Collective neutrino oscillations in non-spherical geometry

TL;DR

This paper extends the study of collective neutrino oscillations to non-spherical geometries, providing a formal framework and analyzing a disk-shaped source as a model for neutron star mergers.

Contribution

It introduces a formalism for collective neutrino oscillations in arbitrary geometries and generalizes the single-angle approximation beyond spherical symmetry.

Findings

Formal definition of single-angle approximation for non-spherical geometries

Application to a disk-shaped source modeling neutron star mergers

Framework applicable to complex astrophysical neutrino sources

Abstract

The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the ``single-angle approximation'' frequently used for supernova neutrinos and allows for a natural generalization to non-spherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.