METAL: The Metal Evolution, Transport, and Abundance in the Large Magellanic Cloud Hubble program. IV. Calibration of Dust Depletions vs Abundance Ratios in the Milky Way and Magellanic Clouds and Application to Damped Lyman-alpha Systems

The evolution of the metal content of the universe can be tracked through rest-frame UV spectroscopy of damped Ly-$α$ systems (DLAs). Gas-phase abundances in DLAs must be corrected for dust depletion effects, which can be accomplished by calibrating the relation between abundance ratios such as [Zn/Fe] and depletions (the fraction of metals in gas, as opposed to dust). Using samples of gas-phase abundances and depletions in the Milky Way (MW), LMC, and SMC, we demonstrate that the relation between [Zn/Fe] and other abundance ratios does not change significantly between these local galaxies and DLAs, indicating that [Zn/Fe] should trace depletions of heavy elements in those systems. The availability of photospheric abundances in young massive stars, a proxy for the total (gas+dust) metallicity of neutral gas, in the MW LMC, and SMC allows us to calibrate the relation between [Zn/Fe] and depletions in these nearby galaxies. We apply the local calibrations of depletions to DLA systems. We find that the fraction of metals in dust, the dust-to-gas-ratio, and total abundances are 2-5 times lower than inferred from previous depletion calibrations based on MW measurements and a different formalism. However, the trend of dust abundance vs. metallicity remains only slightly sub-linear for all existing depletion calibrations, contrary to what is inferred from FIR, 21 cm, and CO emission in nearby galaxies and predicted by chemical evolution models. Observational constraints on the FIR dust opacity and depletions at metallicities lower than 20\% solar will be needed to resolve this tension.