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We consider rotating magnetic stars with winds and disks. We establish atheorem that relates the angular velocity of a disk region with no meridionalmotion to the angular velocity of the star. Also, we show that for a givenvalue of the magnetic field strength, if the rotation rate is too high or theflow velocity into the shock boundary is too low, a Keplerian disk region willnot be formed. We develop a model for the formation of disks in magneticrotators through the processes of fill-up and diffusion into Keplerian orbits.At the end of the fill-up stage the density of the disk increases significantlyand the magnetic force in the disk becomes negligible. We derive analyticalexpressions for the inner and outer radii of Keplerian disks in terms of thestellar rotation rate. A disk can form if the meridional component Bm of thefield at the stellar surface is larger than a minimum value. The radial extentof the Keplerian region becomes larger for larger values of Bm and is largestwhen Bm equals an optimal value. The strengths of the minimum fields requiredfor Keplerian disk formation in B-type stars varies from order 1G to 10G. InO-type stars they must be of order 500G. Also, we suggest that the stellarmagnetic fields may be affected by rotationally driven meridional circulationleading to some of the the observed variations of disks with time.Comment: 44 pages, 1 figure, accepted by Ap

Magnetic Rotator Winds and Keplerian Disks of Hot Stars