Molecular cloud formation by gravitational instabilities in a clumpy interstellar medium

A dispersion relation is derived for gravitational instabilities in a medium with cloud collisional cooling, using a time-dependent energy equation instead of the adiabatic equation of state. The instability extends to much smaller length scales than in the conventional Jeans analysis, and, in regions temporarily without cloud stirring, it has a large growth rate down to the cloud collision mean free path. These results suggests that gravitational instabilities in a variety of environments, such as galactic density wave shocks, swept-up shells, and extended, quiescent regions of the interstellar medium, can form molecular clouds with masses much less than the conventional Jeans mass, e.g., from 100 to 10 million solar masses for the ambient medium, and they can do this even when the unperturbed velocity dispersion remains high. Similar processes operating inside existing clouds might promote gravitationally driven fragmentation. 29 refs