Global three-dimensional flow of a neutron superfluid in a spherical shell in a neutron star

Abstract

We integrate for the first time the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a 1S 0-paired neutron superfluid in a rotating spherical shell, using a pseudo-spectral collocation algorithm coupled with a time-split fractional scheme. Numerical instabilities are smoothed by spectral filtering. Three numerical experiments are conducted, with the following results. (1) When the inner and outer spheres are put into steady differential rotation, the viscous torque exerted on the spheres oscillates quasi-periodically and persistently (after an initial transient). The fractional oscillation amplitude (∼ 10-2) increases with the angular shear and decreases with the gap wid..