Left: outflow regimes as a function of halo mass at z = 6 and halo gas temperature normalized to the virial temperature. The energy-driven limit is considered. The seed BH mass (10⁴M_⊙) and all the other AGN input parameters are kept as in the previous computations. The transitions from supersonic to mixed (i.e. the outflow is part of the time supersonic and part of the time subsonic), and from mixed to subsonic, occur at M_h ~ 3 × 10¹¹M_⊙ and M_h ~ 5 × 10¹²M_⊙, respectively (red curves), and are nearly independent on T_gas. Right: same as in the left panel but as a function of halo mass at z = 6 and initial seed BH mass. Here we assume T_gas = T_vir for simplicity.