THE LARGE-SCALE DISTRIBUTION OF X-RAY-CLUSTERS OF GALAXIES

CLUSTERS of galaxies are not distributed randomly in space, but are themselves clustered, reflecting inhomogeneities in the early Universe(1). The degree of clustering-usually expressed as a correlation length, which measures the characteristic scale for clustering-can therefore be used to determine the size of the initial density fluctuations that gave rise to the clusters(1-3). Optical studies of galaxy clusters(4-7) have indicated a correlation length that conflicts with the predictions of some theories of large-scale structure formation(1-3), leading to the suggestion that these optical samples are biased in that foreground or background galaxies not physi ically associated with a cluster are counted as part of it(8-10). Here we report a measurement of the correlation length for a sample of clusters that were selected based on their X-ray emission, which is free from the bias that is inherent to optical studies. We find a correlation length of 13-15 h(-1) Mpc, where h is the Hubble constant in units of 100 km s(-1) Mpc(-1). There is no evidence for clusters being significantly elongated along the line of sight, contrary to previous suggestions(11,12).