Tracing Molecular Gas in z \(\simeq\) 6 Galaxies with [C\({\rm \scriptsize II}\)]

We investigate the fine-structure [C\({\rm \scriptsize II}\)] line at \(158\,\mu\)m as a molecular gas tracer by analyzing the relationship between molecular gas mass (\(M_{\rm mol}\)) and [C\({\rm \scriptsize II}\)] line luminosity (\(L_{\rm [CII]}\)) in 11,125 \(z\simeq 6\) star-forming, main sequence galaxies from the SIMBA simulations, with line emission modeled by SÍGAME. Though most (\(\sim 50-100\,\%\)) of the gas mass in our simulations is ionized, the bulk (\(> 50\,\%\)) of the [C\({\rm \scriptsize II}\)] emission comes from the molecular phase. We find a sub-linear (slope \(0.78\pm 0.01\)) \(\log L_{\rm [CII]}-\log M_{\rm mol}\) relation, in contrast with the linear relation derived from observational samples of more massive, metal-rich galaxies at \(z \lesssim 6\). We derive a median [C\({\rm \scriptsize II}\)]-to-\(M_{\rm mol}\) conversion factor of \(\alpha_{\rm [CII]} \simeq 18\,{\rm M_{\rm \odot}/L_{\rm \odot}}\). This is lower than the average value of \(\simeq 30\,{\rm M_{\rm \odot}/L_{\rm \odot}}\) derived from observations, which we attribute to lower gas-phase metallicities in our simulations. Thus, a lower, luminosity-dependent, conversion factor must be applied when inferring molecular gas masses from [C\({\rm \scriptsize II}\)] observations of low-mass galaxies. For our simulations, [C\({\rm \scriptsize II}\)] is a better tracer of the molecular gas than CO \(J=1-0\), especially at the lowest metallicities, where much of the gas is 'CO-dark'. We find that \(L_{\rm [CII]}\) is more tightly correlated with \(M_{\rm mol}\) than with star-formation rate (\({\rm SFR}\)), and both the \(\log L_{\rm [CII]}-\log M_{\rm mol}\) and \(\log L_{\rm [CII]}-\log {\rm SFR}\) relations arise from the Kennicutt-Schmidt relation. Our findings suggest that \(L_{\rm [CII]}\) is a promising tracer of the molecular gas at the earliest cosmic epochs.