Volume densities and star formation in nearby molecular clouds

Context. Volume density is a key physical quantity that controls the evolution of the interstellar medium (ISM) and star formation, but it cannot be accessed directly by observations of molecular clouds. Aims. Our aim is to estimate the volume density distribution in nearby molecular clouds in order to measure the relation between column and volume densities and to determine their roles as predictors of star formation. Methods. We developed an inverse modelling method to estimate the volume density distributions of molecular clouds. We applied this method to 24 nearby molecular clouds for which column densities had been derived using Herschel observations and for which star formation efficiencies (SFE) had been derived using observations with the Spitzer space telescope. We then compared the relationships of several column-density-based and volume-density-based descriptors of dense gas with the SFEs of the clouds. Results. We derived volume density distributions for 24 nearby molecular clouds, which represents the most complete sample of such distributions to date. The relationship between column densities and peak volume densities in these clouds is a piecewise power law relation that changes its slope at a column density of 5–10 × 1022 H2 cm−3. We interpret this as a signature of hierarchical fragmentation in the dense ISM. We find that the volume-density-based dense gas fraction is the best predictor of star formation in the clouds, and in particular, it is as anticipated a better predictor than the column-density-based dense gas fraction. We also derived a volume density threshold density for star formation of 2 × 104 H2 cm−3.