Cosmological constraints from the clustering properties of the X-ray Brightest Abell-type Cluster sample

We present an analysis of the two-point correlation function, xi(r), of the X-ray Brightest Abell-type Cluster sample (XBACs) of Ebeling et al, and of the cosmological constraints that it provides. If xi(r) is modelled as a p ower-law, xi(r) = (r(0)/r)(gamma), we find r(0) similar or equal to 26.0 +/ - 4.5 h(-1) Mpc and gamma similar or equal to 2.0 +/- 0.4, with errors corr esponding to 2 sigma uncertainties for one significant fitting parameter. A s a general feature, xi(r) is found to remain positive up to r similar or e qual to 50-55 h(-1) Mpc, after which it declines and crosses zero. Only a m arginal increase of the correlation amplitude is found as the Aux limit is increased from 5 x 10(-12) to 12 x 10(-12) ergs s(-1) cm(-2), thus indicati ng a weak dependence of the correlation amplitude on the cluster X-ray lumi nosity. Furthermore, we present a method to predict correlation functions f or flux-limited X-ray cluster samples from cosmological models. The method is based on the analytical recipe by Mo & White and on an empirical approac h to convert cluster fluxes into masses. We use a maximum likelihood method to place constraints on the model parameter space from the XBACs xi(r) For scale-free primordial spectra, we find that the shape parameter of the pow er spectrum is determined to lie in the 2 sigma range 0.05 less than or sim ilar to Gamma less than or similar to 0.20. As for the amplitude of the pow er spectrum, we find sigma(8) = 0.4-0.8 for Ohm(0) = 1 and sigma(8) = 0.8-2 .0 for Ohm(0) = 0.3. The latter result is in complete agreement with, altho ugh less constraining than, results based on the local cluster abundance.