Constraints on the equation of state from the stability condition of neutron stars

TL;DR

This paper investigates the stability limits of neutron stars using realistic equations of state, deriving a model-independent relation between the critical adiabatic index and compactness, which can constrain the high-density nuclear matter properties.

Contribution

It establishes a model-independent relation between the critical adiabatic index and compactness for neutron stars, supported by numerous equations of state and analytical solutions.

Findings

Derived a model-independent relation between $\gamma_{cr}$ and $eta$

Supported findings with a large set of realistic EoS and analytical models

Discussed implications for maximum rotation rates and observational constraints

Abstract

The stellar equilibrium and collapse, including mainly white dwarfs, neutron stars and supper massive stars, is an interplay between general relativistic effects and the equation of state of nuclear matter. In the present work, we use the Chandrasekhar criterion of stellar instability by employing a large number of realistic equations of state (EoS) of neutron star matter. We mainly focus on the critical point of transition from stable to unstable configuration. This point corresponds to the maximum neutron star mass configuration. We calculate, in each case, the resulting compactness parameter, $\beta=GM/c^2R$, and the corresponding effective adiabatic index, $\gamma_{\rm cr}$. The role of the trial function $\xi(r)$ is presented and discussed in details. We found that it holds a model-independent relation between $\gamma_{\rm cr}$ and $\beta$. This statement is strongly supported by the large number of EoS and it is also corroborated by using analytical solutions of the Einstein's field equations. In addition, we present and discuss the relation between the maximum rotation rate and the adiabatic index close to the instability limit. Accurate observational measurements of the upper bound of the neutron star mass and the corresponding radius, in connection with the present predictions, may help to impose constraints on the high density part of the neutron star equation of state.