The interstellar medium of high-redshift galaxies: Gathering clues from C III] and [C II] lines
A tight relation between [C II] 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 $\Sigma$_[C II] - $\Sigma$_SFR relation. This deviation might be caused by different interstellar medium (ISM) properties in galaxies at early epochs. To test this hypothesis, we combined the [C II] and SFR data with C III] line observations and our physical models. We additionally investigated how ISM properties, such as burstiness, $\kappa_s$, total gas density, $n$, and metallicity, $Z$, affect the deviation from the $\Sigma$_[C II] - $\Sigma$_SFR relation in these sources. We present the VLT/X-SHOOTER observations targeting the C III] ${\lambda}1909$ line emission in three galaxies at 5.5 < z < 7. We include X-SHOOTER and VLT/MUSE archival data of eight galaxies at 2 < z < 7, and eleven star-forming systems at 6 < z < 7.5, with either C III] or [C II] detection reported in the literature. We detected C III] ${\lambda}{\lambda}1907, 1909$ line emission in HZ10 and we derived the intrinsic, integrated flux of the C III] ${\lambda}1909$ line. We constrained the ISM properties for our sample of galaxies, $\kappa_s$ , $n$, 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 $log(\kappa_s) > 1$, that is, they overshoot the Kennicutt-Schmidt (KS) relation by about one order of magnitude, implying that the whole KS relation might be shifted upwards at early times. Furthermore, all the high-z galaxies of our sample lie below the $\Sigma$_[C II] - $\Sigma$_SFR local relation. The total gas density, $n$, shows the strongest correlation with the deviation from the local $\Sigma$_[C II] - $\Sigma$_SFR relation.