Cold gas mass measurements for the era of large optical spectroscopic surveys

Gas plays an important role in many processes in galaxy formation and evolution, but quantifying the importance of gas has been hindered by the challenge to measure gas masses for large samples of galaxies. Data sets of direct atomic and molecular gas measurements are sufficient to establish simple scaling relations, but often not large enough to quantify three-parameter relations, or second-order dependences. As an alternative approach, we derive here indirect cold gas measurements from optical emission lines using photoionization models for galaxies in the Sloan Digital Sky Survey (SDSS) main galaxy sample and the PHANGS-MUSE survey. We calibrate the gas surface density measurements using xCOLD GASS and PHANGS-ALMA molecular gas measurements to ensure that our measurements are reliable. We demonstrate the importance of taking into account the scale dependence of the relation between optical depth (τ_V) and gas surface density (Σ_gas) and provide a general prescription to estimate Σ_gas from τ_V, metallicity, and the dust-to-metal ratio, at any arbitrary physical resolution. To demonstrate that the indirect cold gas masses are accurate enough to quantify the role of gas in galaxy evolution, we study the mass-metallicity relation of SDSS galaxies and show that as a third parameter gas mass is better than star formation rate at reducing the scatter of the relation, as predicted by models and simulations.