Magnetohydrodynamics in superconducting-superfluid neutron stars

Magnetohydrodynamic (MHD) equations are presented for the mixture of superfluid neutrons, superconducting protons and normal electrons believed to exist in the outer cores of neutron stars. The dissipative effects of electron viscosity and mutual friction resulting from electron-vortex scattering are also included. It is shown that Alfven waves are replaced by cyclotron-vortex waves that have not been previously derived from MHD theory. The cyclotron-vortex waves are analogous to Alkven waves with the tension arising from the magnetic energy density replaced by the vortex energy density. The equations are then put into a simplified form useful for studying the effect of the interior magnetic field on the dynamics. Of particular interest is the crust-core coupling time, which can be inferred from pulsar glitch observations. The hypothesis that cyclotron-vortex waves play a significant role in the core spin-up during a glitch is used to place limits on the interior magnetic field. The results are compared with those of other studies.