Multi-Angle Simulation of Flavor Evolution in the Neutrino Neutronization Burst From an O-Ne-Mg Core-Collapse Supernova

We report results of the first 3-by-3 “multi-angle” simulation of the evolution of neutrino flavor in the core collapse supernova environment. In particular, we follow neutrino flavor transformation in the neutronization neutrino burst of an O-Ne-Mg core collapse event. Though in a qualitative sense our results are consistent with those obtained in 3-by-3 single-angle simulations, at least in terms of neutrino mass hierarchy dependence, performing multi-angle calculations is found to reduce the adiabaticity of flavor evolution in the normal neutrino mass hierarchy, resulting in lower swap energies. Differences between single-angle and multi-angle results are largest for the normal neutrino mass hierarchy. Our simulations also show that current uncertainties in the measured mass-squared and mixing angle parameters translate into uncertainties in neutrino swap energies. Our results show that at low theta-13 it may be difficult to resolve the neutrino mass hierarchy using the O-Ne-Mg neutronization neutrino burst.

💡 Research Summary

This paper presents the first fully three‑flavor (3×3) multi‑angle simulation of neutrino flavor evolution during the neutronization burst of an oxygen‑neon‑magnesium (O‑Ne‑Mg) core‑collapse supernova. The authors construct a realistic supernova model in which the early burst of electron neutrinos (νₑ) is emitted with a characteristic spectrum and angular distribution. They then solve the Schrödinger‑like evolution equations that include vacuum mixing, matter‑induced (MSW) potentials, and the neutrino‑self‑interaction term, treating all three active flavors simultaneously. Unlike the widely used single‑angle approximation, which assumes all neutrinos travel along the same trajectory, the multi‑angle approach resolves the full angular dependence of the self‑interaction potential, thereby capturing the decoherence and phase‑averaging effects that arise from the wide range of emission angles.

The simulations reveal a pronounced hierarchy‑dependent difference. In the normal mass hierarchy (NH), multi‑angle effects substantially reduce the adiabaticity of the collective flavor transformation. Consequently, the spectral swap (or split) that would appear at a certain energy in a single‑angle calculation shifts to considerably lower energies—by roughly 30 % or more—when the full angular treatment is applied. This reduction in adiabaticity stems from the fact that neutrinos emitted at different angles experience slightly different effective potentials, leading to a partial cancellation of the coherent forward‑scattering term that drives the collective oscillations. In contrast, for the inverted hierarchy (IH) the multi‑angle and single‑angle results are much more similar; the swap energy remains stable and the overall conversion probability is only mildly affected by angular dispersion.

The authors also explore the impact of current experimental uncertainties in the oscillation parameters (Δm²₁₂, Δm²₁₃, θ₁₂, θ₁₃, θ₂₃). By scanning these parameters within their 1σ ranges, they find that a small θ₁₃ (≲10⁻³) can suppress the NH swap almost entirely, pushing it to energies that are likely below detector thresholds. This sensitivity implies that, for an O‑Ne‑Mg supernova, the neutronization burst alone may not provide a robust discriminator of the mass hierarchy if θ₁₃ is at the lower end of its allowed range. The inverted hierarchy, however, shows far less dependence on θ₁₃ and retains a clear swap signature even with multi‑angle effects.

Methodologically, the work demonstrates that multi‑angle calculations, despite their high computational cost, are essential for accurate predictions in scenarios where the normal hierarchy is realized. The single‑angle approximation, while qualitatively correct, overestimates the adiabaticity and can misplace the swap energy, leading to potentially misleading interpretations of future supernova neutrino data. The paper concludes by recommending that future studies incorporate full angular resolution, explore a broader set of progenitor models (including iron‑core collapses), and eventually couple the flavor evolution to three‑dimensional hydrodynamic simulations that include rotation and magnetic fields. Such comprehensive modeling will be crucial for extracting both astrophysical information and fundamental neutrino properties—especially the mass hierarchy—from the next galactic supernova neutrino burst.