Burstiness parameter κ_s vs. deviation from the local De-Looze relation Δ, color-coded by the C III] surface brightness Σ_C III]. Galaxies detected both in [C II] and C III] emission are annotated and represented as filled circles. Galaxies at 6 < z < 9 from Vallini et al. (2021) are represented as gray stars. Linear fit on the detected sources is shown as a blue line with 1σ uncertainties as a shaded region.