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.
