Direct Measurement of the [C i] Luminosity to Molecular Gas Mass Conversion Factor in High-redshift Star-forming Galaxies

The amount of cold, molecular gas in high-redshift galaxies is typically inferred from proxies of molecular hydrogen (H2), such as carbon monoxide (CO) or neutral atomic carbon ([C i]) and molecular gas mass conversion factors. The use of these proxies, however, relies on modeling and observations that have not been directly measured outside the local universe. Here, we use recent samples of high-redshift gamma-ray burst (GRB) and quasar molecular gas absorbers to determine this conversion factor ${\alpha }_{[{\rm{C}}{\rm{I}}]}={M}_{\mathrm{mol}}/{L}_{[{\rm{C}}\,{\rm{I}}](1-0)}^{{\prime} }$ from the column density of H2, which gives us the mass per unit column, and the [C i](J = 1) column density, which provides the luminosity per unit column. This technique allows us to make direct measurements of the relative abundances in high-redshift absorption-selected galaxies. Our sample spans redshifts of z = 1.9−3.4 and covers two orders of magnitude in gas-phase metallicity. We find that the [C i]-to-Mmol conversion factor is metallicity dependent, with α[C i] scaling linearly with the metallicity: $\mathrm{log}{\alpha }_{[{\rm{C}}{\rm{I}}]}=-1.13\times \mathrm{log}(Z/{Z}_{\odot })+1.33$, with a scatter of σ α[CI] = 0.2 dex. Using a sample of emission-selected galaxies at z ∼ 0–5, with both [C i] and CO line detections, we apply the α[C i] conversion to derive independent estimates of the molecular gas mass and the CO-to-Mmol, αCO, conversion factor. We find a remarkable agreement between the molecular gas masses inferred from the absorption-derived α[C i] compared to typical αCO-based estimates, which we confirm here to be metallicity-dependent as well, with an inferred slope that is consistent with αCI and previous estimates from the literature. These results thus support the use of the absorption-derived α[C i] conversion factor for emission-selected star-forming galaxies and demonstrate that both methods probe the same universal properties of molecular gas in the local and high-redshift universe.