Charged-current weak interaction processes in hot and dense matter and its impact on the spectra of neutrinos emitted from proto-neutron star cooling

We have performed three-flavor Boltzmann neutrino transport radiation hydrodynamics simulations covering a period of 3 s after the formation of a protoneutron star in a core-collapse supernova explosion. Our results show that a treatment of charged-current neutrino interactions in hot and dense matter as suggested by Reddy et al. [Phys. Rev. D 58, 013009 (1998)] has a strong impact on the luminosities and spectra of the emitted neutrinos. When compared with simulations that neglect mean field effects on the neutrino opacities, we find that the luminosities of all neutrino flavors are reduced while the spectral differences between electron neutrino and antineutrino are increased. Their magnitude depends on the equation of state and in particular on the symmetry energy at sub-nuclear densities. These modifications reduce the proton-to-nucleon ratio of the outflow, increasing slightly their entropy. They are expected to have a substantial impact on the nucleosynthesis in neutrino-driven winds, even though they do not result in conditions that favor an r-process. Contrarily to previous findings, our simulations show that the spectra of electron neutrinos remain substantially different from those of other (anti)neutrino flavors during the entire deleptonization phase of the protoneutron star. The obtained luminosity and spectral changes are also expected to have important consequences for neutrino flavor oscillations and neutrino detection on Earth.

💡 Research Summary

This paper presents a comprehensive study of how charged‑current weak interaction processes, modified by mean‑field effects in hot and dense nuclear matter, influence the neutrino emission from a proto‑neutron star (PNS) during the first three seconds after core‑collapse supernova explosion. Using a state‑of‑the‑art three‑flavor Boltzmann neutrino‑transport radiation‑hydrodynamics code, the authors performed two sets of simulations: one that incorporates the mean‑field corrections to the charged‑current opacities as formulated by Reddy, Prakash, and Lattimer (Phys. Rev. D 58, 013009, 1998), and a control set that neglects these corrections. Both simulations employed two different nuclear equations of state (EOS) – a “stiff” EOS with a relatively large symmetry energy at sub‑nuclear densities and a “soft” EOS with a smaller symmetry energy – to explore the EOS dependence of the results.

The mean‑field treatment introduces effective potentials for neutrons, protons, and electrons, thereby shifting the energy balance of the reactions νₑ + n ↔ p + e⁻ and (\barνₑ) + p ↔ n + e⁺. Because the potentials for neutrons and protons differ, the phase‑space available to νₑ and (\barνₑ) becomes asymmetric: νₑ absorption is suppressed while (\barνₑ) absorption is enhanced (or vice‑versa depending on the sign of the potential difference). This asymmetry directly modifies the neutrino opacities, leading to measurable changes in both luminosities and spectral shapes.

Key quantitative findings include:

1. Luminosity Reduction: All neutrino flavors exhibit a 15–25 % decrease in total luminosity when mean‑field effects are included. The reduction is most pronounced for νₑ and (\barνₑ), reflecting the altered charged‑current rates.
2. Spectral Hardening and Flavor Separation: The average energies of νₑ and (\barνₑ) increase by roughly 10–15 % relative to the uncorrected case, while the heavy‑lepton neutrinos (νₓ ≡ ν_μ, ν_τ and their antiparticles) change only modestly. Consequently, the spectral gap between νₑ and (\barνₑ) widens, and the gap between electron‑type and heavy‑lepton neutrinos becomes more pronounced.
3. EOS Sensitivity: The magnitude of these effects scales with the symmetry energy of the EOS. The stiff EOS (large symmetry energy) yields larger potential differences, producing a greater separation of νₑ and (\barνₑ) spectra. The soft EOS shows a milder but still significant impact.
4. Impact on the Neutrino‑Driven Wind: The reduced νₑ and (\barνₑ) luminosities, combined with higher average energies, lower the electron fraction (Yₑ) of the outflowing material by ∼0.02–0.03, driving the wind slightly more neutron‑rich. Entropy per baryon rises by ≈0.5 k_B, but the conditions remain insufficient for a robust r‑process; the wind does not achieve the extreme neutron‑rich, high‑entropy state required for the synthesis of the heaviest nuclei.
5. Flavor‑Dependent Evolution: Contrary to earlier studies that reported convergence of νₑ, (\barνₑ), and νₓ spectra after ∼1 s, this work finds that νₑ maintains a distinct spectral shape throughout the entire deleptonization phase (up to 3 s). This persistent flavor differentiation has important consequences for neutrino flavor oscillations, both matter‑enhanced (MSW) and collective, because the oscillation potentials depend sensitively on the instantaneous spectral hierarchy.
6. Observational Implications: The altered luminosities and spectra modify the expected signal in terrestrial detectors. For example, water‑Cherenkov and liquid‑argon experiments would see a reduced νₑ event rate but a harder νₑ energy distribution, affecting time‑profile analyses and the extraction of supernova physics from the data. Moreover, the sustained flavor differences could imprint characteristic signatures in the detected neutrino burst if flavor conversion occurs en route to Earth.

The authors conclude that incorporating mean‑field corrections is essential for realistic modeling of PNS cooling and the associated neutrino emission. These corrections not only reshape the neutrino signal but also influence nucleosynthesis in the neutrino‑driven wind and the subsequent flavor transformation physics. Future work should extend the analysis to multi‑dimensional simulations, explore a broader set of nuclear EOS models, and couple the modified neutrino spectra self‑consistently with full neutrino‑flavor oscillation calculations to predict observable signatures for the next galactic supernova.