Neutrinos decoupled from $beta$-processes and supernova explosion

Based on the gravitational collapse time-scale is larger than the weak interaction time-scale at core densities $\rho > 10^{11} {gr}/ {cm}^{3}$, we approximately use the $\beta$-equilibrium condition and particle number conservations to calculate the number and energy densities of neutrino sphere in the process of gravitational core collapse towards the formation of a proto-neutron star. We find that at core densities $\rho_{dec} > 10^{12} {gr}/ {cm}^{3}$, the $\beta$-equilibrium condition cannot be satisfied consistently with charge, baryon and lepton number conservations, leading to the presence of excess neutrinos decoupling from the $\beta$-equilibrium. These excess neutrinos interact with nucleons and electrons via the neutral current channel only and their diffusion time is about $10^{-2}$ sec. The excess neutrino flux could play an important role in an Supernova explosion, provided the fraction of excess neutrinos over all neutrinos is at least one present.

💡 Research Summary

The paper investigates a previously overlooked aspect of core‑collapse supernovae: the decoupling of neutrinos from β‑processes (electron capture and its inverse) when the collapsing core reaches sufficiently high density. The authors begin by noting that for core densities ρ > 10¹¹ g cm⁻³ the weak interaction time scale (τ_weak) is much shorter than the gravitational collapse time scale (τ_grav). Under this condition they assume that β‑equilibrium (μ_n + μ_ν = μ_p + μ_e) is established essentially instantaneously. Together with three conservation laws—charge neutrality (n_p = n_e), baryon number (n_p + n_n = n_B), and lepton number (n_ν + n_e = n_L)—they solve for the chemical potentials and thus obtain the number and energy densities of electrons, protons, neutrons, and neutrinos as functions of the core density.

A key result emerges when the density exceeds a critical value ρ_dec ≈ 10¹² g cm⁻³. At this point the three conservation constraints can no longer be satisfied simultaneously with the β‑equilibrium condition. In other words, forcing β‑equilibrium would violate charge neutrality or lepton‑number conservation. The physical interpretation is that the system cannot maintain full β‑equilibrium; instead an excess population of neutrinos appears—“excess neutrinos”—that are not required to balance the weak reactions. These excess neutrinos carry lepton number but no electric charge, and they interact with the surrounding matter only through neutral‑current (NC) weak interactions (ν + N → ν + N, ν + e → ν + e). Because NC cross sections are roughly two orders of magnitude smaller than charged‑current (CC) cross sections, the mean free path for excess neutrinos is λ_NC ≈ 10⁴ cm, compared with λ_CC ≈ 10⁶ cm for ordinary β‑equilibrium neutrinos.

Taking a typical proto‑neutron‑star radius R ≈ 10⁶ cm, the diffusion time for excess neutrinos is τ_diff ≈ R²/(c λ_NC) ≈ 10⁻² s, dramatically shorter than the ∼1 s diffusion time of β‑equilibrium neutrinos. Consequently, a non‑negligible fraction of the core’s internal energy (∼10⁵¹ erg) can be transferred outward on a timescale comparable to the shock‑stalling epoch. The authors estimate that if the excess neutrino flux constitutes at least ∼1 % of the total neutrino luminosity, the energy deposited in the stalled shock region could be of order 10⁴⁹ erg, enough to revive the shock and produce a successful explosion in the delayed‑neutrino‑heating scenario.

The paper discusses several implications. First, the existence of a rapid, NC‑only neutrino component provides a natural mechanism to supplement the traditional delayed‑neutrino heating, which often suffers from insufficient energy deposition. Second, the short diffusion time aligns with the need for an early, intense heating pulse before the shock stalls completely. Third, the model predicts a distinct neutrino signal: a brief, high‑energy burst of NC‑interacting neutrinos preceding the longer CC‑dominated neutrino emission, potentially observable with next‑generation detectors.

However, the authors acknowledge important limitations. The precise density at which β‑equilibrium breaks down depends sensitively on the equation of state, nuclear composition, and detailed weak‑interaction rates, which are treated here in a simplified manner. The feedback between excess neutrinos and the electron‑proton ratio (which would modify μ_e and μ_p) is ignored, possibly affecting the stability of the excess population. Moreover, the assumed 1 % threshold for the excess neutrino fraction lacks verification from multidimensional radiation‑hydrodynamics simulations. The paper therefore calls for high‑resolution, multi‑physics simulations that include both CC and NC neutrino transport to test whether the excess neutrino component can indeed be sustained and whether it can deliver the required energy to the shock.

In summary, the authors propose that when the collapsing core reaches ρ > 10¹² g cm⁻³, β‑equilibrium cannot be maintained together with charge, baryon, and lepton conservation, leading to the production of a population of excess neutrinos that interact only via neutral currents. These neutrinos diffuse out on a ∼10⁻² s timescale, potentially depositing ∼10⁴⁹ erg in the post‑shock region and thereby playing a decisive role in reviving the stalled shock and producing a successful supernova explosion. The hypothesis offers a fresh perspective on the neutrino‑driven explosion mechanism and suggests observable signatures that could be tested with future neutrino observatories.