The spatial correlation function from an X-ray selected sample of Abell clusters

We present here the spatial two-point correlation function for a complete sample of 67 X-ray-selected Abell clusters of galaxies. We find a correlation length of $$16.1\pm 3.4\enspace h^{-1}$$ Mpc, with no significant clustering beyond $$\simeq 40\enspace h^{-1}$$ Mpc. This is the lowest uncorrected value for the correlation length ever derived from the Abell catalogue of clusters. In addition, we have investigated the anisotropy of the correlation function between the radial and tranverse directions. This can be characterized by the magnitude of pairwise cluster peculiar velocities such anisotropy predicts, which we find to be $$\simeq 800\enspace\text {km s}^{-1}$$ for our sample. Again this is the lowest uncorrected value ever seen for the Abell catalogue. We therefore no longer need to invoke high cluster peculiar velocities or line-of-sight clustering to understand the correlation function as derived from an Abell sample of clusters. Furthermore, our result is consistent with recently published correlation functions computed from automated selections of optical and X-ray clusters. We are therefore now approaching a coherent picture for the form of the cluster spatial correlation function, which will be used to place confident constraints on theories of galaxy formation.