Angular Momentum of Cores and Envelopes, and Magnetic Braking

We study the eeect of magnetic braking on the ambipolar-diiusion initiated formation and contraction of protostellar cores in axisymmetric, disklike, model molecular clouds. Magnetic braking rapidly enforces near corotation of the cloud with the background medium during the initial, ambipolar-diiusion controlled, quasistatic contraction. After a magnetically (and thermally) supercritical core forms, rapid contraction of the core ensues, and a power-law angular velocity proole is established within it, while the magnetically supported envelope continues to corotate with the background. The evolution of the central angular velocity is characterized by three distinct stages: (1) an exponential decrease due to eeective magnetic braking; (2) a constant angular velocity phase, which lasts until a supercritical core forms; and (3) a constant angular momentum phase. Predictions are made for the angular momentum, mass, structure, size, etc. of protostellar cores. Even in situations where angular momentum is conserved, we nd that the centrifugal support does not become signiicant for mass shells in the central region of a self-gravitating, nonhomologously contracting thin disk; the gravitational eld increases just as rapidly as the centrifugal acceleration (1=r 3).