Axially symmetric equations for differential pulsar rotation with superfluid entrainment

TL;DR

This paper develops an analytical two-component model for pulsar rotation that incorporates superfluid entrainment and stratification, providing a framework to understand pulsar glitches and angular momentum transfer.

Contribution

It introduces a novel set of differential equations modeling pulsar rotational dynamics with superfluid entrainment and stratification effects, enabling quantitative analysis of glitch phenomena.

Findings

The model can reproduce the largest Vela pulsar glitches with realistic parameters.

Superfluid entrainment significantly influences the angular momentum reservoir.

The equations account for stratification, differential rotation, and vortex-crust coupling.

Abstract

In this article we present an analytical two-component model for pulsar rotational dynamics. Under the assumption of axial symmetry, implemented by a paraxial array of straight vortices that thread the entire neutron superfluid, we are able to project exactly the 3D hydrodynamical problem to a 1D cylindrical one. In the presence of density dependent entrainment the superfluid rotation is non-columnar: we circumvent this by using an auxiliary dynamical variable directly related to the areal density of vortices. The main result is a system of differential equations that take consistently into account the stratified spherical structure of the star, the dynamical effects of non-uniform entrainment, the differential rotation of the superfluid component and its coupling to the normal crust. These equations represent a mathematical framework in which to test quantitatively the macroscopic consequences of the presence of a stable vortex array, a working hypothesis widely used in glitch models. Even without solving the equations explicitly, we are able to draw some general quantitative conclusions; in particular, we show that the reservoir of angular momentum (corresponding to recent values of the pinning forces) is enough to reproduce the largest glitch observed in the Vela pulsar, provided its mass is not too large.