Gravity or Turbulence? The velocity dispersion-size relation

TL;DR

The paper argues that molecular cloud velocity dispersions are influenced by gravity and surface density, supporting a hierarchical gravitational collapse model over turbulence-dominated explanations, aligning with observational data.

Contribution

It introduces a gravitational collapse framework to explain velocity dispersion-size relations, challenging turbulence-only models and incorporating surface density effects.

Findings

Velocity dispersion depends on surface density and size.

Energy balance suggests gravitational binding dominates in cloud evolution.

Hierarchical collapse explains observed velocity and density relations.

Abstract

We discuss the nature of the velocity dispersion vs. 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 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 $|E_g| \sim E_k$, in agreement with observational data, and providing an interpretation for two recent observational results: the scatter in the $\delta v-R$ plane, and the dependence of the velocity dispersion on the surface density ${\delta v^2/ R} \propto \Sigma$. We argue that the observational data are consistent with molecular clouds in a state of hierarchical gravitational collapse, i.e., developing local centers 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.