The Dependence of Star Formation Efficiency on Gas Surface Density

Studies by Lada (2010) and Heiderman (2010) have suggested that star formation mostly occurs above a threshold in gas surface density Sigma of Sigma_c = 120 Msun pc^{-2} (A_K = 0.8). Heiderman infer a threshold by combining low-mass star-forming regions, which show a steep increase in the star formation rate per unit area Sigma_SFR with increasing Sigma, and massive cores forming luminous stars which show a linear relation. We argue that these observations do not require a particular density threshold. The steep dependence of Sigma_SFR, approaching unity at protostellar core densities, is a natural result of the increasing importance of self-gravity at high densities along with the corresponding decrease in evolutionary timescales. The linear behavior of Sigma_SFR vs. Sigma in massive cores is consistent with probing dense gas in gravitational collapse, forming stars at a characteristic free-fall timescale given by the use of a particular molecular tracer. The low-mass and high-mass regions show different correlations between gas surface density and the area A spanned at that density, with A=Sigma^{-3} for low-mass regions and A=Sigma^{-1} for the massive cores; this difference, along with the use of differing techniques to measure gas surface density and star formation, suggests that connecting the low-mass regions with massive cores is problematic. We show that the approximately linear relationship between dense gas mass and stellar mass used by Lada similarly does not demand a particular threshold for star formation, and requires continuing formation of dense gas. Our results are consistent with molecular clouds forming by galactic hydrodynamic flows with subsequent gravitational collapse.