Non-Monotonic Rotation Imprint on Time-Integrated Neutrino Spectral Moments in a 15\,$M_{\odot }$ Core-Collapse Supernova Sequence

Abstract

We study the early post-bounce neutrino signal of the published Garching $15M_{\odot }$ rotating core-collapse supernova (CCSN) sequence consisting of non-rotating (NR), slowly rotating (SR, ${\Omega }_0=0.5$ rad\,s${}^{-1}$), and fast-rotating (FR, ${\Omega }_0=150$ rad\,s${}^{-1}$, artificially boosted $\sim 300\times$) three-dimensional models. We present a new analysis of these publicly available simulation data; no new simulations were performed. Our central result, for this specific model sequence, is that SR and FR shift the integrated spectral moments in \emph{opposite directions} relative to NR: FR drives the spectra toward softer, more-pinched states, while SR moves them weakly toward harder, less-pinched states. Placed in a spectral-shift plane $(\Delta ⟨E{⟩}_L,\Delta {\alpha }_L)$, NR sits at the origin, and SR and FR occupy \emph{diagonally opposite quadrants}, making the non-monotonic response immediately visible as an anti-correlation in two spectral dimensions simultaneously. The focus is the accretion interval $t_{\mathrm{pb}}=0.05$--$0.30$\,s, where the rotation imprint is strongest. Quantitatively, fast rotation produces $\Delta ⟨E_{{\nu }_e}{⟩}_L=-0.513$\,MeV and $\Delta {\alpha }_{{\nu }_e}=+0.161$, with corresponding shifts $\Delta ⟨E_{{\bar{\nu }}_e}{⟩}_L=-0.440$\,MeV and $\Delta {\alpha }_{{\bar{\nu }}_e}=+0.173$; the SR shifts are an order of magnitude smaller and in the opposite sense. The fast-rotation signature is coherent across all $15488$ lines of sight and is established during early accretion. With only three models from a single progenitor family, this result is a phenomenological characterization of one published sequence and a suggestive indication of a non-monotonic, possibly strongly nonlinear, rotational response within this sequence; the functional form and generality of the dependence on ${\Omega }_0$ remain unconstrained.