Star formation rate surface density (Σ_SFR) as a function of the molecular gas surface density (Σ_mol gas). The data points show the locus of the median Σ_SFR and Σ_mol gas of galaxies binned in Δ log(SSFR)_MS and redshift (see Fig. 10). The symbol size increases with redshift, while the color indicates the median Δ log(SSFR)_MS. The solid gray line shows the KS relation reported by Genzel et al. (2010), adapted for a Salpeter IMF. The dotted black line illustrates the best linear fit to all the data points; the dashed thin line shows the best linear fit when we exclude SFGs with Δ log(SSFR)_MS >  0.9. Error bars represent the 16th and 84th percentiles of the inferred Σ_SFR and Σ_mol gas distributions. The molecular gas mass has been approximated by using the prescription of Genzel et al. (2015, see Table 4), where M_mol gas = M_mol gas(z, SSFR, M_⋆ = 10^{10.5 ± 0.5}M_⊙).