We use the Henriques et al. (2015) version of the Munich galaxy formation model (L-GALAXIES) to investigate why the halo and stellar mass scales above which galaxies are quenched are constant with redshift and coincide with the scale where baryons are most efficiently converted into stars. This model assumes that central galaxies are quenched by AGN feedback when hot halo gas accretes onto a supermassive black hole. Nevertheless, we find that supernova (SN) feedback sets both mass scales. As haloes grow above a threshold mass, SNe can no longer eject material so their hot gas content increases, enhancing the cooling rate onto the central galaxy, its cold gas content, its star formation rate and the growth rate of its central black hole. Strong AGN feedback terminates this short-lived phase by suppressing the fuel supply for star formation. Despite strong evolution of the halo mass - temperature relation, quenching occurs at a redshift-independent halo and stellar mass which coincides with the mass where baryons have been converted into stars with maximal efficiency. These regularities and coincidences are a result of the specific parameters selected by MCMC tuning of the model to fit the observed abundance and passive fraction of galaxies over the redshift range 0<z<3. Thus they are required by the observed evolution of the galaxy population, at least in the context of models of this type.
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