The ROSAT-ESO Flux Limited X-ray (REFLEX) Galaxy Cluster Survey II: The Spatial Correlation Function

We report the results of the spatial two-point correlation function xi® for the new X-ray galaxy cluster survey REFLEX, which comprises of 452 X-ray selected clusters (449 with redshifts) detected by the ROSAT satellite during the ROSAT All-Sky-Survey. The REFLEX cluster sample is flux limited to 3x10^{-12} erg s^{-1} cm^{-2} in the ROSAT energy band (0.1-2.4 keV) and spans 3 decades in X-ray luminosity (10^{42} - 10^{45} h^{-2} erg s^{-1}), containing galaxy groups and rich clusters out to a redshift z~0.3. Covering a contiguous area of 4.24 sr REFLEX is the largest X-ray cluster sample to date for which spatial clustering has been analysed. Correlation studies using clusters selected on the basis of their X-ray emission are particularly interesting as they are largely free from the projection biases inherent to optical studies. For the entire flux-limited sample we find that the correlation length (the scale at which the correlation amplitude passes through unity) r_0~20 h^{-1}Mpc. For example, if a power-law fit is made to xi® over the range 4-40 h^{-1} Mpc then r_0=18.8±0.9. An indication of the robustness of this result comes from the high degree of isotropy seen in the clustering pattern on scales close to the correlation length. On larger scales xi® deviates from a power-law, crossing zero at ~45h^{-1} Mpc. From an examination of 5 volume-limited cluster sub-samples we find no significant trend of r_0 with limiting X-ray luminosity. A comparison with recent model predictions for the clustering properties of X-ray flux-limited samples, indicates that Cold Dark Matter models with the matter density Omega_m=1 fail to produce sufficient clustering to account for the data, while Omega_m~0.3 models provide an excellent fit.