A starquake model for Vela pulsar

Various neutron star (NS) models correspond to an unrealistic mass range $\leq 0.5M_\odot$ for the Vela pulsar, if the observational constraints of the glitch healing parameter in the starquake model ($Q = I_{\rm core}/I_{\rm total} \leq 0.2$), are imposed on these models. However, we show that these observational constraints yield a realistic mass range for NS models, corresponding to a core given by the stiffest equations of state (EOS) and the envelope is characterized by the well known EOS of adiabatic polytrope, if the continuity of the adiabatic speed of sound together with pressure, energy-density, and the two metric parameters is assured at the core-envelope boundary of the models and this boundary is worked out on the basis of the `compatibility criterion' for hydrostatic equilibrium. The models yield the surface redshift $z_R \simeq 0.6913$ and mass $M \simeq 2.153 M_\odot$ for the ``central'' weighted mean value, $Q = 0.12 \pm 0.07$, of the glitch healing parameter of the Vela pulsar. These values of mass and surface redshift can increase upto $M \simeq 2.196 M_\odot$ and $z_R \simeq 0.7568$ (which represents an ultra-compact object (UCO; $z_R \geq 0.73$)) respectively for the upper weighted mean value of $Q \simeq 0.19$. However, for the lower weighted mean value of $Q \simeq 0.05$, the mass and surface redshift can decrease upto the values of $M \simeq 2.052 M_\odot$ and $z_R \simeq 0.6066$ respectively. The observation of the lower bound on the energy of a $\gamma$-ray pulse at about 0.30 MeV from the Vela pulsar in 1984 is in excellent agreement with the results of this study, provided this energy could be interpreted as the energy of a gravitationally redshifted electron-positron annihilation radiation from the star's surface.