Modelling large glitches with core superfluidity in mixed phase region.

Many pulsar exhibit a peculiar behaviour in their pulse profile of sudden increase in their rotational period, which is popularly known as pulsar glitch. Some of them shows giant glitches with relative amplitude $\Delta\Omega/\Omega \sim 10^{-6}-10^{-5}$. With the model of pinned neutron vortices inside the the neutron star (NS) crust, this large glitch can not be explained so far. However, the increasing evidence of massive pulsars indicates the appearance of exotic degrees of freedon in the inner core of the pulsars. In view of this we consider the pulsar as a hybrid star (HS) with quark core surrounded by nucleonic matter with a mixed phase region. This model opens up the possibility of votex-pinning inside the core too in the mixed phase region of quark and nucleonic phase. It is believed that at densities $>2\rho_0$ first order phase transition of hadron to quark matter occurs. Under the Gibbs equilibrium conditions it is possible for hadrons and quark phase to coexist.Owing to global charge neutrality condition, quarks pasta structures are formed in the background of hadronic matter. We consider these pasta structures as pinning sites of superfluid vortices which store enough angular momentum to account for larger glitches. Consideration of unpinning of the vortices from this region in addition to the contribution form the crust may lead to large glitches of the pulsars. We show that considering the core contribution the amplitude of glitch is coming to be of the order of $\Delta\Omega/\Omega \sim 10^{-6}$ which is close to the observations showed by Vela pulsar (PSR B0833-45).