On the non-radial oscillations of realistic anisotropic neutron stars: Axial modes

TL;DR

This paper investigates axial non-radial oscillation modes of anisotropic neutron stars, revealing how pressure anisotropy influences mode frequencies, damping times, and universal relations with stellar compactness.

Contribution

It provides a consistent treatment of axial modes in anisotropic neutron stars, demonstrating the impact of anisotropy on oscillation properties and universal scaling relations.

Findings

Lower $w$-mode frequency decreases with stellar mass.

Larger anisotropy leads to more massive stars with lower frequencies.

Frequency and damping time scale quadratically with stellar compactness.

Abstract

Non-radial oscillation modes of neutron stars serve as diagnostics of their internal composition and relativistic structure. In this work, we investigate the perturbations of static and spherically symmetric neutron stars characterized by an anisotropic pressure. Given the background symmetry, perturbations decouple into polar and axial modes. To date, axial modes have remained less explored, primarily because matter and metric perturbations decouple in the isotropic limit. In this work, we provide a consistent treatment of axial modes and demonstrate that pressure anisotropy induces a direct coupling between matter and metric perturbations. We employ parameterized anisotropy models that ensure consistency with the treatment of matter perturbations. We numerically integrate the linearized Einstein field equations for the axial modes, employing a diverse set of realistic equations of state. Our results indicate that as the stellar mass grows, the frequency of the lower $w$-mode generally decreases, while its damping time increases. Softer equation of states typically yield slightly higher oscillation frequencies. Furthermore, larger anisotropy (i.e., when the tangential pressure exceeds the radial pressure) allows for more massive equilibrium configurations, which correspondingly leads to lower oscillation frequencies and prolonged damping times. Finally, we demonstrate that the frequency and damping time, both scaled by the stellar mass, exhibit a nearly universal quadratic dependence on the stellar compactness, remaining largely insensitive to both the underlying equation of state and the specific anisotropy model.