On the Nature of Feedback Heating in Cooling Flow Clusters

We study the feedback between heating and cooling of the intra-cluster medium(ICM) in cooling flow (CF) galaxies and clusters. We adopt the popular viewthat the heating is due to an active galactic nucleus (AGN), i.e. a centralblack hole accreting mass and launching jets and/or winds. We propose that thefeedback occurs with the entire cool inner region (r <~ 5-30 kpc), where thenon-linear over-dense blobs of gas with a density contrast >~2 cool fast andare 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 towardthe central black hole, while others might form stars and cold molecularclouds. We derive the conditions under which the dense blobs formed byperturbations might cool to low temperatures (T <~ 10^4 K), and feed the blackhole. The main conditions are found to be: (1) An over-dense blob must beprevented from reaching an equilibrium position in the ICM: therefore it has tocool fast, and the density profile of the ambient gas should be shallow; (2)Non-linear perturbations are required: they might have chiefly formed byprevious AGN activity; (3) The cooling time of these non-linear perturbationsshould be short relative to few times the typical interval between successiveAGN outbursts. (4) The blobs should be magnetically disconnected from theirsurroundings, in order not to be evaporated by thermal conduction.Comment: Replaced wiht the version accepted by the Ap