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An investigation is made of disk accretion of matter onto a rotating starwith an aligned dipole magnetic field. A new aspect of this work is that whenthe angular velocity of the star and disk differ substantially we argue thatthe $\bf B$ field linking the star and disk rapidly inflates to give regions ofopen 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 magneticallydriven outflows. An analysis is made of the outflows and their back affect onthe disk structure assuming an ``$\ap$" turbulent viscosity model for the diskand a magnetic diffusivity comparable to this viscosity. The outflows are foundto 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 ofthe disk. We find that $r_{to}$ depends on the star's magnetic moment, theaccretion rate, and the disk's magnetic diffusivity. The outflow regime isaccompanied in general by a spin-up of the rotation rate of the star. When$r_{to}$ exceeds the star's corotation radius $r_{cr} = (GM/\om_*^2)^{1\ov 3}$,we argue that outflow solutions do not occur, but instead that ``magneticbraking" of the star by the disk due to field-line twisting occurs in thevicinity of $r_{cr}$. The magnetic braking solutions can give spin-up orspin-down (or no spin change) of the star depending mainly on the star'smagnetic moment and the mass accretion rate. For a system with $r_{to}$comparable to $r_{cr}$, bimodal behavior is possible where extraneousperturbations cause the system to flip between spin-up and spin-down.Comment: 24 pages, Plain TeX, 9 figures available upon request from R.  Lovelace (rvl1@cornell.edu), Submitted to MRNA

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