February5,2008 15:40 WSPC-ProceedingsTrimSize:9inx6in Plionis˙IDM2006 1 7 0 0 2 COSMOLOGY FROM XMM HIGH-Z AGN CLUSTERING n a ManolisPlionis1,2 &SpyrosBasilakos3 J 1 Institute of Astronomy & Astrophysics, National Observatory of Athens, Greece 4 2 INAOE, Puebla, Mexico 2 3 Academy of Athens,Athens, Greece 1 v We review the high-redshift X-ray selected AGN clustering, based on the 6 XMM/2dFsurvey,andcompareitwithother recentXMM-basedresults.Us- 9 ing the recent Hasinger et al. (2005) and La Franca et al. (2005) luminosity 6 functionswefindthatthespatialclusteringlengths,derivedusingLimber’sin- 1 versionequation,are∼17and20h−1Mpcforthesoftandhardbandsources 0 whiletheirmedianredshiftsarez¯∼1.2and0.8,respectively.Thecorrespond- 7 ingbiasfactorsatz=z¯are∼5.3±0.9and∼5.1±1.1,respectively. Within 0 theframeworkofaflatcosmologicalmodel wefindthat ourresultssupporta / modelwithΩm≃0.26,σ8≃0.75,h≃0.72,w≃−0.9(inexcellent agreement h with the 3 year WMAP results). We also find the present day bias of X-ray p AGNstobeb◦∼2. - o r 1. Introduction t s a Active Galactic Nuclei (AGN) can be detected out to high redshifts and : v thus their clustering properties can provide information on the large scale i structure, the underlying matter distribution and the evolution with red- X shift of the AGN phenomenon. Optically selected AGN surveys miss large r a numbersofdustysystemsandthereforeprovideabiasedcensusoftheAGN phenomenon.X-raysurveys,areleastaffectedbydustprovidinganefficient tool for compiling uncensored AGN samples over a wide redshift range. Early studies of the X-ray AGN clustering, using Einstein and ROSAT data, produced contradictory results (eg.;9;43;11;131). Recently, there has been an effort to address this confusing issue and determine the cluster- ing properties of both soft and hard X-ray selected AGNs, based on the new XMM and Chandra missions (eg.;46;47;7,8;21;36;1730). Most of these studies find a relatively largecorrelationlength for the high-z X-ray AGNs (eg.,;7;836).However,the recentXMM-COSMOSsurveyresults30 provided significantly smaller clustering lengths, opening again the contradiction realm. February5,2008 15:40 WSPC-ProceedingsTrimSize:9inx6in Plionis˙IDM2006 2 Fig.1. TheXMM/2dFsurveyangularcorrelationfunctionforthe2bandsconsidered. 2. The XMM/2df survey angular and spatial clustering The XMM-Newton/2dFsurveyis a shallow(2-10ksec per pointing) survey comprising of18 XMM-Newton pointings equally split between a Northern andSouthernGalacticregion.Duetoelevatedparticlebackgroundweanal- ysedatotalof13pointings.Afulldescriptionofthe datareduction,source detection and flux estimation are presented in Georgakakis et al.,1918 We derive the source logN-logS after constructing sensitivity maps in orderto estimate the areaofthe surveyaccessibleto point sourcesabovea given flux limit (see,78). In table 1 we also provide the effective flux-limit ofthe differentsurveys,estimated using the correspondingareacurves,by: Seff ≃ Ω S / Ω , where Ω is the survey solid angle of which the lim i lim,i i i flux limPit is S . P lim,i We calculate the angular correlation function using the estima- tor: w(θ) = f(N /N ) − 1, of which the uncertainty is: σ = DD DR w (1+w(θ))/N ,whereN andN arethe numberofdata-dataand DR DD DR dpata-random pairs, respectively, in the interval [θ−∆θ,θ+∆θ]. The nor- malization factor is f = 2N /(N −1), with N and N the total num- R D D R ber of data and random points, respectively. For each XMM pointing we produce 100 Monte Carlo random catalogues having the same number of points as the real data accounting also for the sensitivity variations across the surveyed area (for details see,78). We use a standard χ2 minimization procedure to fit the measured correlation function assuming a power-law form: w(θ) = (θ◦/θ)γ−1 and fixing γ to 1.8. The fitting is performed for ′′ ′′ angular separations in the range 40 −1000 The resulting raw values of θ◦ are corrected for the integral constraint and the amplification bias (for details see43 and8), althoughsuch correctionsare quite small. The final re- sults arepresentedin Table 1.Now,the spatialcorrelationfunction canbe modeledas(eg.14):ξ(r,z)=(r/r◦)−γ×(1+z)−(3+ǫ),whereǫparametrizes the clustering evolution model. For ǫ = γ −3 (ie., ǫ = −1.2 for γ = 1.8), February5,2008 15:40 WSPC-ProceedingsTrimSize:9inx6in Plionis˙IDM2006 3 Fig. 2. Left Panel: The expected z-distributions using the Hasinger et al23 soft-band luminosity function for the XMM/2dF survey (thick line), the XMM-COSMOSsurvey (blue long-dashed line) and the XMM-ELAIS-S1 survey (red short-dashed line). Right Panel: The corresponding redshift distributions using the LDDE hard-band luminosity function of La Franca et al.28 The histogram in the left panel corresponds to the dis- tributionof the X-raysources inthe ROSAT Lochman Deep Field,39 whilethat of the rightpanel onlimitedspectroscopicandphoto-zdataofour XMM/2dFsurvey. the clustering is constant in comoving coordinates, a model which appears to be appropriate for active galaxies (eg.26). In order to invert the angular correlation function to three dimensions we utilize Limber’s integral equation (eg.34). For a spatially flat Universe, Limber equation can be written as: ∞ 2 ∞ H◦ 1 dN w(θ)=2 E(z)dz ξ(r,z)du (1) c Z (cid:18)N dz (cid:19) Z 0 0 where the number of objects in a surveyof a solidangle Ω and within the s shell (z,z+dz), is given by: dN c =Ω x2φ(x) E−1(z) (2) s dz (cid:18)H◦(cid:19) with φ(x) the selection function and x the proper distance related to the redshift through (see34): c z du x(z)= with E(z)=[Ω (1+z)3+Ω ]1/2 , (3) m Λ H◦ Z0 E(u) Since we do not have complete redshift information for our sources we estimate dN/dz using the X-ray source luminosity function and folding in ∞ theareacurve,viathe relation:φ(x)= Φ(L ,z)dL,whereΦ(L ,z) Lmin(z) x x istheluminositydependentdensityevolRutionluminosity(LDDE)function. In the present analysis we use that of Hasinger et al.23 for the soft-band and that of La Franca et al.28 for the hard-band. In Fig. 2 we present the expected redshift distributions of the soft and hard X-ray sources for all three recent XMM based surveys together with February5,2008 15:40 WSPC-ProceedingsTrimSize:9inx6in Plionis˙IDM2006 4 Table 1. Correlation function analysis results with their 1σ uncertainties for the dif- ferentsurveysandX-raybands.Thecorrelationlengthsassumeaslopeγ=1.8. Band(keV) Survey # Sleifmf θ◦(′′) r◦(h−1 Mpc) z¯ 0.5-2 XMM/2dF 432 1.3×10−14 10.4±3 17±2.2 1.25 0.5-2 XMM-COSMOS 1037 1.9×10−15 1.9±0.3 9.3±0.7 1.33 0.5-2 XMM-ELAIS 395 4.5×10−15 5.2±3.8 13.8±4.5 1.32 2-8 XMM/2dF 177 4.6×10−14 22.2±9 20±3.7 0.80 4.5-10 XMM-COSMOS 151 1.6×10−14 6±2 12±1.8 0.89 2-10 XMM-ELAIS 205 1.8×10−14 12.8±7.8 17±4.6 0.88 the histogramof some limited spectroscopic and photo-z data (see caption fordetails).Itisevidentthatallthreesurveystracesimilardepthsalthough the XMM-COSMO andXMM-ELAISsurveyshaveaslightly largercontri- bution from z∼> 2 in the soft-band. The predicted median redshift of the three XMM surveys for the soft and hard sources are shown in table 1. Then the inversion of eq.(2), using the LDDE luminosity function, ǫ = −1.2, the concordance cosmologicalmodel, and integrating out to z =4.5, provides a correlationlength of r◦ ≃17±2.2h−1 Mpc and ≃20±3.7h−1 Mpc, for the soft and hard bands, respectively (the slight differences with respect to the Basilakoset al.,78 results are due to the different luminosity functions used and a better treatment of the errors). These results are in good agreement with the XMM-ELAIS results36 but significantly larger than the XMM-COSMOS30 results (see table 1). If we assume that all three XMM based surveys provide correct re- sults, and that their differences are due to the cosmic variance, we can volume weight them to obtain an averageestimate of the clustering length of the XMM point sources. The relative volume weights for the XMM- COSMOS, XMM-ELAIS and XMM/2dF surveys are 1:0.9687:0.8527 and 1:0.9947:0.701 for the soft and hard bands, respectively (we have not cor- rected for the slight differences of the hard-bands used in the three sur- veys). Doing so we obtain: hr◦i≃13.2 and 16.0h−1 Mpc, for the soft and hard bands, respectively. These large correlation lengths are comparable to those of Extremely Red Objects,20 of luminous radio sources (;37;3238) and of bright distant red galaxies.15 They are however, significantly larger than those derived from optical AGN surveys: r◦ ≃ 5.4− 8.6 h−1 Mpc (eg.;12;27;13;22;3544). February5,2008 15:40 WSPC-ProceedingsTrimSize:9inx6in Plionis˙IDM2006 5 3. Cosmological Constraints It is well known24 that according to linear biasing the correlationfunction of the mass-tracer (ξ ) and dark-matter one (ξ ), are related by: obj DM ξ (r,z)=b2(z)ξ (r,z) , (4) obj DM where b(z) is the bias evolution function. In this study we use the bias model of Basilakos & Plionis,34 We quantify the underlying matter distri- bution clusteringby presenting the spatialcorrelationfunction ofthe mass ξ (r,z) as the Fourier transform of the spatial power spectrum P(k): DM (1+z)−(3+ǫ) ∞ sin(kr) ξ (r,z)= k2P(k) dk , (5) DM 2π2 Z kr 0 where k is the comoving wavenumber and ǫ= −1.2, according to the con- stantincomovingcoordinatesclusteringevolutionmodel.As forthe power spectrum, we consider that of CDM models, where P(k) = P knT2(k) 0 with scale-invariant (n = 1) primeval inflationary fluctuations. In partic- ular, we use the transfer function parameterization as in,2 with the cor- rections given approximately by Sugiyama.41 Note that we also use the non-linear corrections introduced by Peacock & Dodds.33 We have cho- sen to use either the standard normalization given by: σ ≃ 0.5Ω−γ with 8 m γ ≃0.21−0.22w+0.33Ω ,45 or to leave σ a free parameter. m 8 Firstly, using equations (1), (4) and (5) and evaluating at z = z¯ we derive the bias factor of our sources at the corresponding redshift. We find b(z¯) ≃ 5.1±1.1 and ≃ 5.3±0.9 for the hard and soft bands respectively, which are significantly smaller than the values attributed to our work in Miyaji et al.30 Next, we utilize a χ2 likelihood procedure to compare the measured XMM soft source angular correlation function with the prediction of dif- ferent spatially flat cosmological models (see,56). In particular, we define the likelihoodestimator as:LAGN(c)∝exp[−χ2 (c)/2]with: χ2 (c)= AGN AGN n [w (θ ,c)−w (θ )/σ ]2, where c is a vector containing the cosmo- i=1 th i obs i i lPogical parameters that we want to fit and σ the observed angular corre- i lation function uncertainty. We assume a flat (Ω = 1) cosmology with tot primordial adiabatic fluctuations and baryonic density of Ω h2 ≃ 0.022 b (eg.;2540). In this case the corresponding vector is c ≡ (Ωm,w,σ8,h,b◦) andwedensely samplethe variousparameters.Note thatinordertoinves- tigate possible equations of state, we allow the parameter w to take values below -1, corresponding to the so called phantom cosmologies (eg.10). The resulting best fit parameters for ǫ = −1.2 and the Miyaji et al29 luminosityfunctionarepresentedinTable2.Inthefirsttworowswepresent February5,2008 15:40 WSPC-ProceedingsTrimSize:9inx6in Plionis˙IDM2006 6 Table 2. Cosmological parameters from the likelihood analysis. Errors of the fittedparametersrepresent1σuncertainties.Notethatthefittedparameterscor- respondtoresultsmarginalizedovertheparametersthatdonothaveerrorbars, forwhichweusethevalues indicated. Data Ωm σ8 w h b◦ XMM 0.31+−00..1068 0.93 w=−1 0.72+−00..0128 2.30+−00..7200 XMM/SNIa 0.28±0.02 0.95 −1.05+−00..1200 0.72 2.30 XMM 0.28±0.03 0.75±0.03 w=−1 0.72 2.0+−00..2205 XMM/SNIa 0.26±0.04 0.75 −0.9+−00..1005 0.72 2.0 resultsbasedonthe traditional45 σ normalization.Notethatourestimate 8 oftheHubble parameterhisinverygoodagreementwiththosederivedby the HST key project.16 Inthe lasttwo rowsofTable 2 we leaveσ free but 8 fix the Hubble constantto h=0.72.Inthis caseourfit providesaσ value 8 which is in excellent agreement with the recent 3-years WMAP results40 Therefore,allowingvaluesw<−1wecanderivea(Ω ,σ )relation,agood m 8 fit of which is provided by : σ =0.34(±0.01)Ω−γ(Ωm,w) (6) 8 m withγ(Ω ,w)=0.22(±0.04)−0.40(±0.05)w−0.052(±0.040)Ω .Notethat m m w is degenerate, within the 1σ uncertainty, with respect to Ω . Therefore, m in order to put further constraints on w we additionally use a sample of 172 supernovae SNIa of Tonry et al.42 The joined likelihood analysis is performed by marginalizing the X-ray clustering results over σ , h and b . The vector c 8 0 now becomes: c ≡ (Ω ,w). The SNIa likelihood function can m be written as: LSNIa(c) ∝ exp[−χ2 (c)/2], with: χ2 (c) = SNIa SNIa 172 logDth(z ,c)−logDobs(z )/σ 2, where D (z) is the dimensionless i=1 L i L i i L Plumino(cid:2)sity distance, DL(z) = H◦(1(cid:3)+z)x(z) and zi is the observed red- shift. The joint likelihood function peaks at: Ω = 0.26 ± 0.04 with m w = −0.90+0.1 . Using eq.(6) we find that the normalization of the power −0.05 spectrum that corresponds to these cosmological parameters is σ ≃ 0.73, 8 in excellent agreement with the recent 3-year WMAP results.40 Acknowledgments Many thanks are due to I. Georgantopoulos and A. Georgakakis. References 1. 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