An investigation is made of disk accretion of matter onto a rotating star with an aligned dipole magnetic field. A new aspect of this work is that when the angular velocity of the star and disk differ substantially we argue that the B field linking the star and disk rapidly inflates to give regions of open field lines extending from the polar caps of the star and from the disk. The open field line region of the disk leads to the possibility of magnetically driven outflows. An analysis is made of the outflows and their back affect on the disk structure assuming an "α" turbulent viscosity model for the disk 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 disk. We find that r to depends on the star's magnetic moment, the accretion rate, and the disk'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/ω 2 * ) 1 3 , we argue that outflow solutions do not occur, but instead that "magnetic braking" of the star by the disk 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 behavior is possible where extraneous perturbations (for example, intermittency of α, 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 ) and spin-down (or spin-up) (with no outflows, r to > r cr ).

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A model is developed for magnetic 'propeller'-driven outflows which cause a rapidly rotating magnetized star accreting from a disk to spin-down. Energy and angular momentum lost by the star goes into expelling most of the accreting disk matter. The theory gives an expression for the effective Alfvén radius R A (where the inflowing matter is effectively stopped) which depends on the mass accretion rate, the star's mass and magnetic moment, and the star's rotation rate. The model points to a mechanism for 'jumps' between spin-down and spin-up evolution and for the reverse transition, which are changes between two possible equilibrium configurations of the system. In for example the transistion from spindown to spin-up states the Alfvén radius R A decreases from a value larger than the corotation radius to one which is smaller. In this transistion the 'propeller' goes from being "on" to being "off." The ratio of the spin-down to spin-up torque (or the ratio for the reverse change) in a jump is shown to be of order unity.

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