The magnetic flux problem and ambipolar diffusion during star formation - One-dimensional collapse. I - Formulation of the problem and method of solution

The detailed calculations of collapsing model clouds presented indicate that the flux-to-mass ratio in cloud cores can decrease by between 2 and 4 orders of magnitude in less than one million years, at neutral densities of less than 10 to the 9th/cu cm, due to ambipolar diffusion alone. A solution method is formulated for the problem of the time evolution of isothermal, self-gravitating model clouds which would have been in an exact equilibrium state, with spatially nonuniform density and magnetic field, if ambipolar diffusion had been ignored. In view of this, any degree of evolution is entirely the result of ambipolar diffusion. Attention is given to the cases of both slow and rapid reestablishment of ionization equilibrium, as the ion and electron density changes due to ambipolar diffusion. An analytical mapping of the basic equations from the physical space to a convenient computational space is given.