  This paper reports the study of the cold-feedback heating in cooling flow
clusters. In the cold-feedback model the mass accreted by the central black
hole originates in non-linear over-dense blobs of gas residing in an extended
region (r ~ 5-30 kpc); these blobs are originally hot, but then cool faster
than their environment and sink toward the center. The intra-cluster medium
(ICM) entropy profile must be shallow for the blobs to reach the center as cold
blobs. I build a toy model to explore the role of the entropy profile and the
population of dense blobs in the cold-feedback mechanism. The mass accretion
rate by the central black hole is determined by the cooling time of the ICM,
the entropy profile, and the presence of inhomogeneities. The mass accretion
rate determines the energy injected by the black hole back to the ICM. These
active galactic nucleus (AGN) outbursts not only heat the ICM, but also change
the entropy profile in the cluster and cause inhomogeneities that are the seeds
of future dense blobs. Therefore, in addition to the ICM temperature (or
energy), the ICM entropy profile and ICM inhomogeneities are also ingredients
in the feedback mechanism.
