  In cuspy atmospheres, jets driven by supermassive black holes (BHs) offset
radiative cooling. The jets fire episodically, but often enough that the cuspy
atmosphere does not move very far towards a cooling catastrophe in the
intervals of jet inactivity. The ability of energy released on the sub-parsec
scale of the BH to balance cooling on scales of several tens of kiloparsecs
arises through a combination of the temperature sensitivity of the accretion
rate and the way in which the radius of jet disruption varies with ambient
density. Accretion of hot gas does not significantly increase BH masses, which
are determined by periods of rapid BH growth and star formation when cold gas
is briefly abundant at the galactic centre. Hot gas does not accumulate in
shallow potential wells. As the Universe ages, deeper wells form, and
eventually hot gas accumulates. This gas soon prevents the formation of further
stars, since jets powered by the BH prevent it from cooling, and it mops up
most cold infalling gas before many stars can form. Thus BHs set the upper
limit to the masses of galaxies. The formation of low-mass galaxies is
inhibited by a combination of photo-heating and supernova-driven galactic
winds. Working in tandem these mechanisms can probably explain the profound
difference between the galaxy luminosity function and the mass function of dark
halos expected in the cold dark matter cosmology.
