PreprinttypesetusingLATEXstyleemulateapjv.10/10/03 EVOLUTION OF THE CLUSTER X-RAY LUMINOSITY FUNCTION C.R. Mullis1, A. Vikhlinin2,3, J.P. Henry4, W. Forman2, I.M. Gioia5, A. Hornstrup6, C. Jones2, B.R. McNamara7, and H. Quintana8 To appear in the Astrophysical Journal ABSTRACT We report measurements of the cluster X-ray luminosity function out to z = 0.8 based on the final sample of 201 galaxy systems from the 160 Square Degree ROSAT Cluster Survey. There is little evidence for any measurable change in cluster abundance out to z ∼ 0.6 at luminosities less than a few times 1044 h−2 ergs s−1 (0.5–2.0 keV). However,between0.6 3σ regardless of the adopted local luminosity function or cosmological n framework. Our results and those from several other surveys independently confirm the presence a of evolution. Whereas the bulk of the cluster population does not evolve, the most luminous and J presumably most massivestructures evolveappreciably between z =0.8 andthe present. Interpreted 9 in the context of hierarchicalstructure formation,we are probing sufficiently large mass aggregations 2 atsufficientlyearlytimesincosmologicalhistorywheretheUniversehasyettoassembletheseclusters to present-day volume densities. 1 Subject headings: cosmology: observations — galaxies: clusters: general — X-rays: general v 5 0 1. INTRODUCTION lection functions, it is straight-forward to convert these 6 numbercountsintovolume-normalizedmeasuressuchas 1 Galaxy clusters form via the gravitational amplifica- the luminosity function. Finally, given the strong corre- 0 tionofrare,highpeaksinthecosmicmatterdensityfield. lation between X-ray luminosity and cluster mass, it is 4 The redshift evolution of cluster abundance depends on possible to transform the observed XLF into the cluster 0 thegrowthrateofdensityperturbationswhichis,inturn, mass function which is the fundamental relation in the / sensitive to the mean cosmic matter density (Ω ) and, h M theoretical treatment. to a lesser extent, the dark-energy density (Ω ). Thus p Λ Though the cluster XLF was first measured with observationsof cluster space density with sufficient tem- - an X-ray flux-limited sample over two decades ago o poral sampling can provide powerful cosmological con- r straints(e.g.,Oukbir & Blanchard1992;Eke et al.1998; (Piccinotti et al. 1982), a definitive characterization of t its evolution has proven very difficult. The latter is a s Bahcall et al. 1999). a particularly important test in observational cosmology A directly measurable androbustdiagnostic of cluster : because the variation of the cluster XLF as a function v abundance is the X-ray luminosity function (XLF), that ofredshiftreflectstheevolutionoftheclustermassfunc- i is the volume density of clusters per luminosity interval. X tion. SuchameasureallowsforstrongconstraintsonΩ X-rayselectedgalaxyclustersareparticularlywell-suited M r forthis type ofanalysis. Clusters areefficiently detected even accounting for uncertainty in the luminosity-mass a relation(e.g.,Borgani et al.2001). Earlytheoreticalpre- at X-ray wavelengths to high redshift (currently out to dictions (e.g., Kaiser 1986) postulated dramatic positive z ∼ 1.25) thus providing the leverage for evolutionary evolution in the XLF where the volume density of clus- studies(seereviewbyRosati, Borgani, & Norman2002). ters of a fixed luminosity would increase with redshift. The resulting samples feature high statistical complete- This would be an “observer-friendly” universe since the nesswhichisclearlyimportantforderivingreliablenum- lossinsensitivityathighredshiftinaflux-limitedsurvey ber counts. Since X-ray surveys have well-defined se- would be offset by the growing population of detectable 1 European Southern Observatory, Headquarters, Karl- sources. Contrary to this scenario, observations of the Schwarzschild-Strasse 2, Garching bei Mu¨nchen D-85748, Ger- clusterXLFrangefromzeroevolutionto negativeevolu- many,cmullis@eso.org tiondepending onthe redshiftsandluminositiesprobed. 2 Harvard-Smithsonian Center for Astrophysics, 60 Garden Thesefindingsareconsistentwithcurrentpredictionsfor Street,Cambridge,MA02138,USA 3 SpaceResearchInstitute,Profsoyuznaya84/32,Moscow,Rus- a low-density universe where mild negative evolution is sia restricted to the most luminous, high-redshift clusters 4InstituteforAstronomy,UniversityofHawai‘i,2680Woodlawn while there is little change in the bulk of the population Drive,Honolulu,HI96822,USA (e.g., Borgani & Guzzo 2001, and references therein). 5 Istituto di Radioastronomia del CNR-INAF,viaGobetti 101, Bologna,I-40129,Italy Taking advantage of the first time an X-ray sur- 6 Danish Space Research Institute, Juliane Maries Vej 30, vey extended into cosmologically interesting redshifts, Copenhagen 0,DK-2100,Denmark Gioia et al.(1990a)andHenry et al.(1992)used67clus- 7 Department of Physics and Astronomy, Ohio University, ters (0.14 < z < 0.60) from the pioneering Einstein Ex- Athens,OH45701, USA 8 DepartamentodeAstronomiayAstrofisica,PontificiaUniver- tended Medium Sensitivity Survey (EMSS; Gioia et al. sidadCatolicadeChile,Casilla306,Santiago, 22,Chile 1990b; Stocke et al. 1991; Maccacaro et al. 1994) to 2 MULLIS ET AL. 1045 1] − s s g r e 2 − 01044 5 h ) [ V e k 0 2. − 5 0. 1043 ( x L 160SD EMSS BCS 1042 0.0 0.2 0.4 0.6 0.8 z Fig. 1.—X-rayluminosityand redshiftdistribution of the 160SD (Mullisetal. 2003), the EMSS(Gioia&Luppino 1994 withupdates fromthe literature, e.g.,Henry 2000), and the BCS(Ebeling etal.1998)cluster samples. The dotted curves (left to right)areindicative fluxlimitsof2.7×10−12,1.5×10−13,and3×10−14 ergscm−2 s−1(0.5–2.0keV). TheEMSSandBCSluminositieswereconverted to thisenergybandassumingaRaymond-Smithplasmaspectrum(Raymond&Smith1977)withametallicityof0.3solarandthereported gastemperature(eitherdirectlymeasuredorestimatedfromtheluminosity-temperaturerelation). make the first detection of evolution in the observed (Burke et al. 2003), and WARPS (Scharf et al. 1997; XLF. Based on a steepening of the high-redshift lumi- Perlman et al. 2002). Complementary surveys at low nosity function, they found a deficit of high-luminosity redshifts (z . 0.3) yielded accurate determinations of clusters at z > 0.3 with a statistical significance of ap- the local luminosity function, thus providing the crucial proximately 3σ. Though most subsequent investigations baselineforthedetectionofredshiftevolution. Theselo- corroborate these findings, some questions have been calsurveysinclude the BCS+eBCS(Ebeling et al. 1998, raised concerning the reliability of the EMSS evolution 2000a), RASS1BS (De Grandi et al. 1999a), and RE- detection (e.g., Nichol et al. 1997; Ebeling et al. 2000b; FLEX(Böhringer et al.2001). Fromtheshearnumberof Ellis & Jones2002;Lewis et al.2002). Ofhistoricalnote, projectsitshouldbeclearthatROSAT wasawatershed the only other pre-ROSAT measurement of significant event for X-ray cluster surveys. clusterevolutioncamefromEdge et al.(1990)whofound Critical comparisons of the ROSAT and EMSS lumi- rapid negative evolution in the luminosity function at nosity functions must account for the overlap (or lack z <0.2basedonaHEAO-1sample. Thiswasultimately thereof) of the measurements in redshift and luminos- overruledbyadefinitiveandnon-evolvingmeasureofthe ity. Insufficient attention to this point led to confusion local XLF (Ebeling et al. 1997). in some early analyses and debates. Different combina- SeekinginparttoconfirmorrefutetheEMSS’scontro- tionsofsensitivityandarealcoverageinflux-limitedsur- versial claim of negative cluster evolution, a large num- veys, when convolved with the intrinsic cluster luminos- ber of cluster surveys were initiated in the 1990s based ity function, result in populating different regions of the on ROSAT data (Voges 1992; Tru¨mper 1993). The 160 observedluminosity-redshiftplane(seeindicativeresults SquareDegreeROSAT ClusterSurvey(hereafter160SD, inFigure 1). Inpractice itis difficultto directlytest the Vikhlinin et al.1998a;Mullis et al.2003)isonesuchpro- cluster evolution seen in the EMSS detection because it gram and the subject of this paper. Additional sur- liesattheextremebrightendoftheluminosityfunction. veys probing to high redshift include the NEP (Mullis Thus large search volumes are required to detect ade- 2001; Henry et al. 2001; Gioia et al. 2003), BMW-HRI quate numbers of such rare clusters. The 160SD is one (Moretti et al. 2001; Panzera et al. 2003), BSHARC ofthelargestserendipitousX-raysurveysconductedwith (Romer et al. 2000), MACS (Ebeling, Edge, & Henry ROSAT. With this substantial areal coverage and high 2001), RDCS (Rosati et al. 1995, 1998, 2000), RIXOS sensitivity, the 160SD survey is well-positioned to probe (Castander et al. 1995; Mason et al. 2000), SSHARC cluster evolution. Preliminary analyses of our sample, CLUSTER XLF EVOLUTION 3 shifts. Note that the number of false-detections in the sampleagreesverywellwiththatexpectedfromthecon- 111000000 110000 fusion of point sources as demonstrated in the Monte- Carlo simulations of Vikhlinin et al. (1998a). Two false- detections (Nos. 77 and 141) serendipitously imaged by 22g]g] XMM-Newton andChandra,respectively,areindeedcon- a [dea [de 111000 1100 fused point sources. Finally, the optical survey imaging ee arar was sufficiently deep to demonstrate that none of the urvey urvey false-detections should be galaxy clusters at z .0.9. ss 111 11 Although spatial X-ray extent was our primary selection criterion, detailed comparisons with other surveys demonstrate that no known clusters were missed as unresolved sources (see §4 of Mullis et al. 2003, and ref- 000...111 00..11 erences therein). Thus the 160SD clusters are in ef- 11 00 −− 11 44 11 00 −− 11 33 11 00 −− 11 22 fflluuxx ((00..55−−22..00 kkeeVV)) [[eerrggss ss−−11 ccmm−−22]] fect drawn from a statistically complete, flux-limited survey with an areal coverage (Ω) and sensitivity char- Fig. 2.—Theselection functionofthe160SD surveyspecifying acterized by the selection function shown in Figure the square degrees of area covered as a function of limitingX-ray flux (0.5–2.0keV). These data are tabulated in Vikhlininetal. 2. A total of 158.5 deg2 were surveyed and the me- (1998a,Table5). Theshadingencodes thisinformationforsubse- dian survey flux (where Ω = Ω /2) is 1.2 × 10−13 total quentuseinFigure3. Theverticallineindicatestheminimumflux ergs cm−2 s−1(0.5–2.0keV). We restrict our analysis to alinmailtys(i4s.×10−14 ergscm−2 s−1, 0.5–2.0keV) used inthe present a minimum flux of 4 × 10−14 ergs cm−2 s−1 to avoid anyuncertaintiesintheskycoverageatveryfaintfluxes. Thereare190clustersinthe160SDsurveysampleabove with at-the-time incomplete optical follow-up, seemed thisfluxlimit. Figure 1showsthepositioninluminosity- to confirm the deficit of high-luminosity, high-redshift redshift space of our sample relative to the BCS, one of clusters first seen by the EMSS (Vikhlinin et al. 1998b, thekeyreferencesamplesatlowredshift,andtheEMSS. 2000). Figure 3 shows the 160SD data in greater detail. Here In this paper we present measurements of the clus- the cluster luminosities are plotted as a linear function ter XLF out to z = 0.8 and describe their implications ofcomovingvolumewhichprovidesamoreuniformview for cluster evolution based on the final 160SD sample of ofthe volumesampling. Thegreyscaleinthefigureindi- 201 clusters. In §2 we outline the basic construction of cates the parameter space probed by our survey — sen- our cluster sample and the associated selection function sitivity is maximal in light regions and minimal in dark used herein. The formalism associated with the XLF is regions. defined in §3 and used to measure cluster abundances In our subsequent derivations of the cluster XLF and at both low and high redshifts. In §4 we characterize tests forevolution,weexclude severalobjects(allatz < the evolution in the cluster population using integrated 0.3) to minimize the biasing of our results. To avoid numbercountsandamaximum-likelihoodanalysisofthe potentially skewing the impartiality of the sampling, we observed luminosity-redshift distribution relative to an rejectnineclusterswhoseredshiftsarewithin∆z =0.015 evolving Schechter function. We discuss our results in of the original target of the ROSAT PSPC observations thecontextofpreviousworksanddrawconclusionsin§5. (Nos. 16, 32, 112, 134, 165, 166, 174, 177, 206). Four Throughoutthisanalysisweusethecosmologicalparam- X-ray-overluminous elliptical galaxies or “fossil groups” eters H =50 h km s−1 Mpc−1, Ω =1, and Ω =0 (Nos. 110, 144, 201, and 211) are discounted because 0 50 M Λ (Einstein–de-Sitter, EdS) for direct comparison to pre- thesespecialstructuresareunlikelytomeettheselection vious work in this field. We also repeat calculations in criteriaofthelocalsamples(Vikhlinin et al.1999). Thus the currently preferred cosmology where Ω = 0.3 and thefinalclustersampleusedhereconsistsof177clusters. M Ω = 0.7. X-ray fluxes and restframe luminosities are Λ quoted in the 0.5–2.0 keV energy band unless otherwise 3. THEX-RAYLUMINOSITYFUNCTION stated. We define the cluster differential luminosity function 2. THE160SDCLUSTERSAMPLE to be The 160SDsample of201galaxyclustersisthe largest high-redshift,X-rayselectedsamplepublishedsofar. For d2N φ(L ,z) = (L ,z) (1) instance, there are 73 objects at z > 0.3 and 22 objects X dVdL X X at z > 0.5. The 160SD sample was constructed via the serendipitousdetection ofextendedX-raysourcesin 647 where N is the number of clusters of luminosity L in X archivalROSAT PSPCobservations. Of223clustercan- a volume V at a redshift z. The standard approach didates, we identified 201 as galaxy clusters, 21 as prob- for deriving a nonparametric representation of the dif- able false-detections due to blends of unresolved point ferential cluster XLF is based on the 1/V technique max sources,andonesourceisunidentifiedduetoitsproxim- first proposed by Schmidt (1968) and generalized by ity to a bright star. We have secured spectroscopic red- Avni & Bahcall (1980). Here the observed luminosity shiftsfor200ofthe201clusters. Vikhlinin et al.(1998a) range is parsed into bins of width ∆L, within each of give a complete description of the survey methodol- which there are N observed clusters. The XLF is es- j ogy. Mullis et al. (2003) detail the optical follow-up and timated by summing the density contributions of each present the final cluster catalog with spectroscopic red- cluster in the considered luminosity/redshift bin, 4 MULLIS ET AL. z 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 −1−1s]s] 11004444 s s gg rr ee 22 −− 00 55 hh ) [) [ VV ee 0 k0 k 11004433 2.2. −− 55 0.0. (( xx LL 11004422 00 11 22 33 44 ccoommoovviinngg vvoolluummee VV((< 2.8 × 10−12 ergs cm−2 s−1, In Figure 5 we add the measurements from four addi- X tional deep surveys (RDCS, EMSS, NEP, and WARPS) 0.1–2.4keV). Part of a pilot program of the larger thus producing a compilation of all of the ROSAT (plus REFLEX survey, De Grandi et al. (1999b) presented a EMSS)localXLFspublishedtodatefromX-rayselected, measurement based on 129 RASS1BS clusters (f > X 3–4 × 10−12 ergs cm−2 s−1, 0.5–2.0keV)fromthe south X-ray flux-limited cluster samples. The shallow all-sky surveysaccuratelymeasurethelocalluminosityfunction Galactic cap. Finally, the XLF determination based on at intermediate to high luminosities (& 1043 ergs s−1) thelargestsampletodatecomesfromtheREFLEXsur- butarerelativelyinsensitivetoverylowluminosityclus- vey. Böhringer et al. (2002) made a detailed analysis of ters (.1043 ergs s−1). In a complementary fashion, the 452 clusters extracted from the southern celestial hemi- sphere (f > 3 × 10−12 ergs cm−2 s−1, 0.1–2.4keV). deep surveys better measure the faint end of the local X XLF, provide reasonable precisionat intermediate lumi- Nonparametric determinations of the local XLF (z < nosities,butpoorlyconstraintheverybrightend(&1044 0.3) from the all-sky samples (BCS, RASS1BS, and RE- ergs s−1) due to limited survey volumes at low redshift. FLEX) are shown in Figure 4. We also plot the best- The cluster luminosity-redshift distributions in Figure 1 fitting Schechter functions for these data and list the alsoillustratethisdependenceonfluxlimitandsolidan- associated best-fit parameters in Table 1 for future ref- gle. erence. The results demonstrate that we have accurate knowledgeofthe localclusterluminosity function. Inde- 3.2. The High-Redshift XLF pendentinvestigatorsusingdifferentX-rayselectionpro- ceduresoverdifferentregionsoftheskyagreeonthelocal We measure the distant XLF using the 66 clusters space density of clusters. For example, in the luminos- from the 160SD sample at 0.3 < z < 0.8 and fluxes ity interval 5 × 1043 – 1045 ergs s−1 (0.5–2.0keV), the above 4 × 10−14 ergs cm−2 s−1. The numerical results internalaccuracyofthese XLF measurementsis approx- are shown in Table 3 and plotted in Figure 6. We have imately ±10%–20% (estimated from the ±1σ excursion probed a sufficiently large volume such that we can de- oftheerrorenvelopesplottedinFigure4). Moreover,the rive useful results in two intervals: 0.3 Ncl (1044 h−2 ergss−1) ··· ··· (h5 Mpc−3 (1044 ergss−1)−1) ··· ··· 50 50 0.016 0.013 0.019 5.09×10−4 1.78×10−4 1.18×10−3 0.045 2 0.022 0.019 0.026 2.19×10−4 7.65×10−5 5.07×10−4 0.035 2 0.031 0.026 0.037 1.42×10−4 6.45×10−5 2.81×10−4 0.062 3 0.044 0.037 0.053 2.08×10−5 3.59×10−6 6.85×10−5 0.135 1 0.063 0.053 0.075 4.59×10−5 2.61×10−5 7.69×10−5 0.142 5 0.089 0.075 0.106 2.87×10−5 1.80×10−5 4.42×10−5 0.136 7 0.125 0.106 0.149 1.86×10−5 1.28×10−5 2.65×10−5 0.156 10 0.177 0.149 0.211 6.98×10−6 4.55×10−6 1.04×10−5 0.154 8 0.251 0.211 0.298 7.44×10−6 5.65×10−6 9.72×10−6 0.200 17 0.355 0.298 0.422 5.49×10−6 4.35×10−6 6.89×10−6 0.197 23 0.502 0.422 0.597 1.27×10−6 8.55×10−7 1.86×10−6 0.195 9 0.710 0.597 0.844 9.89×10−7 6.94×10−7 1.39×10−6 0.239 11 1.004 0.844 1.194 3.60×10−7 2.16×10−7 5.76×10−7 0.226 6 1.420 1.194 1.688 8.26×10−8 2.89×10−8 1.92×10−7 0.225 2 2.008 1.688 2.388 5.76×10−8 2.01×10−8 1.34×10−7 0.180 2 2.840 2.388 3.377 2.01×10−8 3.47×10−9 6.63×10−8 0.296 1 †LX isquotedinthe0.5–2.0keVband ergs s−1 (Figure 6: filled circles). Except for the data data points of the latter are offset diagonally down and point near 5 × 1043 ergs s−1 which is 1.9σ off the local to the right approximately along the former. This is relation, there is excellent agreement between these the combined effect of the increase in both the cluster results and the no-evolution benchmark at least out to luminosities and the search volumes in a Λ-dominated intermediate luminosities, L ∼ 2 × 1044 ergs s−1. In universe. The actual positioning of the two XLFs rela- X this regionthe 160SDbest matches the normalizationof tive to each other depends on the cluster redshifts and the REFLEX XLF. At higher luminosities the distant the specific luminosity interval. For example in the RE- XLF is lower than the local population but we will FLEX survey (< z >= 0.08), between 1043 and 1045 demonstrate in §4.1 that this effect is only marginally ergs s−1 the ratio of the fitted XLFs (φ /φ ) is less Λ EdS significant with respect to the local XLF with the than unity with a broad minimum of ∼0.8 around 1044 highest normalization (RASS1BS). The median redshift ergs s−1. REFLEX is the only local sample for which for these depressed data points is < z >= 0.50 (see the XLF in a Λ-cosmology has been explicitly measured Table 3). (Böhringer et al. 2002). However,giventhe similarity of At the highest redshifts probed by the 160SD in the redshift and luminosity distributions, we have used the present analysis, 0.6=0.70. nate cosmology. (Figure 6: open squares). The distant cluster volume It is apparent from Figure 7 that the high-redshift densities are below the local level at all measured lu- 160SD XLFs and the local XLFs shift in similar ways; minosities. We will show that this result is significant thus the apparentdeficitofhigh-luminosityclustersper- (> 3σ) in both the Einstein–de-Sitter and Λ-dominated sists in the Λ-dominated cosmology. The only im- models evenwith respecttothe lowest-normalizationlo- portant difference, of course, is that the point where cal XLF (§4.1). This is a deficit of high luminosity, the 160SD data depart significantly from the non- high redshift clusters in a manner similar to that seen evolution baseline is shifted to larger luminosities, and in the EMSS results. Note that although the optical this is anticipated given the increase in luminosity dis- CCD imaging used to identify the 160SD clusters was tance (L & 3 × 1044 ergs s−1 for 0.3 Ncl (1044 h−2 ergss−1) ··· ··· (h5 Mpc−3 (1044 ergss−1)−1) ··· ··· 50 50 0.3 Ncl (1044 h−2 ergss−1) ··· ··· (h5 Mpc−3 (1044 ergss−1)−1) ··· ··· 50 50 0.3

Evolution of the Cluster X-ray Luminosity Function

Similar Evolution of the Cluster X-ray Luminosity Function