Dynamical collapse of nonrotating magnetic molecular cloud cores:: Evolution through point-mass formation

We present a numerical simulation of the dynamical collapse of a nonrotating, magnetic molecular cloud core and follow the core's evolution through the formation of a central point mass and its subsequent growth into a 1 M. protostar. The epoch of point-mass formation (PMF) is investigated by a self-consistent extension of previously presented models of core formation and contraction in axisymmetric, self-gravitating, isothermal, magnetically supported interstellar molecular clouds. Prior to PMF, the core is dynamically contracting and is not well approximated by a quasi-static equilibrium model. Ambipolar diffusion, which plays a key role in the early evolution of the core, is unimportant during the dynamical pre-PMF collapse phase. However, the appearance of a central mass, through its effect on the gravitational field in the inner core regions, leads to a "revitalization" of ambipolar diffusion in the weakly ionized gas surrounding the central protostar. This process is so efficient that it leads to a decoupling of the field from the matter and results in an outward-propagating hydromagnetic C-type shock. The existence of an ambipolar diffusion-mediated shock of this type was predicted by Li & McKee, and we find that the basic shock structure given by their analytic model is well reproduced by our more accurate numerical results. Our calculation also demonstrates that ambipolar diffusion, rather than Ohmic diffusivity operating in the innermost core region, is the main field-decoupling mechanism responsible for driving the shock after PMF. The passage of the shock leads to a substantial redistribution, by ambipolar diffusion but possibly also by magnetic interchange, of the mass contained within the magnetic flux tubes in the inner core. In particular, ambipolar diffusion reduces the flux initially threading a collapsing similar to 1 M. core by a factor greater than or similar to 10(3) by the time this mass accumulates within the inner radius (similar or equal to 7.3 AU) of our computational grid. This reduction, which occurs primarily during the post-PMF phase of the collapse, represents a significant step toward the resolution of the protostellar magnetic flux problem. Our calculations indicate that a 1 M. protostar forms in similar to 1.5 x 10(5) yr for typical cloud parameters. The mass-accretion rate is time dependent, in part because of the C-shock that decelerates the infalling matter as it propagates outward: the accretion rate rises to similar or equal to 9.4 M. Myr(-1) early on and decreases to similar or equal to 5.6 M. Myr(-1) by the time a solar-mass protostar is formed. The infalling gas disk surrounding the protostar has a mass similar to 10(-2) M. at radii r greater than or similar to 500 AU. A distinguishing prediction of our model is that the rapid ambipolar diffusion after the formation of a protostar should give rise to large (greater than or similar to 1 km s(-1)), and potentially measurable, ion-neutral drift speeds on scales r less than or similar to 200 AU. The main features of our simulation, including the C-shock formation after PMF, are captured by a similarity solution that incorporates the effects of ambipolar diffusion.