A physical model for [C II] line emission from galaxies

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 ([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 [C II] with SFR. However, for SFR 1 M yr−1 kpc−2[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 (κs 1), parametrized by the ‘burstiness’ parameter κs; (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.