CONSTRAINTS ON LARGE-SCALE CLUSTERING FROM THE AUTOCORRELATION PROPERTIES OF THE X-RAY-BACKGROUND

We discuss expectations for the angular correlation function of intensity fluctuations of the extragalactic 2-10 keV X-ray background (XRB) in relation to the two-point spatial correlation functions, ζ(r), of X-ray sources. A simple analytic formula for the amplitude of intensity correlations, Γ(θ), holding in the low-redshift, small-separation approximation, is derived. The HEAO 1 A-2 upper limits on Γ(θ) have been exploited to derive constraints on the local ζ(r) functions of rich clusters of galaxies, of active galactic nuclei (AGNs), and on the AGN-cluster cross-correlation, as well as on evolution of the correlation functions with cosmic time. X-ray data are found to be compatible with the Bahcall and Soneira estimates of ζcluster-cluster as well as with the results of recent studies of quasars clustering. Constraints on evolution models are discussed.