Resonances Driven by a Neutrino Gyroscope and Collective Neutrino Oscillations in Supernovae

Abstract

We show that flavor evolution of a system of neutrinos with continuous energy spectra as in supernovae can be understood in terms of the response of individual neutrino flavor-isospins (NFIS's) to the mean field. In the case of a system initially consisting of nu_e and anti-nu_e with the same energy spectrum but different number densities, the mean field is very well approximated by the total angular momentum of a neutrino gyroscope. Assuming that NFIS evolution is independent of the initial neutrino emission angle, the so-called single-angle approximation, we find that the evolution is governed by two types of resonances driven by precession and nutation of the gyroscope, respectively. The net flavor transformation crucially depends on the adiabaticity of evolution through these resonances. We show that the results for the system of two initial neutrino species can be extended to a system of four species with the initial number densities of nu_e and anti-nu_e significantly larger than those of nu_x and anti-nu_x. Further, we find that when the dependence on the initial neutrino emission angle is taken into account in the multi-angle approximation, nutation of the mean field is quickly damped out and can be neglected. In contrast, precession-driven resonances still govern the evolution of NFIS's with different energy and emission angles just as in the single-angle approximation. Our pedagogical and analytic study of collective neutrino oscillations in supernovae provides some insights into these seemingly complicated yet fascinating phenomena.

41 pages, 20 figures, to appear in Physical Review D

References in corpus (7)

• Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment I: Correlated Neutrino Trajectories
• Collective neutrino flavor transitions in supernovae and the role of trajectory averaging
• Multiple Spectral Splits of Supernova Neutrinos
• Analysis of Collective Neutrino Flavor Transformation in Supernovae
• Adiabaticity and spectral splits in collective neutrino transformations
• N-mode coherence in collective neutrino oscillations
• Symmetries in collective neutrino oscillations

Cited by in corpus (7)

• Effects of neutrino oscillations on nucleosynthesis and neutrino signals for an 18 M supernova model
• Neutrino-nucleus reactions and their role for supernova dynamics and nucleosynthesis
• The neutrino signal at HALO: learning about the primary supernova neutrino fluxes and neutrino properties
• Effect of collective neutrino flavor oscillations on vp-process nucleosynthesis
• Neutrino Oscillations Within the Induced Gravitational Collapse Paradigm of Long Gamma-Ray Bursts
• Neutrino oscillations in a neutrino-dominated accretion disk around a Kerr BH
• Neutrinos and core-collapse supernovae