The panels in the central column show 2D cuts of the logarithmic density distributions in the yz plane for cases A to E, at the time when the cocoon has reached a size of approximately 8 kpc in the y direction (the times of each snapshot is shown in the right panels by the vertical dashed lines). The density is in units of ρ₀. The right panels show plots of the cocoon size along the three axes (black along y, blue along z and red along x) as a function of time up to 3 × 10⁵ yr, we recall that the z direction corresponds to the minor axis, while the x direction corresponds to the intermediate axis. The green lines show the theoretical estimate of the jet head position based on Eq. (10)Since the expansion of cases C, D and E is slower, the insets in the three bottom figures show the evolution for later times. The parameters for each case are given on the left.