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

Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGN also exist in "noncool core" clusters, which brings up the question whether an X-ray cool core is always required for radio feedback. In this work, we present a systematic analysis of BCGs and strong radio AGN in 152 groups and clusters from the Chandra archive. All 69 BCGs with radio AGN more luminous than 2x10^23 W Hz^-1 at 1.4 GHz are found to have X-ray cool cores. The BCG cool cores can be divided into two classes, the large-cool-core (LCC) class and the corona class. Small coronae, easily overlooked at z>0.1, can trigger strong heating episodes in groups and clusters, long before large cool cores are formed. Strong radio outbursts triggered by coronae may destroy embryonic large cool cores and thus provide another mechanism to prevent formation of large cool cores. However, it is unclear whether coronae are decoupled from the radio feedback cycles as they have to be largely immune to strong radio outbursts. Our sample study also shows the absence of groups with a luminous cool core while hosting a strong radio AGN, which is not observed in clusters. This points to a greater impact of radio heating on low-mass systems than clusters. As examples of the corona class, we also present detailed analyses of a BCG corona associated with a strong 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 traditional cool core / noncool core dichotomy is too simple. A better alternative is the cool core distribution function, with the enclosed X-ray luminosity or gas mass.