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The chemical enrichment of dust and metals in the interstellar medium (ISM)of galaxies throughout cosmic time is one of the key driving processes ofgalaxy evolution. Here we study the evolution of the gas-phase metallicities,dust-to-gas (DTG), and dust-to-metal (DTM) ratios of 36 star-forming galaxiesat $1.7 < z < 6.3$ probed by gamma-ray bursts (GRBs). We compile allGRB-selected galaxies with intermediate (R=7000) to high (R>40,000) resolutionspectroscopic data for which at least one refractory (e.g. Fe) and one volatile(e.g. S or Zn) element have been detected at S/N>3. This is to ensure thataccurate abundances and dust depletion patterns can be obtained. We firstderive the redshift evolution of the dust-corrected, absorption-line basedgas-phase metallicity [M/H]$_{\rm tot}$ in these galaxies, for which wedetermine a linear relation with redshift ${\rm [M/H]_{tot}}(z) = (-0.21\pm0.04)z -(0.47\pm 0.14)$. We then examine the DTG and DTM ratios as a functionof redshift and through three orders of magnitude in metallicity, quantifyingthe relative dust abundance both through the direct line-of-sight visualextinction $A_V$ and the derived depletion level. We use a novel method toderive the DTG and DTM mass ratios for each GRB sightline, summing up the massof all the depleted elements in the dust-phase. We find that the DTG and DTMmass ratios are both strongly correlated with the gas-phase metallicity andshow a mild evolution with redshift as well. While these results are subject toa variety of caveats related to the physical environments and the narrowpencil-beam sightlines through the ISM probed by the GRBs, they provide strongimplications for studies of dust masses to infer the gas and metal content ofhigh-redshift galaxies, and particularly demonstrate the large offset from theaverage Galactic value in the low-metallicity, high-redshift regime.

The cosmic build-up of dust and metals. Accurate abundances from GRB-selected star-forming galaxies at $1.7 < z < 6.3$