Baryon Content of Massive Galaxy Clusters (0.57 < z < 1.33)
I. Chiu, J. Mohr, M. Mcdonald, S. Bocquet, M. L. Ashby, M. Bayliss, B. A. Benson, L. E. Bleem, M. Brodwin, S. Desai, J. P. Dietrich, W. R. Forman, C. Gangkofner, A. H. Gonzalez, C. Hennig, J. Liu, C. L. Reichardt, A. Saro, B. Stalder, S. A. Stanford, J. Song, T. Schrabback, R. Suhada, V. Strazzullo, A. Zenteno
aa r X i v : . [ a s t r o - ph . C O ] O c t Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 12 July 2018 (MN L A TEX style file v2.2)
Baryon Content of Massive Galaxy Clusters at . < z < . I. Chiu , , J. Mohr , , , M. McDonald , S. Bocquet , , M. L. N. Ashby ,M. Bayliss , , B. A. Benson , , , L. E. Bleem , , , M. Brodwin , S. Desai , ,J. P. Dietrich , , W. R. Forman , C. Gangkofner , , A. H. Gonzalez , C. Hennig , ,J. Liu , , C. L. Reichardt , A. Saro , , B. Stalder , , S. A. Stanford , , J. Song ,T. Schrabback , R. Šuhada , V. Strazzullo , A. Zenteno , Department of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 München, Germany Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching, Germany Max-Planck-Institut für extraterrestrische Physik, Giessenbachstr. 85748 Garching, Germany Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138 Fermi National Accelerator Laboratory, Batavia, IL 60510-0500 Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 Department of Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, USA 60439 Department of Physics and Astronomy, University of Missouri, 5110 Rockhill Road, Kansas City, MO 64110 Department of Astronomy, University of Florida, Gainesville, FL 32611 School of Physics, University of Melbourne, Parkville, VIC 3010, Australia Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA Department of Physics, University of California, One Shields Avenue, Davis, CA 95616 Institute of Geophysics and Planetary Physics, Lawrence Livermore National Laboratory, Livermore, CA 94550 Korea Astronomy and Space Science Institute 776, Daedeokdae-ro, Yuseong-gu, Daejeon, Republic of Korea 305-348 Argelander-Institut für Astronomie, Auf dem Hügel 71, D-53121 Bonn, Germany Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile
12 July 2018
ABSTRACT
We study the stellar, Brightest Cluster Galaxy (BCG) and intracluster medium (ICM)masses of 14 South Pole Telescope (SPT) selected galaxy clusters with median redshift z = 0 . and mass M = 6 × M ⊙ . We estimate stellar masses for each cluster andBCG using six photometric bands, the ICM mass using X-ray observations, and thevirial masses using the SPT Sunyaev-Zel’dovich Effect signature. At z = 0 . the BCGmass M BCG ⋆ constitutes . ± . of the halo mass for a × M ⊙ cluster, andthis fraction falls as M − . ± . . The cluster stellar mass function has a characteristicmass M = 10 . ± . M ⊙ , and the number of galaxies per unit mass in clusters islarger than in the field by a factor . ± . . We combine our SPT sample withpreviously published samples at low redshift and correct to a common initial massfunction and for systematic virial mass differences. We then explore mass and redshifttrends in the stellar fraction f ⋆ , the ICM fraction f ICM , the collapsed baryon fraction f c and the baryon fraction f b . At a pivot mass of × M ⊙ and redshift z = 0 . ,the characteristic values are f ⋆ = . ± . , f ICM = . ± . , f c = . ± . and f b = . ± . . These fractions all vary with cluster mass at high significance, withhigher mass clusters having lower f ⋆ and f c and higher f ICM and f b . When accountingfor a 15 % systematic virial mass uncertainty, there is no statistically significant redshifttrend at fixed mass. Our results support the scenario where clusters grow throughaccretion from subclusters (higher f ⋆ , lower f ICM ) and the field (lower f ⋆ , higher f ICM ), balancing to keep f ⋆ and f ICM approximately constant since z ∼ . . Key words: galaxy clusters - cosmology - galaxy evolution c (cid:13) Chiu et al.
The utility of galaxy clusters for cosmological param-eter studies was recognized quite early (Frenk et al.1990; Henry & Arnaud 1991; Lilje 1992; White et al.1993; White et al. 1993), but the overwhelming ev-idence of widespread merging in the cluster popu-lation (Geller & Beers 1982; Forman & Jones 1982;Dressler & Shectman 1988; Mohr et al. 1995) togetherwith the high scatter in the X-ray luminosity–temperaturerelation (e.g., Fabian 1994) left many with the impressionthat clusters were too complex and varied to ever beuseful for cosmological studies. It was some time laterthat the first evidence that clusters exhibit significantregularity in their intracluster medium (ICM) propertiesappeared (Mohr & Evrard 1997; Arnaud & Evrard 1999;Cavaliere et al. 1999; Mohr et al. 1999); X-ray obser-vations showed that clusters as a population exhibit asize–temperature scaling relation with ≈ scatter, alevel of regularity comparable to that known in ellipticalgalaxies (i.e., Djorgovski & Davis 1987). This regularitytogether with the emergence of evidence for cosmic accel-eration (Riess et al. 1998; Perlmutter et al. 1999) focusedrenewed interest in the use of galaxy clusters for precisecosmological studies (e.g., Haiman et al. 2001). Moreover,the existence of low scatter, power law relations amongcluster observables provided a useful tool to study thevariation in cluster structure with mass and redshift.Soon thereafter, the regularity seen in the X-ray prop-erties of clusters was shown to exist also in the optical prop-erties of clusters (Lin et al. 2003, hereafter L03). L03 car-ried out an X-ray and near-infrared (NIR) 2MASS K -bandstudy of an ensemble of 27 nearby clusters, measuring themass fraction of the stellar component inside the galaxies( f ⋆ ), the ICM mass fraction ( f ICM ), the total baryon frac-tion ( f b ), the cold baryon fraction ( f c ; hereafter we referto this as the collapsed baryon fraction) and the metal en-richment of the ICM. This study showed an increasing f b and decreasing f ⋆ and f c in the more massive halos, sug-gesting that the star formation efficiency is higher in thelow mass halos as well as that feedback associated with thisenhanced star formation was having a larger structural im-pact in low mass than in high mass halos. Over the lastdecade, additional studies using larger samples and betterdata have largely confirmed this result (e.g., Gonzalez et al.2007; Giodini et al. 2009; Andreon 2010; Zhang et al. 2011,hereafter Zha11; Gonzalez et al. 2013, hereafter GZ13).Understanding how the cluster and group baryon com-ponents evolve with redshift is a key question today. Whilethere have been many detailed studies of intermediate andhigh redshift galaxy clusters, most previous observationalstudies of large cluster samples have focused on nearby sys-tems due to the difficulty of defining high redshift samplesand of following them up in the X-ray and with adequatelydeep optical or near-infrared (NIR) imaging. That is chang-ing now with the recent analyses of Sunyaev-Zel’dovich ef-fect (Sunyaev & Zel’dovich 1970, 1972, hereafter SZE) se-lected clusters and groups at intermediate and high redshift.The SZE results from inverse Compton interactions of thehot ionized ICM with cosmic microwave background (CMB)photons; because it is a CMB spectral distortion rather thana source of emission, it does not suffer from cosmological dimming. Since the first SZE selected clusters were discov-ered in the SPT-SZ survey (Staniszewski et al. 2009), thismethod has been demonstrated to be a useful tool for dis-covering and studying galaxy cluster populations out to highredshift (Zenteno et al. 2011; Hilton et al. 2013, hereafterH13; Bayliss et al. 2014). In addition, NIR selected clustersand groups at high redshift are now also being used to studythe evolution of galaxy populations (e.g. van der Burg et al.2014, hereafter vdB14). In this work we focus on an SZEselected cluster sample at redshift higher than 0.6 that orig-inates from the first 720 deg of the South Pole Telescope(Carlstrom et al. 2011) SZE (SPT-SZ) survey (Song et al.2012b; Reichardt et al. 2013).To study the evolution of f ⋆ one needs robust stellar andvirial mass estimates. Stellar masses are typically estimatedby converting the observed galaxy luminosity into the stel-lar mass using the mean mass-to-light ratio constructed fromtheoretical models. This approach is sensitive to the galaxyspectral templates and needs to be modelled carefully to re-duce possible biases (vdB14). For accurate stellar mass mea-surements with less model-dependence, one requires deepmulti-wavelength observations that allow the spectral energydistribution (SED) to be measured on a galaxy by galaxy ba-sis. For clusters at z ≈ , this typically requires photometryusing 8 m telescopes like the VLT together with space-basedNIR data from the Spitzer
Space Telescope.The cluster virial mass measurements typically havecome from X-ray mass proxies such as the emission weightedmean temperature or from galaxy velocity dispersions. Thecalibration of the X-ray mass proxies has often been basedon the assumption of hydrostatic equilibrium, which in somecircumstances can underestimate the mass by 20 – 40 % due to the non-thermal pressure components in these youngstructures (see Molnar et al. 2010; Chiu & Molnar 2012,and references therein). Velocity dispersion mass estimates,although likely less biased than hydrostatic mass estimates,have been shown to have quite high scatter on a single clus-ter basis (e.g., White et al. 2010; Saro et al. 2013; Ruel et al.2014). Therefore, a study of the redshift variation of f ⋆ would benefit from a low scatter mass proxy from the X-ray or SZE that has been calibrated to mass using low biasmeasurements such as weak lensing or velocity dispersionstogether with a method that accounts for selection effectsand cosmological sensitivity. The masses we use in this anal-ysis are based on the SZE signal-to-noise for each cluster asobserved in the SPT-SZ survey and are calibrated in justsuch a manner (Bocquet et al. 2015).In addition to robust, low scatter mass estimates oneshould use a uniformly selected cluster sample whose selec-tion is not directly affected by variations in f ⋆ . ICM basedobservables such as the X-ray luminosity or the SZE signa-ture enable this, although connections between the physicsof star formation and the structure of the ICM remain aconcern. Also, if one wishes to probe the regime beyondthe group scale at high redshift, one must survey enoughvolume to find significant numbers of the rare, massive clus-ters. Large solid angle SZE surveys like those from SPT, theAtacama Cosmology Telescope (ACT, Fowler et al. 2007)and Planck (Tauber 2000) provide a clean way to discoverclusters. Indeed, because the SZE signature for a cluster of agiven mass evolves only weakly with redshift in an arcminuteresolution SZE survey, the SPT-SZ survey provides a cluster c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters sample that is well approximated as a mass–limited sampleabove redshift z ≈ . (e.g. Vanderlinde et al. 2010).In this paper, we seek to study the baryon content, in-cluding the ICM and the stellar mass components, of mas-sive high redshift clusters discovered within the SPT-SZsurvey. We attempt also to constrain the evolution of thebaryon content of these clusters by combining our high red-shift, massive clusters with other samples, primarily stud-ied at low redshift. The paper is organized as follows. Wedescribe the cluster sample and the data in Section 2. InSection 3 we provide detailed descriptions of the ICM, thestellar mass and the total mass measurements for the clus-ters. We present the stellar mass function (SMF) in Section 4and present results on the mass and redshift trends of thebaryon composition in Section 5. We discuss these results inSection 6 and summarize our conclusions in Section 7.We adopt the concordance ΛCDM cosmologicalmodel with the cosmological parameters measured inBocquet et al. (2015) throughout this paper: Ω M = 0 . , Ω Λ = 0 . and H = 68 . km s − Mpc − . These constraintsare derived from a combination of the SPT-SZ cluster sam-ple, the Planck temperature anisotropy,
WMAP polarisa-tion anisotropy and Baryon Acoustic Oscillation (BAO) andSN Ia distances. Unless otherwise stated all uncertainties areindicated as σ , the quantities are estimated at the overden-sity of 500 with respect to the critical density ( ρ crit ) at thecluster’s redshift, all celestial coordinates are quoted in theepoch J2000, and all photometry is in the AB magnitudesystem. In this section we briefly summarize the SPT cluster sampleand the follow-up data acquisition, reduction, calibration aswell as the literature cluster sample we compare to. The deepoptical observations from the VLT and the
HST , togetherwith the near-infrared observations from the
Spitzer , enableus to measure the integrated stellar masses of our clustersaccurately. The ICM masses are extracted from
Chandra and XMM-
Newton
X-ray observations. Cluster total massesare derived from the SPT SZE observable ξ as calibratedusing the external data sets (see Section 3.1). The litera-ture sample we compare with in this study is described inSection 2.2. The 14 clusters we analyze are drawn from early SPT-SZcluster catalogs, which covered the full 2500 deg with shal-lower data (Williamson et al. 2011) or included the first720 deg of the full depth SPT-SZ survey (Reichardt et al.2013). The full 2500 deg catalog has meanwhile been re-leased (Bleem et al. 2015). These 14 systems have high de-tection significance ( ξ > . ) and were selected for furtherstudy using HST and the VLT. All fourteen have measuredspectroscopic redshifts (Song et al. 2012b).We study the virial region defined by R in each clus-ter, where R is extracted from a virial mass estimate( M ) that is derived from the SPT SZE observable (seeSection 3.1). We adopt the X-ray centroid as the cluster center, because the SZE cluster center measurement uncer-tainties are larger. A previous analysis of the offset betweenthe SPT measured cluster center and the Brightest ClusterGalaxies (BCG) positions in a large ensemble of the SPTclusters (Song et al. 2012b) indicated that once the SPT po-sitional measurement uncertainties are accounted for, thisoffset distribution is consistent with that seen in local sam-ples where the X-ray center is used (e.g., Lin & Mohr 2004).In our sample the BCG positions, X-ray centers and SZEcenters are all in reasonably good agreement (see Figure 1).Importantly, these offsets have a negligible impact on ouranalysis, because we are comparing average properties de-termined within the radius R .We present the names, redshifts and the sky positions inJ2000 ( α, δ ) of the X-ray center and BCG of our SPT samplein Table 1. The virial mass M and the virial radius R for each cluster are listed in Table B1. VLT/FORS2 imaging in the bands b
High ( b H ), I Bessel ( I B ),and z Gunn ( z G ) was obtained for the fourteen clusters underprograms 088.A-0889 and 089.A-0824 (PI Mohr). Observa-tions were carried out in queue mode under clear conditions.The nominal exposure times for the different bands are 480 s( b H ), 2100 s ( I B ) and 3600 s ( z G ). These exposure times areachieved by coadding dithered exposures with 160 s ( b H ),175 s ( I B ), and 120 s ( z G ). Deviations from the nominal ex-posure times are present for some fields due to repeatedobservations when conditions violated specified constraintsor observing sequences that could not be completed duringthe original planned semester. The pseudo-color images ofthe 14 SPT clusters constructed from VLT bands b H , I B ,and z G are shown in Figure 1. Each image shows also SZEcontours (white), the R virial region (green circle) andthe BCG (yellow circle).Data reduction is performed with the THELI pipeline(Erben et al. 2005; Schirmer 2013). Twilight flats are usedfor flatfielding. The I B - and z G -band data are defringed usingfringe maps extracted from night sky flats constructed fromthe data themselves. To avoid over-subtracting the sky back-ground, the background subtraction is modified from thepipeline standard as described by Applegate et al. (2014).The FORS2 field-of-view is so small that only a fewastrometric standards are found in the common astromet-ric reference catalogs. Many of them are saturated in ourexposures. While we use the overlapping exposures fromall passbands to map them to a common astrometric grid,the absolute astrometric calibration is adopted from mo-saics of F606W images centered on our clusters from thecomplementary ACS/
HST programs C18-12246 (PI Stubbs)and C19-12447 (PI High). Each cluster is observed in thewell-dithered mode through
F606W and F814W filters. For
F606W imaging, the cluster is imaged by four pointings withminimal overlap to remove the chip gap; these mosaics spana field of view of 6.7 × centered on the clustercore. For F814W imaging, only one pointing centered oncluster core is acquired. In this work we use only the F606W observations for deriving the stellar masses.Cataloging of the VLT images is carried out using SEx-tractor (Bertin & Arnouts 1996) in dual image mode. Thedetection image is created through the combination of I B c (cid:13) , 000–000 Chiu et al.
Table 1.
Cluster properties and photometric depths: The columns contain the cluster name, redshift and coordinates of the X-ray centerand BCG followed by the 10 σ depths in each band.Cluster Redshift α X [deg] δ X [deg] α BCG [deg] δ BCG [deg] m σ b H m σ F606W m σ I B m σ z G m σ [3 . m σ [4 . SPT-CL J0000 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Figure 1.
VLT pseudo-color images of SPT-CL J2331 − b H , I B and z G . The left and right panels respectivelyshow cluster R and R /3 regions centered on the X-ray peak. The SZE signal-to-noise contours from 0 to 10 with steps of 2 arewhite, the R region is the green circle and the BCG is marked by the yellow circle. The VLT pseudo-color images for the other thirteenclusters are available online. and z G . Cataloging of the HST images is carried out sep-arately, also using SExtractor. Galaxy photometry is ex-tracted using MAG_AUTO. The VLT and HST photometryis matched at the catalog level with a 1 ′′ match radius.Because VLT data are generally not taken in photomet-ric conditions, the photometric calibration is also carried outusing data from the HST programs. We derive a relation be-tween F814W magnitudes and the FORS2 I B filter m I B − m F814W = − .
052 + 0 . m F606W − m F814W ) , from the Pickles (1998) stellar library, which is valid forstars with ( m F606W − m F814W ) < . mag. After deriv-ing the absolute photometric calibration of the FORS2 I B passband from this relation, the relative photometric cal-ibrations of the other bands are fixed using a stellar lo-cus regression (e.g. High et al. 2009; Desai et al. 2012) in the ( m b H , m F606W , m I B , m z G ) color-space. The inclusion of F606W data in this process is necessary because the stellarlocus in ( m b H , m I B , m z G ) colors has no features.All our clusters were observed with the Spitzer
InfraredArray Camera (IRAC; Fazio et al. 2004) at both 3.6 µ mand 4.5 µ m under programs PID 60099, 70053 and 80012(PI Brodwin). The images are acquired in dithered modewith exposure times of × s and × s for 3.6 µ mand 4.5 µ m, respectively. We follow standard data reductionprocedures to reduce the IRAC observations (Ashby et al.2009). For each field we generate a pair of spatially regis-tered infrared mosaics: a relatively deep 3.6 µ m image anda shallower 4.5 µ m image. These images are cataloged withSExtractor in dual image mode, using the 3.6 µ m mosaic asthe detection image. We use the SExtractor MAG_AUTOand its associated uncertainty. We verify our detections by c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters visually inspecting the SExtractor object check image. Be-cause the IRAC point spread function is significantly largerthan in either the HST or VLT imaging, we match our two-band IRAC photometry ( [3 . and [4 . ) to the nearest opti-cal counterpart at the catalog level, using a 1 ′′ match radius.If an object has multiple matches within the Spitzer pointspread function, we then deblend the IRAC fluxes into thecounterparts as described below.For the objects in the
Spitzer /IRAC catalog with multi-ple optical counterparts, we deblend the [3 . and [4 . fluxesusing the properties of the optical counterparts in z G . Specif-ically, we deblend the Spitzer /IRAC fluxes assuming the fluxratios of the neighboring objects in the IRAC band are thesame as in the reddest optical band: R [3 . , [4 . i,j ) ≡ f i f j (cid:12)(cid:12)(cid:12)(cid:12) [3 . , [4 . = f i f j (cid:12)(cid:12)(cid:12)(cid:12) z G , (1)where f i is the flux of object i .We test the relationship between the flux ratios in z G and the two IRAC bands by estimating the flux ratios ofmatched objects without close optical neighbors. We findthat the intrinsic scatter of R [3 . i,j ) and R [4 . i,j ) are of the orderof 0.6 and 0.8 dex, respectively. We add this scatter into theflux uncertainties in [3 . and [4 . of deblended objects.Although the uncertainties in the deblended fluxes arelarge, we find that adding these two IRAC bands– deblendedusing our method– reduces the uncertainties of the stel-lar mass estimates by a mean value of 20 % and reducesthe lognormal scatter of the reduced χ (Section 3.3.1) by29 % . Moreover, through studying an ensemble of pairs ofunblended sources that we first artificially blend and thendeblend, we find that our method does not introduce biasesin the resulting mass estimates.The fraction of blended IRAC sources lying projectedwithin R for the 14 clusters varies from 11 to 20 % witha mean of 16 % and a standard deviation of 2.3 % . From 25to 55 % of the sources are blended within 0.5 R . Thus,the majority ( > ) of sources used in our analysis is notaffected by flux blending.We derive 10 σ depth m σ filter for 6 passbands ( filter =b H , F606W , I B , z G , [3 . , [4 . ) of each cluster in the catalogstage by estimating the magnitude where the median of theMAG_AUTO error distribution is equal to 0.11. These val-ues are listed in Table 1. The m σ filter depths show good con-sistency to the 10 σ depths estimated by measuring the skyvariance in 2 ′′ apertures within the VLT images. The m σ [3 . depths are about 2 magnitudes deeper than our estimated m ∗ for each cluster, and hence the cluster galaxies shouldbe detected without significant incompleteness.We estimate the m ∗ of each passband for each clus-ter using a Composite Stellar Population (CSP) model(Bruzual & Charlot 2003). This model has a burst at z = 3 that decays exponentially with e -folding timescale of τ =0 . Gyr. The tilt of the red sequence is modelled by using6 CSPs with different metallicities and by calibrating thosemodels to reproduce the Coma red sequence (for more de-tails see Song et al. 2012a). This model has been shown tobe adequate to derive accurate red sequence redshifts withinSPT-selected clusters to z > with the root-mean-squareof the cluster’s photo-z error ∆ z/ (1 + z ) , calibrated withspectroscopic clusters, of 0.02 (Song et al. 2012b, Hennig inprep.). This model provides a good representation of the color and tilt of the red sequence and the evolution of m ∗ inSPT selected galaxy clusters extending to z ≈ . (Hennigin prep.). Eleven out of the fourteen clusters in our sample havebeen targeted by the
Chandra
X-ray telescope with pro-gram Nos. 12800071, 12800088, and 13800883. The remain-ing three clusters, SPT-CL J0205 − z = 1 . ; seeStalder et al. 2013), SPT-CL J0615 − z = 0 . ) andSPT-CL J2040 − z = 0 . ) have been observed withXMM- Newton with program 067501 (PI Andersson). TheX-ray follow up observations are designed to observe theSPT clusters uniformly with the goal of obtaining between1500 and 2000 source photons within R . These photonsenable us to measure the ICM projected temperature, thedensity profile and the mass proxy Y X (the product of theICM mass and X-ray temperature) with ∼ % accuracy.The Chandra data reduction is fully described in previ-ous publications (Andersson et al. 2011; Benson et al. 2013;McDonald et al. 2013). We include an additional clusterwith Chandra data (ObsID 12258), the massive merg-ing cluster SPT-CL J0102-4915 (Menanteau et al. 2012;Jee et al. 2014) at z = 0 . , which we analyze in an identi-cal way to those previous works (Benson et al., in prep). Forthe XMM- Newton data, we use SAS 12.0.1 to reduce andreprocess the data. All three cameras (MOS1, MOS2 andpn) are used in our analysis. The background flare periodsare removed in both hard and soft bands using 3 σ clippingafter point source removal. We describe the ICM mass mea-surements in Section 3.2. To place our results in context and to have a more completeview of the possible redshift variation of the baryon contentin galaxy clusters, we compare our measurements with thepublished results from the local universe at z . . Weinclude L03, Zha11 and GZ13 because they all provide esti-mates of f ⋆ , f ICM and f b for large samples over a broadermass range than we are able to sample with the SPT se-lected clusters. L03 study 27 nearby galaxy clusters selectedby optical/X-ray with masses ranging from – M ⊙ ; 13of these have available ICM mass measurements (Mohr et al.1999). There are 19 clusters in Zha11, in which M is es-timated using velocity dispersions. We discard two clusters,A2029 and A2065, from Zha11 because they argue the virialmass estimates are biased due to the substructures. GZ13estimate mass fractions for 15 nearby clusters, 12 of thosehave stellar mass measurements. In addition, we include theclusters and groups from H13 and vdB14 that extend to z > . , allowing a more complete study at high redshifts.H13 study the stellar composition of 10 SZE selected clus-ters from ACT, and vdB14 study the Gemini CLuster Astro-physics Spectroscopic Survey (GCLASS) sample, consistingof 10 low mass clusters selected by Spitzer /IRAC imaging.We restrict the cluster sample to those with virial massesabove × M ⊙ , which is the mass regime probed by theSPT-SZ sample. This results in a total of 34 clusters in thecomparison sample. We note that the majority of the vdB14 c (cid:13) , 000–000 Chiu et al. sample is in the low mass regime and therefore falls belowour mass threshold; our results should not be extrapolatedinto this lower mass regime.There are several important differences between thesestudies and ours. We note that the groups or the clustersin these samples, with the exception of those in H13, areeither selected from X-ray or optical/NIR surveys. Thus,these differences in selection method could potentially leadto observable differences in the samples. In addition to theseselection differences, there are differences in the stellar massand virial mass estimates. We describe below the correctionswe apply to the comparison sample to address these differ-ences, thereby enabling a meaningful combination with theSPT sample.
The most important systematic factor for estimating stellarmass is the choice of the Initial Mass Function (IMF) for thestellar population models that are then employed when con-verting from galaxy light to galaxy stellar mass. Different as-sumed IMFs introduce systematic shifts in the mass to lightratios of the resulting stellar populations (Cappellari et al.2006). For instance, the conventional Salpeter (1955) IMFwith a power law index of -2.35 would predict a massto light ratio higher by a factor of 2 than the one usingthe Kroupa (2001) IMF (Kauffmann et al. 2003; Chabrier2003; Cappellari et al. 2006). For this analysis we adopt theChabrier (2003) IMF (see more detailed discussion in Sec-tion 3.3) and apply a correction to the literature results soall measured stellar masses are appropriate for this IMF.Specifically, we reduce the stellar mass measurements of L03and Zha11 by 24 % (Lin et al. 2012; Zhang et al. 2012), themeasurements of GZ13 by 24 % (or 0.12 dex), and the mea-surements of H13 by 42 % (or 0.24 dex). Because vdB14 usethe same Chabrier IMF as in this work, no IMF correctionis needed. To enable a meaningful comparison of the baryon contentacross samples, it is crucial to use a consistent virial massestimate for all samples. Zha11, H13 and vdB14 estimate M using velocity dispersions, while the other analysesall use X-ray mass proxies (ICM temperature) to estimatevirial masses. Our SPT masses arise from a recent analy-sis (Bocquet et al. 2015) that includes corrections for selec-tion effects, marginalization over cosmological parametersand systematic uncertainties and combination with externalcosmological datasets (see discussion in Section 3.1).The Bocquet et al. (2015) analysis quantifies the sys-tematic mass shifts that result for SPT clusters when usingonly X-ray data, only velocity dispersion data or the fullcombined dataset of X-ray, velocity dispersions and externalcosmological constraints from CMB, BAO and SNe. Namely,when compared to our cluster mass estimates obtained usingthe full combined dataset, the SPT cluster masses inferredfrom the X-ray mass proxy Y X alone have a systematicallylower mass by 44 % , and masses inferred from velocity dis-persions alone have systematically lower masses by 23 % . Asexplained in more detail in Section 3.1, we adopt the full combined dataset masses for the analysis of our SPT clustersample.For the comparison here, it is not crucial to know whichvirial mass estimate is most accurate. What we must do isadopt one mass calibration method for our SPT sample andthen correct the virial mass estimates in the other samplesto a consistent mass definition before making comparisonsof the baryon content. To make these corrections we use theresults from the recent SPT mass analysis (Bocquet et al.2015) to apply a correction to the virial mass scale in eachliterature sample to bring it into better consistency with ourSPT sample.Specifically, we estimate the M of the clusters in L03by using the same T X − M relation (Vikhlinin et al. 2009)used in GZ13; then we increase the L03 and GZ13 massesby 44 % , assuming the systematic offset of Y X derived SPTvirial masses is the same for these clusters whose masses werederived using the T X − M relation. Similarly, we increasethe masses in Zha11, H13 and vdB14 by 23 % , because theirmasses are derived from velocity dispersion measurements.Increasing M increases the virial radius and there-fore also increases the stellar and ICM masses. Specif-ically, a 44 % (23 % ) increase in virial mass leads to a13.2 % (7.4 % ) and 12.9 % (7.1 % ) increment in M ⋆ and M ICM ,respectively, assuming that the cluster galaxies are dis-tributed as an NFW model with concentration c = 1 . and the ICM near the virial radius falls off as a β -model(Cavaliere & Fusco-Femiano 1978) with β = 2 / . In correct-ing the literature results for comparison to the SPT sample,we apply a correction that accounts for the shifts in all thedifferent masses.Correcting previously published masses to account fordifferent data sets and analysis methods allows us to moreaccurately compare the results, but this correction proce-dure has inherent uncertainties. It is challenging to quantifythese remaining uncertainties, but for this analysis we adopta systematic virial mass uncertainty of 15 % (1 σ ) when con-straining the redshift variation with the combined sample.We return to this discussion in Section 5 where we presentour fitting procedure in detail. Also, in the conclusions wecomment on the impact of adopting other systematic uncer-tainties.We note in passing that if we had adopted the SPTmasses calibrated only using the X-ray mass proxy Y X , theSPT cluster virial masses M would decrease on averageby a factor of / . . The new values for the SPT samplequantities M ⋆ , M ICM , f ⋆ , f ICM , f c and f b can be approx-imated by applying the scale factors 0.87, 0.88, 1.26, 1.27,0.99 and 1.27, respectively, to the measurements presentedin Table B1. In this section we describe the method for estimating thevirial, the ICM and the stellar masses. M Measurements
The virial masses ( M ) that we use come from themass calibration and cosmological analysis of Bocquet et al.(2015). They are derived using the SPT SZE observable c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters ξ , the cluster redshift, and a combination of internal andexternal calibration data. These data include direct massinformation from 63 measured cluster velocity dispersions(observed using Gemini South, the VLT, and the Magel-lan Baade and Clay telescopes, see Ruel et al. 2014) and 16 Y X measurements (Andersson et al. 2011; Foley et al. 2011;Benson et al. 2013). In addition, mass information derivesfrom the 100 cluster candidates extracted from the first720 deg of the SPT-SZ survey. These SPT data are thenjointly analyzed in combination with Planck temperatureanisotropy,
WMAP ξ and redshift distributionof the cluster sample. In contrast, the Y X constraints pre-fer lower masses, and the velocity dispersions prefer massesin the middle. By combining all the constraints one endswith a mass calibration that prefers higher masses than themasses one would obtain when using solely the Y X ’s or ve-locity dispersions as calibrators (see also further discussionin Section 2.2.2). We adopt these masses that arise from acombination of internal and external calibration data for theanalysis below.Our SPT masses are corrected for Eddington bias thatarises from the scatter between the mass and the selec-tion variable ξ and the steep cluster mass distribution. Theintrinsic scatter in mass at fixed ξ is approximately 16 % ,and there is an additional measurement scatter that reaches ≈ at ξ = 5 . Final mass uncertainties include marginal-ization over all cosmological and scaling relation parameters.Thus, our masses and mass uncertainties include a combina-tion of the systematic and statistical uncertainties. Typicalfinal mass uncertainties are ∼ . The masses are thenused to calculate R , which has a characteristic uncer-tainty of ≈ . We refer the reader to Bocquet et al. (2015)for additional details. The virial mass systematics correctionfor the comparison sample is described in Section 2.2.2. In this work we adopt the X-ray ICM mass M ICM measure-ments extracted within R . We determine the center of thecluster ( α X , δ X ) iteratively as the centroid of X-ray emissionin the 0.7 – 2.0 keV energy band within a 250 – 500 kpc an-nulus (see Table 1). The final centroid is visually verified onthe smoothed X-ray emission map and is adjusted to matchthe center of the most circularly symmetric isophote if it de-viates significantly from the peak. The ICM density profile isestimated by fitting the X-ray surface brightness profile ex-tracted in the energy range 0.7 – 2.0 keV assuming sphericalsymmetry and centered on the derived centroid. For Chan-dra observations, we fit the modified single β -model (Equa-tion 1 and Equation 2 in Vikhlinin et al. (2006)) to the X-raysurface brightness profile. The details of the X-ray analysisare given elsewhere (Andersson et al. 2011; McDonald et al.2013).Because we cannot simultaneously constrain all the pa-rameters in the modified single β -model for the XMM- Newton observations, we instead fit a single β -model for SPT-CL J0205-5829 ( z = 1 . ), SPT-CL J0615-5746 ( z =0 . ) and SPT-CL J2040-5726 ( z = 0 . ). For these clus-ters the single β -model provides a good fit to the XMM- Newton
X-ray surface brightness profile. The best fit X-raysurface brightness profile then provides the radial distribu-tion of the ICM, and we use the flux of the cluster withinthe 0.15 – 1.0 R annulus to determine the central density(e.g., Mohr et al. 1999). We assume the metal abundanceof the ICM is 0.3 solar, resulting in n e /n p = 1 . and µ ≡ ρ ICM / ( m p n e ) = 1 . , where the subscripts p and edenote proton and electron, respectively.To estimate M ICM , we integrate the measured ICM pro-file to R obtained from the SZE derived M . The un-certainty of M ICM is estimated by propagating the uncer-tainties of the best-fit parameters. Deriving the X-ray tem-perature of the ICM free from the instrumental calibrationbias can be challenging; however, the ICM mass and densityprofile is insensitive to the temperature (Mohr et al. 1999)and to instrumental systematics (Schellenberger et al. 2014;Martino et al. 2014; Donahue et al. 2014). Thus, we do notexpect significant systematics in the ICM masses.
In the sections below we describe the SED fitting to de-termine galaxy stellar masses and our method of making astatistical background correction.
We use the multiband photometry to constrain the spec-tral energy distribution (SED) of each galaxy and to es-timate its stellar mass. The photometry of the six bands( b H F606WI B z G [3 . . ) is used for each galaxy. We usethe Le Phare SED fitting routine (Arnouts et al. 1999;Ilbert et al. 2006) together with a template library that con-sists of stellar templates (Pickles 1998) and galaxy templatesfrom CSP models (Bruzual & Charlot 2003) derived usinga Chabrier (2003) IMF. The systematics correction for thedifferent IMF used in the comparison sample is describedin Section 2.2.1. The stellar templates include all normalstellar spectra together with the spectra of metal-weak F-through K dwarfs and G through K giants. The galaxy li-brary includes templates that cover: (1) a wide range inmetallicity Z = 0 . , . , . ; (2) an e-folding expo-nentially decaying star formation rate with characteristictimescale τ = 0 . , . , . , . , . , . , . , . , . Gyr,(3) a broad redshift range between 0.0 and 3.0 with steps of0.05, and (4) the Calzetti et al. (2000) extinction law eval-uated at E ( B − V ) = 0 . , . , . , . , . , . . Our galaxylibrary contains no templates with emission lines.We run the Le Phare routine with this template li-brary on every object that lies projected within R and isbrighter than m ∗ + 2 . within the z G passband (except thatwe use [3 . for the two clusters at z > . ). This ensureswe are selecting the galaxy population in a consistent man-ner over the full redshift range. For each galaxy, we adopt auniform prior on the extinction law E ( B − V ) between 0.0and 1.0 and a weak, flat prior on the stellar mass between M ⊙ and M ⊙ .For the SED fit we increase the MAG_AUTO flux un-certainties for all 6 passbands by a factor of 2. We estimate c (cid:13) , 000–000 Chiu et al. this correction factor by examining the photometric repeata-bility of the galaxies that appear in multiple individual VLTexposures (Desai et al. 2012; Liu et al. 2014). With this cor-rection the resulting magnitude uncertainties correctly de-scribe the scatter in the repeated photometric measurementsof the same galaxies. Rescaling the uncertainties has no sig-nificant impact on the final result but increases the uncer-tainty of the stellar mass estimate for each galaxy by 25 % .For each cluster we first estimate the stellar mass of theBCG, M BCG ⋆ , fixing the redshift to the cluster redshift. TheBCG is chosen to be the brightest cluster galaxy projectedwithin R ; we select this galaxy visually using the NIRand optical imaging and then confirm in the catalog ( z G and [3 . ) that it is the brightest galaxy. We find that theBCGs in our cluster sample all prefer the templates with thecharacteristic e-folding timescale for the star formation rateto be τ Gyr. This indicates that the rapid star form-ing activity seen in the SPT selected Phoenix Cluster BCG(McDonald et al. 2014) is not present in our cluster sample.This result is consistent with the view that the evolutionof the typical BCG is well described by a CSP model with τ ≈ . Gyr out to redshift 1.5 (Lidman et al. 2012). Forthe final M BCG ⋆ estimates we restrict the template libraryto τ Gyr, which results in a ≈ reduction in the stel-lar mass uncertainties as compared to fitting across the fullrange of τ . This small change in uncertainty has no impacton our final result. We then estimate the stellar mass for theremaining galaxies using the same configuration except thatwe allow the redshift to float and fit the templates withoutrestricting τ .We adjust the Le Phare routine to output the best-fitmass M best ⋆ , the median mass M med ⋆ , the mass at the lower(higher) 68 % confidence level M lo ⋆ ( M hi ⋆ ) and the best-fit χ extracted over the full template library. We discard theobjects from the analysis where the best fit χ arises for astellar template. This stellar removal works well; testing onthe COSMOS field (Capak et al. 2007; Sanders et al. 2007;Ilbert et al. 2009) indicates we have a residual stellar con-tamination and a false identification rate for galaxies under1.5 % and ∼ % , respectively. The mass-to-light ratios Υ and their rms variations in the observed frame [3 . bandfor all clusters are provided in Table B1. These are extractedfrom the subset of galaxies projected within the virial regionthat have photo-z’s that are within ∆ z = 0 . of the clusterspectroscopic redshift.We examine those galaxies with M best ⋆ > M BCG ⋆ closely,because we expect no galaxy to be more massive than theBCG. We find that most of these galaxies can be excludedbecause they have redshifts far higher than the cluster. Intotal, there are 37 out of 2640 galaxies with M best ⋆ > M BCG ⋆ within R of the 14 clusters. That is, about 1.5 % of theobjects are discarded through this process. However, onemust take special care in cases of merging clusters, whichcould host one or more galaxies with masses similar to themost massive one. In a few cases (3 galaxies to be exact)we find through photo-z and visual inspection that thesegalaxies likely lie in the cluster and have mass estimatesslightly larger than the mass of our selected BCG. In thesecases we include those galaxies in the stellar mass estimate.We provide further details of our SED fit performance inAppendix A.The stellar mass estimate for the region within R , including the foreground and background galaxies, is thesum of M best ⋆ . The uncertainty includes the uncertainties onthe single galaxy masses (using M lo ⋆ and M hi ⋆ and assumingthe probability distribution for the stellar mass is Gaussian).We also calculate the fraction of objects f cor with un-physical mass outputs (i.e., log( M med ⋆ ) = − . ), which oc-cur mostly due to data corruption. We correct for these miss-ing galaxies by assuming that they share the same distribu-tion of stellar masses as the uncorrupted galaxies. We notethat this fraction varies between 3 and 10 % . A correction forthe masking of the bright stars is also applied. Thus, for eachcluster we estimate the total stellar mass M field ⋆ projectedwithin R as M field ⋆ = Σ i M best ⋆,i (1 − f mask ) (1 − f cor ) , (2)where f mask is the fraction of area within R that is maskedand M best ⋆,i is the best stellar mass estimate for galaxy i inthe cluster. We correct the stellar mass from the cluster field M field ⋆ forthe contribution from the foreground and background galax-ies M bkg ⋆ using a statistical correction. Because the FORS2field of view is small, the background regions outside R are contaminated by cluster galaxies. Thus, we use the COS-MOS survey to estimate the background correction.The COSMOS survey has 30-band photometry withwavelength coverage from UV to mid-infrared. To minimizesystematics we take two steps to make the COSMOS datasetas similar as possible to our SPT dataset. First, we choosethe passbands which are most similar to ours (from Sub-aru Suprime-Cam and Spitzer ) and apply color correctionswhere needed to convert the COSMOS photometry into ourpassbands. MAG_AUTO photometry is used in the COS-MOS field. Second, we degrade the COSMOS photometryto have the same measurement noise as in our dataset.We then measure the stellar mass for each galaxy in theCOSMOS field using the converted photometry, the same
Spitzer object detection, the same matching algorithm, andthe same fitting strategy as we applied to our own data.We correct this background estimate for the fraction of cor-rupted galaxies as described for the cluster fields in Equa-tion 2.Then, correcting the COSMOS background estimatesto the area of each cluster field, we subtract the backgroundestimate M bkg ⋆ , obtaining our estimate of the cluster stel-lar mass projected within R . We then apply a geometricfactor f geo to correct this projected quantity to the stel-lar mass within the virial volume M ⋆ using a typical radialgalaxy profile with concentration c gal500 = 1 . (Lin et al. 2004,Hennig in prep), which corresponds to a normalization cor-rection of f geo = 0 . . M ∗ = M BCG ⋆ + f geo (cid:16) M field ∗ − M bkg ∗ (cid:17) , (3)where we have defined M ⋆ to include M BCG ⋆ , the BCG stellarmass.In Appendix B, we compare the COSMOS backgroundto the background estimated in the non-cluster portions ofthe VLT imaging where a correction for cluster contami-nation has been applied. We find that the two backgrounds c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters agree at the 10 % level, leading to background corrected clus-ter stellar mass estimates M ⋆ that are consistent at the 4 % level. Thus, we adopt this difference as the amplitude of thesystematic uncertainty associated with our statistical back-ground correction. In this section we present the components of the clusterstellar mass function (SMF). These include the BCGs (Sec-tion 4.1), which we discuss first, followed by the full SMFand the luminosity function (LF) of the satellite galaxies(Section 4.2).
We present M BCG ⋆ for the 14 SPT clusters and compare themwith the measurements of H13 and vdB14, in which groupsand clusters at z > . are studied. H13 estimated M BCG ⋆ based on the mass-to-light technique assuming a passiveevolution model with the [3 . magnitude MAG_AUTO.vdB14 applied the same technique using the K s luminositytogether with the Sersic model fitting to the light profile.As noted in vdB14, the magnitude inferred by the Sersicprofile could differ from MAG_AUTO by up to 0.2 mag,depending on the shape of the light profile. In this workwe estimate M BCG ⋆ using an SED fit to the six bands avail-able in our survey. No special attempt is made to includeor deblend the extended halo or intracluster light (ICL)in any of these studies. We have three clusters in commonwith H13: SPT-CL J0102 − − − − M BCG ⋆ is about a factor of 2 higher, but in the other two clus-ters M BCG ⋆ agrees at better than 10 % . We compare the [3 . photometry of SPT-CL J0546 − − M BCG ⋆ – M relation of M BCG ⋆ = (5 . ± . × (cid:18) M × M ⊙ (cid:19) . ± . , (4)for the combined sample, and this relation is plotted in Fig-ure 2 (black dashed line). Thus, the BCG stellar mass con-stitutes about 0.12 % of the cluster halo mass at M =6 × M ⊙ . Because M BCG ⋆ scales with cluster halo masswith a power law index less than one, the fraction of thecluster mass made up by the BCG falls as M BCG ⋆ /M ∝ M − . ± . .The SPT sample scatters significantly about this rela-tion, providing evidence of intrinsic scatter in M BCG ⋆ at fixedcluster halo mass of σ int = 0 . ± . dex. The full sampleexhibits a consistent value σ int = 0 . ± . dex. Thus, the M [M ⊙ ] M B C G ⋆ [ M ⊙ ] CombinedH13vdB14This work
Figure 2.
The BCG stellar mass ( M BCG ⋆ ) versus cluster virialmass M for the SPT sample (blue), H13 (cyan) and vdB14(red). The H13 sample is corrected to Chabrier IMF. The bluedashed line is the best-fit for the SPT sample alone and the blacksolid line is the best fit for the combined sample (see Equation 4). characteristic scatter of the BCG masses at a fixed clusterhalo mass is 41 % . We extract the [3 . LF and the SMF using a statistical back-ground subtraction with the COSMOS field as the source ofthe background (see Section 3.3.2). We apply a correctionfrom the virial cylinder to the virial volume in the samemanner as in Section 3.3.2. The measured LF and SMF arein physical density units of Mpc − . The uncertainty of eachbin is estimated by the Poisson error associated with thegalaxy counts in the case of the LF and this error combinedwith the galaxy stellar mass measurement uncertainties forthe SMF.We stack the LF and SMF from 14 SPT clusters us-ing inverse-variance weighting within each bin. The numberdensities are corrected to the median redshift of the SPTclusters, z = 0 . , by multiplying by the ratio of the criticaldensities, (cid:16) E (0 . E ( z ) (cid:17) , where E ( z ) ≡ Ω Λ + Ω M (1 + z ) and z is the redshift of the cluster. We stack the LF within thespace of m − m ∗ with magnitude bins of width 0.5, where m ∗ comes from the CSP model described in Section 2.1.1. Giventhat the galaxy population in SPT selected clusters has beenshown to be well described by the CSP model (Song et al.(2012b), Hennig et al, in preparation) stacking LFs with re-spect to the m ∗ predicted at the redshift of each clusterprovides a simple way to extract the information for thenormalization and shape of the composite LF. We stack theSMF in the stellar mass range from – M ⊙ with binwidth of 0.2 dex. Finally, we characterize the stacked LFand SMF with the standard Schechter function (Schechter1976). Specifically, we fit the stacked LF directly in log space c (cid:13) , 000–000 Chiu et al. −2.0−1.5−1.0−0.50.00.51.01.52.02.5 m−m ∗ -1 m a g − ( M p c − ) ( E ( . ) E ( z ) ) m a g − ( M ⊙ ) − m a g − ( M ⊙ ) − Figure 3.
The stacked luminosity function of 14 SPT clusters ex-tracted from the [3 . photometry (black points). The grey pointis fainter than m ∗ +2 and is not included in the fit. The line marksthe best fit Schechter function. The LF is plotted versus m − m ∗ ,where m ∗ is obtained from the passive evolution model describedin the text (Section 2.1.1). The stacked number densities are cor-rected for evolution of the critical density ( ρ crit ∝ E ( z ) ) andnormalized to median redshift z = 0 . . to: Φ L ( m ) = 0 . . φ ∗ × . − . α L +1)( m − m ) × exp( − . − . m − m ) ) , (5)where m is the magnitude, m is the characteristic mag-nitude predicted by the passively evolving model (see Sec-tion 2.1.1), φ ∗ is the characteristic density and α L is thefaint end slope. We fit the stacked SMF directly in log spaceto: Φ M ( M ⋆ ) = ln(10) φ M × ( α M +1)( m ⋆ − M ) × exp( − ( m ⋆ − M ) ) , (6)where m ⋆ is the stellar mass in units of log ( m ⋆ /M ⊙ ) , M is the characteristic mass, φ M is the characteristic density,and α M is the faint end slope. We restrict our fit to thosegalaxies brighter than m ∗ + 2 in the LF analysis. Becausethe stellar mass is not a linearly-rescaled version of the mag-nitude, we choose the conservative depth limit used in theSMF analysis, which is based on the mass-to-light-inferredmass at brighter magnitude, m ∗ +1 . , assuming the passivelyevolving model for SMF analysis.The stacked LF and SMF are shown in Figure 3 andFigure 4, respectively. The best-fit parameters are given inTable 2. We convert the SMF and LF from physical numberdensity to the abundance per mass of M ⊙ (total baryonand dark matter mass) by using the mean density withinthe virial region at z = 0 . , which is ρ crit ( z = 0 . . Thisvalue is shown on the right y -axis. Similarly, to compare toa field LF or SMF one would convert from Mpc − to perunit mass by using the mean density of the universe at thatredshift h ρ i ( z ) = Ω M ( z ) × ρ crit ( z ) .The best-fit m indicates that the LF deviates from log(m ⋆ /M ⊙ ) [dex] -1 d e x − ( M p c − ) ( E ( . ) E ( z ) ) SPT d e x − ( M ⊙ ) − d e x − ( M ⊙ ) − vdB13 field (full) Figure 4.
The measured stellar mass from (SMF) obtained bystacking 14 SPT clusters. The black line is thebest fit Schechterfunction (see Table 2). The grey points are measurements beyondthe depth limit and are not used in the fit. For comparison, weshow the field SMF from vdB13.
Table 2.
Luminosity and Stellar Mass Function Parameters:The luminosity function (top) characteristic density, characteris-tic magnitude, faint end slope and reduced χ are shown followed(below) by the equivalent stellar mass function parameters. φ ∗ m [ Mpc − mag − ] [ mag ] α L χ . ± . − . ± . − . ± . . φ M M [ Mpc − dex − ] [ dex ] α M χ . ± . . ± . − . ± . . the predicted characteristic m ∗ [3 . for the passive evolutionmodel (Section 2.1.1) by − . ± . , suggesting the mildevidence (about 1.8 σ ) of the blue population at the highredshift clusters. The best-fit SMF and LF are consistentwith one another; the characteristic m ∗ [3 . at median red-shift z = 0 . predicted by the passively evolving model corre-sponds to the stellar mass of . M ⊙ , while the measuredcharacteristic mass is . ± . M ⊙ . The faint end slopes andcharacteristic densities are also in good agreement.In a recent paper, van der Burg et al. (2013, hereaftervdB13) compare the SMFs of the GCLASS low mass clus-ters to the field at redshift z = 0 . − . and find thenumber density of galaxies per unit mass (dark matter plusbaryons) in the field SMF is lower than that in the groupsover the mass range M ⊙ to . M ⊙ . This suggeststhat the galaxy formation rate has been lower over time inthe field than in the dense group and cluster environments.A similar picture had previously emerged in the local Uni-verse ( z < . ) (Lin et al. 2004, 2006), where the luminosityfunctions of K-band selected galaxies and of radio sourceswithin clusters are also significantly higher than the field c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters after corrections for the mean matter density differences inthe two environments. As seen in Figure 4, the normaliza-tion of the SMF for the SPT clusters on the massive end( log ( m ⋆ /M ⊙ ) ≈ . − . ) is significantly higher thanthe field (open triangle) measured by vdB13. By integrat-ing the best-fit SMF of SPT above our single galaxy stellarmass threshold of . × M ⊙ , we estimate the number ofgalaxies per unit total mass for SPT clusters is ≈ . ± . times higher than the field at z = 0 . − . . Our result re-inforces this picture that the cluster environment contains amore biased galaxy population than the field. In this section we present our measurements for the stellarmass fraction, ICM mass fraction, collapsed baryon fractionand baryon fraction: f ⋆ ≡ M ⋆ M (7) f ICM ≡ M ICM M (8) f c ≡ M ⋆ M b (9) f b ≡ M b M , (10)where M ⋆ is the stellar mass (see Equation 3), M ICM is theICM mass (see Section 3.2) and M b ≡ M ⋆ + M ICM is thetotal mass in baryons. M is the halo virial mass, estimatedusing the SZE observable (see Section 3.1).In addition, we study mass and redshift trends in ourSPT clusters and in the combined sample that includes theclusters studied in the literature (discussed in Section 2.2).Note that we are not probing the evolution of the baryoncontent by directly tracing the progenitors, because our SPTsample lacks low mass groups at all redshifts. We insteadestimate the baryon content of the massive clusters withrespect to the characteristic mass at the different epochsstatistically by fitting the scaling relation simultaneously inmass and redshift space (see Section 5.1). We also compareour cluster results with more general results coming fromexternal, non-cluster datasets. We use the universal baryonfraction f b estimated using the Planck
CMB anisotropy ob-servations (Planck Collaboration et al. 2014), and we esti-mate the universal stellar density parameter Ω ⋆ , where themean stellar density at z = 0 is extracted from the local K -band galaxy LF (Kochanek et al. 2001) and the mean stellardensity at z = 1 is extracted from the vdB13 analysis. Thesevalues have been corrected to our fiducial cosmology and areappropriate for a Chabrier IMF, enabling comparison to ourcluster measurements. We fit these measurements from our cluster ensemble andalso from the combined sample to a power law relation inboth mass and redshift: f obs ( M , z ) = α obs (cid:18) M M piv (cid:19) β obs (cid:18) z z piv (cid:19) γ obs (11) Table 3.
Mass and Redshift Trends of Baryon Composition with M piv ≡ × M ⊙ : The columns contain the quantity of in-terested, the normalization at the pivot mass and redshift, massdependence and redshift dependence (see Equation 11) for theSPT sample alone (above) and for the SPT sample together withthe literature sample (below). f obs α obs β obs γ obs † SPT Sample Results with z piv ≡ . f ⋆ . ± . − . ± .
27 1 . ± . f ICM . ± .
005 0 . ± .
13 0 . ± . f c . ± . − . ± .
22 0 . ± . f b . ± .
006 0 . ± .
13 0 . ± . Combined Sample Results with z piv ≡ f ⋆ . ± . − . ± .
09 0 . ± . ± . f ICM . ± . . ± . − . ± . ± . f c . ± . − . ± .
10 0 . ± . ± . f b . ± . . ± . − . ± . ± . † The second γ obs uncertainty arises from the 15 % M systematic uncertainty. where M piv and z piv are the mass and redshift pivot points, obs corresponds to the different observables and α obs , β obs and γ obs correspond to normalization of the best fit relation,the power law index of the mass dependence and the powerlaw index of the redshift dependence, respectively. We per-form χ fitting directly in log space using the measurementuncertainties and accounting for intrinsic scatter. For theSPT and combined samples we choose the pivot points tobe the median mass M = 6 × M ⊙ . For the SPT samplewe adopt the redshift pivot z piv = 0 . , consistent with themedian redshift of the sample, but for the combined samplewe adopt a redshift pivot of z piv = 0 .The parameters for the best-fit relations for the SPTsample and for the combined sample are listed in Table 3,while the measured cluster virial masses, ICM masses, stel-lar masses and the derived quantities above are listed inTable B1. These results are summarised in Figures 5 and 6,where the first figure focuses on the mass trends and the sec-ond focuses on the redshift trends. In the subsections belowwe discuss each derived quantity in turn. M Systematic Uncertainties
We account for systematic differences in M estimation be-tween the low redshift comparison sample (L03, Zha11 andGZ13) and the high redshift sample (SPT with two addi-tional samples of H13 and vdB14 added when comparing f ⋆ )by adopting a 15 % (1 σ ) systematic virial mass uncertainty(see discussion in Section 2.2). These virial mass uncertain-ties imply corresponding R uncertainties that lead also tosystematic uncertainties in the stellar mass and ICM massfor each cluster. We estimate the systematic uncertainties inthe redshift variation parameter γ obs (Table 3) by perturb-ing the virial masses of the high redshift sample by ± and extracting the best fit parameters in each case. The 1 σ systematic uncertainty is estimated as half the difference be-tween the two sets of parameters. This virial mass systematicis only important for the measured redshift trends. c (cid:13) , 000–000 Chiu et al.
We also account for systematic differences in the measure-ment uncertainties among the different samples by solvingfor a best fit intrinsic scatter separately for each sample.For the SPT sample, where mass uncertainties include bothmeasurement and systematic uncertainties (Section 3.1), wefind no need for an additional intrinsic scatter. The best fitestimates of the intrinsic scatter for the other samples are9 % for f ICM and f b in L03, 14 % for f ⋆ , f ICM and f b in GZ13,18 % for f ⋆ in H13 and 20 % in vdB14, and 20 to 22 % for thefractions in Zha11. Three of the samples with the largestintrinsic scatter (Zha11, H13 and vdB14) employ velocitydispersions for single cluster mass estimation as opposed toX-ray or SZE mass indicators. This is not surprising, becauseit has been shown that cluster velocity dispersions providehigh scatter single cluster mass estimates (see Saro et al.2013, and references therein). Velocity dispersions can beeffectively used in ensemble to calibrate ICM based singlecluster mass estimates (Bocquet et al. 2015). f ⋆ The stellar mass fraction we estimate here is the mass instars within cluster galaxies. We make no attempt to ac-count for the ICL component. Figure 5 contains a plot ofour results (blue). The mean f ⋆ of our fourteen clusters is . ± . , and the characteristic value at z = 0 . and M = 6 × M ⊙ is . ± . . The SPT sample pro-vides no evidence for a mass or redshift trend, but the largemass trend uncertainty ( f ⋆ ∝ M − . ± . ) means the sam-ple is statistically consistent with the trend for more mas-sive clusters to have lower f ⋆ (L03). In the combined sample,there is 3.7 σ evidence for a mass trend f ⋆ ∝ M − . ± . ,which is also consistent with the L03 result. The com-bined sample exhibits no significant redshift variation ( f ⋆ ∝ (1 + z ) . ± . ± . ), where the second uncertainty reflectsthe 15 % (1 σ ) systematic virial mass uncertainty. The char-acteristic value at z = 0 is f ⋆ = 0 . ± . (statistical),which is in good agreement with the SPT value at z piv = 0 . .Also shown in the shaded region is the f ⋆ constraintemerging from a combination of the stellar mass densityfrom the K -band local luminosity function (Kochanek et al.2001), Ω ⋆ h = 3 . ± . × − with h = 0 . , with themost recent combined results ( Planck + WMAP polariza-tion+SNe+BAO+SPT clusters) on the cosmological matterdensity Ω M = 0 . ± . (Bocquet et al. 2015). The clus-ter f ⋆ is in good agreement with this estimate of the univer-sal average field value f ⋆ = (0 . ± . at z = 0 . However,the average field f ⋆ = 0 . ± . (see Figure 6) inferredfrom the SMF measurements at z=0.85–1.2 (vdB13) is sig-nificantly lower than the cluster f ⋆ . The cluster or group f ⋆ may be altered over time through either the accretion oflower mass clusters or groups (higher f ⋆ ) or through infallfrom the field (lower f ⋆ ). Presumably, these influences mustcombine to produce the transformation in f ⋆ from a lowermass cluster at z = 1 to a higher mass clusters at z = 0 . Wereturn to this discussion in Section 6.We compare the high redshift SPT results to two othersamples at high redshift: vdB14 and H13. The virial massesfor the majority of the vdB14 systems are below × M ⊙ M [10 M ⊙ ] f b ( + z ) γ b f c ( + z ) γ c f I C M ( + z ) γ I C M f ⋆ ( + z ) γ ⋆ L03Zha11 GZ13H13 vdB14 This work
Figure 5.
The baryonic fractions f ⋆ , f ICM , f c and f b are shownas a function of cluster virial mass M for the combined sam-ple. In all cases the measurements have been corrected to z = 0 using the best fit redshift trend. The best fit mass trend isshown in green (Table 3). The color coding and point stylesare defined in the upper panel and is the same throughout.The red shaded region indicates the universal baryon composi-tion from combining the best-fit cosmological parameters fromBocquet et al. (2015) together with the local K -band luminosityfunction (Kochanek et al. 2001). and therefore lower mass than our SPT clusters. The one re-maining system in this mass range falls near the bottom ofour distribution of f ⋆ . The H13 sample shows stellar massfractions that are in good agreement with ours. We havethree clusters in common; combining these measurements wedetermine that the differences are . σ , . σ and . σ for M ⋆ , M and f ⋆ measurements, respectively. vdB14 expressconcern that the M ⋆ estimated by the mass-to-light tech-nique in H13 could possibly be overestimated by as much asa factor of 2. While the largest difference with our sampleis indeed with M ⋆ , the level of agreement between the H13results and our SED fitting results would suggest that thebias is likely smaller (about ± ). f ICM
The majority of the baryonic mass within clusters lies withinthe hot ICM. The arithmetic mean of f ICM for the 14 SPTclusters is . ± . , and the characteristic value at c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters f b ( M /6 × M ⊙ ) β b f c ( M /6 × M ⊙ ) β c f I C M ( M /6 × M ⊙ ) β I C M f ⋆ ( M /6 × M ⊙ ) β ⋆ L03Zha11 GZ13H13 vdB14 This work
Figure 6.
The redshift trends of f ⋆ , f ICM , f c and f b for thecombined cluster sample. The color coding of the points and thered bands are the same as in Figure 5. For f ⋆ and f c we showthe universal value at z = 0 (red) and at z = 0 . − . (blue).Measurements have been corrected using the best fit mass trendsto the mass × M ⊙ , and the best fit redshift trend is shownin green (Table 3). z = 0 . and M = 6 × M ⊙ is . ± . . A clearmass trend ( f ICM ∝ M . ± . ), significant at the . σ level,is seen for SPT clusters. This trend is steeper than (butstatistically consistent with) the trends, β ICM = 0 . ± . and . ± . , presented by Zha11 and GZ13, but steeperat 2.1 σ than the result β ICM = 0 . ± . presented byAndreon (2010). The combined sample has a preferred masstrend β ICM = 0 . ± . , which is 1.5 σ shallower than theSPT sample.These results, extending to redshift z = 1 . , show theclear tendency for f ICM to be suppressed in lower massclusters— first shown in studies of individual low redshiftclusters (David et al. 1993) and later with a uniform anal-ysis of a large sample of low redshift clusters (Mohr et al.1999).The characteristic value of the combined sample at z piv = 0 and M piv = 6 × M ⊙ is f ICM = 0 . ± . (statistical only), which is higher than the z = 0 . SPT sam-ple f ICM = 0 . ± . . However, neither the SPT high red-shift sample nor the combined sample exhibits evidence forredshift variation in f ICM with γ ICM = − . ± . ± . .The impact of the halo mass 15 % systematic uncertainty on the redshift trend introduces an additional systematicuncertainty of σ γ ICM = 0 . which is larger than the statis-tical uncertainty. This underscores the importance of usinga homogeneous sample with consistently derived virial massmeasurements. f c The collapsed baryon fraction f c is the fraction of bary-onic mass that has cooled to form stars that lie in galax-ies and thereby reflects an integral of the star formationefficiency within the halo averaged over cosmic time (e.g.David & Blumenthal 1992). As already noted, we make noattempt to include an estimate of the ICL contributionhere. The arithmetic mean f c of our fourteen clusters is . ± . , and the characteristic value at z = 0 . and M = 6 × M ⊙ is . ± . (statistical).The SPT sample exhibits no evidence for either a mass orredshift trend. The combined sample exhibits a 6.5 σ sig-nificant mass trend f c ∝ M − . ± . with the collapsedbaryon fraction falling to lower values in high mass clus-ters and a characteristic value of . ± . (statisti-cal) at z = 0 . The redshift trend from the combined sample f c ∝ (1 + z ) . ± . ± . is significant at 1.8 σ if we add thestatistical and systematic uncertainties in quadrature.Note that in the case of f c the 15 % systematic uncer-tainty in M has no impact on the f c measurement, be-cause a shift in R has approximately the same impact on M ⋆ and M ICM ,. However, because of the steep mass trendfor f c ( β c ≈ − . ), a shift in the virial mass of the high red-shift sample impacts the best fit redshift trend, because thisshift masquerades as a shift in f c of δf c ∼ − . δM /M .This impacts the estimate of the systematic uncertainty in γ c . This process is also at work for the other fractions, butbecause their mass dependences are weaker, the impact issmaller.In Figure 5 we see that f c decreases with cluster mass,and the scatter about this trend (especially in the Zha11sample) is less than in the case of f ⋆ . This measure is inter-esting because the M measurements come in only throughdefining the virial radius, and if the radial variation in f ICM and f ⋆ are mild, then f c has only a weak dependence on thevirial mass estimates. Thus in cases where the M esti-mates exhibit large uncertainties, the f c can be an effectiveway of exploring trends in the mix of stars and ICM withinclusters.Our study indicates that over cosmic time the collapsedbaryon fraction f c at fixed cluster halo mass falls. This red-shift trend is driven by the slight rise in the ICM mass frac-tion f ICM and slight fall in stellar mass fraction f ⋆ . f b The arithmetic mean of the baryon fraction for our SPT clus-ters is . ± . (statistical only), and the characteristicvalue at z = 0 . and M = 6 × M ⊙ is . ± . (statistical). This is lower than the characteristic values ofthe combined sample at z = 0 of . ± . (statistical).However, neither the SPT sample nor the combined sample( f b ∝ (1 + z ) − . ± . ± . ) provides clear evidence for aredshift trend. The mass systematics between the low and c (cid:13) , 000–000 Chiu et al. high redshift samples introduce an uncertainty in the red-shift trend parameter of σ γ b = 0 . , which is larger than thestatistical uncertainty, implying that controlling mass sys-tematics among the different samples is crucial. The SPTsample exhibits a mass trend f b ∝ M . ± . that has 3 σ significance. The combined sample exhibits a mass trend f b ∝ M . ± . , which is somewhat shallower and is signif-icant at 3.6 σ . Because our sample includes the highest redshift massive( M > × M ⊙ ) clusters studied to date, our analysisis useful for constraining the redshift variation of the ICMand stellar mass components on cluster mass scales. Whilewe do consider intrinsic scatter in fitting the observed prop-erties within our sample, the sample does not provide mean-ingful constraints on this scatter; thus, our results shed nolight on assembly bias, which would link the baryon proper-ties of individual clusters to the properties of the large scaleenvironment within which they formed. A joint analysis ofthe SPT sample and a comparison sample indicates that thecluster collapsed baryon fraction (accounting only for starsin galaxies) within R is decreasing from 10.7 % to 8.6 % on the characteristic mass scale M piv = 6 × M ⊙ since z ≈ . ; the redshift trend is significant at the 1.8 σ confi-dence level when accounting for a 15 % virial mass systematicuncertainty between the literature and SPT samples. More-over our analysis indicates that this change is driven by aweak increase in the ICM fraction ( f ICM changes from 9.6 % to 11.2 % ) and a weak decrease in the stellar fraction from1.1 % to 1.0 % over that same redshift range. These sametrends in f ICM and f ⋆ lead to a weak trend in the baryonfraction (from 10.7 % to 12.3 % ) from z = 0 . to the present,a change that is only 0.7 σ significant given the systematicmass uncertainties between the high redshift and local com-parison samples.To build a physical picture it is important to takenote of the mass trends in the stellar mass fraction f ⋆ ∝ M − . ± . that indicate that high mass clusters have f ⋆ values that lie below those of groups and that are compa-rable to or even higher than the field f ⋆ at z = 0 (see alsoL03, vdB13). The ICM mass fractions f ICM behave oppo-sitely f ICM ∝ M . ± . (see also Mohr et al. 1999), withgroups having lower values than massive clusters, whose f ICM values are approaching but still lower than the uni-versal baryon fraction. These mass trends then give rise tothe trend of falling collapsed baryon fraction f c with mass f c ∝ M − . ± . .Because of the clear mass trends and weak redshifttrends in f ⋆ and f ICM , a simple merging scenario for haloformation, where the accretion of low mass (group-scale)halos is dominating the mass assembly of massive clusters,does not provide an adequate explanation of the observa-tions. In general, such a scenario would lead to f ⋆ that is ap-proximately independent of cluster halo mass (Balogh et al.2008). The massive halos of today form from halos that werelower mass at higher redshift, so if these low mass subclus-ters had lower f ⋆ or higher f ICM at higher redshift, then thesimple merger scenario could in principle be consistent withthe data. However, the weak redshift variation in these frac- tions at fixed halo mass that we estimate here for massivehalos does not help to resolve the situation, because it indi-cates that f ⋆ and f ICM at fixed halo mass have changed onlyweakly over time; if trends on the massive end are coupledwith similar trends on the lower mass end, then the simplemerging scenario must be flawed. The conclusion that infallfrom the field and/or the inclusion of stripping processesthat modify the apparent stellar fraction during the processof the growth of massive, cluster scale halos is inescapable.Infall from the field likely plays a critical role in thegrowth of massive clusters. Studies of the standard hier-archical structure formation scenario on the mass scalesof interest here indicate that ∼ % of the cluster galaxieshave previously been in lower mass group or cluster halos(McGee et al. 2009) and that the rest infall from the field.In the case of f ⋆ , we have shown that the field has lower f ⋆ in comparison to massive clusters at redshift z = 0 . (Sec-tion 4.2) and that it has comparable values of f ⋆ at z = 0 (seeFigure 6). Through an appropriate mix of field and groupaccretion the f ⋆ values in massive clusters could in principleeither increase or decrease with cosmic time. Our results in-dicate that this mix of field and group accretion to build upthe halos of the most massive clusters must produce haloswith f ⋆ that are similar (at ∼ level) up to (or weaklydecreasing since) redshift z ∼ .Add to this the likely stripping of stellar material frominfalling galaxies during the accretion and relaxation pro-cess, and one has an additional mechanism to reduce theobserved f ⋆ over cosmic time, because the ICL from thesestripped stars is not included in the f ⋆ measurements here.Lin & Mohr (2004) suggested just such a mechanism to rec-oncile the falling f ⋆ with halo mass they observed in the localUniverse. They presented a toy model that suggested such amechanism would have to lead to an ICL mass fraction thatincreases with halo mass and reaches high values of ≈ % of the stars in the central galaxy of the clusters. Neitherthis trend nor ICL fractions at this high redshift have beenobserved in recent observational studies (Zibetti et al. 2005;Gonzalez et al. 2013). Presumably, as massive clusters grow,a reduction of f ⋆ through both accretion from the field andstripping of stars from cluster galaxies is counterbalancingthe increase of f ⋆ due to accretion of lower mass subclusters.Together these processes must transform high f ⋆ low massclusters into lower f ⋆ high mass clusters. Moreover, theseprocesses must maintain a roughly constant f ⋆ at fixed halomass over cosmic time on cluster mass scales.A similar scenario of infall from the field and accre-tion of subclusters could explain the trends in f ICM as afunction of halo mass and redshift. In the case of f ICM , thefield value, which is inferred by the
Planck measurement, ishigher than that in the clusters at z = 0 . and remains soto z = 0 (see Figure 6). Thus, given our observed weaklyincreasing cluster f ICM at fixed halo mass since z ∼ , theincreases in f ICM during cluster growth from infall from thefield are compensating for the decreases in f ICM from ac-cretion of subclusters. These constraints, when coupled toa detailed hydrodynamical study, would presumably enableone to constrain processes such as early preheating as well asentropy injection from AGN residing in groups and clusters. c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters In this work we study the stellar mass function and baryoncomposition of 14 high redshift SZE-selected clusters be-tween redshifts 0.572 and 1.32 that have a median mass M of × M ⊙ . We estimate f ⋆ , f ICM , f c and f b within R (Table B1). Our sample provides the highest redshift, uni-formly selected sample to date for the study of the baryoncontent in massive clusters; our measurements together withlow redshift measurements in the literature enable us to con-strain the redshift variation of these quantities. We summa-rize our results here. • We examine the M BCG ⋆ – M relation by combining oursample with the sample of H13 and vdB14 (Section 4.1,Equation 4). On the cluster mass scale of × M ⊙ theBCG stellar mass constitutes . ± . of the halo mass.That fraction falls with cluster mass as M − . ± . . BCGstellar masses scatter about the best fit M BCG ⋆ – M rela-tion with a characteristic value of 41 % , a measure of theconsiderable variation in the BCG population. • We measure the stacked SMF of these clusters and fit itto a Schechter function (Table 2; Section 4.2). The charac-teristic mass is M = 10 . ± . M ⊙ , consistent with valuesderived in low mass clusters at high redshift (vdB14) and atlow redshift (Vulcani et al. 2013). Moreover, through com-parison to constraints on the field SMF in the same redshiftrange (vdB13), we show that the number of galaxies withstellar mass above our threshold ( . × M ⊙ ) per unittotal mass is higher in clusters than in the field by a factorof . ± . .We take the measurements of the baryon compositionin each of our clusters and fit to power law relations in red-shift and mass (Equation 11). We present best fit trends forthe SPT sample and for a combined sample that includesseveral samples from the literature (Table 3). In combiningwith external samples we homogenise the stellar mass mea-surements to the Chabrier IMF (Section 2.2.1), we applycorrections for the differences in the virial mass estimates(Section 2.2.2), we adopt a 15 % (1 σ ) systematic virial massuncertainty (Section 5.1.1), and we account for differencesin the estimates of measurement uncertainties by solving forindependent intrinsic scatter estimates for each subsample(Section 5.1.2). The key results are described below. • The stellar mass fraction has a characteristic value . ± . (statistical) for clusters with mass M = 6 × M ⊙ at z = 0 . and . ± . (statistical) at z = 0 . It falls withcluster halo mass f ⋆ ∝ M − . ± . and mildly decreaseswith cosmic time f ⋆ ∝ (1 + z ) . ± . ± . with 1.45 σ sig-nificance, where the second component of the uncertaintyrepresents the impact of the 15 % systematic mass uncer-tainty between the low and high redshift samples. A similarresult for the mass trend β ⋆ ≈ − . is also seen for lowmass clusters and groups at . z . (Balogh et al.2014). The mass trend and mild redshift trend indicate thatthe infall from subclusters (which would tend to increase f ⋆ )and infall from the field and stripping of stars from clustergalaxies (which would both tend to decrease the observed f ⋆ ) must combine to enable the transformation of f ⋆ from low mass clusters into that of higher mass clusters havingsimilar f ⋆ over the redshift range < z < . Numerical sim-ulations suggest that approximately 40 % of cluster galaxieshave been accreted as members of subclusters, and the re-mainder from the field (McGee et al. 2009), but additionalstudy is warranted to test whether the observed trends in f ⋆ (now constrained both as a function of mass and of redshift)can be reproduced by current structure formation scenarios. • The ICM mass fraction has a characteristic value in clus-ters with mass M = 6 × M ⊙ of . ± . (statis-tical) at z = 0 . and . ± . (statistical) at z = 0 .It rises with cluster halo mass f ICM ∝ M . ± . andevolves weakly with redshift at fixed halo mass as f ICM ∝ (1 + z ) − . ± . ± . , where the . is due to the 15% sys-tematic mass uncertainty between the low and high redshiftsamples. The trend of increasing f ICM with mass has beenpreviously observed (Mohr et al. 1999) and can be explainedthrough entropy injection through early preheating or fromcluster AGN. A weakly varying f ICM with cosmic time couldbe explained by infall from the field, where f ICM is largerthan that in clusters at z = 0 . and z = 0 (see Figure 6).Hydrodyamical studies of this scenario are needed. • The collapsed baryon fraction determines the fraction ofthe baryonic component that has cooled to form stars. Itis the ratio of the stellar mass to the ICM plus stellarmass. The characteristic value at cluster masses M =6 × M ⊙ is . ± . (statistical) at z = 0 . and . ± . (statistical) at z = 0 . It falls with halo massas f c ∝ M − . ± . , indicating with 6.5 σ significance thata smaller fraction of halo baryons is in the form of starsin the most massive halos. The redshift trend is f c ∝ (1 + z ) . ± . ± . , where the second uncertainty is due tothe 15 % systematic mass uncertainty between the low andhigh redshift samples. Thus, there is ≈ . σ evidence thatthe collapsed baryon fraction is falling with cosmic time, andthis is driven by the weak trends of rising f ICM and falling f ⋆ presented above. • The baryon fraction f b is the fraction of the halo mass thatis in ICM and stars. The characteristic value at cluster mass M = 6 × M ⊙ is . ± . (statistical) at z = 0 . and . ± . (statistical) at z = 0 . It rises with halo mass as f b ∝ M . ± . , and this 3.7 σ mass trend is affected both bythe increase in f ICM and the decrease in f ⋆ with cluster mass.The evidence for redshift variation at fixed halo mass is weak f b ∝ (1 + z ) − . ± . ± . , where the second uncertainty isdue to the 15% systematic mass uncertainty between thelow and high redshift samples. If the two uncertainties areadded in quadrature, there is no significant evidence (0.7 σ )that the baryon fraction is evolving.As already discussed in Section 6, these mass and red-shift trends in baryon quantities are not consistent with asimple hierarchical structure formation merger model wheremassive clusters form solely through the accretion of lowermass clusters and groups. Significant accretion of galaxiesand ICM from the field must also occur, and this accre-tion together with infall of subclusters can likely explain theweak variation (at fixed cluster halo mass) in f ⋆ and in f ICM over cosmic time. Additionally, the loss of stellar mass fromgalaxies through stripping is an additional mechanism that c (cid:13) , 000–000 Chiu et al. would allow for f ⋆ to fall as low mass clusters grow to highermass.This analysis of the first homogeneously selected highmass cluster sample extending to high redshift allows forinteresting initial constraints on the redshift trends in thebaryon content; however, these trends are dependent to someextent on the adopted systematic virial mass uncertaintybetween the low and high redshift samples. If the system-atic virial mass uncertainty is 15% there are no statisticallysignificant redshift trends. Higher virial mass systematic un-certainties would further reduce the significance of trends.A reduction of the 15 % systematic virial mass uncertaintyto 10 % or 5 % would result in a fractional reduction (to / or / , respectively) for the redshift trend systematic uncer-tainties γ sysobs . In the case of a 5 % systematic virial mass un-certainty, the significance of the redshift trends for f ⋆ ( f ICM , f c , f b ) would increase from . σ ( . σ , . σ , . σ ) to . σ ( . σ , . σ , . σ ). It is clear that what is needed isa systematic study of a large, homogeneously selected clus-ter sample with high quality mass estimates that spans abroad redshift range.We acknowledge the support by the DFG Cluster ofExcellence “Origin and Structure of the Universe” and theTransregio program TR33 “The Dark Universe”. The cal-culations have been carried out on the computing facilitiesof the Computational Center for Particle and Astrophysics(C2PAP) and of the Leibniz Supercomputer Center (LRZ).BB is supported by the Fermi Research Alliance, LLC underContract No. De-AC02-07CH11359 with the United StatesDepartment of Energy. BS acknowledges the support ofthe NSF grants at Harvard and SAO (AST-1009012, AST-1009649 and MRI- 0723073). TS acknowledges the supportfrom the German Federal Ministry of Economics and Tech-nology (BMWi) provided through DLR under project 50OR 1210. The South Pole Telescope is supported by theNational Science Foundation through grant ANT-0638937.Partial support is also provided by the NSF Physics FrontierCenter grant PHY-0114422 to the Kavli Institute of Cos-mological Physics at the University of Chicago, the KavliFoundation and the Gordon and Betty Moore Foundation.Optical imaging data from the VLT programs 088.A-0889 and 089.A-0824, HST imaging data from programsC18-12246 and C19-12447, and Spitzer Space Telescopeimaging from programs 60099, 70053 and 80012 enable theSED fitting in this analysis. X-ray data obtained with Chan-dra X-ray Observatory programs and XMM- Newton
Obser-vatory program 067501 enable the ICM mass measurements.The SPT survey program SPT-SZ enabled the discovery ofthese high redshift clusters and subsequent analyses haveenabled virial mass estimates of these systems. Optical spec-troscopic data from VLT programs 086.A-0741 and 286.A-5021 and Gemini program GS-2009B-Q-16, GS-2011A-C-3,and GS-2011B-C-6 were included in this work. Additionalspectroscopic data were obtained with the 6.5 m MagellanTelescopes.Facilities: South Pole Telescope,
Spitzer /IRAC, VLT:Antu (FORS2),
HST /ACS,
Chandra , XMM-
Newton , Mag-ellan
REFERENCES
Andersson K. et al., 2011, ApJ, 738, 48Andreon S., 2010, MNRAS, 407, 263Applegate D. E. et al., 2014, MNRAS, 439, 48Arnaud M., Evrard A. E., 1999, MNRAS, 305, 631Arnouts S., Cristiani S., Moscardini L., Matarrese S.,Lucchin F., Fontana A., Giallongo E., 1999, MNRAS, 310,540Ashby M. L. N. et al., 2009, ApJ„ 701, 428Balogh M. L., McCarthy I. G., Bower R. G., Eke V. R.,2008, MNRAS, 385, 1003Balogh M. L. et al., 2014, MNRAS, 443, 2679Bayliss M. B. et al., 2014, ApJ, 794, 12Benson B. A. et al., 2013, ApJ, 763, 147Bertin E., Arnouts S., 1996, AAPS, 117, 393Bleem L. E. et al., 2015, ApJS, 216, 27Bocquet S. et al., 2015, ApJ, 799, 214Bruzual G., Charlot S., 2003, MNRAS, 344, 1000Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koorn-neef J., Storchi-Bergmann T., 2000, ApJ, 533, 682Capak P. et al., 2007, ApJS, 172, 99Cappellari M. et al., 2006, MNRAS, 366, 1126Carlstrom J. E. et al., 2011, PASP, 123, 568Cavaliere A., Fusco-Femiano R., 1978, A&A, 70, 677Cavaliere A., Menci N., Tozzi P., 1999, MNRAS, 308, 599Chabrier G., 2003, PASP, 115, 763Chiu I.-N. T., Molnar S. M., 2012, ApJ, 756, 1David L. P., Blumenthal G. R., 1992, ApJ, 389, 510David L. P., Slyz A., Jones C., Forman W., Vrtilek S. D.,Arnaud K. A., 1993, ApJ, 412, 479Desai S. et al., 2012, ApJ, 757, 83Djorgovski S., Davis M., 1987, ApJ, 313, 59Donahue M. et al., 2014, ApJ, 794, 136Dressler A., Shectman S. A., 1988, AJ, 95, 985Erben T. et al., 2005, Astronomische Nachrichten, 326, 432Fabian A. C., 1994, ARAA, 32, 277Fazio G. G. et al., 2004, ApJS, 154, 10Foley R. J. et al., 2011, ApJ, 731, 86Forman W., Jones C., 1982, ARAA, 20, 547Fowler J. W. et al., 2007, Applied Optics, 46, 3444Frenk C. S., White S. D. M., Efstathiou G., Davis M., 1990,ApJ, 351, 10Geller M. J., Beers T. C., 1982, PASP, 94, 421Giodini S. et al., 2009, ApJ, 703, 982Gonzalez A. H., Sivanandam S., Zabludoff A. I., ZaritskyD., 2013, ApJ, 778, 14Gonzalez A. H., Zaritsky D., Zabludoff A. I., 2007, ApJ,666, 147Haiman Z., Mohr J. J., Holder G. P., 2001, ApJ, 553, 545Henry J. P., Arnaud K. A., 1991, ApJ, 372, 410High F. W., Stubbs C. W., Rest A., Stalder B., Challis P.,2009, AJ, 138, 110Hilton M. et al., 2013, MNRASIlbert O. et al., 2006, A&A, 457, 841Ilbert O. et al., 2009, ApJ, 690, 1236Jee M. J., Hughes J. P., Menanteau F., Sifón C., Mandel-baum R., Barrientos L. F., Infante L., Ng K. Y., 2014,ApJ, 785, 20Kauffmann G. et al., 2003, MNRAS, 341, 33Kochanek C. S. et al., 2001, ApJ, 560, 566Kroupa P., 2001, MNRAS, 322, 231 c (cid:13) , 000–000 aryon Content of Massive Galaxy Clusters Lidman C. et al., 2012, MNRAS, 427, 550Lilje P. B., 1992, ApJ, 386, L33Lin Y., Mohr J. J., Gonzalez A. H., Stanford S. A., 2006,ApJ, 650, L99Lin Y., Mohr J. J., Stanford S. A., 2003, ApJ, 591, 749Lin Y., Mohr J. J., Stanford S. A., 2004, ApJ, 610, 745Lin Y.-T., Mohr J. J., 2004, ApJ, 617, 879Lin Y.-T., Stanford S. A., Eisenhardt P. R. M., VikhlininA., Maughan B. J., Kravtsov A., 2012, ApJ, 745, L3Liu J. et al., 2014, ArXiv e-prints 1407.6001Martino R., Mazzotta P., Bourdin H., Smith G. P., Bar-talucci I., Marrone D. P., Finoguenov A., Okabe N., 2014,MNRAS, 443, 2342McDonald M. et al., 2013, ApJ, 774, 23McDonald M. et al., 2014, ApJ, 784, 18McGee S. L., Balogh M. L., Bower R. G., Font A. S., Mc-Carthy I. G., 2009, MNRAS, 400, 937Menanteau F. et al., 2012, ApJ, 748, 7Mohr J., Evrard A., 1997, ApJ, 491, 38Mohr J. J., Evrard A. E., Fabricant D. G., Geller M. J.,1995, ApJ, 447, 8+Mohr J. J., Mathiesen B., Evrard A. E., 1999, ApJ, 517,627Molnar S. M., Chiu I.-N., Umetsu K., Chen P., Hearn N.,Broadhurst T., Bryan G., Shang C., 2010, ApJ, 724, L1Perlmutter S. et al., 1999, ApJ, 517, 565Pickles A. J., 1998, PASP, 110, 863Planck Collaboration et al., 2014, A&A, 571, A16Reichardt C. L. et al., 2013, ApJ, 763, 127Riess A. G. et al., 1998, AJ, 116, 1009Ruel J. et al., 2014, ApJ, 792, 45Salpeter E. E., 1955, ApJ, 121, 161Sanders D. B. et al., 2007, ApJS, 172, 86Saro A., Mohr J. J., Bazin G., Dolag K., 2013, ApJ, 772,47Schechter P., 1976, ApJ, 203, 297Schellenberger G., Reiprich T. H., Lovisari L., NevalainenJ., David L., 2014, ArXiv e-prints 1404.7130Schirmer M., 2013, ApJS, 209, 21Sifón C. et al., 2013, ApJ, 772, 25Song J., Mohr J. J., Barkhouse W. A., Warren M. S., RudeC., 2012a, ApJ, 747, 58Song J. et al., 2012b, ApJ, 761, 22Stalder B. et al., 2013, ApJ, 763, 93Staniszewski Z. et al., 2009, ApJ, 701, 32Sunyaev R. A., Zel’dovich Y. B., 1970, Comments on As-trophysics and Space Physics, 2, 66Sunyaev R. A., Zel’dovich Y. B., 1972, Comments on As-trophysics and Space Physics, 4, 173Tauber J. A., 2000, in IAU Symposium 201: New Cosmo-logical Data and the Values of the Fundamental Parame-ters, Lasenby A., Wilkinson A., eds., ASPvan der Burg R. F. J. et al., 2013, A&A, 557, A15van der Burg R. F. J., Muzzin A., Hoekstra H., Wilson G.,Lidman C., Yee H. K. C., 2014, A&A, 561, A79Vanderlinde K. et al., 2010, ApJ, 722, 1180Vikhlinin A. et al., 2009, ApJ, 692, 1033Vikhlinin A., Kravtsov A., Forman W., Jones C., Marke-vitch M., Murray S. S., Van Speybroeck L., 2006, ApJ,640, 691Vulcani B. et al., 2013, A&A, 550, A58White M., Cohn J. D., Smit R., 2010, MNRAS, 408, 1818 White S., Navarro J., Evrard A., Frenk C., 1993, Nature,366, 429White S. D. M., Efstathiou G., Frenk C. S., 1993, MNRAS,262, 1023Williamson R. et al., 2011, ApJ, 738, 139Zenteno A. et al., 2011, ApJ, 734, 3Zhang Y.-Y., Laganá T. F., Pierini D., Puchwein E.,Schneider P., Reiprich T. H., 2011, A&A, 535, A78Zhang Y.-Y., Laganá T. F., Pierini D., Puchwein E.,Schneider P., Reiprich T. H., 2012, A&A, 544, C3Zibetti S., White S. D. M., Schneider D. P., Brinkmann J.,2005, MNRAS, 358, 949
APPENDIX A: PERFORMANCE OF SEDFITTING
With the published spectroscopic sample for SPT clus-ters (Sifón et al. 2013; Ruel et al. 2014), we are able toquantify how the uncertainty of the photo-z impacts onthe stellar mass estimates based on the SED fit using thesix band photometry ( b H , F606W , I B , z G , [3 . , [4 . ).We cross-match our photometry identified sample withthe galaxy sample in Ruel et al. (2014) and repeat thewhole SED fit analysis with the redshift fixed to themeasured spectroscopic redshift. We show the comparisonin Figure A1. The photo-z performance is estimated asthe mean ∆ z/ (1 + z ) ≡ ( z photo − z spec ) / (1 + z spec ) to be . ± . . The difference of the stellar mass estimates( log M photoz ⋆ − log M specz ⋆ ) when using z photo and z spec is at the level of / . with a mean ≈ . . Except for thehighest redshift cluster (SPT-CL J0205-5829 at z = 1 . ),which has only 5 spectroscopic redshifts available for thecluster members, the SED fitting using our six band pho-tometry returns unbiased estimates of the stellar masses. APPENDIX B: TESTS OF STATISTICALBACKGROUND CORRECTION
To test the COSMOS background, we extract the local back-ground information from our SPT dataset, applying a cor-rection for the cluster galaxy contamination. We extract thecorrected local background between 1.2 R and 2.5 R foreach cluster. We correct for cluster contamination by as-suming that the cluster galaxies are distributed as an NFWmodel with concentration of c gal500 = 1 . (Lin et al. 2004, Hen-nig in prep), and the Stellar Mass Function (SMF) and theMagnitude Distribution (MD) are the same for the regionwithin the cluster R and for the cluster population thatis contaminating the background region. Together with thearea extracted for the region within R and the local back-ground, we solve for the the surface number densities of theSMF and MD using the corrected local background for eachcluster. The SMF and MD derived using the corrected lo-cal background are noisy for each individual cluster, espe-cially for the lower redshift clusters where the area availablefor the local background is typically less than 5 arcmin .We combine 9 of the 14 independent estimates (those withbackground area larger than 8 arcmin ) to create an aver-age local background estimate. In averaging, we use the area c (cid:13) , 000–000 Chiu et al. −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 ∆z/(1 +z) −0.4−0.3−0.2−0.10.00.10.20.30.4 l og ( M ph o t o z ⋆ ) - l og ( M s p ecz ⋆ ) SPT-CL J0205-5829Mean
Figure A1.
A test of SED fitting using galaxies with spec-troscopic redshifts. The x-axis is the normalized difference ofphoto-z and spec-z and the y-axis is the resulting stellar massdifference averaged on a per-cluster basis. The color code fromblue to red indicates the clusters from the lowest to the high-est redshift. SPT-CL J0205-5829 at z = 1 . is marked as it hasthe largest mass difference. The black dot indicates the mean of( log M photoz ⋆ − log M specz ⋆ ) and ∆ z/ (1 + z ) of the ensembleof clusters. weighted average of the individual background estimates sothat clusters with greater area (but not necessarily highernumber density) receive higher weight.Figure B1 contains a comparison of the COSMOS andlocal background estimates for the SMF (right panels) andMD (left panels). The corrected local background estimates(black) for the SMF and MD are in a good agreementwith the COSMOS backgrounds (magenta). There is pooreragreement on the bright (massive) end with the tendencythat the local background is slightly higher than COSMOS.The cluster plus background SMF and MDs extracted fromwithin R (green) show significant overdensities with re-spect to the background estimates. In both the case of the lo-cal background estimates (black) and the cluster plus back-ground estimates (green), the individual cluster results areshown with dashed lines and the thick solid lines representthe ensemble average.On the other hand, the corrected local background forthe SMF and MD for the red population is generally lowerthan the COSMOS estimates. This suggests we are overcor-recting the local backgrounds for cluster contamination inthe case of the red population, and this is to be expectedgiven that we do not have the right filter combinations (blueband containing 4000 Å break and one band redward of thebreak) for the half of our sample that lies at z > . . Forthese reasons we do not present any analyses of the red se-quence selected subpopulation in this paper.We compare the differences between the cumulativestellar mass estimates for the full population when usingthe two different background corrections. We fit a sim-ple linear relation M local = 10 x × M COSMOS , allowing thenormalization x to float, where M local and M COSMOS log(M ⋆ /M ⊙ ) [dex] -2 -1 a r c m i n − SMF −3 −2 −1 0 1 2 3 mag−m ∗ -2 -1 a r c m i n − MD Figure B1.
The magnitude distribution (MD- left) and stel-lar mass function (SMF- right) for the full population of galax-ies in the SPT clusters. We show the cluster + background es-timates from within R (green), the uncorrected local back-ground (grey), the corrected local background (black), and thebackground estimated from COSMOS (magenta). The SMFs arederived using SED fitting of six band photometry. The dashedlines indicate the results for individual clusters and the heavy-solid lines are the averages over all clusters. The COSMOS andlocal, contamination-corrected background estimates are in goodagreement. We adopt the COSMOS background correction in thiswork. are the mass estimations for using the local and COS-MOS backgrounds, respectively. The resulting best-fit x is − . ± . ( . ± . ) for the cluster (background)stellar mass estimation. That is, using the COSMOS back-ground results in ∼ % higher stellar mass estimates for thecluster and ∼ % lower mass estimates in the backgroundas compared to those using the corrected local background. c (cid:13) , 000–000 a r y o n C o n t e n t o f M a ss i ve G a l a x y C l u s t e r s Table B1.
Measured quantities for the SPT cluster sample: Columns contain the cluster name, spectroscopic redshift, M estimated from the SZE signature, R inferred from thegiven M and redshift, ICM mass M ICM , the BCG mass M BCG ⋆ , the total stellar mass M ⋆ , the stellar mass fraction f ⋆ , the collapsed baryon fraction f c , the baryon fraction f b , theICM mass fractions f ICM and the stellar-mass-to-light ratios Υ (rms in the parenthesis) in [3 . band in the observed frame. M R M ICM M BCG ⋆ M ⋆ f ⋆ f c f b f ICM Υ Cluster Redshift [10 M ⊙ ] [Mpc] [10 M ⊙ ] [10 M ⊙ ] [10 M ⊙ ] [ % ] [ % ] [ % ] [ % ] [ M ⊙ L ⊙ ]SPT-CL J0000-5748 0.702 4.35 ± ± +1 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +1 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +1 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +2 . − . ± ± ± ± ± ± ± +1 . − . ± ± ± ± ± ± ± +1 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± ± ± +0 . − . ± ± ± ± ± c (cid:13) R A S , M N R A S ,,