On the nature of feedback heating in cooling flow clusters

We study the feedback between heating and cooling of the intracluster medium (ICM) in cooling flow (CF) galaxies and clusters. We adopt the popular view that the heating is due to an active galactic nucleus (AGN), i.e., a central black hole accreting mass and launching jets and/or winds. We propose that the feedback occurs within the entire cool inner region (r <= 5-30 kpc), where the nonlinear overdense blobs of gas with a density contrast p/p(a) >= 2 cool fast and are removed from the ICM before experiencing the next major AGN heating event. We term this scenario "cold feedback.'' Some of these blobs cool and sink toward the central black hole, while others might form stars and cold molecular clouds. We derive the conditions under which the dense blobs formed by perturbations might cool to low temperatures (T < 104 K) and feed the black hole. The main conditions are found to be as follows. ( 1) An overdense blob must be prevented from reaching an equilibrium position in the ICM; therefore, it has to cool fast, and the density profile of the ambient gas should be shallow. (2) Nonlinear perturbations are required; they might have chiefly formed by previous AGN activity. (3) The cooling time of these nonlinear perturbations should be short relative to a few times the typical interval between successive AGN outbursts. ( 4) In order not to evaporate the blobs, thermal conduction around the blobs should be suppressed by a factor <= 10(-3).