CoMaLit-IV. Evolution and self-similarity of scaling relations with the
  galaxy cluster mass
  The scaling of observable properties of galaxy clusters with mass evolves
with time. Assessing the role of the evolution is crucial to study the
formation and evolution of massive halos and to avoid biases in the
calibration. We present a general method to infer the mass and the redshift
dependence, and the time-evolving intrinsic scatter of the mass-observable
relations. The procedure self-calibrates the redshift dependent completeness
function of the sample. The intrinsic scatter in the mass estimates used to
calibrate the relation is considered too. We apply the method to the scaling of
mass M_Delta versus line of sight galaxy velocity dispersion sigma_v, optical
richness, X-ray luminosity, L_X, and Sunyaev-Zel'dovich signal. Masses were
calibrated with weak lensing measurements. The measured relations are in good
agreement with time and mass dependencies predicted in the self-similar
scenario of structure formation. The lone exception is the L_X-M_Delta relation
whose time evolution is negative in agreement with formation scenarios with
additional radiative cooling and uniform preheating at high redshift. The
intrinsic scatter in the sigma_v-M_Delta relation is notably small, of order of
14 per cent. Robust predictions on the observed properties of the galaxy
clusters in the CLASH sample are provided as cases of study. Catalogs and
scripts are publicly available at http://pico.bo.astro.it/~sereno/CoMaLit/.
