[C II] surface brightness vs. SFR per unit area, color-coded by the C III] surface brightness, of this sample of galaxies. Filled and empty circles indicate sources with the C III] line detection and upper limits, respectively. Galaxies detected both in [C II] and C III] emission are annotated. Blue × symbols indicate a subsample of galaxies from the ALPINE survey at 4 < z < 6 (Le Fèvre et al. 2020). Σ_[C II] − Σ_SFR relation for local galaxies by De Looze et al. (2014) is represented as a blue dashed line with a 1σ dispersion of 0.32 dex. This relation is extrapolated to cover the distribution of high-z sources in Σ_[C II] − Σ_SFR space, which is shown as a light-blue dashed line. Σ_[C II] − Σ_SFR relation predictions from models of Ferrara et al. (2019) with three different combinations of fixed κ_s, Z, and n parameters (Table 5) are represented as dotted gray lines. Finally, the best-fit model (Z = 0.24 Z_⊙, log(n[cm⁻³]) = 2.98, and log(κ_s) ≈ 1.30) on all the galaxies (excluding Z7_GND_42912) and 100 random samples from the MCMC chain are shown as thick and thin purple solid lines, respectively.