Self-similar Collapse of Rotating Magnetic Molecular Cloud Cores

We present self-similar solutions that describe the gravitational collapse of rotating, isothermal, magnetic molecular cloud cores. These solutions make it possible, for the first time, to study the formation of rotationally supported protostellar disks of the type detected around many young stellar objects in the context of a realistic scenario of star formation in magnetically supported, weakly ionized, molecular cloud cores. This work focuses on the evolution after a point mass first forms at the center and generalizes previous results by Contopoulos, Ciolek, & Königl that did not include rotation. Our semianalytic scheme incorporates ambipolar diffusion and magnetic braking and allows us to examine the full range of expected behaviors and their dependence on the physical parameters. We find that, for typical parameter values, the inflow first passes through an ambipolar diffusion shock (at a radius ra), where the magnetic flux decouples from the matter, and subsequently through a centrifugal shock (at rc), inward of which a rotationally supported disk (of mass Md) is established. By the time (~105 yr) that the central mass Mc grows to ~1 M☉, ra ≳ 103 AU, rc ≳ 102 AU, and Md/Mc ≲ 0.1. The derived disk properties are consistent with data on T Tauri systems, and our results imply that protostellar disks may well be Keplerian also during earlier phases of their evolution. We demonstrate that the disk is likely to drive centrifugal outflows that transport angular momentum and mass, and we show how the radially self-similar wind solution of Blandford & Payne can be naturally incorporated into the disk model. We further verify that gravitational torques and magnetorotational instability-induced turbulence typically do not play an important role in the angular momentum transport. For completeness, we also present solutions for the limiting cases of fast rotation (where the collapse results in a massive disk with such a large outer radius that it traps the ambipolar diffusion front) and strong braking (where no disk is formed and the collapse resembles that of a nonrotating core at small radii), as well as solutions describing the rotational collapse of ideal MHD and of nonmagnetic model cores.