We study the surface brightness profiles of a sample of 25 distant hot clusters, observed with ROSAT, with published temperatures from ASCA. For both open and flat cosmological models, the derived emission measure profiles are scaled according to the self-similar model of cluster formation. We use the standard scaling relations of cluster properties with redshift and temperature, with the empirical slope of the relation derived by Neumann & Arnaud (CITE). Using a test, we perform a quantitative comparison of the scaled emission measure profiles of distant clusters with a local reference profile derived from the sample of 15 hot nearby clusters compiled by Neumann & Arnaud (1999), which were found to obey self-similarity. This comparison allows us to both check the validity of the self-similar model across the redshift range , and to constrain the cosmological parameters. For a low-density flat universe, the scaled distant cluster data were found to be consistent, both in shape and normalisation, with the local reference profile. It indicates that hot clusters constitute a homologous family up to high redshifts, and gives support to the standard picture of structure formation for the dark matter component. Because of the intrinsic regularity in the hot cluster population, the scaled profiles can be used as distance indicators, the correct cosmology being the one for which the various profiles at different redshifts coincide. The intrinsic limitations of the method, in particular possible systematic errors and biases related to the model uncertainties, are discussed. Using the standard evolution model, the present data allow us to put a tight constraint on for a flat Universe: at 90% confidence level (statistical errors only). The critical model () was excluded at the 98% confidence level. Consistently, the observed evolution of the normalisation of the relation was found to comply with the self-similar model for , . The constraint derived on is in remarkable agreement with the constraint obtained from luminosity distances to SNI or from combined analysis of the power spectrum of the 2dF galaxy redshift Survey and the Cosmic Microwave Background anisotropies.
A 2002 study studied this question.