Spacetime Quasi-normal Mode Oscillations of Anisotropic Neutron Stars

TL;DR

This study computes spacetime oscillation (w-mode) frequencies of anisotropic neutron stars, revealing how pressure anisotropy influences mode properties and their relation to stellar compactness, with implications for neutron star physics.

Contribution

First calculation of spacetime (w-mode) oscillations in anisotropic neutron stars using a perturbative framework and phenomenological anisotropy model.

Findings

Both real and imaginary parts of w-mode frequencies decrease with tangential pressure dominance.

No unstable w-modes found within physically viable parameters.

Universal relation between w-mode frequency and stellar compactness, modulated by anisotropy.

Abstract

Neutron star asteroseismology offers a unique opportunity to probe nuclear physics through stellar oscillations. Although the pressure inside of a neutron star is typically assumed to be isotropic, pressure anisotropy can arise from various physical mechanisms, including elasticity, viscosity, and magnetic fields. Previous studies of nonradial stellar quasi-normal mode oscillations with anisotropic pressure have focused primarily on fluid modes. In this paper, we compute, for the first time, spacetime oscillation modes (so-called w-modes) of anisotropic neutron stars. Using a perturbative framework for stellar oscillations with pressure anisotropy, developed previously by some of the authors, together with a phenomenological anisotropy model, we find that both the real and imaginary parts of the w-mode frequencies decrease as the tangential pressure becomes dominant over the radial pressure. Although we do not find any unstable w-modes within the physically viable parameter space, unstable w-modes appear in an unphysical branch of solutions when the tangential pressure strongly dominates the radial one. We also find that the relation between the real part of the w-mode frequency and the stellar compactness is quasi-universal with respect to variations in the equation of state and the degree of pressure anisotropy. In contrast, the relation between the imaginary part of the w-mode frequency and the stellar compactness depends on the degree of anisotropy, but remains equation-of-state universal when the anisotropy is fixed. Finally, we discuss potential mode crossings and the validity of certain approximations that have been shown to work well for w-mode calculations in the isotropic case.