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

An investigation is made of disk accretion of matter on to a rotating star with an aligned dipole magnetic field. A newaspect of this work is that when the angular velocity of the star and disk differ substantially, the B field linking the starand disk 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 ‘α’ 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 generalby a spin-up of the rotation rate of the star. When r_to exceeds the star’s corotation radius $$r_{\text{cr}}=(GM/\omega^2_\ast)^{1/3}$$, 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 thevicinity of r_cr. The magnetic braking solutions can givespin-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 behavior is possible where extraneous perturbations (for example, intermittency of α, B field flux introduced frpm the companaion star, or variations inthe mass accretion rate)cause the system to flip between spin-up(with outflows, r_to < r_cr) and spin-down(or spin-up) (with no ourflws, r_to> r_cr).