Thermal and dynamical balance in dense molecular cloud cores

We consider the thermal and dynamical balance in dense molecular cloud cores. We point out that because such cores are heated throughout their volumes by cosmic rays, but cool radiatively by means of optically thick lines, they are likely to be dynamically unstable and at best in only a form of quasi-static equilibrium. We also draw attention to the possibility that if such cores undergo an external impulse that s large enough to produce a velocity difference Delta upsilon less than or similar to c(s), where c(s) is the thermal sound speed, then the cooling rate rises suddenly and pressure support drops, which leads to gravitational collapse and fragmentation.