Investigating the [C\(\,{\rm \scriptsize II}\)]-to-H\(\,{\rm \scriptsize I}\) conversion factor and the H\(\,{\rm \scriptsize I}\) gas budget of galaxies at \(z\approx 6\) with hydrodynamical simulations

One of the most fundamental baryonic matter components of galaxies is the neutral atomic hydrogen (H\(\,{\rm \scriptsize I}\)). At low redshifts, this component can be traced directly through the 21-cm transition, but to infer H\(\,{\rm \scriptsize I}\) gas content of the most distant galaxies, a viable tracer is needed. We here investigate the fidelity of the fine structure transition of the (\(^2P_{3/2} - ^2P_{1/3}\)) transition of singly-ionized carbon [C\(\,{\rm \scriptsize II}\)] at \(158\,\mu\)m as a proxy for H\(\,{\rm \scriptsize I}\) in a set simulated galaxies at \(z\approx 6\), following the work by Heintz et al. (2021). We select 11,125 star-forming galaxies from the SIMBA simulations, with far-infrared line emissions post-processed and modeled within the SIGAME framework. We find a strong connection between [C\(\,{\rm \scriptsize II}\)] and H\(\,{\rm \scriptsize I}\), with the relation between this [C\(\,{\rm \scriptsize II}\)]-to-H\(\,{\rm \scriptsize I}\) relation (\(\beta_{\rm [C\,{\rm \scriptsize II}]}\)) being anti-correlated with the gas-phase metallicity of the simulated galaxies. We further use these simulations to make predictions for the total baryonic matter content of galaxies at \(z\approx 6\), and specifically the HI gas mass fraction. We find mean values of \(M_{\rm HI}/M_\star = 1.4\), and \(M_{\rm HI}/M_{\rm bar,tot} = 0.45\). These results provide strong evidence for H\(\,{\rm \scriptsize I}\) being the dominant baryonic matter component by mass in galaxies at \(z\approx 6\).