X-ray astronomers often divide galaxy clusters into two classes: cool core (CC) and non-cool core (NCC) objects. The origin of this dichotomy has been the subject of debate in recent years, between evolutionary models (where clusters can evolve from CC to NCC, mainly through mergers) and primordial models (where the state of the cluster is fixed ab initio by early mergers or pre-heating). We found that in a well-defined sample (clusters in the GMRT Radio halo survey with available Chandra or XMM-Newton data), none of the objects hosting a giant radio halo can be classified as a cool core. This result suggests that the main mechanisms which can start a large scale synchrotron emission (most likely mergers) are the same that can destroy CC and therefore strongly supports evolutionary models of the CC-NCC dichotomy. Moreover combining the number of objects in the CC and NCC state with the number of objects with and without a radio-halo, we estimated that the time scale over which a NCC cluster relaxes to the CC state, should be larger than the typical life-time of radio-halos and likely shorter than about 3 Gyr. This suggests that NCC transform into CC more rapidly than predicted from the cooling time, which is about 10 Gyr in NCC systems, allowing the possibility of a cyclical evolution between the CC and NCC states.
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