Scaling relations for galaxy clusters in the Millennium-XXL simulation

We present a very large high-resolution cosmological N-body simulation, the Millennium-XXL or MXXL, which uses 303 billion particles to represent the formation of dark matter structures throughout a 4.1 Gpc box in a Λ cold dark matter cosmology. We create sky maps and identify large samples of galaxy clusters using surrogates for four different observables: richness estimated from galaxy surveys, X-ray luminosity, integrated Sunyaev–Zeldovich (SZ) signal and lensing mass. The unprecedented combination of volume and resolution allows us to explore in detail how these observables scale with each other and with cluster mass. The scatter correlates between different mass–observable relations because of common sensitivities to the internal structure, orientation and environment of clusters, as well as to line-of-sight superposition of uncorrelated structure. We show that this can account for the apparent discrepancies uncovered recently between the mean thermal SZ signals measured for optically and X-ray selected clusters by stacking data from the Planck satellite. Related systematics can also affect inferences from extreme clusters detected at high redshift. Our results illustrate that cosmological conclusions from galaxy cluster surveys depend critically on proper modelling, not only of the relevant physics, but also of the full distribution of the observables and of the selection biases induced by cluster identification procedures.