Left: pixel-by-pixel molecular gas velocity dispersion estimates as a function of molecular gas surface density. For each starburst galaxy, in grey, we show the σ_v, CO values that may be overestimated due to beam-smearing residual effects. The errorbar in the lower-right corner indicates the typical 1-σ uncertainty, whereas the arrow represents the systematic uncertainty given by the use of our α_CO upper limit instead of the adopted value. The “z ∼ 0 ULIRG” sample is taken from Wilson et al. (2019). The “z ∼ 0 SFGs” sample estimates are galactic average values measured for a sub-sample of galaxies taken from the CARMA-EDGE survey (Bolatto et al. 2017; Levy et al. 2018). The “z ∼ 1.5 SFG” data correspond to the ∼kpc-scale measurements for a main-sequence galaxy presented in Molina et al. (2019b). The solid line represents the empirical relationship suggested by Wilson et al. (2019). The dashed line shows the empirical relationship corrected by the average Σ_H2/Σ_Tot and V_rot, CO/σ_v, CO ratios measured for both systems. Middle: pixel-by-pixel σ_v, CO values as a function of the total surface density. Right: molecular gas scale height as a function of the total gas surface density. The last two panels are colour-coded in the same way as the left panel. The vertical pressure equilibrium model gives a reasonable representation of our data.