Evolution (from left to right) of the vertical velocity dispersion σ_z (two bottom rows) and σ_z normalised by the local escape velocity (two top rows). The blue (resp. red) curves represent models with an initial stellar mass of 10^9.5 M_⊙ (resp. above or equal to 10¹⁰ M_⊙, see inset in top left panel). The grey lines are models that do not display a bar at the end of the simulation. The line thickness corresponds to the gas fraction (see inset in the top middle panel). The green shaded areas show vertical velocity dispersions ranging from 10 to 40 km s⁻¹ and the purple shaded areas show a percentage above 5%.