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The reservoir of molecular gas (H$_{\rm 2}$) represents the fuel for the starformation (SF) of a galaxy. Connecting the star formation rate (SFR) to theavailable H$_{\rm 2}$ is key to accurately model SF in cosmological simulationsof galaxy formation. We investigate how modifying the underlying modelling ofH$_{\rm 2}$ and the description of stellar feedback in low-metallicityenvironments (LMF, i.e. low-metallicity stellar feedback) in cosmological,zoomed-in simulations of a Milky Way-size halo influences the formation historyof the forming, spiral galaxy and its final properties. We exploit twodifferent models to compute the molecular fraction of cold gas (f$_{\rm H_{\rm2}}$): $i)$ the theoretical model by Krumholz et al. (2009b) and $ii)$ thephenomenological prescription by Blitz & Rosolowsky (2006). We find that themodel adopted to estimate f$_{\rm H_{\rm 2}}$ plays a key role in determiningfinal properties and in shaping the morphology of the galaxy. The clumpierinterstellar medium (ISM) and the more complex H$_{\rm 2}$ distribution thatthe Krumholz et al. (2009b) model predicts result in better agreement withobservations of nearby disc galaxies. This shows how crucial it is to link theSFR to the physical properties of the star-forming, molecular ISM. Theadditional source of energy that LMF supplies in a metal-poor ISM is key incontrolling SF at high redshift and in regulating the reservoir of SF acrosscosmic time. Not only is LMF able to regulate cooling properties of the ISM,but it also reduces the stellar mass of the galaxy bulge. These findings canfoster the improvement of the numerical modelling of SF in cosmologicalsimulations.

Impact of H$_{\rm 2}$-driven star formation and stellar feedback from low-enrichment environments on the formation of spiral galaxies