A spherical model for starless cores of magnetic molecular clouds and dynamical effects of dust grains

In the current paradigm, isolated low-mass stars form out of magnetic molecular clouds as the clouds evolve because of ambipolar diffusion. A quantitative understanding of this process remains incomplete, because of both physical and technical complexities. As a step toward a quantitative theory for star formation, I explore further the evolution of magnetic clouds with a simplifying spherical geometry, studied first by Safier, McKee, & Stahler. The spherical model has several desirable features as well as some potentially serious difficulties. It highlights the pressing need for two-dimensional, fully dynamic models that treat the coupling between the magnetic field and the cloud matter properly. The model clouds exhibit substantial inward motion during the late stage of core formation, with velocities of order one-half the isothermal sound speed or more over most of the cloud, after a central density enhancement of about 10(2) (say, from 10(3) to 10(5) cm(-3)). Such precollapse motion may have been detected recently by Tafalla et al. and Williams et al. in the starless core L1544. The motion may also explain why starless dense cores typically last for only a few dynamic times and why they have small but significant non-thermal line widths. The clouds that I study have relatively low mass (of order 10 M.) and initial magnetic pressure comparable to thermal pressure. They evolve into a density profile of a flat central plateau surrounded by an envelope whose density decreases with radius roughly as a power law, as found previously. The density decline in the envelope is significantly steeper than those obtained by Mouschovias and collaborators, who considered disklike magnetic clouds whose initial magnetic pressure is much larger than the thermal pressure. As the cloud density increases above approximately 10(5) cm(-3), dust grains become dynamically important. Depending on their size distribution, dust grains can enhance the coupling coefficient between the magnetic field and the neutral cloud matter by as much as an order of magnitude or even more. The enhanced coupling makes it difficult for magnetic flux to escape during the advanced, more dynamic phase of the core formation. In spherical geometry, this trapping of magnetic flux leads to an almost homologous collapse of a central region with substantial mass. The implied extremely rapid assemblage of protostellar mass, with more than 0.5 M. of material reaching the origin in about 10(3) yr or less for a typical set of cloud parameters, poses a serious accretion "luminosity problem. " Magnetic tension in two-dimensional models may help alleviate the problem.