Damping the neutrino flavor pendulum by breaking homogeneity

Abstract

The most general case of self-induced neutrino flavor evolution is described by a set of kinetic equations for a dense neutrino gas evolving both in space and time. Solutions of these equations have been typically worked out assuming that either the time (in the core-collapse supernova environment) or space (in the early universe) homogeneity in the initial conditions is preserved through the evolution. In these cases one can gauge away the homogeneous variable and reduce the dimensionality of the problem. In this paper we investigate if small deviations from an initial postulated homogeneity can be amplified by the interacting neutrino gas, leading to a new flavor instability. To this end, we consider a simple two flavor isotropic neutrino gas evolving in time, and initially composed by only ${\nu }_e$ and ${\bar{\nu }}_e$ with equal densities. In the homogeneous case, this system shows a bimodal instability in the inverted mass hierarchy scheme, leading to the well studied flavor pendulum behavior. This would lead to periodic pair conversions ${\nu }_e{\bar{\nu }}_e\leftrightarrow {\nu }_x{\bar{\nu }}_x$. To break space homogeneity, we introduce small amplitude space-dependent perturbations in the matter potential. By Fourier transforming the equations of motion with respect to the space coordinate, we then numerically solve a set of coupled equations for the different Fourier modes. We find that even for arbitrarily tiny inhomogeneities, the system evolution runs away from the stable pendulum behavior: the different modes are excited and the space-averaged ensemble evolves towards flavor equilibrium. We finally comment on the role of a time decaying neutrino background density in weakening these results.

(7 pages, 5 eps figures. Figure improved. Final version appeared in PRD)

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• Fast Neutrino Flavor Conversion Modes in Multidimensional Core-collapse Supernova Models: the Role of the Asymmetric Neutrino Distributions
• Flavor instabilities in the neutrino line model
• The dispersion relation of the fast neutrino oscillation wave
• Neutrino Flavor Conversions in High-Density Astrophysical and Cosmological Environments
• Simple method for determining asymptotic states of fast neutrino-flavor conversion
• Fast Neutrino Flavor Conversion at Late Time
• Simulations of Fast Neutrino Flavor Conversions with Interactions in Inhomogeneous Media
• Neutrino Oscillations in Core-Collapse Supernovae and Neutron Star Mergers
• Spectral swaps in a two-dimensional neutrino ring model
• Neutrino flavor mixing with moments
• Theory of neutrino slow flavor evolution. Part I. Homogeneous medium
• Three-flavor collective neutrino conversions with multi-azimuthal-angle instability in an electron-capture supernova model
• Fast Flavor Pendulum: Instability Condition
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• Two-beam Multiparticle Many-body simulations of Inhomogeneous FFI
• Single-wave solutions of the neutrino fast flavor system. Part I. Mechanical properties