Abstract
Flavor oscillations can occur on very short spatial and temporal scales in the dense neutrino media in a core-collapse supernova (CCSN) or binary neutron star merger (BNSM) event. Although the dispersion relations (DRs) of the fast neutrino oscillations can be obtained by linearizing the equations of motion (EoM) before the emergence of any significant flavor conversion, one largely depends on numerical calculations to understand this interesting phenomenon in the nonlinear regime. In this work we demonstrate that there exist nontrivial solutions to the flavor EoM that govern the fast oscillations in one-dimensional axisymmetric neutrino gases. These solutions represent a coherent flavor isospin wave similar to the magnetic spin wave in a lattice of magnetic dipoles. We also compute the DRs of such waves in some example cases which are closely related to the DRs of the fast neutrino oscillations obtained in the linear regime. This result sheds new light on the long-term behavior of fast neutrino oscillations which can have various implications for the CCSN and BNSM events.
Highlights
Copious neutrinos are emitted during a core-collapse supernova or binary neutron star merger event which help to shape the physical and chemical evolutions of these fascinating astrophysical systems
The flavor evolution of this model can be inferred from the neutrino electronic lepton number (ELN) distribution and the dispersion relation (DR) when little flavor conversion has occurred [10,11,12], the few numerical explorations that
While our previous works show that fast oscillations can be coherent in space and time [13,14], the calculations from two other groups suggest that flavor depolarization should occur instead [15,16,17]
Summary
Copious neutrinos are emitted during a core-collapse supernova or binary neutron star merger event which help to shape the physical and chemical evolutions of these fascinating astrophysical systems. While our previous works show that fast oscillations can be coherent in space and time [13,14], the calculations from two other groups suggest that flavor depolarization should occur instead [15,16,17]. We try to gain further understanding of the fast oscillation phenomenon by studying the semianalytic solutions to the equations of motion (EoM) that govern the neutrino flavor oscillations in the nonlinear regime. With a suitable initial condition, a gyroscopic pendulum can precess smoothly without any wobbling This corresponds to the pure precession of the flavor Bloch/polarization vectors P [20] or the flavor isospins of the neutrinos [21] in the flavor space. One expects that there should exist nontrivial flavor isospin waves with Pu;3 < 1 which correspond to the flavor pendulum precessing at a latitude lower than the north pole. V we discuss the potential physical significance of the flavor isospin waves and conclude
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