The Effect of Ambipolar Diffusion on Magnetic Braking of Molecular Cloud Cores: an Exact, Time-dependent Solution

It has been shown in earlier papers that magnetic braking in collapsing interstellar clouds is an efficient mechanism for removing angular momentum during star formation. This paper studies quantitatively the effect that ambipolar diffusion within an aligned rotator (core, or fragment, or cloud) can have on its magnetic braking. The rotator is magnetically linked with an external medium (or envelope), in which the magnetic field is frozen in the matter. Although in principle ambipolar diffusion can lengthen the magnetic braking time scale, application of the results to typical molecular cloud cores shows that the quantitative effect is at the level of a few percent. Thus, even the angular momentum problem for single stars can be resolved by magnetic braking operating past the stage at which ambipolar diffusion sets in.