Magnetohydrodynamics in Superconducting-Superfluid Neutron Stars

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 due to electron-vortex scattering are also included. It is shown that Alfvén waves are replaced by cyclotronvortex waves that have not been previously derived from MHD theory. The cyclotronvortex waves are analogous to Alfvén waves with the tension due to the magnetic energy density replaced by the vortex energy density. The equations are then put into a simplified form useful for studing 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.