Massive Neutron Star Models with Parabolic Cores

Abstract

The results of the investigation of the core-envelope model presented in Negi et al. \cite{Ref1} have been discussed in view of the reference \cite{Ref2} . It is seen that there are significant changes in the results to be addressed. In addition, I have also calculated the gravitational binding energy, causality and pulsational stability of the structures which were not considered in Negi et al. \cite{Ref1} . The modified results have important consequences to model neutron stars and pulsars. The maximum neutron star mass obtained in this study corresponds to the mean value of the classical results obtained by Rhodes \& Ruffini \cite {Ref3} and the upper bound on neutron star mass obtained by Kalogera \& Byam \cite {Ref4} and is much closer to the most recent theoretical estimate made by Sotani \cite{Ref5}. On one hand, when there are only few equations of state (EOSs) available in the literature which can fulfil the recent observational constraint imposed by the largest neutron star masses around 2$M_\odot$\cite{Ref6}, \cite{Ref7}, \cite{Ref8}, the present analytic models, on the other hand, can comfortably satisfy this constraint. Furthermore, the maximum allowed value of compactness parameter $u(\equiv M/a$; mass to size ratio in geometrized units) $ \leq 0.30$ obtained in this study is also consistent with an absolute maximum value of $ u_{\rm max} = 0.333^{+0.001}_{-0.005}$ resulting from the observation of binary neutron stars merger GW170817 (see, e.g.\cite{Ref9}).