Dynamical instability of differentially rotating stars

TL;DR

This paper investigates the dynamical instability of differentially rotating stars, revealing that high differential rotation leads to instability at low energy ratios and analyzing the resulting gravitational wave signals.

Contribution

It provides numerical and linear perturbation analysis of star stability, highlighting the instability conditions and gravitational wave characteristics for differentially rotating stars.

Findings

High differential rotation causes instability at low energy ratios

Gravitational waves have frequencies of several hundred Hz

Effective amplitude of gravitational waves is about 5×10^{-22} at 100 Mpc

Abstract

We study the dynamical instability against bar-mode deformation of differentially rotating stars. We performed numerical simulation and linear perturbation analysis adopting polytropic equations of state with the polytropic index $n=1$. It is found that rotating stars of a high degree of differential rotation are dynamically unstable even for the ratio of the kinetic energy to the gravitational potential energy of $O(0.01)$. Gravitational waves from the final nonaxisymmetric quasistationary states are calculated in the quadrupole formula. For rotating stars of mass $1.4M_{\odot}$ and radius several 10 km, gravitational waves have frequency several 100 Hz and effective amplitude $\sim 5 \times 10^{-22}$ at a distance of $\sim 100$ Mpc.