The [C II] line emission as an interstellar medium probe in the MARIGOLD galaxies

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 M ARIGOLD cosmological simulations at redshifts 3 ≤ z ≤ 7 to obtain their [C II ] emission. These simulations were performed with the sub-grid chemistry model, H YACINTH , to track the non-equilibrium abundances of H 2 , 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 ] ∼ 10 9 L ⊙ emitters in 1.4 Gyr.