Dynamical instability of differentially rotating stars

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 non-axisymmetric quasi-stationary states are calculated in the quadrupole formula. For rotating stars of mass 1.4 M⊙ and radius several 10 km, gravitational waves have frequency several 100 Hz and effective amplitude ∼5 × 10−22 at a distance of ∼100 Mpc.