Neutrino Spectral Pinching in 3D Core-Collapse Supernovae: Late-Time Convergence, Failed-Explosion Signatures, and Viewing-Angle Dispersion

Abstract

We present a systematic survey of the neutrino spectral pinching parameter alpha_p(t, M, n-hat) across the Princeton Fornax ensemble of 3D core-collapse supernova simulations. We analyze 25 simulations spanning progenitor masses 8.1-100 M_sun with durations up to 8.47 s post-bounce, computed with the Fornax code and the SFHo equation of state. The pinching parameter alpha_p = (2^2 - E_rms^2)/(E_rms^2 - ^2) is derived from 12-bin spectral moments on a 128x256 sky grid for three neutrino species, enabling time- and angle-resolved spectral characterization. Four results emerge. (1) The nu-bar_e pinching floor is alpha_p = 1.92 +/- 0.10 (N=13 long-running models), lying 0.2-0.4 below 1D predictions due to 3D PNS convection. (2) Both BH-forming models (12.25, 14 M_sun) show anti-pinching (alpha_p < 0.9) before collapse, with deficit Delta alpha_p ~ 0.65 visible from t = 0.5 s. (3) Two of six long-running models exhibit a hierarchy reversal ( > ) after t = 5 s; leptonic flavors carry (40 +/- 3)% of radiated energy. (4) The LESA dipole is suppressed by >3x in BH-forming models; viewing-angle spread Delta alpha_p(68%) ~ 0.8-1.5 dominates spectral-inversion uncertainty. Mollweide sky maps reveal coherent angular structures with alpha_p anticorrelated with luminosity and correlated with mean energy. Detection rates at Hyper-Kamiokande, DUNE, JUNO, and IceCube yield 8-12% NMO/IMO discrimination during Kelvin-Helmholtz cooling. The late-time nu-bar_e pinching floor represents the first 3D characterization of spectral convergence during Kelvin-Helmholtz cooling, lying 0.2-0.4 below 1D predictions, a direct signature of 3D PNS convective transport

Figures (12)

• Figure 1: Neutrino luminosity $L_s(t)$ for all 25 Fornax models, grouped by explosion outcome and mass regime. Colors run from light (low mass) to dark (high mass). Species: $\nu_e$ (blue), $\bar{\nu}_e$ (red), $\nu_x$ (four heavy-lepton flavors; green dashed). The $\nu_e$ neutronization burst is visible as a narrow peak at $t \lesssim 20\,\mathrm{ms}$. The BH-forming models (bottom-right panel) terminate abruptly. The late-time power-law decay $L \propto t^{-n}$ with best-fit index $n \approx 1.4$ (fitted to the 17 and 18.5 M$_\odot$ runs over $t = 2$--$6\,\mathrm{s}$; Eq. \ref{['eq:lum_powerlaw']}) is visible in the longest-duration models.
• Figure 2: Spectral pinching parameter $\alpha_\mathrm{p}(t)$ for all 25 models and three neutrino species. Colors code progenitor mass (light = low mass, dark = high mass). BH-forming models ($12.25$, $14\,M_\odot$) are in red. Gray dashed line: $\alpha_\mathrm{p}=2$ (Maxwell--Boltzmann reference). A $25\,\mathrm{ms}$ rolling average has been applied to suppress convective fluctuations.
• Figure 3: Spectral pinching $\alpha_\mathrm{p}$ vs. progenitor mass at three post-bounce epochs (columns). Quadratic ($k=2$) B-spline interpolation through the mass-sorted successful models for each species ($\nu_e$: blue, $\bar{\nu}_e$: orange, $\nu_x$: green dashed); a quadratic spline is used to suppress Runge-phenomenon oscillations at sparse mass sampling. Shaded vertical bands: BH-forming progenitors (12.25 and $14\,M_\odot$). Gray dashed line: $\alpha_\mathrm{p}=2$ (Maxwell--Boltzmann reference). Horizontal colored solid lines: late-time floor value $\alpha_\mathrm{p}^{\bar{\nu}_e} = 1.92$ (orange), $\alpha_\mathrm{p}^{\nu_e} = 2.05$ (blue), and $\alpha_\mathrm{p}^{\nu_x} = 2.12$ (green), averaged over the $N=13$ long-running models (Section \ref{['sec:alpha_atlas']}). The BH models lie persistently $\sim 0.5$--$0.8$ below the successful-model trend.
• Figure 4: Mean neutrino energy evolution. Left: Time series of $\langle E_{\nu_e}\rangle$ (solid) and $\langle E_{\nu_x}\rangle$ (dashed), both per flavor, for all 25 models colored by progenitor mass (plasma colorbar; BH-forming models shown with dashed/dotted lines). Right: Hierarchy difference $\Delta E = \langle E_{\nu_e}\rangle - \langle E_{\nu_x}\rangle$ (per flavor) for all models with $t_\mathrm{max} > 5\,\mathrm{s}$; each line is annotated at its endpoint with the progenitor mass, uniquely identifying each model independently of color. Dashed line: $\Delta E = 0$ (hierarchy reversal). Six models extend beyond $t = 5\,\mathrm{s}$: $17\,M_\odot$ ($f_+=0.000$), $18.5\,M_\odot$ ($f_+=0.000$), $18\,M_\odot$ ($f_+=0.983$, reversed), $19\,M_\odot$ ($f_+=0.804$, reversed), $23\,M_\odot$ ($f_+=0.000$), and $24\,M_\odot$ ($f_+=0.410$). The $17\,M_\odot$ and $18.5\,M_\odot$ models remain strictly below $\Delta E = 0$ (standard ordering) throughout despite their long durations; see text for discussion of the non-monotonic mass dependence.
• Figure 5: Luminosity (top row) and spectral pinching (bottom row) for all 25 models. Background lines are colored by progenitor mass (plasma colormap, same as Fig. \ref{['fig:energy_hierarchy']}); BH-forming models ($12.25\,M_\odot$, red; $14\,M_\odot$, dark red) are drawn on top with thick solid lines. Columns: $\nu_e$, $\bar{\nu}_e$, $\nu_x$. Shaded region ($\alpha_\mathrm{p} < 1$): extreme anti-pinching regime. The progressive decline to $\alpha_\mathrm{p} \lesssim 0.9$ before collapse is absent in all successful models.