Tidal deformability and radial oscillations of anisotropic polytropic spheres

TL;DR

This paper investigates how anisotropy affects the equilibrium, oscillation frequencies, and tidal deformability of polytropic spheres, providing numerical methods to incorporate anisotropic effects into these calculations.

Contribution

It introduces modified equations to include anisotropic effects in the study of polytropic spheres' equilibrium, oscillations, and tidal responses.

Findings

Anisotropy influences radial pressure and energy density.

Radial stability is affected by anisotropic properties.

Tidal deformability varies with anisotropic parameters.

Abstract

We compute the equilibrium, the fundamental eigenfrequency of oscillations modes, and quadrupolar tidal deformability of anisotropic polytropic spheres. These studies are respectively performed through the numerical solution of the Tolman-Oppenheimer-Volkoff equation, Chandrasekhar radial oscillation equations, and nonlinear first-order Riccati equation for tidal deformability, all modified from their original version to include the anisotropic effects. For the polytropic exponent $\gamma=2$ and the anisotropic model of Cattoen, Faber, and Visser, we show that the anisotropy could be reflected in the radial pressure, energy density, speed of sound, radial stability, and tidal deformability.