The observed concentration–mass relation for galaxy clusters

The properties of clusters of galaxies offer key insights into the assembly process of structure in the universe. Numerical simulations of cosmic structure formation in a hierarchical, dark matter dominated universe suggest that galaxy cluster concentrations, which are a measure of a halo's central density, decrease gradually with virial mass. However, cluster observations have yet to confirm this correlation. The slopes of the run of measured concentrations with virial mass are often either steeper or flatter than that predicted by simulations. In this work, we present the most complete sample of observed cluster concentrations and masses yet assembled, including new measurements for 10 strong-lensing clusters, thereby more than doubling the existing number of strong-lensing concentration estimates. We fit a power law to the observed concentrations as a function of virial mass, and find that the slope is consistent with the slopes found in simulations, though our normalization factor is higher. Observed lensing concentrations appear to be systematically larger than X-ray concentrations, a more pronounced effect than that found in simulations. We also find that at a fixed mass, the bulk of observed cluster concentrations are distributed lognormally, with the exception of a few anomalously high concentration clusters. We examine the physical processes likely responsible for the discrepancy between lensing and X-ray concentrations, and for the anomalously high concentrations in particular. The forthcoming Millennium simulation results will offer the most comprehensive comparison set to our findings of an observed concentration–mass power law relation.