2019MNRAS.489....1F

A tight relation between the [C II] 158 µm line luminosity and star formation rate is measured in local galaxies. At high redshift (z > 5), though, a much larger scatter is observed, with a considerable (15-20 per cent) fraction of the outliers being [C II]-deficient. Moreover, the [C II] surface brightness (Σ_[C II]_) of these sources is systematically lower than expected from the local relation. To clarify the origin of such [C II]-deficiency, we have developed an analytical model that fits local [C II] data and has been validated against radiative transfer simulations performed with CLOUDY. The model predicts an overall increase of Σ_[C II]_ with Σ_SFR. However, for Σ_SFR ≳1 M_☉ yr_^–1 kpc^–2, Σ_[C II]_ saturates. We conclude that underluminous [C II] systems can result from a combination of three factors: (a) large upward deviations from the Kennicutt-Schmidt relation (κ_s ≫ 1), parametrized by the 'burstiness' parameter κ_s; (b) low metallicity; (c) low gas density, at least for the most extreme sources (e.g. CR7). Observations of [C II] emission alone cannot break the degeneracy among the above three parameters; this requires additional information coming from other emission lines (e.g. [O III]88 µm, C III]1909 Å, CO lines). Simple formulae are given to interpret available data for low- and high-z galaxies.