Eigenmode frequency distribution of rapidly rotating neutron stars

We use perturbation theory and the relativistic Cowling approximation to numerically compute characteristic oscillation modes of rapidly rotating relativistic stars which consist of a perfect fluid obeying a polytropic equation of state. We present a code that allows the computation of modes of arbitrary order. We focus here on the overall distribution of frequencies. As expected, we find an infinite pressure mode spectrum extending to infinite frequency. In addition we obtain an infinite number of inertial mode solutions confined to a finite, well-defined frequency range which depends on the compactness and the rotation frequency of the star. For nonaxisymmetric modes we observe how this range is shifted with respect to the axisymmetric ones, moving towards negative frequencies and thus making all m > 2 modes unstable. We discuss whether our results indicate that the star's spectrum must have a continuous part, as opposed to simply containing an infinite number of discrete modes.