$$ \newcommand\Tr{\mathrm{Tr}} \newcommand{\braket}[2]{\langle #1 \mid #2 \rangle} \newcommand\I{\mathbb{I}} \newcommand{\avg}[1]{\left< #1 \right>} \newcommand{\RD}{D} \newcommand{\ri}{\mathrm{i}} \DeclareMathOperator{\sign}{sign} \DeclareMathOperator{\Sign}{Sign} \newcommand{\ii}{\mathrm i} \newcommand{\vv}{\mathrm v} \newcommand{\ff}{\mathrm f} \newcommand{\mm}{\mathrm m} \newcommand{\ee}{\mathrm e} \newcommand{\xx}{\mathrm x} \newcommand{\RR}{\mathrm R} \newcommand{\dd}{\mathrm d} \newcommand{\FF}{\mathrm F} \newcommand{\BB}{\mathrm B} \newcommand{\vph}{v_{\mathrm{ph}}} $$
Neutrino Oscillations

Conclusions and Future Work

Neutrinos are abundantly produced in astrophysical environments such as core-collapse supernovae and binary neutron star mergers. They play important roles in the chemical and physical evolutions of these environments. Since different neutrino flavors have different influence on the environments, identifying the neutrino fluxes in different flavors becomes important. Meanwhile, neutrinos oscillate between different flavors while they propagate through space due to the mismatch of the flavor states and the mass states. Therefore it is important to understand the flavor evolution of dense neutrino media.

The interactions between the neutrino and matter can cause the neutrino to experience flavor transformation through the so called MSW mechanism if the matter profile is smooth. Neutrinos can also experience parametric resonances when there exist oscillatory perturbations to a smooth profile of the matter density. In this book, I showed that this parametric resonance behavior can be understood as Rabi oscillations which provides a simple yet intuitive picture to understand this interesting phenomenon. Interestingly, there exists an infinite number of Rabi modes even for a sinusoidal matter perturbation. I showed that most of these Rabi modes are irrelevant in a real physical system because of their tiny amplitudes, which is also true for multi-frequency matter profiles. I also derived a criterion which can be used to determine whether an off-resonance Rabi mode can significantly alter the behavior of the Rabi oscillation.

For future research, neutrino oscillations can be calculated with realistic matter profiles in supernovae or stars. The criteria I have derived in this book can be used to select the on-resonance and off-resonance Rabi modes that are important to neutrino flavor transformation and to identify the parametric resonances in these environments.

A dense neutrino medium can experience collective flavor oscillations because of the neutrino self-interaction. The linearized flavor stability analysis and the dispersion relations of the collective modes have been used to identify the physical regimes where collective oscillations may occur. In this book, I applied these methods to the neutrino media with discrete and continuous angular emissions. I showed that, contrary to the conjecture by I. Izaguirre et al. in Ref. 1, the flavor instabilities of a neutrino medium are not necessarily associated with the gaps in the dispersion relation curves of the collective modes. More work needs to be done to understand the origin and nature of the flavor instabilities of a dense medium and their relation to the dispersion relations of the collective modes.

The problem of neutrino oscillations in supernovae is further complicated by the presence of the neutrino halo formed by scattered neutrino fluxes. In this book, I have developed a toy model to explore neutrino oscillations in the presence of scattered neutrino fluxes. I have also developed a relaxation method and a parallel numerical code based on this algorithm to solve this toy model. More calculations need to be done to find out how the scattered neutrino fluxes may affect neutrino oscillations.

  1. Ignacio Izaguirre, "Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion Relation Approach", Physical Review Letters 118, 021101 (2017) . ↩︎

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