THE DYNAMICAL STABILITY OF DIFFERENTIALLY ROTATING, SELF-GRAVITATING CYLINDERS

We investigate the dynamical stability of self-gravitating, differentially rotating, incompressible cylinders for three types of rotation law. When the angular velocity decreases outwards, all m = 2 modes exhibit a shear instability due to the presence of a corotation mode. This generalizes a previous result obtained by Balbinski. In most cases this instability also occurs for higher order perturbations. The first point of instability along an equilibrium sequence then belongs to a mode of higher order (m>2) when a sufficient amount of differential rotation is present. For small differential rotation this instability occurs near the secular stability point of the uniformly rotating sequence. There exists a second type of instability which is also present for uniform rotation and occurs for large rotational velocities or angular momenta. Differential rotation has only a moderate influence on this instability, in agreement with previous results. © 1990 Oxford University Press. All rights reserved.