Gravity or turbulence? Velocity dispersion-size relation

We discuss the nature of the velocity dispersion versus size relation for molecular clouds. In particular, we add to previous observational results showing that the velocity dispersions in molecular clouds and cores are not purely functions of the spatial scale but involve surface gas densities as well. We emphasize that hydrodynamic turbulence is required to produce the first condensations in the progenitor medium. However, as the cloud is forming, it also becomes bound, and gravitational accelerations dominate the motions. Energy conservation in this case implies |E_g| ∼E_k, in agreement with observational data, and providing an interpretation for two recent observational results: the scatter in the δv-R plane, and the dependence of the velocity dispersion on the surface density δv²/R∝Σ. We argue that the observational data are consistent with molecular clouds in a state of hierarchical and chaotic gravitational collapse, i.e. developing local centres of collapse throughout the whole cloud while the cloud itself is collapsing, and making equilibrium unnecessary at all stages prior to the formation of actual stars. Finally, we discuss how this mechanism need not be in conflict with the observed star formation rate.