Predicting the clustering of X-ray selected galaxy clusters in flux-limited surveys

We present a model to predict the clustering properties of X-ray selected c lusters in flux-limited surveys. Our technique correctly accounts for past light-cone effects on the observed clustering and follows the non-linear ev olution in redshift of the underlying dark matter correlation function and cluster bias factor. The conversion of the limiting flux of a survey into t he corresponding minimum mass of the hosting dark matter haloes is obtained by using theoretical and empirical relations between mass, temperature and X-ray luminosity of galaxy clusters. Finally, our model is calibrated to r eproduce the observed cluster counts adopting a temperature-luminosity rela tion moderately evolving with redshift, We apply our technique to three exi sting catalogues: the ROSAT Brightest Cluster Sample (BCS); the X-ray Brigh test Abell-type Cluster sample (XBACs); and the ROSAT-ESO Flux-Limited X-ra y sample (REFLEX). Moreover, we consider an example of possible future spac e missions with fainter limiting flux. In general, we find that the amplitu de of the spatial correlation function is a decreasing function of the limi ting flux and that the Einstein-de Sitter models always give smaller correl ation amplitudes than open or flat models with low matter density parameter Omega(om). In the case of the XBACs catalogue, the comparison with previou s estimates of the observational spatial correlation shows that only the pr edictions of models with Omega(om) = 0.3 are in good agreement with the dat a, while the Einstein-de Sitter models have too low a correlation strength. Finally, we use our technique to discuss the best strategy for future surv eys. Our results show that, to study the clustering properties of X-ray sel ected clusters, the choice of a wide area catalogue, even with a brighter l imiting flux, is preferable to a deeper, but smaller area, survey.