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

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