Insights into non-axisymmetric instabilities in three-dimensional rotating supernova models with neutrino and gravitational-wave signatures

Abstract

We present a detailed analysis to clarify what determines the growth of the low-$T/|W|$ instability in the context of rapidly rotating core-collapse of massive stars. To this end, we perform three-dimensional core-collapse supernova (CCSN) simulations of a $27 M_{\odot}$ star including several updates in the general relativistic correction to gravity, the multi-energy treatment of heavy-lepton neutrinos, and the nuclear equation of state. Non-axisymmetric deformations are analyzed from the point of view of the time evolution of the pattern frequency and the corotation radius. The corotation radius is found to coincide with the convective layer in the proto neutron star (PNS). We propose a new mechanism to account for the growth of the low-$T/|W|$ instability in the CCSN environment. Near the convective boundary where a small Brunt-V\"ais\"al\"a frequency is expected, Rossby waves propagating in the azimuthal direction at mid latitude induce non-axisymmetric unstable modes, in both hemispheres. They merge with each other and finally become the spiral arm in the equatorial plane. We also investigate how the growth of the low-$T/|W|$ instability impacts the neutrino and gravitational-wave signatures.