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We use imaging from the first three years of the Dark Energy Survey tocharacterize the dynamical state of 288 galaxy clusters at $0.1 \lesssim z\lesssim 0.9$ detected in the South Pole Telescope (SPT) Sunyaev-Zeldovich (SZ)effect survey (SPT-SZ). We examine spatial offsets between the position of thebrightest cluster galaxy (BCG) and the center of the gas distribution as tracedby the SPT-SZ centroid and by the X-ray centroid/peak position from Chandra andXMM data. We show that the radial distribution of offsets provides no evidencethat SPT SZ-selected cluster samples include a higher fraction of mergers thanX-ray-selected cluster samples. We use the offsets to classify the dynamicalstate of the clusters, selecting the 43 most disturbed clusters, with half ofthose at $z \gtrsim 0.5$, a region seldom explored previously. We find thatSchechter function fits to the galaxy population in disturbed clusters andrelaxed clusters differ at $z>0.55$ but not at lower redshifts. Disturbedclusters at $z>0.55$ have steeper faint-end slopes and brighter characteristicmagnitudes. Within the same redshift range, we find that the BCGs in relaxedclusters tend to be brighter than the BCGs in disturbed samples, while inagreement in the lower redshift bin. Possible explanations includes a highermerger rate, and a more efficient dynamical friction at high redshift. Thered-sequence population is less affected by the cluster dynamical state thanthe general galaxy population.

A joint SZ-Xray-optical analysis of the dynamical state of 288 massive galaxy clusters