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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 (τV) and gas surface density (Σgas) and provide a general prescription to estimate Σgas from τV, 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.

Star formation histories (SFHs) are integral to our understanding of galaxy evolution. We can study recent SFHs by comparing the star formation rate (SFR) calculated using different tracers, as each probes a different time-scale. We aim to calibrate a proxy for the present-day rate of change in SFR, dSFR/dt, which does not require full spectral energy distribution (SED) modelling and depends on as few observables as possible, to guarantee its broad applicability. To achieve this, we create a set of models in cigale and define an SFR change diagnostic as the ratio of the SFR averaged over the past 5 and 200 Myr, $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$, probed by the H α–FUV colour. We apply $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$ to the nearby spiral NGC 628 and find that its star formation activity has overall been declining in the recent past, with the spiral arms, however, maintaining a higher level of activity. The impact of the spiral arm structure is observed to be stronger on $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$ than on the star formation efficiency. In addition, increasing disc pressure tends to increase recent star formation, and consequently $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$. We conclude that $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$ is sensitive to the molecular gas content, spiral arm structure, and disc pressure. The $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$ indicator is general and can be used to reconstruct the recent SFH of any star-forming galaxy for which H α, FUV, and either mid- or far-IR photometry is available, without the need of detailed modelling.