2025A&A...697A.174K

Context. The [C II] fine-structure line at 157.74 μm is one of the brightest far-infrared emission lines in galaxies and an important probe of galaxy properties such as the star formation rate (SFR) and the molecular gas mass (M_mol).
Aims. Using high-resolution numerical simulations, we tested the reliability of the [C II] line as a tracer of M_mol in high-redshift galaxies and investigated secondary dependences of the [C II]-M_mol relation on the SFR and metallicity. We also investigated the time evolution of the [C II] luminosity function (LF) and the relative spatial extent of [C II] emission and star formation.
Methods. We post-processed galaxies from the MARIGOLD cosmological simulations at redshifts 3 ≤ z ≤ 7 to obtain their [C II] emission. These simulations were performed with the sub-grid chemistry model, HYACINTH, to track the non-equilibrium abundances of H₂, CO, C and C⁺ on the fly. Based on a statistical sample of galaxies at these redshifts, we investigated correlations between the [C II] line luminosity (L_[C II]_) and the SFR, the M_mol, the total gas mass and the metal mass in gas phase (M_metal).
Results. We find that accounting for secondary dependencies in the L_[C II]_-M_mol relation improves the M_mol prediction by a factor of 2.3 at all redshifts. Our simulations predict a mild evolution in the slope of the L_[C II]_-SFR relation (≲0.15 dex) and an increase in the intercept by 0.5 dex in the above redshift range. Among the various galaxy properties we explore, the [C II] emission in our simulated galaxies shows the tightest correlation with M_metal, indicating the potential of this line to constrain the metallicity of high-redshift galaxies. About 20% (10%) of our simulated galaxies at z = 5 (z = 4) have [C II] emission extending ≥2 times farther than the star formation activity. The [C II] LF evolves rapidly and is always well approximated by a double power law that does not show an exponential cut-off at the bright end. We record a 600-fold increase in the number density of L_[C II]_ ∼ 10⁹ L_⊙ emitters in 1.4 Gyr.