Collective neutrino flavor transitions in supernovae: analytical and numerical aspects

Abstract

Non-linear effects on supernova neutrino oscillations, associated with neutrino-neutrino interactions, are known to induce collective flavor transformations near the supernova core for θ13 ≠ 0. For typical electron density profiles (as taken from shock-wave simulations at a few seconds after bounce) these transformations precede ordinary matter effects, and 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, using thermal spectra and a representative value sin2 θ13 = 10-4. Our results neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, with analytically understandable features. They also suggest that averaging over neutrino trajectories plays a minor role in the final outcome. The split/swap of (anti)neutrino spectra emerges as an unmistakable signature of the inverted neutrino hierarchy.