Equilibrium models of differentially-rotating polytropic cylinders

The equilibrium structure of differentially rotating polytropic cylinders is determined numerically. We setn=3 and use a quadratic function for the law of differential rotation. We construct different models by varying the angular velocity at the axis and the ratio of the angular velocity at the surface to the angular velocity at the axis. By taking a decreasing function for the rotation law we are able to treat models with an angular velocity at the axis greater than the break-up velocity of uniformly rotating cylinders. We also determine whether a Richardson-like criterion for stability is violated in the models.