A&A 465, 35-40 (2007)
N. Cappelluti1 - H. Böhringer1 - P. Schuecker1 - E. Pierpaoli2,6 - C. R. Mullis3 - I. M. Gioia4 - J. P. Henry5,1
1 - Max Planck Institute für Extraterrestrische Physik, Postfach 1312, 85741 Garching, Germany
2 - California Institute of Technology, Mail Code 130-33, Pasadena, CA 91125, USA
3 - Department of Astronomy, University of Michigan, 918 Dennison, 500 Church Street, Ann Arbor, 48109-1042, USA
4 - Istituto di Radioastronomia INAF, via P. Gobetti 101, 40129 Bologna, Italy
5 - Institute for Astronomy, University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
6 - Physics and Astronomy Department, University of Southern California, Los Angeles, CA 90089-0484, USA
Received 27 June 2006 / Accepted 16 November 2006
Context. X-ray surveys facilitate investigations of the environment of AGNs. Deep Chandra observations have revealed that the AGN source surface density rises near clusters of galaxies. The natural extension of this finding is the measurement of spatial clustering of AGNs around clusters and the investigation of relative biasing between active galactic nuclei and galaxies near clusters.
Aims. We aim to measure the correlation length of AGNs around clusters and the average clustering properties of a complete sample of AGNs in a dense environment.
Methods. We present the first measurement of the soft X-ray cluster-AGN cross-correlation function in redshift space using the data of the ROSAT-NEP survey. The survey covers 9 9 deg2 around the North Ecliptic Pole where 442 X-ray sources were detected and almost completely spectroscopically identified.
Results. We detected a >3 significant clustering signal on scales s 50 h70-1 Mpc. We performed a classical maximum-likelihood power-law fit to the data and obtained a correlation length s0 = 8.7 +1.2-0.3 h70-1 Mpc and a slope = 1.7 +0.2-0.7 (1 errors).
Conclusions. This is strong evidence that AGNs are good tracers of the large scale structure of the Universe. Our data were compared to the results obtained by cross-correlating X-ray clusters and galaxies. We observe, with a large uncertainty, a similar behaviour of AGN clustering around clusters similar to the clustering of galaxies around clusters.
Key words: galaxies: clusters: general - galaxies: active - X-rays: galaxies: clusters - cosmology: large-scale structure of Universe - cosmology: dark matter
The current paradigm of galaxy formation assumes that all types of galaxies reside in dark matter (DM) haloes, and that the properties of these haloes determine to some extent the properties of the galaxies inside (White & Rees 1978). In general, the clustering amplitudes of haloes depend on halo mass. The relation between the clustering properties of both DM haloes and galaxies (biasing) should thus tell us something about the physical processes leading to the formation and evolution of galaxies. Clusters of galaxies are the highest peaks in the global mass distribution of the Universe and should follow a direct and simple biasing scheme - mainly related to the underlying primordial Gaussian random field (Kaiser 1987). A simple means towards a better understanding of galaxy biasing is thus provided by studies of the relative biasing between galaxies and clusters of galaxies.
As a first step, previous investigations estimated two-point statistics like the auto-correlation function (Mullis et al. 2004a; Gilli et al. 2005; Basilakos et al. 2005; Yang et al. 2006). They could show that, AGNs trace the underlying cosmic large-scale structure. In addition, the large-scale structure of X-ray selected galaxy clusters could be studied in some detail (e.g. Schuecker et al. 2001), but without investigating the link between clusters and AGNs.
In the present paper, we concentrate on the study of the relative clustering between X-ray selected AGNs and galaxy clusters. Our work improves on most previous work on the large-scale structure of X-ray selected AGNs in two important aspects. First, with the exception of Mullis et al. (2004a), our sample is the only one that is spectroscopically complete (99.6%). Gilli et al. (2005) used the CDFS (35%) and the CDFN (50%). The Basilakos et al. (2005) sample had almost no spectroscopic redshifts. Yang et al. (2006) used the CLASXS sample (52% complete) and the CDFN (56% complete).
Another motivation for our work is that over the last several years, X-ray observations revealed that a significant fraction of high-z clusters of galaxies show overdensities of AGNs in their outskirts (i.e. between 3 h70-1 Mpc and 7 h70-1 Mpc from the center of the cluster) (Henry et al. 1991; Cappi et al. 2001; Ruderman & Ebeling 2005; Cappelluti et al. 2005, and references therein). These overdensities were however detected in randomly selected archive targeted observations of galaxy clusters. While these overdensities are highly significant (up to 8) when compared to cluster-free fields, the incompleteness of the samples does not allow one to draw any conclusion about the average clustering properties of AGNs around clusters. The majority of the sources making these overdensities have no spectroscopic identification and therefore any information on their spatial clustering is lost. More recently Branchesi et al. (2007) showed that at high-z the source surface density of AGNs significantly increases, even in the central regions of the clusters. These results imply that further progress will come from studying the three dimensional spatial distribution of AGNs around clusters. A natural way to characterize this specific type of clustering is given by the three-dimensional cross-correlation of AGNs and galaxy clusters, the computation of which needs complete redshift information for all objects, which is rare in X-ray surveys.
In this respect, the ROSAT North Ecliptic Pole (NEP) survey (Henry et al. 2001, 2006; Voges et al. 2001) is one of the few X-ray surveys covering a sufficiently large volume with an almost complete follow-up identification of AGNs and clusters (i.e. 440 sources spectroscopically identified of 442 detected). This survey thus provides a very useful basis for more precise investigations of the relative clustering properties of these two types of objects.
We organized the present paper in the following way. In Sect. 2, we describe the ROSAT-NEP survey data that we use for our investigations of the spatial distribution of X-ray selected AGNs and galaxy clusters. For the statistical analysis we estimate their cross-correlation. A useful estimator for this statistic and the mock samples needed for its determination are described in Sects. 3 and 4, respectively. The results are presented in Sect. 5, and are discussed in Sect. 6. In this paper, we assume a (concordance) Friedmann-Lemaitre Universe characterized by the Hubble constant given in units of , the normalized cosmic matter density , and the normalized cosmological constant . Unless otherwise stated, errors are reported at the confidence level.
The ROSAT NEP survey covers a region of 9 9 deg2around the North Ecliptic Pole (17 , 62 ) observed with the PSPC proportional counter as part of the ROSAT All Sky Survey (Henry et al. 2001; Voges et al. 2001) with a flux limit of 2 10-14 erg cm-2 s-1 in the 0.5-2 keV energy band. 442 X-ray sources were detected and 440 optically identified. Spectroscopic redshift information is available for 219 AGNs and 62 clusters of galaxies. The clusters have redshifts 0.81 with a median of 0.18 and the AGNs have 3.889 with a median of 0.4 (Fig. 1). For the purpose of this work we selected all the clusters and the 185 AGNs with 1 (Gioia et al. 2003).
Such a dataset was used also by Mullis et al. (2004a) for the calculation of the 3-D auto correlation function of X-ray selected AGNs. Mullis and collaborators find significant clustering on scales smaller than 43 h70-1 Mpc with a correlation length of 10.4 h70-1 Mpc, and a slope of the correlation best-fit power law of = 1.8.
The cross-correlation function
of clusters and AGNs is
defined by the joint probability of finding, at a distance r, one cluster in the infinitesimal comoving volume element
and one AGN in the comoving volume element
|Figure 1: Top panel: the redshift distribution of the AGNs in the NEP survey ( shaded histogram) and of the randomly generated AGNs with the same selection effects ( filled histogram). Bottom panel: the redshift distribution of the galaxy clusters in the NEP survey ( shaded histogram) and of randomly generated clusters ( filled histogram). The deviations at low z between the data and the random sample are mainly caused by the NEP supercluster of galaxies (Mullis et al. 2001).|
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Equation (2) indicates that an accurate estimate of the
distribution function of the random samples is crucial in order to
obtain a reliable estimate of
Several effects must be taken
into account when generating a sample of objects in a flux limited survey.
Simulated AGNs were randomly placed within the ROSAT NEP survey area.
In order to reproduce the flux distribution of the real sample, we followed
the method of Mullis et al. (2004a). In practice, since the cumulative AGN
source count distribution can be described by a power law,
the differential probability scales as
Using a transformation method (e.g. Press et al. 1986, Chap. 7) we see that the
random flux above a certain X-ray flux
is distributed as
where p is a random number uniformly
distributed between 0 and 1 and
10-14 erg cm-2 s-1, i.e. the flux limit of the NEP survey. All random AGNs
with a flux lower than the flux limit map (see Fig. 4 in Henry et al. 2006) at the source position were excluded. In order to assign a redshift to these "sources'' we computed the predicted redshift distribution at the position of each accepted source. Once the flux limit
at the position where the source was randomly placed is known,
and denoting with
the luminosity function,
then the number of sources per redshift interval dz is given by
|Figure 2: The cluster-AGN soft X-ray cross correlation function plus one. The error bars are quoted at 1 level. The dashed line represents the best fit maximum-likelihood power-law fit s0=8.7 +1.2-0.3 h70-1 Mpc and = 1.7 +0.2-0.7. The shaded region illustrates the 1 confidence region of the power-law fit in the distance range in which it was performed.|
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We present the spatial cross-correlation function between clusters and AGNs in
Fig. 2. A positive clustering signal is detected in the
h70-1 Mpc. In order to test the strength of
the clustering we performed a canonical power-law fit,
|Figure 3: The distribution of the angular radial separations translated into redshift space distances at = 0.38.|
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|Figure 4: The 1, 2 and 3 confidence contours in the space for the power-law fit to for two interesting parameters. The cross represents the best fit values.|
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The integral constraint (Peebles 1980), which is a systematic shift in correlation functions introduced by the limited volume observed, was computed following the prescription of Roche et al. (1993). This can be obtained numerically with a fit by assuming that the correlation function is represented by a power law of fixed index (here we used = 1.7) on all scales sampled by the survey. The underestimate of due to the integral constraint is found to be of the order of 2%.
In order to determine the stability of these results the procedure was repeated first by separating the field in two subfields twice, the North and South, and West and East parts of the survey. The fluctuations due to sample variance are found to be smaller than the typical amplitude of the uncertainties. A similar result is obtained by recomputing the for clusters with 0.18 (i.e. the cluster median redshift) and z>0.18. The dependence of on the cluster X-ray luminosity () was evaluated, dividing the cluster sample into two subsamples with h70-2 erg s-1. Though no significant dependent behaviour was detected, we cannot yet conclude that there is no luminosity or redshift dependent cross-correlation length because of the statistics of the sub-samples. The stability of the result was also checked by fitting the data with the likelihood estimator used by Mullis et al. (2004a), returning no significant deviations from our results at a 1-2 level.
We presented here the first direct evidence of spatial clustering of soft X-ray selected AGNs around X-ray selected clusters of galaxies. Indirect evidence was presented by Henry et al. (1991), Cappi et al. (2001), Cappelluti et al. (2005) (and references therein). These authors found significant X-ray point source overdensities (about a factor 2) around distant clusters of galaxies when compared to cluster-free fields. If the overdensities were at the cluster redshift they would arise at scales smaller than 7 h70-1 Mpc. Since the correlation function is proportional to , a = 1 implies an overdensity of a factor of 2 with respect to a randomly distributed field. We can conclude that, since the correlation length found in this work reflects the scale of the overdensities known up to now, we observe a physical overdensity (of at least a factor of 2) of AGNs around clusters between 2 and 8 h70-1 Mpc from the center of the clusters.
Because of the shallowness of the NEP survey, the AGN surface density
(i.e. <30 deg2 in the central region) does not allow detection of such a correlation via overdensity analysis since it
would be dominated by small number statistics. From our results we expect to detect
AGN overdensities on scales <7-8
h70-1 Mpc from the center of clusters. At
0.18 (i.e. the
median z of the cluster sample of the NEP survey) these overdensities arise on scales
of 0.6 deg-2 which are easily resolved by the NEP survey.
However, to significantly detect these overdensity on single clusters,
a large number of sources is necessary to disentangle real overdensities
from shot noise. This problem could be easily resolved
by high angular resolution telescopes like Chandra and partially by XMM-Newton.
In this direction deep and wide Chandra and XMM-Newton surveys like COSMOS,
which will return an AGN surface density of up to 2700 deg-2,
would allow seeing in a 0.015 deg2 region (i.e. the size of an ACIS-I chip) a population of at least 40 AGNs belonging to the cluster environment (i.e. assuming an average overdensity of a factor 2, we expect 40 sources belonging
to the cluster and 40 to the background).
As an example, at the limiting flux of the C-COSMOS survey, the AGN population of a cluster at z = 1 would be observed with a 0.5-2 keV limiting luminosity
1042 erg s-1.
At z = 1 the size of an ACIS chip (i.e. 8 arcmin) corresponds to a linear dimension
h70-1 Mpc. Having 40 AGNs in a sphere with this radius corresponds to a space density of AGN with
According to the result presented here,
clusters of galaxies could be detected by AGN overdensities (rather than
galaxy overdensities) if the depth of the survey provides
an AGN surface density sufficient to overcome the Poisson noise on the AGN number.
In general, in order to understand the galaxy evolution in dense environments
the measure of cross correlation between clusters and different kind of galaxies is an important tool. We already know that infrared dusty galaxies avoid dense environments,
therefore showing a large cross-correlation length and a weak clustering signal in the small
separations region (Sánchez et al. 2005).
We also know that blue galaxies avoid low-z rich clusters cores (Butcher & Oemler 1984).
It is therefore important to compare the cluster-AGN cross correlation length to that of
clusters and different galaxy types.
Mo et al. (1993) computed the cross-correlation function of Abell clusters
and QDOT IRAS galaxies. They found an average correlation length and
a slope in agreement with the results presented here. Moreover
Lilje & Efstathiou (1988) showed that the cross-correlation function of Abell clusters with Lick galaxies is positive on scales 29
h70-1 Mpc with a slope
2.2 and a correlation length of 12.6
h70-1 Mpc. These results are also in
agreement within 1
with our findings on AGNs. These
first comparisons suggest that AGNs are clustered around
galaxy clusters just like galaxies.
As a final check we compared our
to the X-ray cluster-galaxy cross-correlation
function (hereinafter CGCCF) computed by Sánchez et al. (2005).
They used the X-ray selected clusters of the REFLEX survey (Böhringer et al. 2002)
and the galaxies from the APM survey (Maddox et al. 1990) limited to bj = 20.5 mag.
They found that the CGCCF behaves like a broken power-law with a cut-off
distance of 2
h70-1 Mpc with a steeper slope at small distances.
We can define the following approximate biasing relations:
|Figure 5: The ratio between the observed ROSAT NEP and the best fit obtained by Sánchez et al. (2005). Errors are quoted at the 1 level. The shaded region shows the expected level of = 1 if the cross-correlation functions were compared in the same space.|
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We derived for the first time the soft X-ray spatial cross-correlation function between clusters and AGNs using the data of the ROSAT NEP survey. A strong clustering signal was detected on scale s< 50 h70-1 Mpc. The best power-law fit parameters are s0 = 8.7 +1.2-0.3 h70-1 Mpc and = 1.7 +0.2-0.7. In this work we observed that the source density of AGNs is higher near clusters than in the field. This result confirms earlier findings of overdensities of AGNs around clusters reported by many authors and improves the evidence connecting the overdensities to the large scale structure of the Universe. We also derived the relative bias between AGNs and galaxies which is consistent with one on almost all scales investigated here. This result still allows, within the errors, a factor of 2 fluctuation. New wide field surveys (such as XMM-COSMOS) performed with the new generation X-ray telescopes will be useful to enlarge the statistics, to better understand the physics of AGNs in clusters and to extend the analysis to the inner regions of clusters.
N.C. thanks Günther Hasinger for useful discussions, and Marica Branchesi for advanced communication of her results. E.P. is an ADVANCE fellow (NSF grant AST-0340648), also supported by NASA grant NAG5-11489. J.P.H. thanks the Alexander von Humboldt Foundation for support to visit the MPE. We also thank the anonymous referee for her/his useful comments and suggestions.
In memory of Peter Schuecker.