a shell with outer (shock) radius $R_s(t)$ which sweeps the gas around the AGN; the effect is similar to that resulting in the simulations by Di Matteo et al. (2005), although the latter have been performed only in selected cases of major mergers, while our treatment applies also to less energetic events (the accretion rate, and hence the energy $\Delta E$ injected by the AGN, is determined by eq. 2).

The mass $\Delta m$ expelled out of the virial radius by the blowout is computed as a function of the ratio $\Delta E/E$ where $E$ is the gas binding energy; The values of $\Delta m$ and $\beta$ for any given ratio $\Delta E/E$ are tabulated in Cavaliere, Lapi & Menci (2002), the former being well approximated (to better than 10 %) by $\Delta m/m\approx 0.5 \Delta E/E$ for $\Delta E/E<1.4$.

In our semi-analytic model, for any galaxy undergoing an active AGN phase (see sebsection 2.1), we compute $\Delta E=f\,L\,\tau$ assuming the AGN feedback efficiency $10^{-2}\lesssim f\lesssim  10^{-1}$ as a free parameter, the lower value being more appropriate to radio-quiet AGNs because of the flat spectrum and the low photon momenta; observations of wind speeds up to $v_W\approx 0.4 c$ suggest 