Characterizing the conversion factor between CO emission and column density of molecular hydrogen, X CO, is crucial in studying the gaseous content of galaxies, its evolution, and relation to star formation. In most cases the conversion factor is assumed to be close to that of giant molecular clouds (GMCs) in the Milky Way, except possibly for mergers and star-bursting galaxies. However, there are physical grounds to expect that it should also depend on the gas metallicity, surface density, and strength of the interstellar radiation field. The X CO factor may also depend on the scale on which CO emission is averaged due to effects of limited resolution. We study the dependence of X CO on gas properties and averaging scale using a model that is based on a combination of results of sub-parsec scale magnetohydrodynamic simulations and on the gas distribution from self-consistent cosmological simulations of galaxy formation. Our model predicts X CO ≈ (2-4) × 1020 K–1 cm–2 km–1 s, consistent with the Galactic value, for interstellar medium conditions typical for the Milky Way. For such conditions the predicted X CO varies by only a factor of two for gas surface densities in the range . However, the model also predicts that more generally on the scale of GMCs, X CO is a strong function of metallicity and depends on the column density and the interstellar UV flux. We show explicitly that neglecting these dependencies in observational estimates can strongly bias the inferred distribution of H2 column densities of molecular clouds to have a narrower and offset range compared to the true distribution. We find that when averaged on ~kiloparsec scales the X-factor depends only weakly on radiation field and column density, but is still a strong function of metallicity. The predicted metallicity dependence can be approximated as X CO∝Z –γ with γ ≈ 0.5-0.8.
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