2020ApJ...896...60P

We explore the relation between the stellar mass surface density and the mass surface density of molecular hydrogen gas in 12 nearby molecular clouds that are located at <1.5 kpc distance. The sample clouds span an order-of-magnitude range in mass, size, and star formation rates. We use thermal dust emission from Herschel maps to probe the gas surface density and the young stellar objects from the most recent Spitzer Extended Solar Neighborhood Archive catalog to probe the stellar surface density. Using a star-sampled nearest neighbor technique to probe the star-gas surface density correlations at the scale of a few parsecs, we find that the stellar mass surface density varies as a power law of the gas mass surface density, with a power-law index of ∼2 in all the clouds. The consistent power-law index implies that star formation efficiency is directly correlated with gas column density, and no gas column density threshold for star formation is observed. We compare the observed correlations with the predictions from an analytical model of thermal fragmentation and with the synthetic observations of a recent hydrodynamic simulation of a turbulent star-forming molecular cloud. We find that the observed correlations are consistent for some clouds with the thermal fragmentation model and can be reproduced using the hydrodynamic simulations.