Fast neutrino flavor conversion: Roles of dense matter and spectrum crossing

Abstract

The flavor conversion of a neutrino usually occurs at densities GF-1ω, whether in ordinary matter or a dense neutrino medium, and on time/distance scales of order ω-1, where GF is the Fermi weak coupling constant and ω is the typical vacuum oscillation frequency of the neutrino. In contrast, fast neutrino flavor conversions or fast neutrino oscillations can occur on scales much shorter than ω-1 in a very dense, anisotropic neutrino gas such as that in a core-collapse supernova or a binary neutron star merger. The origin of fast neutrino oscillations still seems elusive except that it is a mathematical solution to the equation of motion. It has been suggested that the fast oscillations in stationary neutrino gases require a crossing in the electron lepton number angular distribution of the neutrino and that they are suppressed at large matter densities as normal oscillations are. By inspecting a simple four-beam neutrino model we illustrate how the multi-angle effects that were once found to suppress collective neutrino oscillations now give rise to fast flavor conversions. As a result, a large matter density can induce fast oscillations in certain astrophysical scenarios such as at the early epoch of a core-collapse supernova. We also provide an explicit proof of the necessity of a crossed neutrino angular distribution for fast oscillations to occur in an outward flowing, axially symmetric neutrino flux such as in the multi-bulb supernova model. However, fast oscillations can occur without a crossed angular distribution when both inward and outward flowing neutrino fluxes are present in a stationary neutrino gas.