Nonradial instabilities in anisotropic neutron stars

TL;DR

This paper develops a general relativistic framework to study non-radial oscillation modes in anisotropic neutron stars, revealing that anisotropy can induce instabilities in certain oscillation modes, which may limit the internal anisotropic configurations.

Contribution

It introduces a consistent method to analyze quasi-normal modes in anisotropic neutron stars within general relativity, highlighting the impact of anisotropy on mode stability.

Findings

Anisotropy can cause the imaginary parts of certain modes to change sign.

Some anisotropic neutron star models are potentially unstable.

The study constrains possible internal anisotropic configurations.

Abstract

Non-radial oscillation modes of a neutron star possess valuable information about its internal structure and nuclear physics. Starting from the quadrupolar order, such modes under general relativity are known as quasi-normal modes since they dissipate energy through gravitational radiation and their frequencies are complex. The stability of these modes is governed by the sign of the imaginary part of the frequency, which determines whether the mode would decay or grow over time. In this Letter, we develop a fully consistent framework in general relativity to study quasi-normal modes of neutron stars with anisotropic pressure, whose motivation includes strong internal magnetic fields and non-vanishing shear or viscosity. We employ parametrized models for the anisotropy and solve the perturbed Einstein field equations numerically. We find that, unlike the case for isotropic neutron stars, the imaginary parts of some of the pressure ($p$-)modes flip signs as the degree of anisotropy deviates from zero, depicting a transition from stable modes to unstable modes. This finding indicates that some anisotropic neutron star models are unstable, potentially restricting the form of sustained anisotropy.