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

We study numerically the collapse of rotating, magnetized molecular cloud cores, focusing on rotation and magnetic braking during the main accretion phase of isolated star formation. Motivated by previous numerical work and analytic considerations, we idealize the pre-collapse core as a magnetized singular isothermal toroid, with a constant rotational speed everywhere. The collapse starts from the center, and propagates outwards in an inside-out fashion, satisfying exact self-similarity in space and time. For rotation rates and field strengths typical of dense low-mass cores, the main feature remains the flattening of the mass distribution along field lines -- the formation of a pseudodisk, as in the nonrotating cases. The density distribution of the pseudodisk is little affected by rotation. On the other hand, the rotation rate is strongly modified by pseudodisk formation. Most of the centrally accreted material reaches the vicinity of the protostar through the pseudodisk. The specific angular momentum can be greatly reduced on the way, by an order of magnitude or more, even when the pre-collapse field strength is substantially below the critical value for dominant cloud support. The efficient magnetic braking 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 to outside. The excess angular momentum is carried away in a low-speed outflow that has, despite claims made by other workers, little in common with observed bipolar molecular outflows. We discuss the implications of our calculations for the formation of true disks that are supported against gravity by rotation.