Revisited Cold Gas Content with Atomic Carbon [C I] in z = 2.5 Protocluster Galaxies

We revisit the cold gas contents of galaxies in a protocluster at z = 2.49 using the lowest neutral atomic carbon transition [C I] ³P₁ - ³P₀ from Atacama Large Millimeter/submillimeter Array observations. We aim to test if the same gas-mass calibration adopted in field galaxies can be applied to protocluster galaxies. Five galaxies out of 16 targeted galaxies are detected in the [C I] line, and these are all previously detected in CO (3-2) and CO (4-3) and three in 1.1 mm dust continuum. We investigate the line luminosity relations between CO and [C I] in the protocluster and compare with other previous studies. We then compare the gas mass based on three gas tracers of [C I], CO(3-2), and dust if at least one of the last two tracers are available. Using the calibration adopted for field main-sequence galaxies, the [C I]-based gas measurements are lower than or comparable to the CO-based gas measurements by -0.35 dex at the lowest with the mean deviation of -0.14 dex. The differences between [C I]- and the dust- based measurements are relatively mild by up to 0.16 dex with the mean difference of 0.02 dex. Taking these all together with calibration uncertainties, with the [C I] line, we reconfirm our previous findings that the mean gas fraction is comparable to field galaxies for a stellar-mass range of $\mathrm{log}({M}_{\mathrm{star}}/{M}_{\odot })=[10.6,11.3]$ <!-- --> . However, at least for these secure five detections, the depletion timescale decreases more rapidly with stellar mass than field galaxies that might be related to earlier quenching in dense environments.