Time evolution of the bubble radius produced by a growing SMBH in a dark matter halo growing to 10¹³M_⊙ at z = 6 in the energy-driven case (black curves). The dashed curve shows the evolution of the bubble radius when only the gravitational pull of the halo is considered. The solid curve also considers the external pressure P_ext by the halo gas. The mass and luminosity of the accreting SMBH are as in Fig. 2. The evolution of the halo virial radius is also shown (grey curve). For comparison, the evolution of the bubble radius in the case of a uniform density field as assumed in Fig. 2 is also plotted (green curve). The vertical dotted lines are as in Fig. 2.