X-RAY-CLUSTERS AND GRAVITATIONAL-INSTABILITY THEORIES

We discuss the expected evolution of X-ray clusters of galaxies in different models for structure formation: these are cold dark matter, hybrid, and baryonic isocurvature models. We compare the theoretical predictions 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 luminosities and fluxes. We find that the most effective correction comes from considering the finite size of the EMSS detection cell in the HEAO 2 Imaging Proportional Counter cluster images. The available X-my data are extremely selective. They allow to reject baryonic isocurvature models, as well as hybrid models where hot dark matter provides approximately 30% of the critical density. The model which performs by far better 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 initial density field. This implies that optical galaxies are biased tracers of the mass density field, unless the cluster collapse occurs on timescales longer than those of the ideal pressureless sphere. We discuss our results in the light of the COBE-DMR detection of large scale anisotropy of the cosmic microwave background.