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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 cosmologicalmodels, the derived emission measure profiles are scaled according to theself-similar model of cluster formation. We use the standard scaling relationsof cluster properties with z and temperature, with the empirical slope of theMgas-T relation derived by Neumann & Arnaud (2001). Using a \chi^2 test, weperform a quantitative comparison of the scaled emission measure profiles ofdistant clusters with a reference profile derived from the sample of 15 hotnearby clusters compiled by Neumann & Arnaud (1999), which were found to obeyself-similarity. For a low density flat universe, the distant cluster scaleddata were found to be consistent, both in shape and normalisation, with thereference local profile.It indicates that hot clusters constitute a homologousfamily up to high z, and supports the standard picture of structure formationfor the dark matter component. Because of the intrinsic regularity in the hotcluster population, the scaled profiles can be used as distance indicators, thecorrect cosmology being the one for which the profiles at different redshiftscoincide. The present data allow us to put a tight constraint on Omega0 for aflat Universe: Omega0=0.40^{+0.15}_{-0.12} at 90% confidence level (statisticalerrors only). The critical model was excluded at the 98% confidence level.Consistently, the observed evolution of the normalisation of the Lx-T relationwas found to comply with the self-similar model for Omega0=0.4, Lambda=0.6. Theconstraint derived on Omega0 is in remarkable agreement with the constraintobtained from SNI or from combined analysis of the power spectrum of the 2dFGRSand the CMB anisotropy. ABRIDGEDComment: Astronomy & Astrophysics in press; revision: further discussion added  section 3.1, 4.2, 5.2 and 7.2; analytical fit of the reference profile given  in Appendix; 18 pages, 6 figure

The X-ray surface brightness profiles of hot galaxy clusters up to $\vec z$ ~ 0.8: Evidence for self-similarity and constraints on $\Omega_\mathsf{0}$