text: 148,180,1494636885674799107,1247125153110204416,Roland Szakacs,"Paper day! ""The Column Densities of Molecular Gas across Cosmic Time: Bridging Observations and Simulations"" is accepted for publication in #MNRAS! In this paper we study the evolution of the molecular gas column density distribution in sim. and obs.: <LINK>",https://arxiv.org/abs/2202.08777,"Observations of the cosmic evolution of different gas phases across time indicate a marked increase in the molecular gas mass density towards $z\sim 2-3$. Such a transformation implies an accompanied change in the global distribution of molecular hydrogen column densities ($N_{\rm{H_2}}$). Using observations by PHANGS-ALMA/SDSS and simulations by GRIFFIN/IllustrisTNG we explore the evolution of this H$_2$ column density distribution function [$f(N_{\rm{H}_2})$]. The H$_2$ (and HI) 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 $f(N_{\rm{H}_2})$ of individual main-sequence star-forming galaxies are correlated with the star formation rate (SFR), stellar mass (${M_*}$), and H$_2$ mass ($M_{\rm{H}_2}$) in both observations and simulations. TNG100, combined with H$_2$ post-processing models, broadly reproduces observations, albeit with differences in slope and normalization. Also, an analytically modelled $f(N)$, based on exponential gas disks, matches well with the simulations. The GRIFFIN simulation gives first indications that the slope of $f(N_{\rm{H}_2})$ might not majorly differ when including non-equilibrium chemistry in simulations. The $f(N_{\rm{H}_2})$ 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, H$_2$ starts dominating compared to HI only at column densities above log($N_{\rm{H}_2} / \rm{cm}^{-2}) \sim 21.8-22$ 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 $z=3$. ","The Column Densities of Molecular Gas across Cosmic Time: Bridging