Magnetic Braking, Ambipolar Diffusion, and the Formation of Cloud Cores and Protostars. III. Effect of the Initial Mass-to-Flux Ratio

Abstract

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 μd,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 (μd,c0 = 0.1) to initially critical (μd,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 μd,c0; specifically, we find that Mcore ∝ μd,c0, and (J/M)core μ2d,c0. The observationally guided range of values of μd,c0 in our parameter study can explain naturally a range of core masses 3-30 M_{0 }and specific angular momenta 1019-1021 cm2 s-1.