The interstellar medium of high-redshift galaxies: Gathering clues from C III] and [C II] lines

Context. A tight relation between [C II] 158 μm line luminosity and the star formation rate (SFR) has been observed for local galaxies. At high redshift (z > 5), galaxies instead deviate downwards from the local Σ[C II] − ΣSFR relation. This deviation might be caused by different interstellar medium (ISM) properties in galaxies at early epochs. Aims. To test this hypothesis, we combined the [C II] and SFR data with C III] 1909 Å line observations and our physical models. We additionally investigated how ISM properties, such as burstiness, κs, total gas density, n, and metallicity, Z, affect the deviation from the Σ[C II] − ΣSFR relation in these sources. Methods. We present the VLT/X-shooter observations targeting the C III] λ1909 line emission in three galaxies at 5.5 < z < 7.0. We include archival X-shooter data of two other sources at 5.5 < z < 7.0 and the VLT/MUSE archival data of six galaxies at z ∼ 2. We extend our sample of galaxies with eleven star-forming systems at 6 < z < 7.5, with either C III] or [C II] detection reported in the literature. Results. We detected C III] λλ1907, 1909 line emission in HZ10 and we derived the intrinsic, integrated flux of the C III] λ1909 line. We constrained the ISM properties for our sample of galaxies, κs, n, and Z, by applying our physically motivated model based on the MCMC algorithm. For the most part, high-z star-forming galaxies show subsolar metallicities. The majority of the sources have log(κs) ≳ 1, that is, they overshoot the Kennicutt–Schmidt (KS) relation by about one order of magnitude. Conclusions. Our findings suggest that the whole KS relation might be shifted upwards at early times. Furthermore, all the high-z galaxies of our sample lie below the Σ[C II] − ΣSFR local relation. The total gas density, n, shows the strongest correlation with the deviation from the local Σ[C II] − ΣSFR relation, namely, low-density high-z systems have lower [C II] surface brightness, in agreement with theoretical models.