Neutrino Luminosity and Matter-Induced Modification of Collective Neutrino Flavor Oscillations in Supernovae

We show that the bump in the electron number density profile at the base of the hydrogen envelope in O-Ne-Mg core-collapse supernovae causes an interesting interplay between neutrino-electron and neutrino-neutrino forward scattering effects in the flavor evolution of low-energy nu_e in the neutronization burst. The bump allows a significant fraction of the low-energy nu_e to survive by rendering their flavor evolution nonadiabatic. Increasing the luminosity of the neutronization burst shifts the bump-affected nu_e to lower energy with reduced survival probability. Similarly, lowering the luminosity shifts the bump-affected neutrinos to higher energies. While these low energy neutrinos lie near the edge of detectability, the population of bump-affected neutrinos has direct influence on the spectral swap formation in the neutrino signal at higher energies.

💡 Research Summary

The paper investigates how a modest bump in the electron number density (nₑ) at the base of the hydrogen envelope of an O‑Ne‑Mg core‑collapse supernova influences the flavor evolution of the neutronization burst neutrinos, especially the low‑energy νₑ component. In O‑Ne‑Mg progenitors the hydrogen envelope has a high electron fraction (Yₑ≈0.85) while the underlying layers have Yₑ≈0.5. Because the matter density ρ varies smoothly with radius, the abrupt change in Yₑ creates a localized increase—a “bump”—in nₑ. For the normal mass hierarchy this bump renders the MSW resonance for low‑energy νₑ non‑adiabatic, allowing a sizable fraction of these neutrinos to remain in the electron flavor.

The authors model the burst as a pure νₑ emission from a neutrinosphere at Rν=60 km with a total luminosity Lν ranging from 10⁵² to 10⁵⁴ erg s⁻¹. The emitted spectrum follows a Fermi‑Dirac distribution (η=3, T=2.75 MeV) with an average energy ⟨Eν⟩≈11 MeV. Using the single‑angle approximation, the neutrino‑neutrino forward‑scattering potential μ(r)=2√2 G_F n_ν(r) is expressed in terms of Lν and falls off as r⁻⁴. The flavor evolution is described by the neutrino flavor isospin (NFIS) formalism, where each mode s_ω (ω=Δm²/2E) obeys

  ds_ω/dr = s_ω × (H_v + H_e – μ S),

with H_v the vacuum term (set by Δm²_atm and θ₁₃), H_e the matter term (∝√2 G_F nₑ), and S the collective NFIS vector. The bump introduces an additional resonance condition ω cos 2θ_v = |H_e| + B, where B≡μ² cos 2θ_m>0. As Lν increases, μ grows, B becomes larger, and the resonance energy E_res ∝ 1/(|H_e|+B) shifts to lower values. Consequently, for high luminosities the bump‑affected νₑ occupy the sub‑MeV regime, whereas for lower luminosities they peak around 4–5 MeV.

The probability for a νₑ to hop from the heavy to the light mass eigenstate after passing the resonance is given by a Landau‑Zener expression

  P_hop = exp