On the relationship between molecular hydrogen and carbon monoxide abundances in molecular clouds

The most usual tracer of molecular gas is line emission from CO. However, the reliability of this tracer has long been questioned in environments different from the Milky Way. We study the relationship between H-2 and CO abundances using a fully dynamical model of magnetized turbulence coupled to a chemical network simplified to follow only the dominant pathways for H-2 and CO formation and destruction, and including photodissociation using a six-ray approximation. We find that the abundance of H-2 is primarily determined by the amount of time available for its formation, which is proportional to the product of the density and the metallicity, but insensitive to photodissociation. Photodissociation only becomes important at extinctions under a few tenths of a visual magnitude, in agreement with both observational and prior theoretical work. On the other hand, CO forms quickly, within a dynamical time, but its abundance depends primarily on photodissociation, with only a weak secondary dependence on H-2 abundance. As a result, there is a sharp cut-off in CO abundance at mean visual extinctions A(V) less than or similar to 3. At lower values of A(V), we find that the ratio of H-2 column density to CO emissivity X-CO proportional to A-3.5(V). This explains the discrepancy observed in low metallicity systems between cloud masses derived from CO observations and other techniques such as infrared emission. Our work predicts that CO-bright clouds in low metallicity systems should be systematically larger or denser than Milky Way clouds, or both. Our results further explain the narrow range of observed molecular cloud column densities as a threshold effect, without requiring the assumption of virial equilibrium.