The Spatial Correlation Function from an X--ray Selected Sample of Abell Clusters

Abstract

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 $16.1\pm3.4\mpc$ with no significant clustering beyond $\simeq40\mpc$. 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 transverse directions. This can be characterised by the magnitude of pair--wise cluster peculiar velocities such anisotropy predicts, which we find to be $\simeq800{\rm km\,s^{-1}}$ 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. Therefore, we are 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.