Asymmetric emissions of neutrinos in the cooling of rotating proto-neutron stars

TL;DR

This paper addresses the problem of neutrino-emission asymmetry during the cooling of rapidly rotating proto-neutron stars by constructing axisymmetric rotating PNS models and performing 2D GR Boltzmann neutrino transport on fixed backgrounds. The authors reveal observer-dependent neutrino luminosities that evolve from pole-dominated to intermediate-dip and eventually equatorial-dominated patterns, and they show that anisotropic neutrino emission generates deci-Hz gravitational waves potentially detectable for Galactic events; they also assess fast flavor conversions in a post-processed manner, finding near-surface zero-crossings in the electron-type sector. The key contributions include a rigorous framework for combining rotating equilibria with GR neutrino transport, quantified luminosity anisotropies, GW predictions in the deci-Hz band, and initial FFC diagnostics, highlighting the astrophysical significance for CCSN remnants and multi-messenger signals. The work provides a stepping stone toward fully dynamical, multi-physics modeling that includes convection and flavor feedback, with implications for interpreting future neutrino and gravitational-wave observations from core-collapse events.

Abstract

We evaluate global asymmetry in the luminosities of neutrinos emitted from rapidly-rotating proto-neutron stars (PNS's). We build axisymmetric models of PNS's in mechanical equilibrium with rotation by adding prescribed angular momentum distributions by hand to non-rotational PNS models, which are extracted from a one-dimensional (spherically symmetric) PNS cooling calculation at different times: \(t=2, 6, 10, 20, 30\)s after a supernova explosion. We then conduct two-dimensional (spatially axisymmetric) neutrino transport calculations on top of them with the matter profiles (and the spacetime geometry) fixed. We find for the rapidly-rotating models with \(T/|W|\sim 5\times 10^{-2}\) that the neutrino luminosity changes by \(\sim 3 \% \) depending on the observer position. We give detailed analyses of the neutrino-hemispheres as well as the neutrino luminosities that are defined observer-wise. We also calculate the low-frequency (\(\lesssim 1{\rm Hz}\)) gravitational waves produced by the neutrinos radiated asymmetrically. We find that those gravitational waves, if emitted from the Galactic center, can be detected by planned detectors such as B-DECIGO, DECIGO and AILA. Finally, we look for crossings in the energy-integrated angular distributions in momentum space for the electron neutrino sector, a signature of the fast flavor conversion. We find them near the PNS surface in all models.

Figures (16)

• Figure 1: Schematic picture of the coordinate system employed in this paper. The momentum space coordinates are locally defined with respect to the tetrad deployed there.
• Figure 2: Schematic picture showing the relation of the observer's position and the neutrino angles: $\vec{e}_r$, $\vec{e}_\theta$, $\vec{e}_\phi$ are local orthogonal unit vectors; $\vec{n}_o$ is the unit vector in the direction of the observer; $\vec{n}_p$ is the unit vector of the projection of $\vec{n}_o$ in the $\vec{e}_\theta$-$\vec{e}_\phi$ plane and $\vec{n}_{axis}$ denotes the direction of the rotation axis.
• Figure 3: Scheme for locating the neutrino-hemispheric position. (a) The schematic picture of the rays, along which the optical depth is calculated. (b) The starting points of the rays (red dots).
• Figure 4: 2D profiles with contours of the temperature (top left quadrant), density (top right quadrant), electron fraction (bottom left quadrant) and lapse function for non-rotating and uniformly-rotating models or angular velocity for the differentially-rotating model (bottom right quadrant) at $t=2$s (first row), $6$s (second row), $10$s (third row), $20$s (fourth row) and $30$s (fifth row) for the non-rotating (left column), rigidly-rotating (central column) and differentially-rotating (right column) models.
• Figure 5: Observer-dependent luminosity as a function of the observer's position for $\nu_e$ (top row), $\bar{\nu}_e$ (central row) and $\nu_x$ (bottom row) at $t=2$s (left column), $10$s (central column) and $30$s (right column) for the two rotational models. The non-rotational model is also plotted for reference.