The Structure and Evolution of Magnetized Cloud Cores in a Zero‐Density Background

Molecular-line observations of star-forming cloud cores indicate that theyare not the flattened structures traditionally considered by theory. Rather,they are elongated, perhaps in the direction of their internal magnetic field.We are thus motivated to consider the structure and evolution of axisymmetric,magnetized clouds that start from a variety of initial states, both flattened(oblate) and elongated (prolate). We devise a new technique, dubbed the$q$-method, that allows us to construct magnetostatic equilibria of anyspecified shape. We find, in agreement with previous authors, that the fieldlines in oblate clouds bend inward. However, those in prolate clouds bowoutward, confining the structures through magnetic tension. We next follow the quasi-static evolution of these clouds via ambipolardiffusion, under the assumption of constant core mass. An oblate cloud eitherrelaxes to a magnetically force-free sphere or, if sufficiently massive,flattens along its polar axis as its central density runs away. A prolate cloudalways relaxes to a sphere of modest central density. We finally consider theevolution of an initially spherical cloud subject to the tidal gravity ofneighboring bodies. Although the structure constricts equatorially, it alsoshortens along the pole, so that it ultimately flattens on the way to collapse.In summary, none of our initial states can evolve to the point of collapsewhile maintaining an elongated shape. We speculate that this situation willchange once we allow the cloud to gain mass from its environment.Comment: 19 pages, plus 20 postscript figures. Accepted by Ap