A Two Component Model of the Vela Pulsars with Large Fractional Moment of Inertia of the Crust

We construct a two-component analytic model of the Vela pulsar which can reproduce the fractional crustal moment of inertia, $I_{\rm crust}/I_{\rm total} \geq 0.074$ ( where $I_{\rm crust}$ represents the moment of inertia of the crust and $ I_{\rm total}$ is the total moment of inertia of the star) for the mass range $M/M_\odot \geq 1.0 - 1.96$. The models are assumed to be self-bound at the surface density $E_a = 2\times 10^{14}\rm g{cm}^{-3}$ (like, Brecher and Caporaso \cite{Ref1}) which yields the transition density at the core-crust boundary $E_b \geq 2.105 \times 10^{14}\rm g{cm}^{-3}$ and pressure/energy-density ratio, $P_b/E_b \geq 0.00589$.The central density, $E_0$, of the models ranges from 1.263 - 1.600 $\times 10^{15}\rm g{cm}^{-3}$. The total moment of inertia, $I_{\rm total}$, and the moment of inertia of the crust component, $ I_{\rm crust}$ lie in the range $I_{\rm 45} = $0.076 - 2.460 and 0.0056 - 0.8622 respectively (where $I_{45}=I/10^{45}\rm g{cm}^2$. The total radii, $a$, of the models have the values from 9.252km - 11.578km and the crustal thickness, $a_{\rm crust}$, lies in the range 0.234km - 1.551km. The mass of the crust, $M_{\rm crust}/M_\odot$, of the models varies from 0.025 - 0.263. The pressure/energy-density ratio, $P_b/E_b$, at the core-crust boundary and other physical parameters obtained in this study for the Vela pulsar are compared with the corresponding parameters obtained in the literature on the basis of various equations of state (EOSs). That few studies available in the literature \cite{Ref2}, \cite{Ref3} which predict the fractional crustal moment of inertia about 7\% for the Vela mass as large as 1.7$M_\odot$, the present study has been able to reproduce the minimum fractional crustal moment of inertia about 7.4\% and larger for all the values of the mass in the range 1.0 - 1.96$M\odot$ considered for the Vela pulsar.