The Nature of Low T/|W| Dynamical Instabilities in Differentially Rotating Stars

Recent numerical simulations indicate the presence of dynamical instabilities of the f-mode in differentially rotating stars even at very low values of T/|W|, the ratio of kinetic to potential energy. In this Letter we argue that these are shear instabilities which occur when the degree of differential rotation exceeds a critical value and the f-mode develops a corotation point associated with the presence of a continuous spectrum. Our explanation, which is supported by detailed studies of a simple shell model, offers a straightforward way of understanding all of the key features of these instabilities.