Modeling molecular hydrogen in low metallicity galaxies

Abstract: We use a suite of hydrodynamics simulations of the interstellar medium (ISM) within a galactic disk, which include radiative transfer, a non-equilibrium model of molecular hydrogen, and a realistic model for star formation and feedback, to study the structure of the ISM and H$2$ abundance as a function of local ISM properties. We show that the star formation rate and structure of the ISM are sensitive to the metallicity of the gas with a progressively smoother density distribution with decreasing metallicity. In addition to the well-known trend of the HI-H$_2$ transition shifting to higher densities with decreasing metallicity, the maximum achieved molecular fraction in the interstellar medium drops drastically at $Z \lesssim 0.2 \, Z\odot$ as the formation time of H$2$ becomes much longer than a typical lifetime of dense regions of the ISM. We present accurate fitting formulae for both volumetric and projected $f\mathrm{H_2}$ measured on different scales as a function of gas metallicity, UV radiation field, and gas density. We show that when the formulae are applied to the patches in the simulated galaxy the overall molecular gas mass is reproduced to better than a factor of $\lesssim 1.5$ across the entire range of metallicities and scales. We also show that the presented fit is considerably more accurate than any of the previous $f_\mathrm{H_2}$ models and fitting formulae in the low-metallicity regime. The fit can thus be used for modeling molecular gas in low-resolution simulations and semi-analytic models of galaxy formation in the dwarf and high-redshift regimes.