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Ambipolar diffusion and star formation: Formation and contraction of axisymmetric cloud cores. I. Formulation of the problem and method of solution

We formulate the problem of the formation and contraction of axially symmetric, isothermal, self-gravitating, molecular cloud fragments (or cores) due to ambipolar diffusion in magnetically supported parent clouds. The initial reference states are taken to be static and uniform with the magnetic field parallel to the axis of symmetry. The two-fluid MHD equations describing the evolution contain three dimensionless free parameters: α 0 , the ratio of magnetic and thermal pressures in the initial state, ν ff,0 , essentially the initial ratio of the free-fall and neutral-ion collision times, and the exponent k in the relation between the ion and neutral densities n i ∞n n k