The X-ray surface brightness profiles of hot galaxy clusters up to z~0.8: evidence for self-similarity and constraints on Omega_0

We study the ROSAT surface brightness profiles of a sample of 25 distant (0.3<z<0.83) hot (kT>3.5keV) clusters. 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 z and temperature, with the empirical slope of the Mgas-T relation derived by Neumann & Arnaud (2001). Using a \chi^2 test, we perform a quantitative comparison of the scaled emission measure profiles of distant clusters with a reference profile derived from the sample of 15 hot nearby clusters compiled by Neumann & Arnaud (1999), which were found to obey self-similarity. For a low density flat universe, the distant cluster scaled data were found to be consistent, both in shape and normalisation, with the reference local profile.It indicates that hot clusters constitute a homologous family up to high z, and supports 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 profiles at different redshifts coincide. The present data allow us to put a tight constraint on Omega0 for a flat Universe: Omega0=0.40^{+0.15}_{-0.12} 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 Lx-T relation was found to comply with the self-similar model for Omega0=0.4, Lambda=0.6. The constraint derived on Omega0 is in remarkable agreement with the constraint obtained from SNI or from combined analysis of the power spectrum of the 2dFGRS and the CMB anisotropy. ABRIDGED