Condition for the formation of micron-sized dust grains in dense molecular cloud cores

We investigate the condition for the formation of micron-sized grains in dense cores of molecular clouds. This is motivated by the detection of the mid-infrared emission from deep inside a number of dense cores, the so-called `coreshine,' which is thought to come from scattering by micron-sized grains. Based on numerical calculations of coagulation starting from the typical grain size distribution in the diffuse interstellar medium, we obtain a conservative lower limit to the time $t$ to form micron-sized grains: $t/t_\mathrm{ff}>3 (5/S) (n_\mathrm{H}/10^5 \mathrm{cm}^{-3})^{-1/4}$ (where $t_\mathrm{ff}$ is the free-fall time at hydrogen number density $n_\mathrm{H}$ in the core, and $S$ the enhancement factor to the grain-grain collision cross-section to account for non-compact aggregates). At the typical core density $n_\mathrm{H}=10^5 \mathrm{cm}^{-3}$, it takes at least a few free-fall times to form the micron-sized grains responsible for coreshine. The implication is that those dense cores observed in coreshine are relatively long-lived entities in molecular clouds, rather than dynamically transient objects that last for one free-fall time or less.