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

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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 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_{0 }and specific angular momenta 1019-1021 cm2 s-1.

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