Introduction

The Autocorrelation Function (ACF) of the intensity fluctuations of the X-ray background (XRB) is an integrated view of the clustering properties of the source populations contributing to the XRB, so studies of the ACF provide information on the origin of the XRB as well as on clustering evolution of the underlying sources.

Recently ROSAT Deep Surveys have shown that about 40% of the soft XRB (E ≤ 3keV, henceforth SXRB) is contributed by sources brighter than S(0.5–2keV) ≥ 7 × 10−15 erg s−1 cm−2 (Hasinger et al. 1991; Shanks et al. 1991). On the other hand only a few percent of the hard XRB (3 < E < 60keV, henceforth HXRB) has already been resolved into sources. ROSAT observations also show that the SXRB is actually very smooth on arcminute scales with a current upper limit on the ACF in the 0.9–2.4keV band W(9′) ≤ 2 × 10−3 (Hasinger 1992). As regards the HXRB, the results of the ACF analyses on sub-degree angular scales have been used to put significant constraints on clustering of AGNs and galaxy clusters (Martín-Mirones et al. 1991; Carrera et al. 1992). Here we will discuss data on ACFs to obtain limits on clustering, clustering evolution and volume emissivity of X-ray sources contributing to the SXRB and HXRB.

Constraints on the clustering scale and the clustering evolution of AGNs and on their contribution to the XRB

Recent analyses of large samples of optically selected QSOs have produced consistent values of the clustering scale, 12 ≲ r0 ≲ 20 Mpc (H0 = 50kms−1 Mpc−1), and of the evolution of the correlation function with ∈ ≥ −1.2, a constant comoving clustering scale being slightly favoured (Boyle 1991; Andreani & Cristiani 1992).