Studies by Lada et al .
( 45 ) and Heiderman et al .
( 31 ) have suggested that star formation mostly occurs above a threshold in gas surface density \Sigma of \Sigma _ { c } \sim 120 M _ { \odot } { pc ^ { -2 } } ( A _ { K } \sim 0.8 ) . Heiderman et al .
( 31 ) 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 \sim \Sigma ^ { -3 } for low-mass regions and A \sim \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 et al .
( 45 ) 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 .