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 clusters in flux-limited surveys. Our technique correctly accounts for past light-cone effects on the observed clustering and follows the non-linear evolution in redshift of the underlying dark matter correlation function and cluster bias factor. The conversion of the limiting flux of a survey into the 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 reproduce the observed cluster counts adopting a temperature-luminosity relation moderately evolving with redshift, We apply our technique to three existing catalogues: the ROSAT Brightest Cluster Sample (BCS); the X-ray Brightest Abell-type Cluster sample (XBACs); and the ROSAT-ESO Flux-Limited X-ray sample (REFLEX). Moreover, we consider an example of possible future space missions with fainter limiting flux. In general, we find that the amplitude of the spatial correlation function is a decreasing function of the limiting flux and that the Einstein-de Sitter models always give smaller correlation amplitudes than open or flat models with low matter density parameter Omega(om). In the case of the XBACs catalogue, the comparison with previous estimates of the observational spatial correlation shows that only the predictions of models with Omega(om) = 0.3 are in good agreement with the data, while the Einstein-de Sitter models have too low a correlation strength. Finally, we use our technique to discuss the best strategy for future surveys. Our results show that, to study the clustering properties of X-ray selected clusters, the choice of a wide area catalogue, even with a brighter limiting flux, is preferable to a deeper, but smaller area, survey.