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 μm 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 Mh = 1.17 × 1011 Mo) 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 (Fdiff/Ftot) for different SFR and Z values. We find that the [C II] emission arises predominantly from PDRs: regardless of the galaxy properties, Fdiff/Ftot ≤ 10%, since at these early epochs the CMB temperature approaches the spin temperature of the [C II] transition in the cold neutral medium (TCMB ∼ TCNMs ∼ 20 K). Our model predicts a high-z [C II]-SFR relation, consistent with observations of local dwarf galaxies (0.02 < Z/Zo < 0.5). The [C II] deficit suggested by actual data (LCii < 2.0 × 107 Lo 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 Zo).