Evolution of Dust-to-Metal Ratio in Galaxies

This paper investigates the evolution of the dust-to-metal ratio in galaxies based on a simple evolution model for the amount of metal and dust with infall. We take into account grain formation in stellar mass-loss gas, grain growth by the accretion of metallic atoms in a cold dense cloud, and grain destruction by SNe shocks. Especially, we propose that the accretion efficiency is independent of the star-formation history. This predicts various evolutionary tracks in the metallicity ($Z$)–dust-to-gas ratio ($\mathcal{D}$) plane depending on the star-formation history. In this framework, the observed linear $Z$–$\mathcal{D}$ relation of nearby spiral galaxies can be interpreted as a sequence of a constant galactic age. We emphasize that an observational study of the $Z$–$\mathcal{D}$ relation of galaxies at $z\sim 1$ is very useful to constrain the efficiencies of dust growth and destruction. We also suggest that the Lyman break galaxies at $z\sim 3$ have a very low dust-to-metal ratio, typically $\text{ltsim}0.1$. Although the effect of infall on the evolutionary tracks in the $Z$–$\mathcal{D}$ plane is quite small, the dispersion of the infall rate can disturb the $Z$–$\mathcal{D}$ relation with a constant galactic age.