Magnetic braking, ambipolar diffusion, and the formation of cloud cores and protostars. II. a parameter study

The formulation of the problem of the formation of protostellar cores in self-gravitating, magnetically supported, rotating, isothermal model molecular clouds was presented in a previous paper, where detailed numerical simulations for two different model clouds were also discussed. In this paper, we study the effect of varying five dimensionless free parameters: the ratio ρ̃ of external density and central density in a reference state (which is related simply to an initial equilibrium state), the initial radial length scale ι̃_ref of the column density of the cloud, the central angular velocity of the reference state Ω̃_c,ref, the central neutral-ion collision time in the reference state τ̃_ni,ref (which is inversely proportional to the collapse retardation factor v_ff ≡ τ_ff/τ_ni), and the exponent k in the relation between the ion and neutral densities n_i ∝ n^k_n. In addition to the models previously presented, seven more models are investigated here. Different values (1/1000 to 1/100) of the initial magnetic-braking efficiency parameter ρ̃(>0) do not significantly affect the evolution; magnetic braking remains effective during the quasistatic phase and ineffective during the (dynamic) collapse of the magnetically and thermally supercritical core. The initially very effective magnetic braking also means that the solution is insensitive to values of Ω̃_c,ref. Different values of ι̃_ref yield qualitatively similar evolution, with smaller cloud sizes leading to slightly smaller core sizes. Increasing the value of τ̃_ni,ref leads to a more rapid evolution and larger, more rapidly rotating cores. A smaller k leads to relatively more rapid evolution in the core and a better core-envelope separation. We also give an analytical explanation of the previously presented result, that the gravitational field acting on an infalling mass shell in the central region of a nonhomologously contracting thin disk increases as 1/r³_m, where r_m is the Lagrangian radius of the shell.