Modelling self-similar appearance of galaxy clusters in X-rays

Context. The largest uncertainty for cosmological studies using clusters of galaxies is introduced by our limited knowledge of the statistics of galaxy cluster structure and the related scaling relations between observables and cluster mass. A large effort has therefore been made to compile global galaxy cluster properties, in particular those obtained through X-ray observations, and to study their scaling relations. However, the scaling schemes used in the literature differ.
Aims: The present paper aims to clarify this situation by providing a thorough review of the scaling laws within the standard model of large-scale structure growth and to discuss various steps in practical approximations.
Methods: We derived the scaling laws for X-ray observables and cluster mass within the pure gravitational structure growth scenario. Using N-body simulations we tested the recent formation approximation used in earlier analytic approaches. It involves a redshift-dependent overdensity parameter. We find this approximation less precise than using a fiducial radius based on a fixed overdensity with respect to critical density.
Results: Inspired by the comparison of the predicted scaling relations with observations, we propose a first-order modification of the scaling scheme to include the observed effects of hydrodynamics in structure formation. This modification involves a cluster-mass dependent gas-mass fraction. We also discuss the observational results of the reshift evolution of the most important scaling relations and find that a redshift dependence of the gas mass to total mass relation also has to be invoked within our modification scheme.
Conclusions: We find that the current observational data are, within their uncertainties, consistent with the proposed modified scaling laws.