The 3D soft X-ray cluster-AGN cross-correlation function in the ROSAT NEP survey
N. Cappelluti, H. Boehringer, P. Schuecker, E. Pierpaoli, C. R. Mullis, I. M. Gioia, J. P. Henry
aa r X i v : . [ a s t r o - ph ] A p r **FULL TITLE**ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION****NAMES OF EDITORS** The 3D soft X-ray cluster-AGN cross-correlation functionin the
ROSAT
NEP survey
N. Cappelluti , H. B¨ohringer P. Schuecker , E. Pierpaoli , ,C. R. Mullis , I. M. Gioia , J. P. Henry , Abstract.
X-ray surveys facilitate investigations of the environment of AGNs.Deep C handra observations revealed that the AGNs source surface density risesnear clusters of galaxies. The natural extension of these works is the mea-surement of spatial clustering of AGNs around clusters and the investigationof relative biasing between active galactic nuclei and galaxies near clusters.Themajor aims of this work are to obtain a measurement of the correlation length ofAGNs around clusters and a measure of the averaged clustering properties of acomplete sample of AGNs in dense environments. We present the first measure-ment of the soft X-ray cluster-AGN cross-correlation function in redshift spaceusing the data of the ROSAT -NEP survey. The survey covers 9 × aroundthe North Ecliptic Pole where 442 X-ray sources were detected and almost com-pletely spectroscopically identified. We detected a > σ significant clusteringsignal on scales s ≤ h − Mpc. We performed a classical maximum-likelihoodpower-law fit to the data and obtained a correlation length s =8.7 +1 . − . h − Mpcand a slope γ =1.7 +0 . − . ( 1 σ errors). This is a strong evidence that AGNs aregood tracers of the large scale structure of the Universe. Our data were com-pared to the results obtained by cross-correlating X-ray clusters and galaxies.We observe, with a large uncertainty, that the bias factor of AGN is similar tothat of galaxies.
1. Introduction
In the present paper, we concentrate on the study of the relative clustering be-tween X-ray selected AGNs and galaxy clusters. Our work improves on mostprevious work on the large-scale structure of X-ray selected AGNs in two im-portant aspects. First, with the exception of Mullis et al. (2004), our sample isthe only one that is spectroscopically complete (99.6%). Gilli et al. (2005) usedthe CDFS (35%) and the CDFN (50%). The Basilakos et al. (2005) sample hadalmost no spectroscopic redshifts. Yang et al. (2006) used the CLASXS sample(52% complete) and the CDFN (56% complete). Second, with the exception Max Planck Institute f¨ur Extraterrestrische Physik, Postfach 1312, 85741, Garching, Germany California Institute of Technology, Mail Code 130-33,Pasadena, CA 91125, USA Department of Astronomy, University of Michigan, 918 Dennison, 500 Church Street, AnnArbor, 48109-1042 Istituto di Radioastronomia INAF, Via P. Gobetti 101, 40129 Bologna, Italy Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Drive, Honolulu, HI 96822 Physics and Astronomy Department, University of Southern California, Los Angeles, CA 90089-0484, USA N. Cappelluti et al. of Mullis et al. (2004) and part of Yang et al. (2006), we measure a threedimensional redshift space correlation function as opposed to deprojecting thetwo dimensional angular correlation function.Another motivation for our work is that over the last several years, X-ray ob-servations revealed that a significant fraction of high- z clusters of galaxies showoverdensities of AGNs in their outskirts (i.e. between 3 h − Mpc and 7 h − Mpcfrom the center of the cluster) (Henry et al., 1991; Cappi et al., 2001; Ruderman& Ebeling 2005, Cappelluti et al., 2005, and references therein). These overden-sities were however detected in randomly selected archive targeted observationsof galaxy clusters. While these overdensities are highly significant (up to 8 σ )when compared to cluster-free fields, the incompleteness of the samples does notallow drawing any conclusion about the average clustering properties of AGNsaround clusters. The majority of the sources making these overdensities haveno spectroscopical identification and therefore any information on their spatialclustering is lost. More recently Branchesi et al. (2007) showed that at high- z the source surface density of AGNs significantly increases even in the centralregions of the clusters. These results imply that further progress will come fromstudying the three dimensional spatial distribution of AGNs around clusters. Anatural way to characterize this specific type of clustering is given by the three-dimensional cross -correlation of AGNs and galaxy clusters, the computation ofwhich needs complete redshift information for all objects, which is rare in X-raysurveys.
2. The Cluster AGN cross-correlation function
The cross-correlation function ξ CA of clusters and AGNs is defined by the jointprobability to find, at a distance r , one cluster in the infinitesimal comovingvolume element δV C and one AGN in the comoving volume element δV A , δ P = n C n A [1 + ξ CA ( r )] δV C δV A , where n C and n A are the mean comoving numberdensities of clusters and AGNs, respectively. In calculating the differential cross-correlation in redshift space we used an adapted version of the Landy–Szalayestimator (Landy & Szalay, 1993; see also e.g. Blake et al., 2006).We present the spatial cross-correlation function between clusters and AGNsin left panel of Fig. 1. A positive clustering signal is detected in the distanceinterval s ≤ h − Mpc. In order to test the strength of the clustering weperformed a canonical power-law fit, ξ CA ( s ) = ( ss ) − γ , with s and γ as freeparameters. The best fit parameters obtained are s =8.7 +1 . − . h − Mpc and γ =1.7 +0 . − . where the uncertainty is at the 1 σ confidence level. With γ fixed to1.8 (i.e. a typical value found in galaxy-galaxy correlation function) we find s ∼ . h − Mpc. A similar value was obtained by extending the fitting regionto 60 h − Mpc and restricting it to the 2.5–40 h − Mpc.
3. Discussion
We presented here the first direct evidence of spatial clustering of soft X-rayselected AGNs around X-ray selected clusters of galaxies. Indirect evidence waspresented by Henry et al. (1991), Cappi et al. (2001), Cappelluti et al. (2005) oft X-ray cluster-AGN cross-correlation Figure 1.
Lef t P anel : The Cluster-AGN soft X-ray cross correlation func-tion plus one. The error bars are quoted at 1 σ level. The dashed line rep-resents the best fit maximum-likelihood power-law fit s =8.7 +1 . − . h − Mpcand γ =1.7 +0 . − . . The shaded region illustrates the 1 σ confidence region of thepower-law fit in the distance range in which it was performed. Right P anel :The ratio between the observed
ROSAT
NEP ξ CA (s) and the best fit ξ CG (r)obtained by S´anchez et al. (2005). Errors are quoted at the 1 σ level. Theshaded region shows the expected level of b A b G ( s )=1 if the cross-correlationfunctions were compared in the same space. (and references therein). These authors found significant X-ray point sourceoverdensities (about a factor 2) around distant clusters of galaxies when com-pared to cluster-free fields. If the overdensities were at the cluster redshift theywould arise at scales smaller than ∼ h − Mpc. Since the correlation function isproportional to ( δρρ ) , a ξ CA =1 implies an overdensity of a factor 2 with respectto a randomly distributed field. We can conclude that, since the correlationlength found in this work reflects the scale of the overdensities known up tonow, we observe a physical overdensity (of at least a factor 2) of AGNs aroundclusters between 2 and ∼ h − Mpc from the center of the clusters.Because of the shallowness of the NEP survey, the AGN surface density (i.e. <
30 deg − in the central region) does not allow detection of such a correlationvia overdensity analysis since it would be dominated by small number statis-tics. In fact, from our results we expect to detect AGNs overdensities on scales < h − Mpc from the center of clusters. At < z > ∼ z of the cluster sample of the NEP survey) these overdensities arise on scalesof ∼ − which are easily resolved by the NEP survey. However to sig-nificantly detect these overdensity on single clusters, a conspicuous number ofsources is necessary to disentangle real overdensities from shot noise. As a finalcheck we compared our ξ CA to the X-ray cluster-galaxy cross-correlation func-tion (hereinafter CGCCF) computed by S´anchez et al. (2005). They used theX-ray selected clusters of the REFLEX survey (B¨ohringer et al. 2002) and thegalaxies from the APM survey (Maddox et al. 1990) limited to b j =20.5 mag.They found that the CGCCF behaves like a broken power-law with a cut-offdistance of ∼ h − Mpc with a steeper slope at small distances. We can define