The Chocolate Chip Cookie Model: dust-to-metal ratio of HII regions

Using a sample of face-on star-forming galaxies selected from the Sloan Digital Sky Survey, we statistically derive the typical optical depth $\tau_{\rm{cl}}$ of individual HII regions based on the ``Chocolate Chip Cookie" model of Lu2022. By binning galaxies into stellar mass and gas-phase metallicity bins and interpreting $\tau_{\rm{cl}}$ as the dust to gas ratio (DGR) of HII regions, we further investigate the correlations among DGR and stellar mass, 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-metalliciy relation, DTM increases with increasing metallicity with a power-law index 1.45 in the low metallicity region, while remains constant at the high metallicity end.