The formation of stars shapes the structure and evolution of entire galaxies. The rate and efficiency of this process are affected substantially by the density structure of the individual molecular clouds in which stars form. The most fundamental measure of this structure is the probability density function of volume densities (density-PDF), which determines the star formation rates predicted with analytical models. This function has remained unconstrained by observations. We have developed an approach to quantify the density-PDFs and establish their relation to star formation. The density-PDFs instigate a density threshold of star formation and allow us to quantify the star formation efficiency above it. The density-PDFs provide new constraints for star formation theories and correctly predict several key properties of the star-forming interstellar medium.
Density-PDFs reconstructed (A) in Serpens South (a star-forming cloud) and (B) in Chamaeleon III (a quiescent cloud). The dense-gas fraction (shown in brown) is significantly larger in the star-forming cloud, demonstrating how the density-PDF controls star-formation activity.