The Chocolate Chip Cookie Model: Dust-to-metal Ratio of H ii Regions

Using a sample of face-on star-forming galaxies selected from the Sloan Digital Sky Survey, we statistically derive the typical optical depth tau (cl) of individual H ii regions based on the "Chocolate Chip Cookie" model of Lu et al. (2022). By binning galaxies into stellar mass and gas-phase metallicity bins and interpreting tau (cl) as the dust-to-gas ratio (DGR) of H ii regions, we further investigate the correlations between DGR and stellar mass and between DGR and gas-phase metallicity, respectively. We find that DGR increases monotonically with the stellar mass of galaxies. At a given stellar mass, DGR shows a linear correlation with the gas-phase metallicity, which implies a constant dust-to-metal ratio (DTM) of galaxies at a given stellar mass. These results adequately indicate that the DTM of galaxies is simply a function of their stellar masses. In terms of gas-phase metallicity, because of the mass-metallicity relation, DTM increases with increasing metallicity with a power-law index 1.45 in the low-metallicity region, while it remains constant at the high-metallicity end.