A Theoretical Calibration of ^{13}CO LTE Column Density in Molecular Clouds

In this work we use models of molecular clouds (MC), and non-LTE radiative transfer calculations, to obtain a theoretical calibration of the relation between LTE 13CO column density and true column density in MCs. The cloud models consist of 3 dimensional grids of density and velocity fields obtained as solutions of the compressible magneto-hydrodynamic equations in a 128x128x128 periodic grid in both the supersonic and super-Alfvenic regimes. Due to the random nature of the velocity field and the presence of shocks, the density spans a continuous range of values covering over 5-6 orders of magnitude (from ~0.1 to ~10^5 cm^-3). As a result, the LTE column density can be calibrated over 3 orders of magnitude. We find that LTE column density of molecular clouds typically underestimates the mean 13CO true column density by a factor 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.