Collective neutrino flavor transitions in supernovae and the role of trajectory averaging

TL;DR

This paper investigates how collective neutrino flavor transitions in supernovae are affected by different density profiles and trajectory averaging, highlighting the conditions under which these effects are observable and their dependence on neutrino hierarchy.

Contribution

It provides a detailed analysis of collective neutrino oscillations considering higher electron densities and the impact of trajectory averaging, offering new insights into spectral features and hierarchy signatures.

Findings

Collective flavor transitions are decoupled from matter effects at higher densities.

Trajectory averaging has minimal impact on the final spectral outcomes.

Spectral swaps in inverted hierarchy serve as potential signatures for neutrino hierarchy.

Abstract

Non-linear effects on supernova neutrino oscillations, associated with neutrino self-interactions, are known to induce collective flavor transitions near the supernova core for theta_13 \neq 0. In scenarios with very shallow electron density profiles, these transformations have been shown to couple with ordinary matter effects, jointly producing spectral distortions both in normal and inverted hierarchy. In this work we consider a complementary scenario, characterized by higher electron density, as indicated by post-bounce shock-wave simulations. In this case, early collective flavor transitions are decoupled from later, ordinary matter effects. Moreover, such transitions become more amenable to both numerical computations and analytical interpretations in inverted hierarchy, while they basically vanish in normal hierarchy. We numerically evolve the neutrino density matrix in the region relevant for self-interaction effects. In the approximation of averaged intersection angle between neutrino trajectories, our simulations neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, recently discussed in the literature. In the more realistic (but computationally demanding) case of non-averaged neutrino trajectories, our simulations do not show new significant features, apart from the smearing of ``fine structures'' such as bipolar nutations. Our results seem to suggest that, at least for non-shallow matter density profiles, averaging over neutrino trajectories plays a minor role in the final outcome. In this case, the swap of nu_e and nu_{\mu,\tau} spectra above a critical energy may represent an unmistakable signature of the inverted hierarchy, especially for theta_{13} small enough to render further matter effects irrelevant.