L_[C II]-to-M_H2 conversion factor α_[CII] (dark pink) and L_[C II]-to-M_HI conversion factor β_[CII] (orange) as a function of stellar metallicity Z_⋆, at z = 10, 8, 7, and 6 combined. The solid dark pink and orange lines represent the mean values obtained from CDM HR for α_[C II] and β_[C II], respectively. The darker (lighter) shaded regions represent the 1σ (2σ) standard deviation. The grey points are α_[C II] estimates from observations of local galaxies (Cormier et al. 2015; Accurso et al. 2017; Contursi et al. 2017; Hughes et al. 2017) and z = 2 − 4 galaxies (Huynh et al. 2014; Schaerer et al. 2015). The black squares are β_[C II] derived by observations of γ-ray burst afterglows in star-forming galaxies at z = 2 − 5 (Heintz et al. 2021). The COLDSIM results agree well with lower-redshift observations and provide predictions for future observational works. Both α_[C II] and β_[C II] increase by ∼3 dex at low stellar metallicities.