forward peaked in the radial direction with an angular spread that is largest for $\nu_e$, smaller for $\bar\nu_e$, and smallest for $\nu_x$, where $x=\mu$ or $\tau$. While the energy-integrated $\nu_e$ minus $\bar\nu_e$ angle distribution has a dip in the forward direction, it does not turn negative in any of our investigated cases.