Left column: time evolution of the bubble radius (upper panel) and velocity (lower panel) produced by a growing SMBH in a dark matter halo growing to 10¹³M_⊙ by z = 6 in the energy-driven case (black curves) as compared with the evolution of the halo virial radius and sound speed of the halo gas, respectively (grey curves). For such a massive halo the outflow expansion is always subsonic. Right column: as in the left column but for a smaller halo that grows to 3 × 10¹¹M_⊙ by z = 6. In this case the outflow expansion is always supersonic. The meaning of the vertical dotted lines is as in the previous figures.