Gauging the mass of metals in the gas phase of galaxies from the Local Universe to the Epoch of Reionization

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.