Ambipolar diffusion, cloud cores, and star formation: Two-dimensional, cylindrically symmetric contraction, II. Results and a length scale for protostellar cores

Ambip olar diffusion initiates the formation and collapse of cores in self-gravitating, thermally supercritical model clouds which would be in exact equilibrium states if the magnetic field were frozen in the matter. We follow the contraction to an increase of the central density by a factor of 10⁶ (e.g., from 3 × 10³ to 3 × 10⁹ cm^-3). The results are interpreted in terms of the thermal (λ_T.cr = 1.4Cτ_ff), magnetic (λ_M = v_A τ_ff), and Alfvén (λ = πv_A τ_ni) length scales, discussed recently elsewhere, where C, v_A, τ_ff and τ_ni are, respectively, the isothermal sound speed, the Alfvén speed in the neutrals, the free-fall time, and the neutral-ion collision time. Typically, a nearly uniform-density core forms and shrinks in time, leaving behind a "tail" of infalling matter in which a power-law density profile tends to be established. Magnetic forces (typically) remain the dominant opposition to gravity in the envelope and introduce a break in the slope of the log ρ-log r profile; at larger radii the structure of the cloud throughout the evolution is primarily determined by the physical conditions prevailing in the parent cloud. In the core and the innermost part of the tail, magnetic forces tend to relinquish to thermal-pressure forces the role of primary opposition to gravity, and a (second) break in the slope of log ρ-log r appears in the tail as well; it is more pronounced the more bimodal the opposition to gravity (by thermal-pressure forces in the core and magnetic forces in the envelope) becomes. As time progresses, the tail extends inward in radius because of the decreasing size of the uniform-density core. The mass infall (or accretion) rate from the envelope is controlled by (usually slow) ambipolar diffusion, whose time scale is typically 3-4 orders of magnitude longer in the envelope than in the core, as found analytically in 1979 by Mouschovias. The dependence of the results on the three free parameters present in the two-fluid equations is studied. For initially thermally supercritical, primarily magnetically supported clouds, the evolution of the cores is insensitive to the other (at most two) free parameters that enter through the boundary conditions-the initial conditions introduce no new free parameters. In a following paper, we extend the parameter study and discuss further the two breaks in the slope of the log ρ-log r profile, the mass infall rate, and the dependence of the exponent k in the relation B_c ∝ ρ_c^k between the magnetic field strength and the gas density in the core on the free parameters.