Star formation law in the epoch of reionization from [C II] and CIII] lines

We present a novel method to simultaneously characterize the star formation law and the interstellar medium properties of galaxies in the epoch of reionization (EoR) through the combination of [C II] 158 mu m (and its known relation with star formation rate) and C III] lambda 1909 angstrom emission line data. The method, based on a Markov chain Monte Carlo algorithm, allows us 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 [C II] and C III]. We show that COS-3018 is a moderate starburst (kappa(s) approximate to 3), with Z approximate to 0.4Z(circle dot), and n approximate to 500 cm(-3). Our method will be optimally applied to joint ALMA and James Webb Space Telescope targets.