Spin-up/spin-down of magnetized stars with accretion discs and outflows

Abstract

An investigation is made of disc accretion of matter on to a rotating star with an aligned dipole magnetic field. A new aspect of this work is that we argue that, when the angular velocities of the star and disc differ sustantially, the B field linking the star and disc rapidly inflates to give regions of open field lines extending from the polar caps of the star and from the disc. The open field line region of the disc leads to the possibility of magnetically driven outflows. An analysis is made of the outflows and their back effect on the disc structure, assuming an `alpha' turbulent viscosity model for the disc and a magnetic diffusivity comparable to this viscosity. The outflows are found to extend over a range of radial distances inward to a distance close to r_to, which is the distance of the maximum of the angular rotation rate of the disc. We find that r_to depends on the star's magnetic moment, the accretion rate, and the disc's magnetic diffusivity. The outflow regime is accompanied in general by a spin-up of the rotation rate of the star. When r_to exceeds the star's corotation radius r_cr=(GM/omega^2*)^1/3, we argue that outflow solutions do not occur, but instead that `magnetic braking' of the star by the disc due to field-line twisting occurs in the vicinity of r_cr. The magnetic braking solutions can give spin-up or spin-down (or no spin change) of the star, depending mainly on the star's magnetic moment and the mass accretion rate. For a system with r_to comparable to r_cr, bimodal behaviour is possible where extraneous perturbations (for example, intermittency of alpha, B field flux introduced from the companion star, or variations in the mass accretion rate) cause the system to flip between spin-up (with outflows, r_to r_cr).