The correlation function of X-ray galaxy clusters in the ROSAT All-Sky Survey 1 Bright Sample

We analyse the spatial clustering properties of the ROSAT All-Sky Survey (R ASS) 1 Bright Sample, an X-ray flux-limited catalogue of galaxy clusters se lected from the southern part of the survey. The two-point correlation func tion xi(r) of the whole sample is well fitted (in an Einstein-de Sitter mod el) by the power law xi=(r/r(0))(-gamma), with r(0) = 21.5(-4.4)(+3.4) h(-1 ) Mpc and gamma=2.11(-0.56)(+0.53) (95.4 per cent confidence level with one fitting parameter). We use the RASS 1 Bright Sample as a first application of a theoretical model that aims to predict the clustering properties of X -ray clusters in flux-limited surveys for different cosmological scenarios. The model uses the theoretical and empirical relations between mass, tempe rature and X-ray cluster luminosity, and fully accounts for the redshift ev olution of the underlying dark matter clustering and cluster bias factor. T he comparison between observational results and theoretical predictions sho ws that the Einstein-de Sitter models display too low a correlation length, while models with a matter density parameter Omega(0m)=0.3 (with or withou t a cosmological constant) are successful in reproducing the observed clust ering. The dependence of the correlation length r(0) on the X-ray limiting flux and luminosity of the sample is generally consistent with the predicti ons of all our models. Quantitative agreement is however only reached for O mega(0m)=0.3 models. The model presented here can be reliably applied to fu ture deeper X-ray cluster surveys: the study of the clustering properties w ill provide a useful complementary tool to the traditional cluster abundanc e analyses used to constrain the cosmological parameters.