The insignificant evolution of the richness-mass relation of galaxy   clusters
  We analysed the richness--mass scaling of 23 very massive clusters at $0.15<z<0.55$ with homogenously measured weak-lensing masses and richnesses within a fixed aperture of $0.5$ Mpc radius. We found that the richness--mass scaling is very tight (the scatter is $<0.09$ dex with 90 \% probability) and independent of cluster evolutionary status and morphology. This implies a close association between infall and evolution of dark matter and galaxies in the central region of clusters. We also found that the evolution of the richness-mass intercept is minor at most, and, given the minor mass evolution across the studied redshift range, the richness evolution of individual massive clusters also turns out to be very small. Finally, it was paramount to account for the cluster mass function and the selection function. Ignoring them would led to biases larger than the (otherwise quoted) errors. Our study benefits from: a) weak-lensing masses instead of proxy-based masses thereby removing the ambiguity between a real trend and one induced by an accounted evolution of the used mass proxy; b) the use of projected masses that simplify the statistical analysis thereby not requiring consideration of the unknown covariance induced by the cluster orientation/triaxiality; c) the use of aperture masses as they are free of the pseudo-evolution of mass definitions anchored to the evolving density of the Universe; d) a proper accounting of the sample selection function and of the Malmquist-like effect induced by the cluster mass function; e) cosmological simulations for the computation of the cluster mass function, its evolution, and the mass growth of each individual cluster. 
S. Andreon, P. Congdon
astro-ph.CO astro-ph.GA astro-ph.IM stat.AP