X-RAY-CLUSTERS AND GRAVITATIONAL-INSTABILITY THEORIES

We discuss the expected evolution of X-ray clusters of galaxies in dif ferent models for structure formation: these are cold dark matter, hyb rid, and baryonic isocurvature models. We compare the theoretical pred ictions with the observed X-ray local luminosity function and with the counts obtained from the Extended Medium Sensitivity Survey (EMSS) of the HEAO 2 satellite. For properly comparing our predictions with the EMSS data we apply several corrections to the theoretical X-ray lumin osities and fluxes. We find that the most effective correction comes f rom considering the finite size of the EMSS detection cell in the HEAO 2 Imaging Proportional Counter cluster images. The available X-my dat a are extremely selective. They allow to reject baryonic isocurvature models, as well as hybrid models where hot dark matter provides approx imately 30% of the critical density. The model which performs by far b etter than the others considered here is a low-density (OMEGA0 = 0.2 h = 0.75) vacuum-dominated cold dark matter model with an initial scale -free density fluctuation spectrum. In all models, the brighter X-ray clusters are rare objects originating from the high peaks of the initi al density field. This implies that optical galaxies are biased tracer s of the mass density field, unless the cluster collapse occurs on tim escales longer than those of the ideal pressureless sphere. We discuss our results in the light of the COBE-DMR detection of large scale ani sotropy of the cosmic microwave background.