Angular Correlations of the X–ray Background and Clustering of Extragalactic X–ray Sources

The information content of the autocorrelation function (ACF) of intensity fluctuations of the X–ray background (XRB) is analyzed. The tight upper limits set by ROSAT deep survey data on the ACF at arcmin scales imply strong constraints on clustering properties of X–ray sources at cosmological distances and on their contribution to the soft XRB. If quasars have a clustering radius r0 = 12–20 Mpc (H0 = 50), and their two point correlation function, ξ(r), is constant in comoving coordinates (ǫ = −1.2), as indicated by optical data, they cannot make up more 40– 50% of the soft XRB (higher contributions corresponding to lower r0); the maximum contribution may reach 80% in the case of stable clustering (ǫ = 0). If r0 ≥ 12Mpc, a slow decrease of the ξ(r) of the AGNs with increasing redshift (ǫ ≃ −3) is ruled out since it would imply an implausibly low contribution to the XRB. Active Starforming (ASF) galaxies clustered like normal galaxies (r0 ≃ 12Mpc) can yield up to 20% or up to 40% of the soft XRB for ǫ = −1.2 or ǫ = 0, respectively. The ACF on degree scales, typical of existing hard X–ray surveys, essentially reflects the clustering properties of local sources and is proportional to their volume emissivity. The upper limits on scales of a few degrees imply that hard X–ray selected AGNs have r0 ≤ 25Mpc if ǫ = 0 or r0 ≤ 20Mpc if ǫ = −1.2. No significant constraints are set on clustering of ASF galaxies, due to their low local volume emissivity. The possible signal on scales ≥ 6, if real, may be due to AGNs with r0 ≃ 20Mpc; the contribution from clusters of galaxies with r0 ≃ 50Mpc is a factor ≃ 2 lower. Other classes of sources clustered like normal galaxies could only account for such signal if their local volume emissivity is ≈ 6 × 10 erg s Mpc. This value is somewhat in contrast with larger estimates based on alternative methods, and implies that the bulk of the XRB is not local.