Dynamical stability of the modified Tolman VII solution

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.

arXiv comment10 pages, 7 figures. Updated Figs. 2 and 7. Few minor changes in presentation. Corrected some statements on the realistic EOSs in Sec. IV. Extended conclusions and discussion. Accepted for publication in PRD

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• New interior model of neutron stars
• On the maximum compactness of neutron stars
• Slowly rotating Tolman VII solution
• Horizonless star based on regular black hole with finite radius and its observational signatures
• Configurational entropy and stability conditions of fermion and boson stars
• The Tolman VII Space-time in the Presence of a Charge and a Cosmological Constant
• Statistical complexity as a probe of mass and phase structure in compact objects