On the Self-Similar Appearance of Galaxy Clusters in X-rays
  The largest uncertainty for cosmological studies using clusters of galaxies
is introduced by our limited knowledge of the statistics of galaxy cluster
structure, and of the scaling relations between observables and cluster mass. A
large effort is therefore undertaken to compile global galaxy cluster
properties in particular obtained through X-ray observations and to study their
scaling relations. However, the scaling schemes used in the literature differ.
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 discus various steps of practical approximations. We derive the scaling
laws for X-ray observables and cluster mass within the pure gravitational
structure growth scenario. Using N-body simulations we test the recent
formation approximation used in earlier analytic approaches which involves a
redshift dependent overdensity parameter.We find this approximation less
precise than the use of a fiducial radius based on a fixed overdensity with
respect to critical density. 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 also a redshift
dependence of the gas mass to total mass relation has to be invoked within our
modification scheme. We find that the current observational data are within
their uncertainties consistent with the proposed modified scaling laws.
