Accretion Disk Magnetic Braking

A protostellar disk is threaded by a static magnetic field that is perpendicular to the disk-surface. The magnetic field acts to brake the protostellar disk and cause the disk material to move towards the protostar. General analytic equations are derived for the accretion speed, and mass accretion rate. Simplified analytic equations are also obtained for the disk energy dissipation, accretion timescale and the disk radial position plus disk surface density, as a function of time. In addition to providing physical insight, such equations might be useful as a check on computational models for protostar and protostellar disk formation.