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Fast flavor conversions of supernova neutrinos: Classifying instabilities via dispersion relations
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abstract
Supernova neutrinos can exhibit a rich variety of flavor conversion mechanisms. In particular, they can experience "fast" self-induced flavor conversions almost immediately above the core. Very recently, a novel method has been proposed to investigate these phenomena, in terms of the dispersion relation for the complex frequency and wave number ($\omega$,$k$) of disturbances in the mean field of the $\nu_e\nu_x$ flavor coherence. We discuss a systematic approach to such instabilities, originally developed in the context of plasma physics, and based of the time-asymptotic behavior of the Green's function of the system. Instabilities are typically seen to emerge for complex $\omega$, and can be further characterized as convective (moving away faster than they spread) and absolute (growing locally), depending on $k$-dependent features. Stable cases emerge when $k$ (but not $\omega$) is complex, leading to disturbances damped in space, or when both $\omega$ and $k$ are real, corresponding to complete stability. The analytical classification of both unstable and stable modes leads not only to qualitative insights about their features but also to quantitative predictions about the growth rates of instabilities. Representative numerical solutions are discussed in a simple two-beam model of interacting neutrinos. As an application, we argue that supernova and binary neutron star mergers exhibiting a "crossing" in the electron lepton number would lead to an absolute instability in the flavor content of the neutrino gas.
Forward citations
Cited by 6 Pith papers
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Flavomons in Matter Gradients: Ray Tracing and Amplitude Evolution
Matter gradients slow but do not suppress neutrino-mass-induced flavor instabilities, so flavomon ray tracing is required instead of local stability analysis alone.
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Neutrino quantum kinetics for fast flavor conversion in a time-dependent environment
Fast flavor conversion in a time-varying supernova background proceeds through three episodes and broadly agrees with static two-step model results.
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Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior
For shallow angular crossings, the nonlinear evolution of a single-wave fast flavor instability is a flavor pendulum whose amplitude and period are set by the linear growth rate.
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Theory of neutrino slow flavor evolution. Part II. Space-time evolution of linear instabilities
All weak fast and slow neutrino flavor instabilities are convective, so they grow spatially along neutrino directions rather than locally in time.
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Pauli blocking: probing beyond-mean-field effects in neutrino flavor evolution
Adding heuristic Pauli-blocking factors to neutrino self-interactions shifts fast flavor stability regions: two instabilities weaken, and one stable case becomes unstable.
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Fast Flavor Pendulum: Instability Condition
The Nyquist criterion for homogeneous fast flavor instability is corrected to N = W - Ns/2, where W is the subluminal winding number and Ns counts real superluminal solutions.
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