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 ( \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 .