7 OUTER CRUST Composition: electrons + (ions) nuclei Electrons (e): constitute a strongly degenerate,almost ideal gas, give the main contributioninto the pressureIons (A,Z): fully ionized by electron pressure, givethe main contribution into the densityElectron background
8 INNER CRUST Composition: electrons + nuclei + free (dripped) neutrons Electrons (e): constitute a strongly degenerate, ultra-relativistic gasIons (A,Z): neutron-rich, occupy substantial fraction of volumeFree neutrons (n): constitute a stronglydegenerate Fermi-liquid, which can besuperfuide+n background
22 Pinning force・condensation energy (Alpar et al. 1984)pinning energy Ep ~ 1MeVcoherence length ξ~10-12 cmlattice constant a ~5× cm・cancellation of the elementary pinning force (Jones 1991)rigid vortex --> equal number of pinning sites on either side ofthe line --> fp ~ 0・bending of vortex lines (Link & Epstein 1993)finite tension --> kink --> much more efficient pinning
24 vortices move together with superfluids Kinkspropagation alongthe vortex linesy-componentof velocityvortices move togetherwith superfluidsJones et al. 1998almost no pinning
25 Vortex configurations ・equation of motion of vortex lines・configurationskinksminimize
26 Dispersion relation for the vortex oscillations kink supply raterequired in Vela~2×１015 s-1~1×１016 rad s-1
27 Discussion on vortex pinning We find no unstable mode that grows with time. The vortexequilibrium configurations with static kink structures are stable.Hence, the kink motion as required by Jones is less likely.(2) The kink solution can be expressed as a sum of fouriercomponents of different wave numbers. The dispersion relationshows that the phase velocity of vortex waves depends on the wavenumber. Hence, even if a kink is formed and start to move, the kinkfeature will be smeared out during propagation.(3) The vortex equilibrium configuration is composed of the statickink and straight segments. A vortex line in equilibrium lies deepin the pinning potential well and is strongly pinned to the latticenuclei in its most part, especially when the vortex line is close tothe main axis of a crystal lattice.Pinning may be strong enough to explain the large glitchesobserved in Vela pulsar.