Magnetic braking, ambipolar diffusion, and the formation of cloud cores and protostars. III. Effect of the initial mass-to-flux ratio

Two previous papers have formulated the problem of the formation and contraction of protostellar cores in isothermal, rotating, self-gravitating, magnetically supported model molecular clouds and have presented results, respectively, for a typical case and for the effects of varying five dimensionless free parameters of the problem. In this paper, we study the effect of varying the sixth parameter μ_{d, c0}, the initial central mass-to-flux ratio in units of the critical value for collapse. Clouds with initial central mass-to-flux ratio ranging from highly subcritical (μ_{d, c0} = 0.1) to initially critical (μ_{d, c0} = 1.0) are studied. Core formation is initially quasistatic (i.e., negligible acceleration) for the subcritical clouds but dynamic for the critical cloud. In the case of the critical cloud, magnetic-tension forces bring an end to the magnetic-braking-induced, initial phase of (dynamic) collapse (caused by the rapid loss of rotational support); quasistatic contraction follows. After ambipolar diffusion increases (quasistatically) the central mass-to-flux ratio above the critical value cores in all model clouds enter a dynamic phase of contraction. We find that, by the end of the isothermal phase of contraction, at a central density enhancement of about 10⁶ (e.g., from 3 × 10³ cm^-3 to 3 × 10⁹ cm^-3), the widest range of core masses and angular momenta is obtained from the variation of the free parameter μ_{d, c0}; specifically, we find that M_core ∝ μ_{d, c0}, and (J/M)_core ∝ μ²_{d, c0}. The observationally guided range of values of μ_{d, c0} in our parameter study can explain naturally a range of core masses 3-30 M_⊙ and specific angular momenta 10¹⁹-10²¹ cm² s^-1.