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The co-evolution of molecular hydrogen and the grain size distribution in an isolated galaxy

Understanding the evolution of dust and molecular hydrogen (H$_2$) is a critical aspect of galaxy evolution, as they affect star formation and the spectral energy distribution of galaxies. We use the $N$-body/smoothed-particle-hydrodynamics code {\sc Gadget-4} to compute the evolution of dust and H$_2$ in a suite of numerical simulations of an isolated Milky-Way-like galaxy. The evolution of the full grain size distribution (GSD) is solved by sampling the grain size on a logarithmically spaced grid with 30 bins. The evolution of a primordial chemistry network with twelve species is solved consistently with the hydrodynamic evolution of the system, including star formation, metal and energy ejections from stars into the interstellar medium through supernova feedback and stellar winds. The formation model for H$_2$ considers the GSD and photo-dissociation through the UV radiation of young stars. We identify the processes needed for producing a sizeable amount of H$_2$, verify that the resulting star formation law in the later stages of galaxy evolution is consistent with observations of local spirals, and show that our model manages to produce a galactic molecular gas fraction in line with observations of Milky-Way-like galaxies. We stress the importance of the co-evolution of the GSD and H$_2$, as models assuming a fixed MRN shape for the GSD overestimate the production of H$_2$ in regimes where the dust abundance is dominated by large grains and underestimate it in the regime where the dust is dominated by small grains, both of which are realized in simulations of dust evolution.