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Brightest Cluster Galaxies and Core Gas Density in REXCESS Clusters

We investigate the relationship between brightest cluster galaxies (BCGs) and their host clusters using a sample of nearby galaxy clusters from the Representative XMM Cluster Structure Survey (REXCESS). The sample was imaged with the Southern Observatory for Astrophysical Research (SOAR) in R band to investigate the mass of the old stellar population. Using a metric radius of 12h^-1 kpc, we found that the BCG luminosity depends weakly on overall cluster mass as L_BCG \propto M_cl^0.18+-0.07, consistent with previous work. We found that 90% of the BCGs are located within 0.035 r_500 of the peak of the X-ray emission, including all of the cool core (CC) clusters. We also found an unexpected correlation between the BCG metric luminosity and the core gas density for non-cool core (non-CC) clusters, following a power law of n_e \propto L_BCG^2.7+-0.4 (where n_e is measured at 0.008 r_500). The correlation is not easily explained by star formation (which is weak in non-CC clusters) or overall cluster mass (which is not correlated with core gas density). The trend persists even when the BCG is not located near the peak of the X-ray emission, so proximity is not necessary. We suggest that, for non-CC clusters, this correlation implies that the same process that sets the central entropy of the cluster gas also determines the central stellar density of the BCG, and that this underlying physical process is likely to be mergers.