The core of the relaxed cluster AWM 4 is characterized by a unique combination of properties which defy a popular scenario for ANG heating of cluster cores. A flat inner temperature profile is indicative of a past, major heating episode which completely erased the cool core, as testified by the high central cooling time (~ 3 Gyr) and by the high central entropy level (~ 60 keV cm^2). Yet the presence of a 1.4 GHz active central radio galaxy with extended radio lobes out to 100 kpc, reveals recent feeding of the central massive black hole. A system like AWM 4 should have no radio emission at all if only feedback from the cooling hot gas regulates the AGN activity.
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