  The universe's largest galaxies reside at the centers of galaxy clusters and
are embedded in hot gas that, if left unchecked, would cool prodigiously and
create many more new stars than are actually observed. Cooling can be regulated
by feedback from accretion of cooling gas onto the central black hole, but
requires an accretion rate finely tuned to the thermodynamic state of the hot
gas. Theoretical models in which cold clouds precipitate out of the hot gas via
thermal instability and accrete onto the black hole exhibit the necessary
tuning. We have recently presented observational evidence showing that the
abundance of cold gas in the central galaxy increases rapidly near the
predicted threshold for instability. Here we present observations showing that
this threshold extends over a large range in cluster radius, cluster mass, and
cosmic time, and incorporate the precipitation threshold into a comprehensive
framework of theoretical models for the thermodynamic state of hot gas in
galaxy clusters. According to that framework, precipitation regulates star
formation in some giant galaxies, while thermal conduction prevents star
formation in others, if it can compensate for radiative cooling and shut off
precipitation.
