We present the results of a numerical study designed to address the question of whether there is a column density threshold for star formation within molecular clouds .
We have simulated a large number of different clouds , with volume and column densities spanning a wide range of different values , using a state-of-the-art model for the coupled chemical , thermal and dynamical evolution of the gas .
We show that star formation is only possible in regions where the mean ( area-averaged ) column density exceeds 10 ^ { 21 } \ > { cm ^ { -2 } } .
Within the clouds , we also show that there is a good correlation between the mass of gas above a K-band extinction A _ { K } = 0.8 and the star formation rate ( SFR ) , in agreement with recent observational work .
Previously , this relationship has been explained in terms of a correlation between the SFR and the mass in dense gas .
However , we find that this correlation is weaker and more time-dependent than that between the SFR and the column density .
In support of previous studies , we argue that dust shielding is the key process : the true correlation is one between the SFR and the mass in cold , well-shielded gas , and the latter correlates better with the column density than the volume density .