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One of the most fundamental baryonic matter components of galaxies is theneutral atomic hydrogen (H$\,{\rm \scriptsize I}$). At low redshifts, thiscomponent can be traced directly through the 21-cm transition, but to inferH$\,{\rm \scriptsize I}$ gas content of the most distant galaxies, a viabletracer is needed. We here investigate the fidelity of the fine structuretransition 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$\,{\rm \scriptsizeI}$ in a set simulated galaxies at $z\approx 6$, following the work by Heintzet al. (2021). We select 11,125 star-forming galaxies from the SIMBAsimulations, with far-infrared line emissions post-processed and modeled withinthe SIGAME framework. We find a strong connection between [C$\,{\rm \scriptsizeII}$] 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 thesimulated galaxies. We further use these simulations to make predictions forthe total baryonic matter content of galaxies at $z\approx 6$, and specificallythe 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 evidencefor H$\,{\rm \scriptsize I}$ being the dominant baryonic matter component bymass in galaxies at $z\approx 6$.

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