  Star formation in the universe's largest galaxies---the ones at the centers
of galaxy clusters---depends critically on the thermodynamic state of their hot
gaseous atmospheres. Central galaxies with low-entropy, high-density
atmospheres frequently contain multiphase star-forming gas, while those with
high-entropy, low-density atmospheres never do. The dividing line between these
two populations in central entropy, and therefore central cooling time, is
amazingly sharp. Two hypotheses have been proposed to explain the dichotomy.
One points out that thermal conduction can prevent radiative cooling of cluster
cores above the dividing line. The other holds that cores below the dividing
line are subject to thermal instability that fuels the central AGN through a
cold-feedback mechanism. Here we explore those hypotheses with an analysis of
the H-alpha properties of ACCEPT galaxy clusters. We find that the two
hypotheses are likely to be complementary. Our results support a picture in
which cold clouds inevitably precipitate out of cluster cores in which cooling
outcompetes thermal conduction and rain down on the central black hole, causing
AGN feedback that stabilizes the cluster core. In particular, the observed
distribution of the cooling-time to freefall-time ratio is nearly identical to
that seen in simulations of this cold-feedback process, implying that
cold-phase accretion, and not Bondi-like accretion of hot-phase gas, is
responsible for the AGN feedback that regulates star formation in large
galaxies.
