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In this article we present an analytical two-component model for pulsarrotational dynamics. Under the assumption of axial symmetry, implemented by aparaxial array of straight vortices that thread the entire neutron superfluid,we are able to project exactly the 3D hydrodynamical problem to a 1Dcylindrical one. In the presence of density dependent entrainment thesuperfluid rotation is non-columnar: we circumvent this by using an auxiliarydynamical variable directly related to the areal density of vortices. The mainresult is a system of differential equations that take consistently intoaccount the stratified spherical structure of the star, the dynamical effectsof non-uniform entrainment, the differential rotation of the superfluidcomponent and its coupling to the normal crust. These equations represent amathematical framework in which to test quantitatively the macroscopicconsequences of the presence of a stable vortex array, a working hypothesiswidely used in glitch models. Even without solving the equations explicitly, weare able to draw some general quantitative conclusions; in particular, we showthat the reservoir of angular momentum (corresponding to recent values of thepinning forces) is enough to reproduce the largest glitch observed in the Velapulsar, provided its mass is not too large.

Axially symmetric equations for differential pulsar rotation with superfluid entrainment