Star Formation in Cold, Spherical, Magnetized Molecular Clouds

We present an idealized, spherical model of the evolution of a magnetizedmolecular cloud due to ambipolar diffusion. This model allows us to follow thequasi-static evolution of the cloud's core prior to collapse and the subsequentevolution of the remaining envelope. By neglecting the thermal pressuregradients in comparison with magnetic stresses and by assuming that the ionvelocity is small compared with the neutral velocity, we are able to find exactanalytic solutions to the MHD equations. We show that, in the case of acentrally condensed cloud, a core of finite mass collapses into the originleaving behind a quasi-static envelope, whereas initially homogeneous cloudsnever develop any structure in the absence of thermal stresses, and collapse asa whole. Prior to the collapse of the core, the cloud's evolution ischaracterized by two phases: a long, quasi-static phase where the relevanttimescale is the ambipolar diffusion time (treated in this paper), and a short,dynamical phase where the characteristic timescale is the free-fall time. Thecollapse of the core is an "outside-in" collapse. The quasi-static evolutionterminates when the cloud becomes magnetically supercritical; thereafter itsevolution is dynamical, and a singularity develops at the origin-a protostar.After the initial formation of the protostar, the outer envelope continues toevolve quasi-statically, while the region of dynamical infall grows withtime-an "inside-out" collapse. We use our solution to estimate the magneticflux trapped in the collapsing core and the mass accretion rate onto the newlyformed protostar. Our results agree, within factors of order unity, with thenumerical results of Fiedler & Mouschovias (1992) for the physical quantitiesin the midplane ofComment: 18 postscript figures Accepted by The Astrophysical Journa