Time evolution of the linear perturbations of a rotating Newtonian polytrope

We present the results of numerical time evolutions of the linearized perturbations of rapidly and rigidly rotating Newtonian polytropes while making the Cowling approximation. The evolution code runs stably for hundreds of stellar rotations, allowing us to compare our results with previously published eigenmode calculations, for instance the f-mode calculations of Ipser & Lindblom, and the r-mode calculations of Karino et al. The mode frequencies were found to be in agreement within the expected accuracy. We have also examined the inertial modes recently computed by Lockitch & Friedman and Yoshida & Lee, and we were able to extend their slow-rotation results into the rapid-rotation regime. In the longer term, this code will provide a platform for studying a number of poorly understood problems in stellar oscillation theory, such as the effect of differential rotation and gravitational radiation reaction on normal-mode oscillations and, with suitable modifications, mode-mode coupling in the mildly non-linear regime.