On the Timescale for the Formation of Protostellar Cores in Magnetic Interstellar Clouds

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Abstract
We revisit the problem of the formation of dense protostellar cores due to ambipolar diffusion within magnetically supported molecular clouds, and derive an analytical expression for the core formation timescale. The resulting expression is similar to the canonical expression = t_{ff}^2/t_{ni} ~ 10 t_{ni} (where t_{ff} is the free-fall time and t_{ni} is the neutral-ion collision time), except that it is multiplied by a numerical factor C(\mu_{c0}), where \mu_{c0} is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C(\mu_{c0}) is typically ~ 1 in highly subcritical clouds (\mu_{c0} << 1), although certain conditions allow C(\mu_{c0}) >> 1. For clouds that are not highly subcritical, C(\mu_{c0}) can be much less than unity, with C(\mu_{c0}) --> 0 for \mu_{c0} --> 1, significantly reducing the time required to form a supercritical core. This, along with recent observations of clouds with mass-to-flux ratios close to the critical value, may reconcile the results of ambipolar diffusion models with statistical analyses of cores and YSO's which suggest an evolutionary timescale \~ 1 Myr for objects of mean density ~ 10^4 cm^{-3}. We compare our analytical relation to the results of numerical simulations, and also discuss the effects of dust grains on the core formation timescale.

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