Spectral swaps in a two-dimensional neutrino ring model

TL;DR

This paper investigates collective neutrino flavor transformations in a 2D supernova model, revealing two distinct scenarios of flavor swapping depending on the initial conditions and symmetry breaking.

Contribution

It demonstrates the existence of two limiting cases of collective oscillations in a 2D neutrino ring model, highlighting the role of spatial symmetry breaking and restoration.

Findings

Flavor transformations can start at different radii with varying neutrino densities.

Spatial symmetry can be broken and restored during flavor evolution.

Partial spectral swaps occur similarly to 1D models under certain conditions.

Abstract

Neutrinos emitted deep within a supernova explosion experience a self-induced index of refraction. In the stationary, one-dimensional (1D) supernova "bulb model", this self-induced refraction can lead to a collective flavor transformation which is coherent among different neutrino momentum modes. Such collective oscillations can produce partial swaps of the energy spectra of different neutrino species as the neutrinos stream away from the proto-neutron star. However, it has been demonstrated that the spatial symmetries (such as the spherical symmetry in the bulb model) can be broken spontaneously by collective neutrino oscillations in multi-dimensional models. Using a stationary, 2D neutrino ring model we demonstrate that there exist two limiting scenarios where collective oscillations may occur. In one limit, the collective flavor transformation begins at a radius with relatively high neutrino densities and develops small-scale flavor structures. The loss of the spatial correlation in the neutrino flavor field results in similar (average) energy spectra for the anti-neutrinos of almost all energies and the neutrinos of relatively high energies. In the other limit, the flavor transformation starts at a radius where the neutrino densities are smaller (e.g., due to the suppression of the high matter density near the proto-neutron star). Although the spatial symmetry is broken initially, it is restored as the neutrino densities decrease, and the neutrinos of different flavors partially swap their energy spectra as in the 1D bulb model. This finding may have interesting ramifications in other aspects of supernova physics.