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The amount of cold, molecular gas in high-redshift galaxies is typicallyinferred from proxies of molecular hydrogen (H$_2$), such as carbon monoxide(CO) or neutral atomic carbon ([CI]) and molecular gas mass conversion factors.The use of these proxies, however, relies on modeling and observations thathave not been directly measured outside the local universe. Here, we use recentsamples of high-redshift gamma-ray burst (GRB) and quasar molecular gasabsorbers to determine this conversion factor $\alpha_{\rm [CI]}$ from thecolumn density of H$_2$, which gives us the mass per unit column, and the[CI]($J=1$) column density, which provides the luminosity per unit column. Thistechnique allows us to make direct measurements of the relative abundances inhigh-redshift absorption-selected galaxies. Our sample spans redshifts ofz=1.9-3.4 and covers two orders of magnitude in gas-phase metallicity. We findthat $\alpha_{\rm [CI]}$ scales linearly with the metallicity: $\log\alpha_{\rm [CI]} = -1.13\times \log(Z/Z_{\odot}) + 1.33$, with a scatter of$\sigma_{\alpha_{\rm [CI]}} = 0.2$ dex. Using a sample of emission-selectedgalaxies at z~0-5, with both [CI] and CO line detections, we apply the$\alpha_{\rm [CI]}$ conversion to derive independent estimates of the moleculargas mass and $\alpha_{\rm CO}$. We find a remarkable agreement between themolecular gas masses inferred from the absorption-derived $\alpha_{\rm [CI]}$compared to typical $\alpha_{\rm CO}$-based estimates, and an inferredmetallicity evolution of $\alpha_{\rm CO}$ that is consistent with $\alpha_{\rm[CI]}$ and previous estimates from the literature. These results thus supportthe use of the absorption-derived $\alpha_{\rm [CI]}$ conversion factor foremission-selected star-forming galaxies and demonstrate that both methods probethe same universal properties of molecular gas in the local and high-redshiftuniverse.

Direct measurement of the [CI] luminosity to molecular gas mass conversion factor in high-redshift star-forming galaxies