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We study numerically the collapse of rotating, magnetized molecular cloudcores, focusing on rotation and magnetic braking during the main accretionphase of isolated star formation. Motivated by previous numerical work andanalytic considerations, we idealize the pre-collapse core as a magnetizedsingular isothermal toroid, with a constant rotational speed everywhere. Thecollapse starts from the center, and propagates outwards in an inside-outfashion, satisfying exact self-similarity in space and time. For rotation ratesand field strengths typical of dense low-mass cores, the main feature remainsthe flattening of the mass distribution along field lines -- the formation of apseudodisk, as in the nonrotating cases. The density distribution of thepseudodisk is little affected by rotation. On the other hand, the rotation rateis strongly modified by pseudodisk formation. Most of the centrally accretedmaterial reaches the vicinity of the protostar through the pseudodisk. Thespecific angular momentum can be greatly reduced on the way, by an order ofmagnitude or more, even when the pre-collapse field strength is substantiallybelow the critical value for dominant cloud support. The efficient magneticbraking is due to the pinched geometry of the magnetic field in the pseudodisk,which strengthens the magnetic field and lengthens the level arm for braking.Both effects enhance the magnetic transport of angular momentum from inside tooutside. The excess angular momentum is carried away in a low-speed outflowthat has, despite claims made by other workers, little in common with observedbipolar molecular outflows. We discuss the implications of our calculations forthe formation of true disks that are supported against gravity by rotation.Comment: 38 pages, 9 figures. To appear in v599 n1 ApJ December 10, 2003 issu

Collapse of Magnetized Singular Isothermal Toroids. II. Rotation and Magnetic Braking