  We find that the power of jets that inflate bubble pairs in cooling flow
clusters of galaxies correlates with the size of the inner region where the
entropy profile is flat, as well as with the gas mass in that region and the
entropy floor (the entropy value at the center of the cluster). These
correlations strengthen the cold feedback mechanism that is thought to operate
in cooling flow clusters and during galaxy formation. In the cold feedback
mechanism the central super-massive black hole (SMBH) is fed with cold clumps
that originate in an extended region of the cooling flow volume, in particular
from the inner region that has a flat entropy profile. Such a process ensures a
tight feedback between radiative cooling and heating by the SMBH (the AGN). The
derived expressions should be used instead of the Bondi accretion rate when
studying AGN feedback. We find that the mass of molecular gas also correlates
with the entropy profile parameters, despite that the jet power does not
correlate with the molecular gas mass. This further suggests that the entropy
profile is a fundamental parameter determining cooling and feedback in cooling
flow clusters.
