The nature of low T/vertical bar W vertical bar 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 may be shear instabilities that occur when the degree of differential rotation exceeds a critical value and when 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.