The Equilibrium Structure of Prolate Magnetized Molecular Cores

The structure of molecular cloud cores supported by thermal pressure and a poloidal magnetic field is reinvestigated in the magnetohydrostatic and axisymmetric approximation. In addition to oblate configurations found in earlier work, solutions yielding prolate spheroidal shapes have also been obtained for a reference state described by a uniform sphere threaded by a uniform background magnetic field. The solutions for prolate configurations are found to be relevant for lower masses than for their oblate counterparts. Of particular importance is the result that the prolate cloud cores have radii less than a maximum given by $0.25 pc (a/0.2km/s)^2 (P_{\rm ext}/10^{-12} dyne/cm^2)^{-1/2}$, where $a$ is the sound speed and $P_{\rm ext}$ is the external pressure of the background medium. The existence of such solutions obviates the presence of toroidal fields in such modeled structures.