Ambipolar diffusion, interstellar dust, and the formation of cloud cores and protostars. III. Typical axisymmetric solutions

In a previous paper we formulated the problem of the formation of protostellar cores by ambipolar diffusion in axisymmetric, isothermal, self-gravitating, thermally supercritical but magnetically subcritical model molecular clouds, accounting for a cosmic abundance of interstellar grains (both charged and neutral). Using an implicit code with an adaptive mesh, we follow the evolution to a central density enhancement of 10⁶ (e.g., from 2.6 × 10³ cm^-3 to 2.6 × 10⁹ cm^-3). First, ambipolar diffusion slowly increases the mass-to-flux ratio of a cloud's central flux tubes, leading to the formation and contraction of thermally supercritical but magnetically subcritical cores. The timescale for this process is essentially the initial central flux-loss timescale, which exceeds the dynamical timescale (≃free-fall timescale) typically by a factor 10-20. Eventually, the mass-to-flux ratio exceeds the critical value for collapse. The subsequent contraction of the thermally and magnetically supercritical cores becomes progressively more dynamic, while the envelopes remain relatively well supported by magnetic forces, in agreement with early theoretical predictions by Mouschovias. A typical supercritical core consists of a uniform-density central region and a "tail" of infalling matter with a power-law density profile n_n ∝ r^s, -1.5 ≳ s ≳ -1.85. The mass infall (or accretion) rate from the subcritical envelopes is controlled by ambipolar diffusion, and differs both qualitatively and quantitatively from estimates based on non-magnetic models and their extrapolations to magnetic clouds. Model clouds that include the macroscopic (collisional) effects of grains have their evolution retarded (typically by 50%) with respect to models accounting only for neutral-ion drag. Neutral-grain drag typically dominates the neutral-ion drag at core densities n_n,c ≳ 10⁸ cm^-3. Electrostatic attraction by electron-shielded ions ("quasiparticles") keeps charged grains partially attached to the magnetic field for densities n_n,c ≳ 3 × 10⁵ cm^-3, at which detachment would otherwise occur because of collisions with neutrals. Neutral grains also couple to the magnetic field by inelastic charge-capture processes. The grains lengthen the timescale for the formation of a core, accentuate the core-envelope separation, and, by any given central density enhancement, increase a core's size, mass, and magnetic flux.