2015ApJ...813...36V

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 M_h= 1.17x10¹¹ 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∼ T_s^CNM ∼ 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_Cii< 2.0x10⁷ 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_☉).