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

Abstract

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 is formulated. The numerical method of solution involves a new, very general, fully adaptive, filtered mesh to accurately follow the quasi-static and dynamical phases of evolution. In a test run on a 30 x 30 grid with flux-freezing in the neutrals, the evolution of a supercritical fragment to a central density enhancement of 100,000 was traced. The height and width of the innermost zone decreased by factors of 180 and 45, respectively, and the mass in the central flux tube changed by less than 0.2 percent, which is a negligible amount compared to the change expected when ambipolar diffusion is included.