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Radio AGN feedback in X-ray cool cores has been proposed as a crucialingredient in the evolution of baryonic structures. However, it has long beenknown that strong radio AGN also exist in "noncool core" clusters, which bringsup the question whether an X-ray cool core is always required for radiofeedback. In this work, we present a systematic analysis of BCGs and strongradio AGN in 152 groups and clusters from the Chandra archive. All 69 BCGs withradio AGN more luminous than 2x10^23 W Hz^-1 at 1.4 GHz are found to have X-raycool cores. The BCG cool cores can be divided into two classes, thelarge-cool-core (LCC) class and the corona class. Small coronae, easilyoverlooked at z>0.1, can trigger strong heating episodes in groups andclusters, long before large cool cores are formed. Strong radio outburststriggered by coronae may destroy embryonic large cool cores and thus provideanother mechanism to prevent formation of large cool cores. However, it isunclear whether coronae are decoupled from the radio feedback cycles as theyhave to be largely immune to strong radio outbursts. Our sample study alsoshows the absence of groups with a luminous cool core while hosting a strongradio AGN, which is not observed in clusters. This points to a greater impactof radio heating on low-mass systems than clusters. As examples of the coronaclass, we also present detailed analyses of a BCG corona associated with astrong radio AGN (ESO 137-006 in A3627) and one of the faintest coronae known(NGC 4709 in the Centaurus cluster). Our results suggest that the traditionalcool core / noncool core dichotomy is too simple. A better alternative is thecool core distribution function, with the enclosed X-ray luminosity or gasmass.

Every BCG with a strong radio AGN has an X-ray cool core: is the cool core - noncool core dichotomy too simple?