Symmetries, magnetic fields, and the shape of molecular cloud cores

We develop a formalism wherein the solution of the equations of equilibrium for a self-gravitating, magnetized interstellar cloud may be accomplished analytically, under the only hypotheses that (a) the cloud is scale-free, and (b) is electrically neutral. All variables are represented as series of scalar and vector spherical harmonics, and the equilibrium equations are reduced to a set of coupled algebraic equations for the expansion coefficients of the density and the magnetic vector potential. Previously known axisymmetric solutions are recovered and new non-axisymmetric solutions are found and discussed as models for pre-protostellar molecular cloud cores.