Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars

We study nonaxisymmetric perturbations of rotating relativistic stars modeled as perfect-fluid equilibria. Instability to a mode with angular dependence exp (imϕ) sets in when the frequency of the mode vanishes. The locations of these zero-frequency modes along sequences of rotating stars are computed for the first time in the framework of general relativity. We consider models of uniformly rotating stars with polytropic equations of state, finding that the relativistic models are unstable to nonaxisymmetric modes at significantly smaller values of rotation than in the Newtonian limit. Most strikingly, the m = 2 bar mode can become unstable even for soft polytropes of index N ≤ 1.3, while in Newtonian theory it becomes unstable only for stiff polytropes of index N ≤ 0.808. If rapidly rotating neutron stars are formed by the accretion-induced collapse of white dwarfs, instability associated with these nonaxisymmetric, gravitational-wave driven modes may set an upper limit on neutron-star rotation. Consideration is restricted to perturbations that correspond to polar perturbations of a spherical star. A study of axial perturbations is in progress.