Dynamical instability is shown to occur in differentially rotating polytropes with N = 3.33 and T / |W| \gtrsim 0.14 .
This instability has a strong m = 1 mode , although the m = 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 radiation emitted by such unstable cores may be detectable with advanced ground-based 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 .