Dynamical stability of the modified Tolman VII solution

TL;DR

This paper investigates the dynamical stability of a modified Tolman VII neutron star model, incorporating an additional parameter, and finds it remains stable under radial oscillations for a range of configurations, supporting its physical plausibility.

Contribution

It introduces a modified Tolman VII solution with an extra parameter and analyzes its stability, enhancing the model's realism for neutron star interior structures.

Findings

The modified model remains stable for various compactness and parameter values.

The additional parameter does not compromise the model's stability.

Supports the model's use as a realistic neutron star approximation.

Abstract

Studies of neutron stars are at their peak after the multi-messenger observation of the binary merger event GW170817, which strongly constraints the stellar parameters like tidal deformability, masses and radii. Although current and future observations will provide stronger limits on the neutron stars parameters, knowledge of explicit interior solutions to Einstein's equations, which connect observed parameters with the internal structure, are crucial to have a satisfactory description of the interior of these compact objects. A well known exact solution, which has shown a relatively good approximation to a neutron star, is the Tolman VII solution. In order to provide a better fitting for the energy density profile, with the realistic equations of state for neutron stars, recently Jiang and Yagi proposed a modified version of this model which introduces an additional parameter $\alpha$ reflecting the interplay of the quadratic and the newly added quartic term in the energy density profile. Here we study the dynamical stability of this modified Tolman VII solution using the theory of infinitesimal and adiabatic radial oscillations developed by Chandrasekhar. For this purpose, we determine values of the critical adiabatic index, for the onset of instability, considering configurations with varying compactness and $\alpha$. We found that the new models are stable against radial oscillations for a considerable range of values of compactness and the new parameter $\alpha$, thus supporting their applicability as a physically plausible approximation of realistic neutron stars.