In this work we use models of molecular clouds and non-LTE radiative transfer calculations to compare the column densities of molecular clouds with their LTE 13CO column densities. The cloud models consist of three-dimensional grids of density and velocity fields obtained as solutions of the compressible magnetohydrodynamic equations in a 1283 periodic grid in both the supersonic and super-Alfvénic regimes. Because of the random nature of the velocity field and the presence of shocks, the densities span a continuous range of values covering about 6 orders of magnitude (from ~0.1 to ~105 cm-3). As a result, the LTE column densities can be calculated over 3 orders of magnitude. We find that LTE column densities of molecular clouds typically underestimate the mean 13CO true column densities by factors ranging from 1.3 to 7. These results imply that the standard LTE methods for the derivation of column densities from CO data systematically underestimate the true values independent of other major sources of uncertainty such as the relative abundance of CO.
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