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

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 ≃ τ/τni ~ 10τff (where τff is the free-fall time and τni is the neutral-ion collision time), except that it is multiplied by a numerical factor 𝒞(μc0), where μc0 is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. 𝒞(μc0) is typically ~1 in highly subcritical clouds (μc0 ≪ 1), although certain conditions allow 𝒞(μc0) ≫ 1. For clouds that are not highly subcritical, 𝒞(μc0) can be much less than unity, with 𝒞(μc0) → 0 for μc0 → 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.