A Comparative Study of the Ground State Transitions of CO and [C I] as Molecular Gas Tracers at High Redshift
The CO(1--0) and [\ion{C}{1}](1--0) emission lines are well-established tracers of cold molecular gas mass in local galaxies. At high redshift, where the interstellar medium (ISM) is likely to be denser, there have been limited direct comparisons of both ground state transitions. Here we present a study of CO(1--0) and [\ion{C}{1}](1--0) emission in a sample of 20 unlensed dusty, star-forming galaxies at $z=2-5$. The CO(1--0)/[\ion{C}{1}](1--0) ratio is constant up to at least $z=5$, supporting the use of [CI](1-0) as a gas mass tracer. PDR modelling of the available data indicates a median H$_2$ density of log$(n~[$cm$^{-3}])=4.7\pm0.2$, and UV radiation field log$(G_{\mathrm{UV}} [G$_0$])=3.2\pm0.2$. We use the CO(1--0), [\ion{C}{1}](1--0) and 3mm dust continuum measurements to cross--calibrate the respective gas mass conversion factors, finding no dependence of these factors on either redshift or infrared luminosity. Assuming a variable CO conversion factor then implies [\ion{C}{1}] and dust conversion factors that differ from canonically assumed values but are consistent with the solar/super-solar metallicities expected for our sources. Radiative transfer modelling shows that the warmer CMB at high redshift can significantly affect the [\ion{C}{1}] as well as CO emission, which can change the derived molecular gas masses by up to 70\% for the coldest kinetic gas temperatures expected. Nevertheless, we show that the magnitude of the effect on the ratio of the tracers is within the known scatter of the $L'_\mathrm{CO}-L'_\mathrm{[CI]}$ relation. Further determining the absolute decrease of individual line intensities will require well-sampled spectral line energy distributions (SLEDs) to model the gas excitation conditions in more detail.