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 semianalytically, combining a simple model for the cluster gas properties with the distribution functions of halo formation epochs proposed by Lacey & Cole and Kitayama & Suto. In contrast to several previous approaches that apply the Press-Schechter mass function in a straightforward manner, our method can take into account explicitly the temperature and luminosity evolution of clusters. In order to make quantitative predictions in a specific cosmological context, me adopt cold dark matter universes. Assuming the baryon density parameter Omega(B) = 0.0125 h(-2) (h is the Hubble constant in units of 100 km s(-1) Mpc(-1)) and the COBE normalization of matter fluctuations, temperature and luminosity functions of X-ray clusters depend sensitively on the density parameter Omega(0). Allowing for several uncertainties in observational data as well as in our simplified assumptions, we conclude that Omega(0) similar to 0.2-0.5 and h similar to 0.7 CDM models with/without the cosmological constant reproduce simultaneously the observed temperature and luminosity functions of X-ray clusters at redshift z similar to 0.