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ABSTRACT  We study the distribution of projected offsets between the cluster X‐ray centroid and the brightest cluster galaxy (BCG) for 65 X‐ray‐selected clusters from the Local Cluster Substructure Survey, with a median redshift of   z = 0.23 . We find a clear correlation between X‐ray/BCG projected offset and the logarithmic slope of the cluster gas density profile at  0.04 r  500 (α ), implying that more dynamically disturbed clusters have weaker cool cores. Furthermore, there is a close correspondence between the activity of the BCG, in terms of detected Hα and radio emission, and the X‐ray/BCG offset, with the line‐emitting galaxies all residing in clusters with X‐ray/BCG offsets of ≤15 kpc. Of the BCGs with  α &lt; −0.85  and an offset &lt;0.02 r  500 , 96 per cent (23/24) have optical emission and 88 per cent (21/24) are radio active, while none has optical emission outside these criteria. We also study the cluster gas fraction ( f  gas ) within  r  500  and find a significant correlation with X‐ray/BCG projected offset. The mean  f  gas  of the ‘small offset’ clusters (&lt;0.02 r  500 ) is  0.106 ± 0.005 (σ= 0.03 ) compared to  0.145 ± 0.009 (σ= 0.04 ) for those with an offset &gt;0.02 r  500 , indicating that the total mass may be systematically underestimated in clusters with larger X‐ray/BCG offsets. Our results imply a link between cool core strength and cluster dynamical state consistent with the view that cluster mergers can significantly perturb cool cores, and set new constraints on models of the evolution of the intracluster medium.

LoCuSS: the connection between brightest cluster galaxy activity, gas cooling and dynamical disturbance of X‐ray cluster cores