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Abstract We investigate the fine-structure [Cii] line at 158μm as a molecular gas tracer by analyzing the relationship between molecular gas mass (M_mol) and [Cii] line luminosity (L_[CII]) in 11,125z≃ 6 star-forming, main-sequence galaxies from thesimbasimulations, with line emission modeled by the Simulator of Galaxy Millimeter/Submillimeter Emission. Though most (∼50%–100%) of the gas mass in our simulations is ionized, the bulk (>50%) of the [Cii] emission comes from the molecular phase. We find a sublinear (slope 0.78 ± 0.01) $\log L_{\left[\mathrm{C}\mathrm{II}\right]}–\log M_{\mathrm{mol}}$relation, in contrast with the linear relation derived from observational samples of more massive, metal-rich galaxies atz≲ 6. We derive a median [Cii]-to-M_molconversion factor ofα_[CII]≃ 18M_⊙/L_⊙. This is lower than the average value of ≃30M_⊙/L_⊙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 [Cii] observations of low-mass galaxies. For our simulations, [Cii] is a better tracer of the molecular gas than COJ= 1–0, especially at the lowest metallicities, where much of the gas isCO-dark. We find thatL_[CII]is more tightly correlated withM_molthan with star formation rate (SFR), and both the $\log L_{\left[\mathrm{C}\mathrm{II}\right]}–\log M_{\mathrm{mol}}$and $\log L_{\left[\mathrm{C}\mathrm{II}\right]}–\log \mathrm{SFR}$relations arise from the Kennicutt–Schmidt relation. Our findings suggest thatL_[CII]is a promising tracer of the molecular gas at the earliest cosmic epochs. 

We studied the molecular gas properties of AzTEC/C159, a star-forming disk galaxy at $z=4.567$. We secured $$^{12}$$CO molecular line detections for the $$J=2\to1$$ and $$J=5\to4$$ transitions using the Karl G. Jansky VLA and the NOEMA interferometer. The broad (FWHM$$\sim750\,{\rm km\,s}^{-1}$$) and tentative double-peaked profiles of both $$^{12}$$CO lines are consistent with an extended molecular gas reservoir, which is distributed in a rotating disk as previously revealed from [CII] 158$$\mu$$m line observations. Based on the $$^{12}$$CO(2$$\to$$1) emission line we derived $$L'_{\rm{CO}}=(3.4\pm0.6)\times10^{10}{\rm \,K\,km\,s}^{-1}{\rm \,pc}^{2}$$, that yields a molecular gas mass of $$M_{\rm H_2 }(\alpha_{\rm CO}/4.3)=(1.5\pm0.3)\times 10^{11}{\rm M}_\odot$$ and unveils a gas-rich system with $$\mu_{\rm gas}(\alpha_{\rm CO}/4.3)\equiv M_{\rm H_2}/M_\star=3.3\pm0.7$$. The extreme star formation efficiency (SFE) of AzTEC/C159, parametrized by the ratio $$L_{\rm{IR}}/L'_{\rm{CO}}=(216\pm80)\, {\rm L}_{\odot}{\rm \,(K\,km\,s}^{-1}{\rm \,pc}^{2})^{-1}$$, is comparable to merger-driven starbursts such as local ultra-luminous infrared galaxies (ULIRGs) and SMGs. Likewise, the $$^{12}$$CO(5$$\to$$4)/CO(2$$\to$$1) line brightness temperature ratio of $$r_{52}= 0.55\pm 0.15$$ is consistent with high excitation conditions, similar to that observed in SMGs. We constrained the value for the $$L'_{\text{CO}}-{\rm H}_2$$ mass conversion factor in AzTEC/C159, i.e. $$\alpha_{\text{CO}}=3.9^{+2.7}_{-1.3}{\rm \,M}_{\odot}{\rm \,K}^{-1}{\rm \,km}^{-1}{\rm \,s\,pc}^{-2}$$, that is consistent with a self-gravitating molecular gas distribution as observed in local star-forming disk galaxies. Cold gas streams from cosmological filaments might be fueling a gravitationally unstable gas-rich disk in AzTEC/C159, which breaks into giant clumps forming stars as efficiently as in merger-driven systems and generate high gas excitation.