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

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Abstract
Molecular-line observations of star-forming cloud cores indicate that they are 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). In this first contribution, the clouds are of fixed mass, and are surrounded by a fictitious medium of zero density and finite pressure. We devise a new technique, dubbed the q-method, that allows us to construct magnetostatic equilibria of any specified shape. The mass loading of the field lines then follows from the self-consistent model solution, just the reverse of the standard procedure. We find, in agreement with previous authors, that the field lines in oblate clouds bend inward. However, those in prolate clouds bow outward, confining the structures through magnetic tension. We next follow the quasi-static evolution of these clouds via ambipolar diffusion. An oblate cloud either relaxes to a magnetically force-free sphere or, if sufficiently massive, flattens along its polar axis as its central density runs away. A prolate cloud always relaxes to a sphere of modest central density. We finally consider the evolution of an initially spherical cloud subject to the tidal gravity of neighboring bodies. Although the structure constricts equatorially, it also shortens 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 collapse while maintaining an elongated shape. We speculate that this situation will change once we allow the cloud to gain mass from its environment.
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