ANGULAR-CORRELATIONS OF THE X-RAY-BACKGROUND AND CLUSTERING OF EXTRAGALACTIC X-RAY SOURCES

The information content of the autocorrelation function (ACF) of inten sity fluctuations of the X-ray background (XRB) is analyzed. The tight upper limits set by ROSAT deep survey data on the ACF at arcminute sc ales imply strong constraints on clustering properties of X-ray source s at cosmological distances and on their contribution to the soft XRB. If quasars have a clustering radius r0 = 12-20 Mpc (H-0 = 50), and th eir two-point correlation function, xi(r), is constant in comoving coo rdinates (epsilon = - 1.2), as indicated by optical data, they cannot make up more than 40%-50% of the soft XRB (higher contributions corres ponding to lower r0); the maximum contribution may reach 80% in the ca se of stable clustering (epsilon = 0). If r0 greater-than-or-equal-to 12 Mpc, a slow decrease of the xi(r) of the AGNs with increasing redsh ift (epsilon congruent-to - 3) is ruled out since it would imply an im plausibly low contribution to the XRB. Active star-forming (ASF) galax ies clustered like normal galaxies (r0 congruent-to 12 Mpc) can yield up to 20% or up to 40% of the soft XRB for epsilon = - 1.2 or epsilon = 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 lim its on scales of a few degrees imply that hard X-ray-selected AGNs hav e r0 less-than-or-equal-to 25 Mpc if epsilon = 0 or r0 less-than-or-eq ual-to 20 Mpc if epsilon = - 1.2. No significant constraints are set o n clustering of ASF galaxies, due to their low local volume emissivity . The possible signal on scales greater-than-or-equal-to 6-degrees, if real, may be due to AGNs with r0 congruent-to 20 Mpc; the contributio n from clusters of galaxies with r0 congruent-to 50 Mpc is a factor co ngruent-to 2 lower. Other classes of sources clustered like normal gal axies could only account for such signal if their local volume emissiv ity is almost-equal-to 6 x 10(38) ergs s-1 Mpc-3. This limit is lower than the values indicated by recent, indirect, estimates and implies t hat the bulk of the XRB is not local. We have also computed the expect ed ACF in the 2-10 keV energy band on arcminute scales, that will be u seful for comparison to the upcoming data from the Astro-D satellite. Although the nature of sources producing the bulk of the soft and of t he hard XRB is likely to be different, their clustering properties app ear to be not much different from those of normal galaxies.