Equations (3.2) and (6.12) finally yield the connection between the hydrogen and CO column densities:
Here, there is an estimated uncertainty of 50 percent in the proportionality constant. Returning one last time to our Taurus example, we derive NH = 6.6 x 1021 cm~2.
One should bear in mind that the correlations underlying equation (6.13) represent an average within the solar neighborhood. Under a variety of circumstances, such as the exposure of a cloud to intense ultraviolet emission from nearby stars, the concentration of CO relative to hydrogen changes. Moreover, a given cloud might well have substantial optical thickness even to 13C16O. The derivation of Ar013 through equation (6.1) is then no longer feasible. To apply equation (6.13), one must first observe the cloud in a rarer CO isotope and then relate the new column density to that of 13C16O through the natural abundance ratios of the respective isotopes.
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