Comparison of hydrostatic and convecting models. Panel a: Temperature as a function of height from a 1D hydrostatic model (black solid line) and convective runs A0 (red dashed line), A6 (blue dashed line), and A9 (orange dashed line). The black (red) dotted line shows a polytropic gradient corresponding to index n_rad = 3.25 (n_ad = 1.5) for reference. Panel b: Absolute value of the superadiabatic temperature gradient Δ∇ from the same runs as indicated by the legend. Red (blue) indicates convectively unstable (stable) stratification. The dotted vertical lines at z = 0 and z/d = 1 denote the base and top of the initially isentropic layer.