Collective Neutrino Flavor Instability Requires a Crossing

TL;DR

This paper proves that for neutrino collective flavor instability to occur, the difference in their momentum distributions must cross zero, providing a key criterion for understanding neutrino behavior in astrophysical environments.

Contribution

It establishes a rigorous, unified condition for neutrino flavor instability based on the crossing of momentum distribution differences, applicable to various astrophysical scenarios.

Findings

Necessary condition for instability: zero crossing in distribution difference.

Applicable to Hamiltonian flavor evolution with damping.

Unifies slow and fast instability criteria.

Abstract

Neutrinos in supernovae, neutron stars, and in the early Universe may change flavor collectively and unstably, due to neutrino-neutrino forward-scattering. We prove that for collective instability to occur, the difference of momentum distributions of two flavors must change sign, i.e., there is a zero crossing. This necessary criterion, which unifies slow and fast instabilities, is valid for Hamiltonian flavor-evolution of ultra-relativistic Standard Model neutrino occupation matrices, including damping due to collisions in the relaxation approximation. It provides a simple but rigorous condition for collective flavor transformations that are believed to be important for stellar dynamics, nucleosynthesis, and neutrino phenomenology.