ON THE [C ii]–SFR RELATION IN HIGH REDSHIFT GALAXIES

After two Atacama Large Millimeter/submillimeter Array (ALMA) observing cycles, only a handful of [C ii ] 158 μ m emission line searches in z > 6 galaxies have reported a positive detection, questioning the applicability of the local [C ii ]–star formation rate (SFR) relation to high- z systems. To investigate this issue we use the Vallini et al. (V13) model,based on high-resolution, radiative transfer cosmological simulations to predict the [C ii ] emission from the interstellar medium of a z ≈ 7 (halo mass M h = 1.17 × 10 11 M ⊙ ) galaxy. We improve the V13 model by including (a) a physically motivated metallicity ( Z ) distribution of the gas, (b) the contribution of photodissociation regions (PDRs), and (c) the effects of cosmic microwave background (CMB) on the [C ii ] line luminosity. We study the relative contribution of diffuse neutral gas to the total [C ii ] emission ( F diff / F tot ) for different SFR and Z values. We find that the [C ii ] emission arises predominantly from PDRs: regardless of the galaxy properties, F diff / F tot ≤ 10%, since at these early epochs the CMB temperature approaches the spin temperature of the [C ii ] transition in the cold neutral medium ( T CMB ∼ ∼ 20 K). Our model predicts a high- z [C ii ]–SFR relation, consistent with observations of local dwarf galaxies (0.02 < Z / Z ⊙ < 0.5). The [C ii ] deficit suggested by actual data ( L C ii < 2.0 × 10 7 L ⊙ in BDF3299 at z ≈ 7.1) if confirmed by deeper ALMA observations, can be ascribed to negative stellar feedback disrupting molecular clouds around star formation sites. The deviation from the local [C ii ]–SFR would then imply a modified Kennicutt–Schmidt relation in z > 6 galaxies. Alternatively/in addition, the deficit might be explained by low gas metallicities ( Z < 0.1 Z ⊙ ).