Axial instability of rotating relativistic stars

TL;DR

This paper investigates axial perturbations in rotating relativistic stars, revealing a low-m instability that can lead to instability or marginal stability even at slow rotation rates, contrasting with polar mode behavior.

Contribution

It demonstrates the existence of axial instabilities in rotating relativistic stars for all m≥2, extending understanding of stellar stability beyond polar perturbations.

Findings

Negative canonical energy for axial perturbations at all m≥2

Axial instability timescale scales with high power of rotation rate

Viscosity likely stabilizes hot, rapidly rotating neutron stars

Abstract

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{im\phi}$ for all values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $\Omega$, to be proportional to a high power of $\Omega$. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.