SUPERFLUID CORE ROTATION IN PULSARS .1. VORTEX CLUSTER DYNAMICS

Starting from conservation laws, a magnetohydrodynamic theory for rotating neutron-proton superfluid mixture in neutron star cores is formulated. The theory incorporates the effects of energy dissipation and mutual friction. In particular, the equations of motion of uncoupled neutron and proton vortices in the bulk and at the boundaries of the superfluid core are derived. As a result of the entrainment of superconducting proton currents by the superfluid neutron vortex circulation, rotation induced supercurrents and magnetic fields are generated in the neutron-proton superfluid mixture. The magnetic field enters the vicinity of each neutron vortex line by forming a triangular two- dimensional lattice (vortex cluster) confined around the neutron vortex line within a macroscopic length scale delta(n) similar to 10(-5) cm. The net number of proton vortices bound in each vortex cluster is found to be [n(p)] similar to 10(12)-10(13), producing a mean magnetic field induction of the cluster [B-C] similar to 10(14) G. The axisymmetric magnetic field induction averaged over the core of neutron star is of order [B] similar to 10(11)-10(12) G. This is a generated component of neutron star magnetic field, which in contrast to a possible fossil field of the star, is independent of its magnetic history prior to the nucleation of the superconducting phase and nucleation process as well. The arrangement of vortices in clusters imposes constraints on the equations of motion of uncoupled vortices. We determine the effective dynamical equations of motion of vortex clusters by establishing the form of effective Magnus and frictional forces. Vortex cluster friction is dominated by the scattering of relativistic electrons from magnetic field of proton vortices and leads to a strong coupling of the clusters to the normal electron liquid. The resulting dynamical coupling times are found to be from few days to 10(3) days for different density regions of the superfluid core. These timescales are compatible with the observed postjump relaxation times of pulsars.