  Our Chandra X-ray Observatory archival study of intracluster entropy in a
sample of 222 galaxy clusters shows that H-alpha and radio emission from the
brightest cluster galaxy are much more pronounced when the cluster's core gas
entropy is < 30 keV cm^2. The prevalence of H-alpha emission below this
threshold indicates that it marks a dichotomy between clusters that can harbor
multiphase gas and star formation in their cores and those that cannot. The
fact that strong central radio emission also appears below this boundary
suggests that AGN feedback turns on when the intracluster medium starts to
condense, strengthening the case for AGN feedback as the mechanism that limits
star formation in the Universe's most luminous galaxies.
