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A Comparison of Methods for Determining the Molecular Content of Model Galaxies

Recent observations indicate that star formation occurs only in the molecular phase of a galaxy's interstellar medium. A realistic treatment of star formation in simulations and analytic models of galaxies therefore requires that one determine where the transition from the atomic to molecular gas occurs. In this paper we compare two methods for making this determination in cosmological simulations where the internal structures of molecular clouds are unresolved: a complex time-dependent chemistry network coupled to a radiative transfer calculation of the dissociating ultraviolet (UV) radiation field, and a simple time-independent analytic approximation. We show that these two methods produce excellent agreement at all metallicities >~10^-2 of the Milky Way value across a very wide range of UV fields. At lower metallicities the agreement is worse, likely because time-dependent effects become important; however, there are no observational calibrations of molecular gas content at such low metallicities, so it is unclear if either method is accurate. The comparison suggests that, in many but not all applications, the analytic approximation provides a viable and nearly cost-free alternative to full time-dependent chemistry and radiative transfer.