Evolution of the shock radius r(t) (blue) and head position d(t) (orange) for different jet powers L₀: 10³⁹ W (solid curves), 10³⁷ W (dashed curves) and 10³⁵ W (dotted curves). The horizontal lines, limiting the evolution phases 1 to 4, indicate the galactic core radius, a_g, (green), the position at which the galactic density reaches the cluster one, l_gc (red), and the cluster core radius, a_c (purple). The symbols indicate the values obtained from multi-dimensional relativistic (RHD) simulations. The empty symbols represent 2D, axisymmetric numerical simulations: The rhombs stand for the 5 × 10³⁴ W simulations in Perucho et al. (2014a), the triangles for the 10³⁷ W simulations in Perucho & Martí (2007), Perucho et al. (2014a,b), and the circles and squares for the 10³⁸ and 10³⁹ W simulations, respectively, in Perucho et al. (2014b). The solid symbols indicate the results obtained from 3D simulations (Perucho et al. 2019, 2022, 2023). As for the lines, blue symbols correspond to shock radii and orange ones to head positions.