The dispersion relation of the fast neutrino oscillation wave

Abstract

A dense neutrino medium can support flavor oscillation waves which are coherent among different momentum modes of the neutrinos. The dispersion relation (DR) branches of such a wave with complex frequencies and/or wave numbers can lead to the exponential growth of the wave amplitude which in turn will engender a collective flavor transformation in the neutrino medium. In this work we propose that the complex DR branches of the neutrino oscillation wave should be bound by the critical points of the DR. We demonstrate how this theory can be applied to the neutrino medium with an (approximate) axial symmetry about the propagation direction of the neutrino oscillation wave. We also show how the flavor instabilities in this medium can be identified by tracing the critical points of the DR as the electron lepton number distribution of the neutrino medium is changed continuously.

11 pages, 4 figures. Small textual changes for clarification

References in corpus (6)

• Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion-Relation Approach
• Coherent Development of Neutrino Flavor in the Supernova Environment
• Fast neutrino flavor conversions near the supernova core with realistic flavor-dependent angular distributions
• Fast flavor conversions of supernova neutrinos: Classifying instabilities via dispersion relations
• Flavor instabilities in the neutrino line model
• Damping the neutrino flavor pendulum by breaking homogeneity

Cited by in corpus (8)

• Neutrino oscillations in supernovae: angular moments and fast instabilities
• A new possibility of the fast neutrino-flavor conversion in the pre-shock region of core-collapse supernova
• Fast Neutrino Flavor Conversion Modes in Multidimensional Core-collapse Supernova Models: the Role of the Asymmetric Neutrino Distributions
• Fast-pairwise collective neutrino oscillations associated with asymmetric neutrino emissions in core-collapse supernova
• On the characteristics of fast neutrino flavor instabilities in three-dimensional core-collapse supernova models
• Fast flavor oscillations in dense neutrino media with collisions
• A change of direction in pairwise neutrino conversion physics: The effect of collisions
• Fast Neutrino Flavor Conversion at Late Time