The equilibrium view on dust and metals in galaxies: Galactic outflows drive low dust-to-metal ratios in dwarf galaxies

Most galaxy evolution simulations as well as a variety of observational methods assume a linear scaling between the (galaxy-averaged) dust-to-gas ratio D and metallicity Z of the interstellar medium (ISM). Indeed, nearby galaxies with solar or moderately sub-solar metallicities clearly follow this trend albeit with significant scatter. However, a growing number of observations show that the linear scaling breaks down for metal-poor galaxies (Z<0.2 Z_sun), highlighting the need for a more sophisticated modeling of the dust-to-metal ratio of galaxies. Here we study the co-evolution of dust and metal abundances in galaxies with the help of a dynamical, one-zone model that incorporates dust formation and destruction processes in addition to gas inflows, outflows, and metal enrichment. The dynamical model is consistent with various observational constraints, including the stellar mass -- metallicity relation, the stellar mass -- halo mass relation, and the observed Z -- D relation for both metal-poor and metal-rich galaxies. The functional form of the Z -- D relation follows from a basic equilibrium ansatz, similar to the ideas used previously to model the stellar mass -- metallicity relation. Galactic outflows regulate the inflow rate of gas from the cosmic web for galaxies of a given star formation rate. The mass loading factor of outflows thus dictates the rate at which the dust and metal content of the ISM is diluted. The stellar mass dependence of the mass loading factor drives the evolution of metallicities, dust-to-gas ratios, and dust-to-metal ratios in galaxies.