| Summary: | Observations of the cosmic evolution of different gas phases across time indicate a marked increase in the molecular gas mass density towards z ∼2-3. Such a transformation implies an accompanied change in the global distribution of molecular hydrogen column densities (NH2). Using observations by PHANGS-ALMA/SDSS and simulations by GRIFFIN/IllustrisTNG we explore the evolution of this H2 column density distribution function [f(NH2)]. The H2 (and H i) column density maps for TNG50 and TNG100 are derived in post-processing and are made available through the IllustrisTNG online API. The shape and normalization of f(NH2) of individual main-sequence star-forming galaxies are correlated with the star formation rate (SFR), stellar mass (M∗), and H2 mass (MH2) in both observations and simulations. TNG100, combined with H2 post-processing models, broadly reproduces observations, albeit with differences in slope and normalization. Also, an analytically modelled f(N), based on exponential gas discs, matches well with the simulations. The GRIFFIN simulation gives first indications that the slope of f(NH2) might not majorly differ when including non-equilibrium chemistry in simulations. The f(NH2) by TNG100 implies that higher molecular gas column densities are reached at z = 3 than at z = 0. Further, denser regions contribute more to the molecular mass density at z = 3. Finally, H2 starts dominating compared to H i only at column densities above log(NH2cm-2) ∼ 21.8-22 at both redshifts. These results imply that neutral atomic gas is an important contributor to the overall cold gas mass found in the ISM of galaxies including at densities typical for molecular clouds at z = 0 and 3. © 2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.
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