Effect of entrainment on stress and pulsar glitches in stratified neutron star crust

The build up of the stress whose relaxation is presumed to account for pulsar frequency glitches can be attributed to various mechanisms, of which the most efficient involve differential rotation of the neutron superfluid in the inner layers of the (magnetically braked) solid crust of a rotating neutron star. In such a case it is usually supposed that the stress is attributable to pinning of superfluid vortices to crust nuclei, but it has been suggested that, even if the pinning effect is too weak, a comparably large stress might still arise just from the deficit of centrifugal buoyancy in the slowed down crust. The present work is a re-examination that investigates the way such processes may be affected by considerations that were overlooked in the previous work – notably uncertainties about the “effective” masses that have to be attributed to the “free” superfluid neutrons to allow for their entrainment by the ionic crust material. Though restricted to a Newtonian formulation, this analysis distinguishes more carefully than has been usual between true velocities, which are contravariantly vectorial, and so called “superfluid velocities” that are proportional to momenta, which are essentially covectorial, a technicality that is important when more than one independent current is involved. The results include a Proudman type theorem to the effect that the superfluid angular velocity must be constant on slightly deformed Taylor cylinders in the force free case, and it is shown how to construct a pair of integral constants of the motion that determine the solution for the pinned case assuming beta equilibrium.