Gravitational radiation from rotational instabilites in compact stellar cores with stiff equations of state

We carry out 3D numerical simulations of the dynamical instability in rapidly rotating stars initially modeled as polytropes with $n=1.5, 1.0, \mathrm{and} 0.5$. The calculations are done with a SPH code using Newtonian gravity, and the gravitational radiation is calculated in the quadrupole limit. All models develop the global $m=2\mathrm{}$ bar mode, with mass and angular momentum being shed from the ends of the bar in two trailing spiral arms. The models then undergo successive episodes of core recontraction and spiral arm ejection, with the number of these episodes increasing as $n$ decreases: this results in longer-lived gravitational wave signals for stiffer models. This instability may operate in a stellar core that has expended its nuclear fuel and is prevented from further collapse due to centrifugal forces. The actual values of the gravitational radiation amplitudes and frequencies depend sensitively on the radius of the star $R_{\mathrm{eq}}$ at which the instability develops.