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The universe's largest galaxies reside at the centers of galaxy clusters andare embedded in hot gas that, if left unchecked, would cool prodigiously andcreate many more new stars than are actually observed. Cooling can be regulatedby feedback from accretion of cooling gas onto the central black hole, butrequires an accretion rate finely tuned to the thermodynamic state of the hotgas. Theoretical models in which cold clouds precipitate out of the hot gas viathermal instability and accrete onto the black hole exhibit the necessarytuning. We have recently presented observational evidence showing that theabundance of cold gas in the central galaxy increases rapidly near thepredicted threshold for instability. Here we present observations showing thatthis threshold extends over a large range in cluster radius, cluster mass, andcosmic time, and incorporate the precipitation threshold into a comprehensiveframework of theoretical models for the thermodynamic state of hot gas ingalaxy clusters. According to that framework, precipitation regulates starformation in some giant galaxies, while thermal conduction prevents starformation in others, if it can compensate for radiative cooling and shut offprecipitation.

Regulation of star formation in giant galaxies by precipitation, feedback, and conduction