Star formation law in the EoR from [CII] and CIII] lines

Abstract: We present a novel method to simultaneously characterise the star formation law and the interstellar medium properties of galaxies in the Epoch of Reionization (EoR) through the combination of [CII] 158$\mu$m (and its known relation with star formation rate) and CIII]$\lambda$1909{\AA} emission line data. The method, based on a Markov Chain Monte Carlo algorithm, allows to determine the target galaxy average density, $n$, gas metallicity, $Z$, and burstiness parameter, $\kappa_s$, quantifying deviations from the Kennicutt-Schmidt relation. As an application, we consider COS-3018 (z=6.854), the only EoR Lyman Break Galaxy so far detected in both [CII] and CIII]. We show that COS-3018 is a moderate starburst ($\kappa_s \approx 3$), with $Z\approx 0.4\, Z_{\odot}$, and $n \approx 500\, {\rm cm^{-3}}$. Our method will be optimally applied to joint ALMA and JWST targets.