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. 
Andreas Burkert, Lee Hartmann
astro-ph.GA