Using a sample of 123 X-ray clusters and groups drawn from the XMM-Cluster Survey first data release , we investigate the interplay between the brightest cluster galaxy ( BCG ) , its black hole , and the intra-cluster/group medium ( ICM ) .
It appears that for groups and clusters with a BCG likely to host significant AGN feedback , gas cooling dominates in those with T _ { X } > 2 keV while AGN feedback dominates below .
This may be understood through the sub-unity exponent found in the scaling relation we derive between the BCG mass and cluster mass over the halo mass range 10 ^ { 13 } < M _ { 500 } < 10 ^ { 15 } M _ { \odot } and the lack of correlation between radio luminosity and cluster mass , such that BCG AGN in groups can have relatively more energetic influence on the ICM .
The L _ { X } - T _ { X } relation for systems with the most massive BCGs , or those with BCGs co-located with the peak of the ICM emission , is steeper than that for those with the least massive and most offset , which instead follows self-similarity .
This is evidence that a combination of central gas cooling and powerful , well fuelled AGN causes the departure of the ICM from pure gravitational heating , with the steepened relation crossing self-similarity at T _ { X } = 2 keV .
Importantly , regardless of their black hole mass , BCGs are more likely to host radio-loud AGN if they are in a massive cluster ( T _ { X } \gtrsim 2 keV ) and again co-located with an effective fuel supply of dense , cooling gas .
This demonstrates that the most massive black holes appear to know more about their host cluster than they do about their host galaxy .
The results lead us to propose a physically motivated , empirical definition of ‘ cluster ’ and ‘ group ’ , delineated at 2 keV .