The amount of cold , molecular gas in high-redshift galaxies is typically inferred from proxies of molecular hydrogen ( H _ { 2 } ) , 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 _ { [ CI ] } = M _ { mol } / L ^ { \prime } _ { [ CI ] ( 1 - 0 ) } from the column density of H _ { 2 } , 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- M _ { mol } conversion factor is metallicity dependent , with \alpha _ { [ CI ] } scaling linearly with the metallicity : \log \alpha _ { [ CI ] } = -1.13 \times \log ( Z / Z _ { \odot } ) +1.33 , with a scatter of \sigma _ { \alpha _ { [ CI ] } } = 0.2 dex .
Using a sample of emission-selected galaxies at z \sim 0 - 5 , with both [ C i ] and CO line detections , we apply the \alpha _ { [ CI ] } conversion to derive independent estimates of the molecular gas mass and the CO-to- M _ { mol } , \alpha _ { CO } , conversion factor .
We find a remarkable agreement between the molecular gas masses inferred from the absorption-derived \alpha _ { [ CI ] } compared to typical \alpha _ { CO } -based estimates , which we confirm here to be metallicity-dependent as well , with an inferred slope that is consistent with \alpha _ { [ CI ] } and previous estimates from the literature .
These results thus support the use of the absorption-derived \alpha _ { [ CI ] } 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 .