Dynamical rotational instability at low T/W

Dynamical instability is shown to occur in differentially rotating polytrop es with N = 3.33 and T/\W \ greater than or similar to 0.14. This instabili ty has a strong m = 1 mode, although them = 2, 3, and 4 modes also appear. Such instability may allow a centrifugally hung core to begin collapsing to neutron star densities on a dynamical timescale. The gravitational radiati on emitted by such unstable cores may be detectable with advanced ground-ba sed detectors, such as LIGO-II. If the instability occurs in a supermassive star, it may produce gravitational radiation detectable by the space-based detector LISA.