2023A&A...678A..30H

The chemical enrichment of dust and metals are vital processes in constraining the star formation history of the universe. These are important ingredients in the formation and evolution of galaxies overall. 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 ≳ 2. Here, we present a new method of inferring the metal mass in the interstellar medium (ISM) of galaxies out to z ≈ 8, using the far-infrared [C II]-158 μm emission line as a proxy. We calibrated the [C II]-to-M_Z, ISM_ conversion factor based on a benchmark observational sample at z ≈ 0, in addition to gamma-ray burst sightlines at z > 2 and cosmological hydrodynamical simulations of galaxies at z ≈ 0 and z ≈ 6. We found a universal scaling across redshifts of log(M_Z, ISM_/M_⊙) = log(L_[CII]/L_⊙)-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 [C II] in galaxies at z ≳ 2 and compared their inferred M_Z, ISM_ to their stellar mass (M_⋆). In particular, we determined the fraction of metals retained in the gas-phase ISM, M_Z, ISM_/M_⋆, as a function of redshift and we showed 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 (Ω_Z, ISM_) at z ≈ 5 and ≈7 based on recent estimates of the [C II]-158 μm luminosity functions at these epochs, yielding $ \Omega_{Z,\mathrm{ISM}} = 6.6^{+13}_{-4.3}\times 10^{-7}\,M_\odot\,\mathrm{Mpc}^{-3} $ (z ≈ 5) and $ \Omega_{Z,\mathrm{ISM}} = 2.0^{+3.5}_{-1.3}\times 10^{-7}\,M_\odot\,\mathrm{Mpc}^{-3} $ (z ≈ 7), respectively. 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 ≳ 5 are confined to the ISM, with strong implications that disfavor efficient outflow processes at these redshifts. Instead, these results suggest that the extended [C II] halos predominantly trace the extended neutral gas reservoirs of high-z galaxies.