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

The flavor conversion of a neutrino usually occurs at densities G₅^-1, whether in ordinary matter or a dense neutrino medium, and on time/distance scales of order ^-1, where G₅ is the Fermi weak coupling constant and 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 ^-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.