Superfluid Spin-up: 3D Simulations of Postglitch Dynamics in Neutron Stars Cores

Following a glitch, a neutron star interior undergoes a transfer of angular momentum from the star's crust to the core, resulting in the spin-up of the latter. The crust-core coupling, which determines how quickly this spin-up proceeds, can be achieved through various physical processes, including Ekman pumping, superfluid vortex-mediated mutual friction, and magnetic fields. While the complexity of the problem has hindered studies of the mechanisms' combined action, analytical work on individual processes suggests different spin-up timescales depending on the relative strength of Coriolis, viscous, and mutual friction forces, and the magnetic field, respectively. However, experimental and numerical validations of these results are limited. In this paper, we focus on viscous effects and mutual friction and conduct non-linear hydrodynamical simulations of the spin-up problem in a two-component fluid by solving the incompressible Hall$-$Vinen$-$Bekarevich$-$Khalatnikov (HVBK) equations in the full sphere (i.e., including $r=0$) for the first time. We find that the viscous (normal) component accelerates due to Ekman pumping, although the mutual friction coupling to the superfluid component alters the spin-up dynamics compared to the single-fluid scenario. Close to the sphere's surface, the response of the superfluid is accurately described by the mutual friction timescale irrespective of its coupling strength with the normal component. However, as we move deeper into the sphere, the superfluid accelerates on different timescales due to the slow viscous spin-up of the internal normal fluid layers. We discuss potential implications for neutron stars and requirements for future work to build more realistic models.