Tidal deformability and radial oscillations of anisotropic polytropic spheres

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.