Transport Moment Equations of Oscillating Neutrinos and Applications to Core-Collapse Supernovae

Abstract

Understanding neutrino flavor evolution is not only important for correctly interpreting neutrino signals from core-collapse supernovae, but also potentially for understanding their mechanisms of explosion. The dense environment in a core-collapse supernova induces a variety of neutrino oscillation phenomena: in particular, self-induced collective oscillations, MSW conversion, vacuum oscillations, as well as scattering and absorption. In the past, scattering, absorption and emission have been studied in detail using Boltzmann transport, while oscillation effects have been studied in more idealistic contexts. Recent developments in the subject have pointed out that understanding the flavor evolution of neutrinos in a core-collapse supernova requires careful considerations of the interplay among all these effects, and thus attention has been paid to more complete formalisms. In this thesis we derive for the first time the moment transport equations of oscillating neutrinos, with which the problem can be solved in full. Using a natural definition of the single-angle approximation, we solve the moment equations for the flavor evolution of neutrinos in both the accretion phase and cooling phase of a typical supernova with progenitor mass around 10Msun, ignoring the effects of scattering. We observed bipolar spectral swap for the inverted hierarchy in both phases. For the accretion phase, however, the high matter density suppresses collective phenomena to a radius outside the shock and thus makes collective behavior irrelevant to shock revival. Furthermore, the high density in the accretion phase causes the spectrum to be only partially swapped, and thus at higher densities in the earlier accretion phase collective oscillations may not even affect the spectrum at infinity. Decoherence effects can further inhibit collective oscillations. To discuss such effects however, the equations need to be solved in full with scattering effects. This requires generalizing the equations to comoving frame and abandoning the single-angle approximation and is thus outside the scope of this thesis.