Black holes, cuspy atmospheres and galaxy formation

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 haloes expected in the cold dark matter cosmology.