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

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 $T\mathrm{/}\mathrm{\mid }W\mathrm{\mid }\sim 5\times {10}^{-2}$ that the neutrino luminosity changes by $\sim 3\mathrm{\%}$ 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 ($\lesssim 1\mathrm{H}\mathrm{z}$) 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.