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.
Highlights
Through the neutrino-neutrino forward scattering [1,2,3], the dense neutrino gases present in the early universe, corecollapse supernovae and binary neutron star mergers can experience collective flavor transformation
We have studied the critical points of the dispersion relation (DR) of the fast flavor conversion of the neutrino medium
These critical points are the end points of the DR branches with complex frequencies and/or wave numbers. Applying this theory to the neutrino medium with the axial symmetry, we demonstrated how the DR branches and instabilities emerge and evolve as the electron lepton number (ELN) distribution is changed continuously
Summary
Through the neutrino-neutrino forward scattering [1,2,3], the dense neutrino gases present in the early universe, corecollapse supernovae and binary neutron star mergers can experience collective flavor transformation (see, e.g., Refs. [4,5,6,7] among many other works, and Ref. [8] for a review). [11] that the complex DR branches of the neutrino oscillation wave always exist between the gaps of the real branches This conclusion turns out to be limited to the toy model with only two neutrino beams whose DR function is a quadratic polynomial of the wave number and frequency [31]. [13] were still limited to the two-beam toy model This is because the theories by Sturrock and Briggs require the knowledge of the overall analytic properties of the DR function which can be difficult to obtain for a general medium. Due to this difficulty, it was later proposed in Ref.
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