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The chemical enrichment of dust and metals are vital processes in constraining the star formation history of the universe. Previously, the dust masses of high-redshift star-forming galaxies have been determined through their far-infrared continuum, however, equivalent, and potentially simpler, approaches to determining the metal masses have yet to be explored at $z\gtrsim 2$. Here, we present a new method of inferring the metal mass in the interstellar medium (ISM) of galaxies out to $z\approx 8$, using the far-infrared [CII]$-158\mu$m emission line as a proxy. We calibrated the [CII]-to-$M_{\rm Z,ISM}$ conversion factor based on a benchmark observational sample at $z\approx 0$, in addition to gamma-ray burst sightlines at $z>2$ and cosmological hydrodynamical simulations of galaxies at $z\approx 0$ and $z\approx 6$. We found a universal scaling across redshifts of $\log (M_{\rm Z,ISM}/M_\odot) = \log (L_{\rm [CII]}/L_\odot) - 0.45,$ with a 0.4 dex scatter, which is constant over more than two orders of magnitude in metallicity. We applied this scaling to recent surveys for [CII] in galaxies at $z\gtrsim 2$ and determined the fraction of metals retained in the gas-phase ISM, $M_{\rm Z,ISM} / M_\star$, as a function of redshift showing that an increasing fraction of metals reside in the ISM of galaxies at higher redshifts. We place further constraints on the cosmic metal mass density in the ISM ($\Omega_{\rm Z,ISM}$) at $z\approx 5$ and $\approx 7$, yielding $\Omega_{\rm Z,ISM} = 6.6^{+13}_{-4.3}\times 10^{-7}\,M_\odot\, {\rm Mpc}^{-3}$ ($z\approx 5$) and $\Omega_{\rm Z,ISM} = 2.0^{+3.5}_{-1.3}\times 10^{-7}\,M_\odot\, {\rm Mpc}^{-3}$ ($z\approx 7$). These results are consistent with the expected metal yields from the integrated star formation history at the respective redshifts. This suggests that the majority of metals produced at $z\gtrsim 5$ are confined to the ISM of galaxies., Comment: Accepted in A&A, abstract abridged

We present the average rest-frame spectrum of the final catalog of dusty star-forming galaxies (DSFGs) selected from the South Pole Telescope SZ survey (SPT-SZ) and measured with Band 3 of the Atacama Large Millimeter/submillimeter Array (ALMA). This work builds on the previous average rest-frame spectrum, given in Spilker et al. (2014) for the first 22 sources, and is comprised of a total of 78 sources, normalized by their respective apparent dust masses. The spectrum spans $1.9$$<$z$<$$6.9$ and covers rest-frame frequencies of 240$-$800 GHz. Combining this data with low-J CO observations from the Australia Telescope Compact Array (ATCA), we detect multiple bright line features from $^{12}$CO, $[$CI$]$, and H$_2$O, as well as fainter molecular transitions from $^{13}$CO, HCN, HCO$^+$, HNC, CN, H$_2$O$^+$, and CH. We use these detections, along with limits from other molecules, to characterize the typical properties of the interstellar medium (ISM) for these high redshift DSFGs. We are able to divide the large sample into subsets in order to explore how the average spectrum changes with various galaxy properties, such as effective dust temperature. We find that systems with hotter dust temperatures exhibit differences in the bright $^{12}$CO emission lines, and contain either warmer and more excited dense gas tracers, or larger dense gas reservoirs. These observations will serve as a reference point to studies of the ISM in distant luminous DSFGs (L$_{\mathrm{IR}}$$>$$10^{12}$L$_\odot$), and will inform studies of chemical evolution before the peak epoch of star formation at $z=2-3$., Comment: 26 pages, 10 figures, accepted for publication in ApJ

High-redshift dusty star-forming galaxies with very high star formation rates (500 -- 3000 M$_{\odot}$ yr$^{-1}$) are key to understanding the formation of the most extreme galaxies in the early Universe. Characterising the gas reservoir of these systems can reveal the driving factor behind the high star formation. Using molecular gas tracers like high-J CO lines, neutral carbon lines and the dust continuum, we can estimate the gas density and radiation field intensity in their interstellar media. In this paper, we present high resolution ($\sim$0.4$^{\prime\prime}$) observations of CO(7-6), [CI](2-1) and dust continuum of 3 lensed galaxies from the SPT-SMG sample at $z\sim$ 3 with the Atacama Large Millimeter/submillimeter Array. Our sources have high intrinsic star-formation rates ($>$850 M$_{\odot}$yr$^{-1}$) and rather short depletion timescales ($<$100 Myr). Based on the L$_{[\rm CI](2-1)}$/L$_{\rm CO(7-6)}$ and L$_{[\rm CI](2-1)}$/L$_{\rm IR}$ ratios, our galaxy sample has similar radiation field intensities and gas densities compared to other submillimetre galaxies. We perform visibility-based lens modelling on these objects to reconstruct the kinematics in the source plane. We find that the cold gas masses of the sources are compatible with simple dynamical mass estimates using ULIRG-like values of the CO-H$_2$ conversion factor $\alpha_{\rm CO}$ but not Milky Way-like values. We find diverse source kinematics in our sample: SPT0103-45 and SPT2147-50 are likely rotating disks while SPT2357-51 is possibly a major merger. The analysis presented in the paper could be extended to a larger sample to determine better statistics of morphologies and interstellar medium properties of high-$z$ dusty star-forming galaxies., Comment: 29 pages, 26 figures, Accepted for publication in A&A. Figure 16 and the related conclusions have been revised