Torque bistability in the interaction between a neutron star magnetosphere and a thin accretion disc

We present a time-dependent model of the interaction between a neutron star magnetosphere and a thin (Shakura-Sunyaev) accretion disk, where the extent of the magnetosphere is determined by balancing outward diffusion and inward advection of the stellar magnetic field at the inner edge of the disc. The nature of the equilibria available to the system is governed by the magnetic Prandtl number Pm and the ratio ξ of the corotation radius to the Alfvén radius. For ξ & Pm, the system can occupy one of two stable states where the torques are of opposite signs. If the star is spinning up initially, in the absence of extraneous perturbations, ξ decreases until the spin-up equilibrium vanishes, the star subsequently spins down, and the torque asymptotes to zero. Vortex-in-cell simulations of the Kelvin-Helmholtz instability suggest that the transport speed across the mixing layer between the disc and magnetosphere is less than the shear speed when the layer is thin, unlike in previous models.