Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars

TL;DR

This paper investigates the stability of rotating relativistic stars against nonaxisymmetric perturbations, revealing that relativistic effects cause instabilities at lower rotation rates than Newtonian predictions, with implications for neutron star formation.

Contribution

It provides the first computation of zero-frequency nonaxisymmetric modes in relativistic stars, showing increased instability compared to Newtonian models, especially for softer polytropes.

Findings

Relativistic models become unstable at lower rotation rates than Newtonian models.

The m=2 bar mode can be unstable for softer polytropes with N ≤ 1.3.

Instability may limit the rotation speed of newly formed neutron stars.

Abstract

We study nonaxisymmetric perturbations of rotating relativistic stars. modeled as perfect-fluid equilibria. Instability to a mode with angular dependence $\exp(im\phi)$ sets in when the frequency of the mode vanishes. The locations of these zero-frequency modes along sequences of rotating stars are computed 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 $N \leq 1.3$, while in Newtonian theory it becomes unstable only for stiff polytropes of index $N \leq 0.808$. 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.