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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 haloes 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_\ versus line-of-sight galaxy velocity dispersion σv, optical richness, X-ray luminosity, LX, and Sunyaev–Zel'dovich signal. Masses were calibrated with weak lensing measurements. The measured relations are in good agreement with time and mass dependences predicted in the self-similar scenario of structure formation. The lone exception is the L_ \ - M_\ 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 \ _ \ - M_\ relation is notably small, of the order of 14 per cent. Robust predictions on the observed properties of the galaxy clusters in the Cluster Lensing And Supernova survey with Hubble sample are provided as cases of study. Catalogues and scripts are publicly available at http: //pico. bo. astro. it/small tildesereno/CoMaLit/.
Sereno et al. (Wed,) studied this question.