Dynamical evolution of high-z galaxies. Top: Intrinsic velocity dispersion σ₀ as a function of redshift for our disk sample (black hexagons with green outline) compared with the literature values (see Appendix D Table D.1). Bottom: Same but for the ratio between rotational velocity and σ₀, V_rot/σ₀. The solid and dashed black lines are the Übler et al. (2019)’s best-fit relations for galaxies at z < 4, for ionised and cold molecular gas, respectively. Where available, the points are colour-coded by their MS offset, ΔMS, relative to the Speagle et al. (2014) relation, otherwise in grey. The insets show the literature sample (see Table D.2) of the same galaxy with two gas tracers tracing different phases. The insets include the galaxies with large uncertainties, which are omitted in the main plots. The grey shading encloses the corresponding range in σ₀ and V_rot/σ₀ for Q ∈ [0.6, 2.0]. The definition of the Toomre Q parameter is presented in Sect. 6.3.