The Cosmic Build-Up of Dust and Metals. Accurate Abundances from GRB-selected Star-Forming Galaxies at $1.7 < Z < 6.3$

The chemical enrichment of dust and metals in the interstellar medium (ISM) of galaxies throughout cosmic time is one of the key driving processes of galaxy 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 galaxies at $1.7 < z < 6.3$ probed by gamma-ray bursts (GRBs). We compile all GRB-selected galaxies with intermediate (R=7000) to high (R>40,000) resolution spectroscopic 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 that accurate abundances and dust depletion patterns can be obtained. We first derive the redshift evolution of the dust-corrected, absorption-line based gas-phase metallicity [M/H]$_{\rm tot}$ in these galaxies, for which we determine a linear relation with redshift ${\rm [M/H]_{tot}}(z) = (-0.21\pm 0.04)z -(0.47\pm 0.14)$. We then examine the DTG and DTM ratios as a function of redshift and through three orders of magnitude in metallicity, quantifying the relative dust abundance both through the direct line-of-sight visual extinction $A_V$ and the derived depletion level. We use a novel method to derive the DTG and DTM mass ratios for each GRB sightline, summing up the mass of all the depleted elements in the dust-phase. We find that the DTG and DTM mass ratios are both strongly correlated with the gas-phase metallicity and show a mild evolution with redshift as well. While these results are subject to a variety of caveats related to the physical environments and the narrow pencil-beam sightlines through the ISM probed by the GRBs, they provide strong implications for studies of dust masses to infer the gas and metal content of high-redshift galaxies, and particularly demonstrate the large offset from the average Galactic value in the low-metallicity, high-redshift regime.