The Nature of Low <i>T</i> /| <i>W</i> | Dynamical Instabilities in Differentially Rotating Stars
Anna L. WattsLaboratory for High Energy Astrophysics, Mail Code 662, NASA Goddard Space Flight Center, Greenbelt, MD 20771Nils AnderssonSchool of Mathematics, University of Southampton, Southampton SO17 1BJ, UKD. I. JonesCenter for Gravitational Wave Physics, Pennsylvania State University, 104 Davey Laboratory, University Park, PA 16802-6300
2004en
ABI
Abstract
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 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.
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