Challenges at the neutron star core-crust boundary

The Ekman layer problem in a neutron star crust-core boundary is studied, taking into account possible slippage between the core flow (modelled as a single r-mode oscillation) and the crust, and allowing for a background magnetic field. With the help of a simple toy problem we derive basic estimates for the layer thickness and damping timescales, and show that the slippage enters linearly (instead of quadratically as previously assumed ) in the dissipation expression. In the case of a strong magnetic field we show that the main damping mechanism is the energy stored in the magnetic field itself in the form of propagating Alfvén waves, rather than viscous dissipation. These results are then combined with a revised viscosity coefficient, discussed in a companion paper, and used to compute revised r-mode damping timescales.