Semianalytic Predictions for Statistical Properties of X-Ray Clusters of Galaxies in Cold Dark Matter Universes

Temperature and luminosity functions of X-ray clusters are computed semi-analytically, combining a simple model for the cluster gas properties with the distribution functions of halo formation epochs proposed by Lacey \\& Cole (1993) and Kitayama \\& Suto (1996). In contrast to several previous approaches which apply the Press--Schechter mass function in a straightforward manner, our method can explicitly take into account the temperature and luminosity evolution of clusters. In order to make quantitative predictions in a specific cosmological context, we adopt cold dark matter (CDM) universes. Assuming the baryon density parameter \\ ₁=0. 0125 h^-2 (h is the Hubble constant in units of 100 km\^-1\^-1) and the \ COBE normalization of matter fluctuations, temperature and luminosity functions of X-ray clusters depend sensitively on the density parameter \₀. Allowing for several uncertainties in observational data as well as in our simplified assumptions, we conclude that \₀ \ 0. 2-0. 5 and h\ 0. 7 CDM models with/without the cosmological constant reproduce simultaneously the observed temperature and luminosity functions of X-ray clusters at redshift z\0.