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

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 $Zapprox 0.4, Z_{odot}$, and $n approx 500, {rm cm^{-3}}$. Our method will be optimally applied to joint ALMA and JWST targets.