  The core-envelope models presented in {Ref1}; {Ref2}, corresponding to the
values of compactness parameter, $u \equiv M/a$ = 0.30 and 0.25 (mass to size
ratio in geometrized units) have been studied under slow rotation. It is seen
that these models are capable of explaining all the observational values of
glitch healing parameter, $G_h = I_{\rm core}/I_{\rm total} < 0.55$ {Ref3} for
the Vela pulsar. The models yield the maximum values of mass, $M$, surface
redshift, $z_a$, and the moment of inertia, $I_{\rm Vela}$ for the Vela pulsar
in the range $M = 3.079M_\odot - 2.263M_\odot$; $z_a = 0.581 - 0.414$ and
$I_{\rm Vela,45} =6.9 - 3.5$ (where $I_{45}=I/10^{45}\rm g{cm}^2$) respectively
for the values of $u = $ 0.30 and 0.25 and for an assigned value of the surface
density, $E_a = 2\times 10^{14}\rm g{cm}^{-3}$ {Ref4}. The values of masses
lower than the above mentioned values ( so called the realistic mass range, $M
= 1.4\pm0.2 M_\odot$, in the literature) but significantly higher than that of
the unrealistic mass range $M \leq 0.5M_\odot$ (obtained for the Vela pulsar in
the literature on the basis of parametrized neutron star (NS) models based on
equations of state (EOSs) of dense nuclear matter {Ref3}) and other parameters
may be obtained likewise for the above mentioned range of the values of $G_h$
corresponding to the values of $u < 0.25$. The models are found to be causally
consistent, gravitational bound and pulsationally stable. The upper bound on
neutron star (NS) mass obtained in this study which is applicable for the Vela
pulsar, in fact, corresponds to the mean value of the upper bound on NS mass
obtained in the classical result {Ref5} and that obtained on the basis of
modern EOSs for neutron star matter {Ref6} and is in a good agreement with the
most recent theoretical estimate {Ref7}.
