Dust and Grain Size Evolution in Galaxy Simulations: What Matters and What Does Not

We present the first implementation of an evolving dust grain size distribution (GSD) within a semi-analytic cosmological model (SAM) of galaxy evolution. This flexible model self-consistently accounts for stellar dust production, shattering, coagulation, accretion of gas-phase metals, and destruction in supernova-driven shocks and hot gas, successfully reproducing key observational constraints. The purpose of this paper is to present the key physical elements of this novel dust implementation in a SAM and to explore controlled numerical experiments to identify the mechanisms shaping the GSD and extinction law in galaxies. Our results show that the GSD evolves from a large-grain-dominated regime at high redshift to a flatter, MRN-like shape at low redshift. This transition occurs earlier for massive galaxies, at a characteristic metallicity determined by the galaxy depletion time. The resulting extinction curves show an increase of the UV/optical slope and a pronounced $2175$ A bump toward lower redshift, in good agreement with the extinction properties of the MW. Through numerical experiments, we find that once stars provide the initial reservoir of large grains, shattering and ISM accretion are the principal mechanisms driving the growth of small grains. When accretion is included, the model robustly reproduces the observed $z \approx 0$ dust masses, largely independent of the specific assumptions adopted for grain-size physics. The extinction properties of MW-like galaxies are also generally recovered, except in extreme cases, such as when grain velocities in turbulent media are assumed to be independent of grain size.