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 similar or equal to tau (2)(ff)/tau (ni) similar to 10 tau (ff) (where tau (ff) is the free-fall time and tau (ni) is the neutral-ion collision time), except that it is multiplied by a numerical factor C(mu (cO)) where mu (cO) is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C (mu (cO)) is typically similar to1 in highly subcritical clouds (mu (cO) much less than 1) although certain conditions allow C(mu (cO)) much greater than 1. For clouds that are not highly subcritical, C(mu (cO)) can be much less than unity, with C(mu (cO)) --> 0 for mu (cO) --> 1, for 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 similar to1 Myr for objects of mean density similar to 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.