Axial -modes of anisotropic neutron stars
Phys. Rev. D 113, 123003 – Published 2 June, 2026
DOI: https://doi.org/10.1103/bf6z-6xtn
Abstract
We investigate the axial -mode oscillations of anisotropic neutron stars. Equilibrium stellar configurations are constructed using two realistic equations of state, BSk21 and SLy4, together with two prescriptions for pressure anisotropy, namely the Horvat Ansatz and the Bowers-Liang Ansatz. Only neutron-star models satisfying the stability and physical acceptability criteria are considered. On these backgrounds, the complex axial -mode frequencies are computed by solving the linearized perturbation equations using a continued-fraction method. We find that, for each fixed anisotropy strength, the axial -mode frequency decreases monotonically with increasing stellar mass along the stable branch, with its magnitude depending on both the equation of state and the nature of the anisotropy. At relatively low stellar masses, configurations with dominant radial pressure () exhibit higher frequencies than those with dominant tangential pressure, whereas toward the upper end of the stable branch this ordering is reversed, and configurations with attain higher frequencies at the same mass. When expressed as a function of compactness, the axial -mode frequency displays an approximately linear dependence on , with anisotropy modifying both the slope and the intercept of the relation. The Bowers-Liang prescription produces a wider spread in the frequency values compared to the Horvat Ansatz. We also analyze the damping times associated with the axial -modes and find that they increase with stellar mass, with a rapid rise toward the upper end of the stable branch. At a fixed mass, increasing the tangential pressure relative to the radial pressure leads to shorter damping times, while configurations with dominant radial pressure exhibit longer damping times. The sensitivity of the damping time to anisotropy is more pronounced for more compact stars, and the Bowers-Liang prescription yields systematically larger damping times than the Horvat Ansatz. Finally, motivated by the numerical results, we provide empirical expressions for the axial -mode frequency and damping time as functions of stellar compactness and anisotropy strength. These relations accurately capture the behavior of the axial -mode spectrum within the physically allowed parameter space considered in this study.
