The source of mass accreted by the central black hole in cooling flow clusters

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.