The Clustering of XMM-Newton Hard X-ray Sources

This paper presents the clustering properties of hard (2-8 keV) X-ray selected sources detected in a wide field ($\approx \rm 2 deg^{2}$) shallow [$f_X(\rm 2-8 keV)\approx 10^{-14}\rm erg cm^{-2} s^{-1}$] and contiguous XMM-{\it Newton} survey. We perform an angular correlation function analysis using a total of 171 sources to the above flux limit. We detect a $\sim 4\sigma$ correlation signal out to 300 arcsec with $w(\theta < 300^{''})\simeq 0.13 \pm 0.03$. Modeling the two point correlation function as a power law of the form $w(\theta)=(\theta_{\circ}/\theta)^{\gamma-1}$ we find: $\theta_{\circ}=48.9^{+15.8}_{-24.5}$ arcsec and $\gamma=2.2\pm {0.30}$. Fixing the correlation function slope to $\gamma=1.8$ we obtain $\theta_{\circ}=22.2^{+9.4}_{-8.6}$ arcsec. Using Limber's intergral equation and a variety of possible luminosity functions of the hard X-ray population, we find a relatively large correlation length, ranging from $r_{\circ}\sim 9$ to 19 $h^{-1}$ Mpc (for $\gamma=1.8$ and the {\em concordance} cosmological model), with this range reflecting also different evolutionary models for the source luminosities and clustering characteristics. The relatively large correlation length is comparable to that of extremely red objects and luminous radio sources.