2001ApJ...547..272C

We revisit the problem of the formation of dense protostellar cores caused by 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 ≃τ²_ff/τ_ni∼10τ_ff (where τ_ff is the free-fall time and τ_ni is the neutral-ion collision time), except that it is multiplied by a numerical factor C(µ_c0), where µ_c0 is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C(µ_c0) is typically ∼1 in highly subcritical clouds (µ_c0{Lt}1), although certain conditions allow C(µ_c0){Gt}1. For clouds that are not highly subcritical, C(µ_c0) can be much less than unity, with C(µ_c0)⟶0 for µ_c0⟶1, which significantly reduces 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 young stellar objects that suggest an evolutionary timescale ∼1 Myr for objects of mean density ∼10⁴ 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.