Ambipolar diffusion, cloud cores, and star formation: Two-dimensional, cylindrically symmetric contraction. III. A further parameter study and magnetically controlled accretion rate

The self-initiated formation and contraction of protostellar cores (due to ambipolar diffusion) and its dependence on the three dimensionless free parameters present in the two-fluid magnetohydrodynamic equations are investigated further. We follow the evolution of four thermally supercritical, primarily magnetically supported model clouds up to a central density enhancement of 10⁶ (e.g., from 3 × 10³ to 3 × 10⁹ cm^-3). Together with the 10 models studied in Paper II, they reveal and quantify the crucial and unavoidable role of ambipolar diffusion in the formation of stars in otherwise quiescent molecular clouds. The physical origin of two breaks in the slope of the log ρ-log r neutral density profile, one in the envelope and one just outside the shrinking, nearly uniform-density core, is discussed. The ambipolar-diffusion limited mass infall (or accretion) rate is both qualitatively and quantitatively very different from that of nonmagnetic calculations and their extrapolations to magnetic clouds. The dependence on the free parameters of the exponent k in the relation B_c ∝ ρ_c^k between the magnetic field strength and the gas density in contracting cores is studied thoroughly in this (cylindrical) geometry. For completeness, the evolution of a thermally subcritical (but still initially primarily magnetically supported) model cloud is also followed until a final equilibrium state is reached.