Asymmetric emissions of neutrinos in the cooling of rotating protoneutron stars

We evaluate global asymmetry in the luminosities of neutrinos emitted from rapidly rotating protoneutron stars (PNSs). We build axisymmetric models of PNSs in mechanical equilibrium with rotation by adding prescribed angular momentum distributions by hand to nonrotational PNS models, which are extracted from a one-dimensional (spherically symmetric) PNS cooling calculation at different times: <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>t</a:mi><a:mo>=</a:mo><a:mn>2</a:mn></a:math>, 6, 10, 20, and 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>T</c:mi><c:mo>/</c:mo><c:mo stretchy="false">|</c:mo><c:mi>W</c:mi><c:mo stretchy="false">|</c:mo><c:mo>∼</c:mo><c:mn>5</c:mn><c:mo>×</c:mo><c:msup><c:mn>10</c:mn><c:mrow><c:mo>−</c:mo><c:mn>2</c:mn></c:mrow></c:msup></c:math> that the neutrino luminosity changes by <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo>∼</g:mo><g:mn>3</g:mn><g:mo>%</g:mo></g:math> depending on the observer position. We give detailed analyses of the neutrino hemispheres, as well as the neutrino luminosities that are defined observerwise. We also calculate the low-frequency (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mo>≲</i:mo><i:mn>1</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>Hz</i:mi></i:math>) 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.