Self‐similar Collapse of Rotating Magnetic Molecular Cloud Cores

We present self-similar solutions that describe the gravitational collapse ofrotating, isothermal, magnetic molecular-cloud cores, relevant to the formationof rotationally supported protostellar disks. This work focuses on theevolution after a point mass first forms at the center and generalizes previousresults by Contopoulos, Ciolek, & Konigl that did not include rotation. Ourmodel includes ambipolar diffusion and magnetic braking and allows us toexamine the full range of expected behaviors and their dependence on thephysical parameters. For typical parameter values, the inflow first passesthrough an ambipolar-diffusion shock (at a radius r_a, where the magnetic fluxdecouples from the matter), and later through a centrifugal shock at r=r_c, theouter edge of a rotationally supported disk of mass M_d. By the time (~10^5 yr)that the central mass M_c grows to ~1 M_\sun, r_a may be larger than 1000 AU,r_c larger than 100 AU, and M_d/M_c smaller than 10%. Disk properties areconsistent with data on T Tauri systems, and our results imply thatprotostellar disks may well be Keplerian also during earlier phases. We showthat the disk is likely to drive centrifugal outflows transporting angularmomentum and mass, and we incorporate these effects into the model. We verifythat gravitational torques and magnetorotational instability-induced turbulencetypically do not play an important role in the angular momentum transport. Wealso present solutions for the limiting cases of fast rotation (where collapseresults in a massive disk with such a large outer radius that it traps theambipolar diffusion front) and strong braking (where no disk is formed and thecollapse resembles that of a nonrotating core at small radii), as well assolutions for the rotational collapse of ideal-MHD and nonmagnetic model cores.Comment: 25 pages, including 10 figures. Accepted for publication in ApJ, scheduled for vol. 580, December 1, 200