A Multi-Wavelength Mass Analysis of RCS2 J232727.6-020437, a ~3x10 15 M ⊙ Galaxy Cluster at z=0.7
K. Sharon, M.D. Gladders, D.P. Marrone, H. Hoekstra, E. Rasia, H. Bourdin, D. Gifford, A.K. Hicks, C. Greer, T. Mroczkowski, L.F. Barrientos, M. Bayliss, J.E. Carlstrom, D.G. Gilbank, M. Gralla, J. Hlavacek-Larrondo, E. Leitch, P. Mazzotta, C. Miller, S.J.C. Muchovej, T. Schrabback, H.K.C. Yee
AApJ in press: draft date October 23, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
A MULTI-WAVELENGTH MASS ANALYSIS OF RCS2 J232727.6-020437, A ∼ × M (cid:12) GALAXY CLUSTERAT Z=0.7
K. Sharon , M.D. Gladders , D.P. Marrone , H. Hoekstra , E. Rasia , H. Bourdin , D. Gifford , A.K. Hicks ,C. Greer , T. Mroczkowski , L.F. Barrientos , M. Bayliss , J.E. Carlstrom , D.G. Gilbank , M.Gralla , J. Hlavacek-Larrondo , E. Leitch , P. Mazzotta , C. Miller , S.J.C. Muchovej , T.Schrabback , H.K.C. Yee , and RCS-Team ApJ in press: draft date October 23, 2018
ABSTRACTWe present an initial study of the mass and evolutionary state of a massive and distant cluster,RCS2 J232727.6-020437. This cluster, at z=0.6986, is the richest cluster discovered in the RCS2project. The mass measurements presented in this paper are derived from all possible mass proxies:X-ray measurements, weak-lensing shear, strong lensing, Sunyaev Zel’dovich effect decrement, thevelocity distribution of cluster member galaxies, and galaxy richness. While each of these observablesprobe the mass of the cluster at a different radius, they all indicate that RCS2 J232727.6-020437 isamong the most massive clusters at this redshift, with an estimated mass of M ∼ × h − M (cid:12) . Inthis paper, we demonstrate that the various observables are all reasonably consistent with each otherto within their uncertainties. RCS2 J232727.6-020437 appears to be well relaxed – with circular andconcentric X-ray isophotes, with a cool core, and no indication of significant substructure in extensivegalaxy velocity data. Subject headings: galaxies: clusters: individual (RCS2 J232727.6-020437) INTRODUCTION
High redshift clusters have been successfully identifiedin dedicated surveys working with a range of cluster- Department of Astronomy, University of Michigan, 1085 S.University Ave, Ann Arbor, MI 48109, USA Department of Astronomy and Astrophysics, The Universityof Chicago, Chicago, IL 60637, USA Kavli Institute for Cosmological Physics, The University ofChicago, Chicago, IL 60637, USA Steward Observatory, University of Arizona, 933 NorthCherry Avenue, Tucson, AZ 85721, USA Leiden Observatory, Leiden University, P.O. Box 9513, 2300RA Leiden, The Netherlands Department of Physics,450 Church St, University of Michi-gan, 500 Church Street, Ann Arbor, MI 48109, USA INAF-Osservatorio Astronomico of Trieste, via Tiepolo 11,34121, Trieste, Italy Dipartimento di Fisica, Universit`a di Roma Tor Vergata, viadella Ricerca Scientifica, I-00133, Roma, Italy Sustainable Engineering Group, 7475 Hubbard Avenue Suite201, Middleton, WI 53562 Pontificia Universidad Cat´olica de Chile, Santiago 22, Chile Department of Physics, Harvard University, 17 OxfordStreet, Cambridge, MA 02138 Harvard-Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138, USA South African Astronomical Observatory, P.O. Box 9, Ob-servatory 7935, South Africa Department of Physics and Astronomy, Johns Hopkins Uni-versity, Baltimore, MD 21218, USA Departement de Physique, Universite de Montreal, C.P.6128, Succ. Centre-Ville, Montreal, Quebec H3C 3J7, Canada National Research Council Fellow, National Academy ofSciences. U.S. Naval Research Laboratory, 4555 Overlook Ave SW,Washington, D.C. 20375, USA. California Institute of Technology - Owens Valley RadioObservatory, Big Pine, CA 93513, USA Argelander Institute for Astronomy, University of Bonn,Auf dem H¨ugel 71, 53121 Bonn, Germany Department of Astronomy and Astrophysics, University ofToronto, 50 St. George Street, Toronto, Ontario M5S 3H4,Canada selecting techniques and wavelengths. These includecluster discoveries in deep X-ray observations (e.g., Gioia& Luppino 1994; Rosati et al. 1998; Romer et al. 2000;Ebeling et al. 2001; Rosati et al. 2004; Mullis et al. 2005;Stanford et al. 2006; Rosati et al. 2009); optical+near in-frared imaging (e.g., Gladders & Yee 2005; Stanford et al.2005; Brodwin et al. 2006; Elston et al. 2006; Wittmanet al. 2006; Eisenhardt et al. 2008; Muzzin et al. 2009;Wilson et al. 2009; Papovich et al. 2010; Brodwin et al.2011; Santos et al. 2011; Gettings et al. 2012; Stanfordet al. 2012; Zeimann et al. 2012; Stanford et al. 2014),and detection of the the Sunyaev Zel’dovich (SZ) ef-fect (Staniszewski et al. 2009; Vanderlinde et al. 2010;Williamson et al. 2011; Marriage et al. 2011; Planck Col-laboration et al. 2013; Hasselfield et al. 2013; Reichardtet al. 2013; Brodwin et al. 2014; Bleem et al. 2015).Nevertheless, despite this extensive effort, these sur-veys resulted in a modest number of high redshift ( z (cid:38) .
5) and massive ( M (cid:38) M (cid:12) ) galaxy clusters. Thisrelative paucity of distant massive clusters is a reflectionboth of the challenges inherent in detecting such clustersand of their intrinsic rarity (e.g., Crocce et al. 2010).Such clusters are the earliest and largest collapsed halos;the observed density of distant massive clusters is thusexquisitely sensitive to several cosmological parameters(e.g., Eke et al. 1996) and indeed the presence of a sin-gle cluster in prior cluster surveys has been used to limitcosmological models (e.g., Bahcall & Fan 1998). Suchclusters also offer, at least in principle, the opportunityto test for non-gaussianity on cluster scales if the cosmol-ogy is otherwise constrained (e.g., Sartoris et al. 2010).At 0 . < z < .
0, the most massive galaxy clus-ters known to date are CL J1226+3332 (Maughanet al. 2004) at z = 0 .
89 with mass of M =1 . ± . × h − M (cid:12) (Jee & Tyson 2009), ACT-CL J0102–4915 at z = 0 .
87 and with M = 2 . ± a r X i v : . [ a s t r o - ph . C O ] N ov Sharon et al.0 . × h − M (cid:12) (Menanteau et al. 2012), andMACS0744.8+3927 at z = 0 .
698 with M ( < . . ± . × h − M (cid:12) (Applegate et al. 2014).Recently discovered z > . z = 1 . M = 1 . ± . × h − M (cid:12) ;Foley et al. 2011), SPT-CL J2040–4451 ( z = 1 . M = 5 . ± . × h − M (cid:12) ; Bayliss et al. 2014b)and IDCS J1426.5+3508 ( z = 1 . M = 4 . ± . × h − M (cid:12) ; Brodwin et al. 2012).Massive clusters at any redshift are amenable to de-tailed study with a density of data that less massive sys-tems do not present. The X-ray luminosity of clustersscales as M . (Pratt et al. 2009), the SZ decrement asM . (Bonamente et al. 2008), the weak-lensing shearapproximately as M / , and the galaxy richness in afixed metric aperture (and hence the available numberof cluster galaxy targets for spectroscopic and dynami-cal studies within a given field of view) scales as M . (Yee & Ellingson 2003) at these masses. Similarly it isexpected that the most massive clusters dominate thecross-section for cluster-scale strong lensing (Hennawi etal. 2007). Thus the most massive clusters offer a wealthof potentially well-measured observables which can beused, for example, to study the correspondance betweendifferent mass proxies; such study is critical to the suc-cess of surveys which aim to use the redshift evolution ofthe cluster mass function as a cosmological probe.We present here detailed observations of a single mas-sive cluster selected from the Second Red-Sequence Clus-ter Survey (RCS2; Gilbank et al. 2011). This cluster,RCS2 J232727.6-020437 (hereafter RCS2327), was se-lected from RCS2 in an early and partial cluster cat-alog. Its optical properties indicated that it is a verymassive cluster, and justified an extensive followup cam-paign with ground-based and space-based observatoriesat all wavelengths, from X-ray to radio. Since its dis-covery, some of the properties of RCS2327 have beenreported on in the literature. Gralla et al. (2011) firstmeasured its mass from Sunyaev Zel’dovich array obser-vations and its Einstein radius from strong lens model-ing. RCS2327 was rediscovered as the highest signifi-cance cluster in the Atacama Cosmology Telescope sur-vey (Hasselfield et al. 2013), and Menanteau et al. (2012)also report on mass estimates from archival optical andX-ray observations.Although the discovery publication of RCS2327 hasbeen delayed, it was advertised in the past decade invarious oral presentations and conferences – in order tomotivate more extensive followup effort by the commu-nity. Indeed deeper and more detailed observations havebeen conducted since, and will be the basis of future pub-lications. This paper presents mass estimates from theinitial survey and early multi-wavelength followup obser-vations of RCS2327, which collectively indicate that it isan unusually massive high-redshift cluster of galaxies.This paper is organized as follows. The appearance ofthe cluster in the RCS2 data and catalogs is discussed in §
2. We describe the various datasets and correspondinganalyses (richness and galaxy photometry, dynamics, X-ray, SZ decrement, weak- and strong-lensing) in detail in §
3. We discuss the implications of these observations in § § M ( M , M ) to denote the enclosed masswithin a radius R ( R , R ), where the overden-sity is 200 (500, 2500) the critical matter density at thecluster redshift. Unless otherwise stated, we used theWMAP 5-year cosmology parameters (Komatsu et al.2009), with Ω Λ = 0 .
73, Ω m = 0 .
27, and H = 70 km s − Mpc − . In this cosmology, 1 (cid:48)(cid:48) corresponds to 7.24 kpc atthe cluster redshift, z = 0 . THE SECOND RED-SEQUENCE CLUSTER SURVEY ANDTHE DISCOVERY OF RCS2327
The Second Red-Sequence Cluster Survey (RCS2) isan imaging program executed using the Megacam facil-ity at CFHT. RCS2 is described in full in Gilbank etal. (2011). In short, images have been acquired in the g , r , and z filters, with integration times of 4, 8, and 6minutes respectively, and all with sub-arcsecond seeingconditions via observations in queue mode. The RCS2data are approximately 1-2 magnitudes deeper than theSloan Digital Sky Survey imaging (York et al. 2000), witha 5- σ point-source limiting magnitudes of 24.4, 24.3, and22.8 mag in g , r , and z respectively. The RCS2 sur-vey data comprise 785 unique pointings of the nominally1 square degree CFHT Megacam camera; the surveyedarea is somewhat less than 700 square degrees once datamasking and pointing overlaps are accounted for. Thecluster and group catalog from RCS2 extend to z ∼ . g -band imaging improves the over-all performance at lower redshifts (compared to RCS1;Gladders & Yee 2005), and makes the survey more adeptat detecting strong lensing clusters, since lensed sourcestend to have blue colors.RCS2327 was discovered in 2005 in an early and par-tial version of the RCS2 cluster catalog. An examinationof the RCS2 survey images made it clear that it was anunusually massive object. A color image of RCS2327is shown in Figure 1. The original RCS2 imaging dataclearly showed at least one strongly lensed arc, and theindicated cluster photometric redshift was z ∼ .
7. Aplot of the detection significance versus photometric red-shift for clusters from the RCS2 cluster catalog is shownin Figure 2. The RCS2 imaging data are fairly uniform,and so at a given redshift the detection significance is ameaningful quantity that is not strongly affected by dataquality from region to region of the survey. At high red-shifts RCS2327 is the most significant cluster detected.Furthermore, a cluster of a given richness and compact-ness (both of which influence detection significance) willbe detected as a more significant object at lower red-shifts; the fact that RCS2327 is detected with a signifi-cance as great as any lower redshift clusters implies thatit is likely the most massive cluster in this sample. Evenfrom these basic data and considering the volume probedit is apparent that RCS2327 is a remarkably massive clus-ter, worthy of significant followup.The cluster is located at R.A.=23:27:27.61 (J2000) andDecl.= − § Fig. 1.—
A composite gri color image of RCS2327 from imaging from the LDSS-3 instrument on Magellan (see § FOLLOWUP OBSERVATIONS AND MASS ESTIMATES
In this section we describe the multi-wavelength fol-lowup observations of RCS2327. Based on these observa-tions, we are able to estimate the mass of RCS2327 fromrichness, galaxy dynamics, X-ray, Sunyaev Zel’dovich ef-fect, weak lensing and strong lensing. The different massproxies naturally measure either spherical mass or a pro-jected mass along the line of sight (usually referred toas cylindrical mass or aperture mass). Moreover, eachmass proxy is sensitive to mass at a different radial scale:strong lensing measures the projected mass density atthe innermost parts of the cluster, typically ∼ ) and lack the resolution atthe center of the cluster; weak lensing reconstructs theprojected mass density out to R , with poor resolutionat the center as well. Dynamical mass (from the veloc-ity distribution of cluster galaxies) is used to estimatethe virial mass. We note that these mass proxies are notalways independent, and rely on scaling relations and as-sumptions. In the following subsections, we describe thedata and our analysis to derive the cluster mass fromeach mass proxy. In § D e t e c t i o n S i g n i f i c a n c e Fig. 2.—
The detection significance versus redshift of RCS2327compared to the distribution of these properties for clusters fromthe RCS2 cluster catalog. RCS2327 is indicated as a heavy symboland is an obvious outlier; it is as significant as any cluster detectedat lower redshifts.
Deep Multi-color Imaging, Galaxy Distribution andRichness
In addition to the RCS2 survey imaging data, avail-able imaging data on RCS2327 includes images from theLDSS-3 imaging spectrograph on the 6.5m Clay tele-scope, taken during a run in September 2005. Total inte-gration times were 16, 12, and 10 minutes in the g , r and i filters respectively. The point-spread-function widthat half maximum in the final stacked images is 0 . (cid:48)(cid:48)
60 ( i ),0 . (cid:48)(cid:48)
65 ( r ), and 0 . (cid:48)(cid:48)
80 ( g ) with some image elongation due towind shake present principally in the bluest band. Thesedata cover a circular field of view 8’ in diameter, centeredon the BCG. Figure 1 is constructed from these data.The RCS2 data are best suited to measurements ofcluster richness, as they are well calibrated and natu-rally include excellent background data, and are readilyconnected to the cosmological context and calibration ofthe mass-richness relation provided by the RCS1 pro-gram (Gladders & Yee 2005; Gladders et al. 2007). Themulti-band LDSS-3 images are deeper, with better see-ing than the RCS2 images, and we use these data forcomputing detailed photometric properties - principallycolor-magnitude diagrams. For this we focus our analysisbelow on the r and i observations, since this filter pairhas the best image quality, and almost perfectly straddlesthe 4000˚A break at the cluster redshift.Figure 3 shows an r − i color-magnitude diagram ofall galaxies at projected radii less than 1 Mpc from thecluster center. The red sequence of early-type clustermembers is obvious, emphasizing the extraordinary rich-ness of this cluster in comparison to most other clus-ters in the literature at a similar redshift (e.g., De Lu-cia et al. 2007; Gladders & Yee 2005). Figure 4 showsonly galaxies for which a spectroscopic redshift is avail-able, plotted by SED type. As expected, galaxies whichare both cluster members and have early-type spectraare almost all red-sequence members. From the spec-troscopically confirmed early-type cluster galaxies, withsimple iterated 3- σ clipping (e.g., as in Gladders et al.1998), we fit a linear red sequence relation, given by( r − i ) = − . × ( i − i ∗ ) + 1 .
18 19 20 21 22 23 24i Magnitude0.00.51.01.52.0 r (cid:239) i C o l o r Fig. 3.—
The color-magnitude diagram for a 1 Mpc radius fieldof view centered on RCS2327, in the r and i filters. Galaxies havebeen divided into three radials bins of equal radius; galaxies in theoutermost bin are plotted as small pluses, and those in the centralbin as heavy squares. Only galaxies with photometric uncertaintiesin both filters of less than 0.2 magnitudes are shown.
18 19 20 21 22 23 24i Magnitude0.00.51.01.52.0 r (cid:239) i C o l o r Fig. 4.—
The color-magnitude diagram for galaxies with spectro-scopic redshifts, regardless of position, in the r and i filters. Spec-troscopic early-type cluster members are shown as red diamonds;other cluster members are shown as green squares. Non-membersare shown as small squares. Only galaxies with uncertainties inboth filters of less than 0.2 magnitudes are shown. The best fittingred-sequence model, derived as described in § i ∗ indicated by the heavy blacksquare. ass Measurements of RCS2 J232727.6-020437 5acteristic magnitude for cluster galaxies in RCS2327 as i ∗ = 21 .
3, consistent to within 0.05 magnitudes with themodels in both Gladders & Yee (2005) and Koester etal. (2007). These models include a correction for passiveevolution. The measured scatter of early-type galaxiesabout the best fit red sequence is less than 0.05, con-sistent with that seen in other rich clusters at a rangeof redshifts (Hao et al. 2009; Mei et al. 2009). Thebest fitting model is indicated in Figure 4. These datademonstrate that RCS2327 appears as expected for awell-formed high-redshift cluster, albeit an extraordinar-ily rich example.We derive a total richness for RCS2327 of B gcT =3271 ±
488 Mpc . , and a corresponding red-sequence richness of B gcRS =2590 ±
413 Mpc . (seeGladders & Yee 2005, for a detailed explanation ofthe B gc parameter). Calibrations relevant to themeasurement of this richness have been taken from theRCS1 survey, which also uses the z (cid:48) -band as the reddestsurvey filter. A direct comparison of the total richnessto the scaling relations in Yee & Ellingson (2003) nom-inally corresponds to a mass of M = 4 . +1 . − . × h − M (cid:12) with a significant uncertainty, given the knownscatter in richness as a mass proxy (Gladders et al. 2007;Rozo et al. 2009), and the lack of direct calibration ofthe richness-mass relation at the redshift of RCS2327.Furthermore, the relevant richness to use in comparisonto the scaling relation in Yee & Ellingson (2003) is notobvious; though the richness values in Yee & Ellingson(2003) are for all galaxies, the small blue fraction in thatsample and the significant observed evolution in thegeneral cluster blue fraction (Loh et al. 2008) from theredshift of that sample (mean z=0.32) to the redshift ofRCS2327 suggests that the (less evolving) red-sequencerichness may be a more appropriate measure. With thatin mind we note that the mass corresponding to B gcRS is M = 3 . +0 . − . × h − M (cid:12) . Given the limitations ofthis analysis however, we do not use a richness-derivedmass extensively in the analysis in §
4, but simply notehere that RCS2327 is remarkably rich.
Optical Spectroscopy
Spectroscopic observation of galaxies in the field ofRCS2327 has been conducted using the Magellan tele-scopes. Data were acquired in both normal and nod-and-shuffle modes using LDSS-3, during runs in August andNovember, 2006, and a total of 3 masks with the GISMOinstrument in June 2008. RCS2327 was also observed us-ing the GMOS instrument on the Gemini South telescopein queue mode in semester 2007B, yielding redshifts ofpotential lensed sources; the Gemini data are discussedin more detail in § .The bulk of the LDSS-3 observations (apart from a sin-gle early mask, which established the cluster redshift at z ∼ .
70) were acquired using a 6000˚A-7000˚A band-limiting filter; this allows for a high density of slits, at theexpense of a significant redshift failure rate (specifically,[O II] λλ . < z < . http://obs.carnegiescience.edu/Code/cosmos of 0 . < z < . − , and the un-certainty within observations using a single instrument ismeasured to be less than 100 km sec − . Neither of theseuncertainties is significant in the analysis below. Red-shifts were measured using a combination of cross corre-lation and line measurement techniques, and cross cor-relation measurements of absorption systems were onlyretained if (at minimum) the H and K lines were individ-ually visible. Apart from possible mis-interpreted singleemission line redshifts in the LDSS-3 spectra, the mea-sured redshifts are robust. Each spectrum was also clas-sified as either an emission or absorption type, with post-starburst (showing strong Balmer lines) or AGN featuresalso noted when present.A histogram of the galaxy velocities around the meancluster redshift of 0.6986 ± ±
95 km sec − with uncertainties measuredfrom a bootstrap analysis. The cluster is well separatedfrom other structures. The velocity dispersion usingonly the 110 galaxies with early type spectra is 1398 ± − , and similarly using all other cluster memberswe derive 1757 ±
139 km sec − – a factor of 1.27 ± ± ±
127 km sec − ,1268 ±
147 km sec − , and 1034 ±
201 km sec − , respec-tively. The radial distribution of emission line membersrelative to absorption line cluster members is also as ex-pected, with proportionately more actively star-formingsystems found at large radii. A clear interpretation ofthis result is difficult given the complexity of the sam-pling from multiple masks from multiple instrumentswith differing fields of view, and the weighting of slitassignments toward photometric red-sequence members;the data shown in Figure 7 are at least consistent withexpectations. Finally, a KS test of the velocity distri-bution shows at best marginal evidence for velocity sub-structure, with the velocity distribution inconsistent witha normal distribution at a modest 1.3 sigma using allgalaxies. Using only early type members, there is noteven marginal evidence for velocity substructure.We also note the presence of a secondary structure sep-arated from the main cluster by 5700 km sec − . Thisstructure is dominated by emission line galaxies, has a Sharon et al. -200 -100 0 100 200 (cid:54) R.A. (arcsec)-200-1000100200 (cid:54) D ec l . ( a r c s ec ) Fig. 5.—
The distribution of red-sequence galaxy light (red contours) smoothed with a 150 kpc FWHM gaussian, and the full band X-raylight (blue contours) similarly smoothed. Blue diamonds mark X-ray point sources; the correspondance between some of these sourcesto optical counterparts validates the astrometric matching between these data. Individual galaxies are indicated by squares, with symbolsize proportional to brightness; solid red squares have colors consistent with the cluster red-sequence and are the basis for the overplottedcontours, and solid yellow squares show spectroscopically confirmed members of the secondary structure noted in Figures 6 and 7 and § (cid:48) × (cid:48) region with the same data, with the strong lensing main halo mass distribution also indicated (greencontours). The contour levels have been chosen to highlight the core position and outer shape of the light distributions. velocity dispersion of 400 km sec − , and is located to theedge of the spectroscopic field of view, as can been seenin Figures 5, 6, and 7. It is not significant for any of theanalyses below. Dynamical Mass Estimates from Velocity Dispersion
The observed velocity dispersion is converted to massthrough the virial scaling relation derived from simula-tions (Evrard et al. 2008). This relationship is described as M = 10 h ( z ) (cid:18) σ obs σ (cid:19) α , (1)where σ obs is the observed 1-d velocity dispersion of thecluster, σ is the velocity dispersion normalized for a10 M (cid:12) cluster, and α is the slope of the scaling rela-tion. Evrard et al. (2008) find the best fit parametersfor a multitude of cosmologies and velocity dispersionsmeasured from dark matter particles to be σ = 1082 . (cid:239) (cid:239) ±95 (cid:60) (cid:60) (cid:60) (cid:60) Fig. 6.—
The velocity distribution of galaxies about the meancluster redshift for all galaxies (top), absorption line only galaxies(middle), and all emission line galaxies (bottom). Velocity disper-sions in the restframe in km sec − are as indicated. R e d s h i f t Fig. 7.—
Redshifts versus cluster-centric radius for absorption-line-only galaxies (red diamonds) and all other galaxies (greensquares) for all galaxies within ∆ z = 0 .
05 of the RCS2327. Thefield of view of the GISMO instrument is approximately 0.7 Mpc inthese coordinates; the denser sampling this provides in the clustercore, combined with the details of slit placements in the LDSS-3instrument yields a complex slit weighting with radius which isresponsible for the apparent deficit of galaxies at ∼ km s − and α = 2 . M = 2 . +1 . − . × h − M (cid:12) . Theuncertainties in mass assume a 13% total uncertaintyin velocity dispersion. This included both the statis-tical uncertainty, which is small for the large numberof galaxies observed in this sample, and the system-atic uncertainty, which includes line-of-sight effects, clus-ter shape/triaxiality, and foreground/background con-tamination (Gifford et al. 2013, Saro et al. 2013). Saro et al. (2013) re-fit the scaling relation to a semi-analytic galaxy catalog for the Millennium Simulationand find the parameters to be σ = 938 . − and α = 2 .
91. The resulting mass using these parameters is M = 3 . +1 . − . × h − M (cid:12) . Dynamical Mass Estimates from the Caustic Method
The distribution of radial velocities of cluster galaxiesas a function of cluster-centric radius can be used to es-timate its mass using the caustic technique (Diaferio &Geller 1997, Gifford et al. 2013, Gifford & Miller 2013).This method relies on the expectation that cluster galax-ies that have not escaped the potential well of the clus-ter halo occupy a well-defined region in a radius-velocityphase space confined by the escape velocity from thatpotential, v esc ( r ). We follow the techniques outlined inGifford et al. (2013), and refer to that publication for afull description of the methods applied here.Figure 8 shows the radius-velocity space of ∼ v esc as indicated by the velocity edge in phase-spacedensity. The enclosed mass can be derived as GM = (cid:90) r F β ( r ) A ( r ) dr, (2)where A ( r ) is the square of the line-of-sight escape ve-locity, and F β ( r ) is a function of the potential, density,and velocity anisotropy, corrected for projection effects.We apply the common convention of assuming that F β is constant. Physically, this parameter depends on theunknown concentration and velocity anisotropy profileof the cluster. Disagreement on the constant value of F β that results in unbiased mass estimates on averagepersists in the literature with values ranging from 0.5 to0.7. Gifford et al. (2013) find that F β = 0 .
65 resultsin mass estimates with less than 4% mass bias for sev-eral semi-analytic catalogs available for the MillenniumSimulation, and we adopt this value for this study.We derive a dynamical mass of M = 2 . +1 . − . × h − M (cid:12) . The uncertainty in the derived mass usingthe caustics technique depends on the number of galaxiesused; from caustic mass analysis of the Millenium Simu-lation semi-analytic galaxy catalogs, Gifford et al. (2013)find that for N gal ≥
150 the scatter is ≤
30% with a biasof < ±
58 km s − , in agreement with the estimates in § Chandra Observations, X-ray properties and MassEstimates
RCS2327 was observed on two separate occasions withthe
Chandra X-ray Observatory . A first 25 ks observationwas carried out on 2007 August 12 (Cycle 8 Proposal08801039; PI: Gladders) using the ACIS-S array. Theearly analysis suggested that the cluster was massive, X-ray regular, and possibly hosting a cool core. These hintsjustified the need of deeper data obtained in 2011 withACIS-I (Cycle 13 Proposal 13800830; PI: Hicks).The two deep Cycle 13 ACIS-I pointings (150 ks total)sample a more extended field around the cluster, and Sharon et al. V e l o c i t y ( k m / s ) Fig. 8.—
The projected radius vs line-of-sight velocity phasespace for galaxies identified as members by the caustic algorithm(red circles) and non-members (open circles). The estimated escapevelocity surfaces (or caustics) are represented by solid red lineswhich are symmetric with respect to the cluster velocity. result in a higher signal-to-noise ratio than the Cycle8 observation. Since the background is better under-stood than that of the ACIS-S configuration, combinedwith the very small increase in signal-to-noise ratio thatwould be gained by combining both datasets, we choseto analyse the 2011 data separately and not co-add thetwo epochs.The X-ray data reduction follows Martino et al. (2014)and Bartalucci et al. (2014), with minor modifications.We use both the count statistics and the control on sys-tematics offered by a multi-component modeling of thebackground noise (see Bartalucci et al. 2014, for details).Filtering the hard and soft event light curve reducesthe total exposure time by 10% to ∼
130 ks. We binthe photon events in sky coordinates with a fixed an-gular resolution of 1 . (cid:48)(cid:48) Chandra
Calibrationdatabase CALDB 4.6.1, when computing the effective ex-posure we take into account the spatially variable mirroreffective area, quantum efficiency of the detector, CCDgaps, bad pixels, and a correction for the motion of thetelescope. Our background noise model includes Galac-tic foreground, cosmic X-ray background, and false de-tections due to cosmic ray induced particles. For the par-ticle background spectrum, we use the analytical modelproposed by Bartalucci et al. (2014). The amplitude ofall the other components was determined from the dataoutside the region of the field of view covered by thetarget. We derive the temperature map following tech-niques described in Bourdin & Mazzotta (2008). Figure 9shows the X-ray flux isophotes overplotted on the false-color temperature map. The cluster has a regular X-raymorphology and does not show significant substructureor X-ray cavities (Hlavacek-Larrondo et al. 2014).
X-ray surface brightness, temperature, and metallicityprofiles
We extract the surface brightness profile (Figure 10a)from an effective exposure and background-corrected soft band ([0.5-2.5] keV) image, after excluding point sources.The profile averages the surface brightness in concentricannulli centered on the maximum of a wavelet-filteredimage of the cluster. The temperature and metallicityprofiles (Figure 10b,c) were calculated in five radial binsout to ∼
840 kpc, each containing at least 2000 counts inthe [0.7-5] keV band. The measurements of temperatureand metallicity assume redshifted and absorbed emissionspectra modeled with the Astrophysical Plasma EmissionCode (APEC, Smith et al. 2001), adopting the elementabundances of Grevesse & Sauval (1998) and neutral hy-drogen absorption cross sections of Balucinska-Church &McCammon (1992). The spectra, modified by the effec-tive exposure and background, are also convolved with afunction of the redistribution of the photon energies bythe detector. The assumed column density value is fixedat 4 . × cm from measurements obtained near ourtarget by the Leiden/Argentine/Bonn (LAB) Survey ofgalactic HI (Kalberla et al. 2005). The redshift is fixedto z = 0 . ∼ . R to ∼ . . − × R region(roughly out to 1Mpc, see § T X = 13 . +2 . − . keV. We also estimate the cooling times as a functionof cluster-centric radius (following the prescription de-scribed in Hlavacek-Larrondo et al. 2013), and find thatthe cooling time profile decreases mildly towards the cen-ter from ∼
40 Gyr at 400 kpc, to ∼ § ±
28 keV cm − . X-ray Mass Estimate.
To measure the X-ray mass we follow the forward pro-cedure described in Meneghetti et al. (2010) and Rasiaet al. (2012). In short, analytic models are fitted to theprojected surface density and temperature profiles andsubsequently analytically de-projected. The 3D infor-mation are then folded into the hydrostatic mass equa-tion (Vikhlinin et al. 2006). The surface brightness isparametrized via a modified β − model with a power-lawtrend in the center and a steepening behavior in the out-skirts, plus a second β − model to describe the core: n p n e ( r ) = n ( r/r c ) − α (1 + r /r c ) β − α/ + n (1 + r /r c ) β , (3)where n e and n p are the electron and proton densities,respectively. We allow all parameters to vary.We model the temperature profile with a simple power-law: T ( r ) = T ( r/r t ) − a . (4)This profile is then projected along the line of sight usingthe formula of the spectroscopic-like temperature: T los = (cid:82) W T dV (cid:82) W dV , (5)where W = ( n p n e ) / ( T . ). All the best fit parametersare determined using a χ minimization technique ap-plied to the models and the data. Finally, the 3D densityass Measurements of RCS2 J232727.6-020437 9and temperature profiles are used to estimate the totalgravitational mass through the equation of hydrostaticequilibrium (HSE; Sarazin 1988): M ( r ) = − . × T ( r ) r (cid:18) d log ρ g dr + d log Tdr (cid:19) h − M (cid:12) , (6)where the numerical factor includes the gravity con-stant, proton mass, and the mean molecular weight, µ = 0 . M realization − M original ] , where the sum extendsto all radial bins). We consider the 68% of the profiles(340 in number) with the smallest associated value and,finally, for each radial bin, we consider the maximumand minimum values of the selected profiles. The re-sulting mass profile and its uncertainties are plotted inFigure 10d. The HSE radius and mass at overdensity∆ =2500 are R = 471 +54 − h − kpc, and M =3 . +0 . − . × h − M (cid:12) , respectively, and the gas masswithin this radius is M gas , = 4 . +0 . − . × h − M (cid:12) .On average, HSE masses are expected to be biased lowby 10-15% as evident from simulations (Rasia et al. 2006;Nagai et al. 2007; Battaglia et al. 2013) and observations(Mahdavi et al. 2008, 2013). This offset is smaller thanour statistical uncertainty.The value of R is within the region probed by theobservation, and thus its measurement is conservativeand robust. However, the lower overdensities ∆ = 500and ∆ = 200 are not within the observed region, andwe therefore need to extrapolate. For that purpose, wefollow two different approaches.
1: NFW-mass extrapolation — We fit the 500 realizationswith the Navarro-Frenk-White (NFW, Navarro et al.1995, 1996, 1997) formula: M NFW = 4 πM r s (cid:20) log(1 + r/r s ) − r/r s r/r s ) (cid:21) , (7)where r s is the scale radius and M the normalization ofthe mass profile. The fitting is carried out only withinthe observed radial region. The results lead to R =1 . +0 . − . h − Mpc and R = 1 . +1 . − . h − Mpc. Theerrors represent the minimum and maximum values ofthe 68% of the analytic expressions that are the clos-est to the NFW fit of the original mass profile. Theresulting extrapolated masses are M = 1 . +0 . − . × h − M (cid:12) and M = 1 . +1 . − . × h − M (cid:12) . M − Y X relation. — To derive R we also apply theiterative method based on the M − Y X (= M gas × T X )relation proposed by Kravtsov et al. (2006). We startwith an initial guess for the radius (we consider twicethe value of the measured R ). We evaluate the gasmass at that radius from the surface brightness profileand compute the X-ray temperature from the spectra Fig. 9.—
A 4’ ×
4’ temperature map of RCS2327, derived fromthe deep
Chandra
Cycle 13 data. The image is centered onRA=23:27:27.53, Dec= − extracted in the spherical shell with maximum and mini-mum radii equal to the specific radius and 15% its value.The obtained Y X is compared with the Y X − M relationcalibrated from hydrostatic mass estimates in a nearbysample of clusters observed with Chandra (Vikhlinin etal. 2009). This returns an estimate of M and, thus, anew value for R . The process is repeated until con-vergence in the radius estimate is reached. The result-ing radius is R = 1 . +0 . − . h − Mpc, corresponding to M = 1 . +0 . − . × h − M (cid:12) .While the two extrapolation methods agree within er-rors, we note that the NFW-mass extrapolation results inmuch larger uncertainty. This is due to the fact that theHSE mass profile is constrained at a small radius (justabove R ) and thus the external slope of the clusteris poorly constrained from X-ray observations. Sunyaev Zel’dovich Array Observations and SZMass Estimates
The Sunyaev Zel’dovich Array (SZA) observedRCS2327 for a total of 48 hours between 2007 Septem-ber and November. The SZA is an eight-element inter-ferometer with 30 and 90 GHz receivers. The SZA wasconfigured in a standard configuration with 6 telescopesarranged in a compact, short-baseline configuration withtwo outlying telescopes ∼
30 m from the central group.The correlated bandwidth was 8 GHz, centered on 31GHz, resulting in projected lengths of 350 − λ on theshort (SZ-sensitive) baselines and 2000 − λ on thelonger baselines. The data were calibrated and flaggedusing the MATLAB pipeline described in Muchovej etal. (2007); 41% of the data were removed, largely dueto shadowing in the compact array, which is increased inequatorial and lower declination objects. The rms noiselevel in the short-baseline data is 0.21 mJy beam − , cor-responding to a 15 µ K rms brightness temperature inthe 1.9 (cid:48) × (cid:48) synthesized beam. A bright radio sourceis detected nearly 9 (cid:48) to the west of the cluster, but it0 Sharon et al. Fig. 10.—
Radial profiles derived from the analysis of
Chandra
Cycle 13 150 ks X-ray observation, extended out to 800 kpc. (a)
Top-left:
Radial profile of the X-ray surface brightness in the soft band [0.5-2.5] keV (data points). The dotted line represents the best fit model.(b)
Top-right:
Projected temperature profile, clearly showing a temperature decrease towards the center of the cluster, indicating a coolcore. The dotted line represents the best fit model. (c)
Bottom-left:
Metallicity profile (d)
Bottom-right:
Hydrostatic mass profile (solidline) and its 1- σ uncertainty (shaded area). The vertical line indicates R . does not affect the SZ detection. There is one faintradio source coincident with the cluster which we jointlymodel when presenting data. This source is present inthe NRAO VLA Sky Survey (NVSS, Condon 1998). Thedeconvolved image of the cluster, after subtraction of theradio sources, is shown in Figure 11. The peak signifi-cance in this image is 22 σ .The SZA interferometer acts as a spatial filter sensi-tive to the Fourier transform of sky emission on angu-lar scales determined by the baseline lengths. To re-cover the integrated Compton- y parameter, Y , we fit ourFourier plane data to the transform of the generalizedNFW pressure profile presented in Nagai et al. (2007),which was motivated by simulations and X-ray observa-tions (Mroczkowski et al. 2009). In this five-parametermodel we fix the three shape parameters ( α , β , γ ) to thebest fit values derived from X-ray observations of clus-ters (1.0620, 5.4807, 1.156; Arnaud et al. 2010). We fitthe profile normalization and scale radius. The clustercentroid and the flux of one emissive source are allowed to vary as well. The models are fit to the data directlyin the uv -plane, which correctly accounts for the noise inthe data.To determine the significance of the cluster detection,we compare the χ of the best fit model including thecluster and emissive source with the χ of the best fitmodel including only the emissive source. Expressed interms of Gaussian standard deviations, the significanceof the SZ detection is 30.2 σ . Estimates of the Y parameter
We compute two estimates of the Y parameter, Y sph and Y cyl . Y sph is a spherical integral of the pressure pro-file. It is relatively insensitive to unconstrained modesin the interferometer-filtered data and proportional tothe total integrated pressure of the cluster, making it arobust observable (see Marrone et al 2011).To compute Y sph , we volume-integrate the radial pro-ass Measurements of RCS2 J232727.6-020437 11file to an overdensity radius, r ∆ , Y ∆ ,sph = σ T m e c (cid:90) r ∆ P ( r/r s ) dV, (8)as in Marrone et al. (2012). We determine the overden-sity radius of integration by enforcing consistency withthe Y ,sph − M scaling relation derived by Anderssonet al. (2011). To enforce consistency, we iteratively chosethe integration radius (and, by extension, the mass) un-til the mass and Y ∆ lie on the mean relation. Thisanalysis yields Y ,sph = 13 . ± . × − Mpc with R = 1 . ± .
02 Mpc (this radius is 3-15% smallerthan the R that we derive from extrapolating the X-ray data in Section 3.3). Y cyl is a cylindrical integral of the pressure profile alongthe line of sight, Y ∆ ,cyl = σ T m e c (cid:90) r ∆ d Ω (cid:90) ∞−∞ P e dl (9)(see also Mroczkowski et al. 2009). Y cyl corresponds tothe aperture integrated SZ flux, and is sensitive to theline of sight contribution of pressure beyond the radiusof interest. For our gNFW fits, the ratio of Y cyl / Y sph in the 211 . (cid:48)(cid:48) . Y ,cyl todirectly compare our results with the SZ observations ofRCS2327 reported by Hasselfield et al. (2013) with datafrom the Atacama Cosmology Telescope (ACT). Fromtheir “Universal Pressure Profile” (UPP) analysis, whichimplicitly imposes the Y − M scaling relation of Arnaud(2010), they obtain Y ,cyl = 19 . ± . × − Mpc within an aperture of R = 2 . ± . . ± . Y ,cyl = 16 . +1 . − . × − Mpc , within 1 . σ of the Hasselfield et al. (2013) measurement. SZ Mass Estimates
We estimate the cluster mass from the value of Y sph quoted above, which corresponds to M = 8 . ± . × h − M (cid:12) using the Andersson et al. (2011) scalingrelation. The uncertainty assumes 21% scatter in Y atfixed mass in the Andersson et al. (2011) scaling relation(Buddendiek et al. 2014).We also estimate the cluster mass by applying themethod outlined in Mroczkowski (2011, 2012) to the SZAdata. This method assumes the gas is virialized and inthermal hydrostatic equilibrium within the cluster grav-itational potential. Further, we assume the total matterdensity ρ tot follows an NFW dark matter profile (Navarroet al. 1995), with the gas density ρ gas is a constant frac-tion of the total density ( ρ gas = f gas ρ tot ), and the pres-sure and density profiles are spherically symmetric. Thismethod has been applied successfully and compared withother mass estimates in several works (e.g., Reese et al.2012; Umetsu et al. 2012; Medezinski et al. 2013). Afit to a gNFW profile described above yields R =0 . ± .
01 Mpc, M = 4 . ± . × h − M (cid:12) , assum-ing an average gas fraction within R of f gas = 0 . § R = 1 . ± .
04 Mpc, M = 8 . ± . × h − M (cid:12) ,assuming an average gas fraction in this radius of f gas =0 .
12 from Menanteau et al. (2012). We estimate a ∼ Right Ascension (J2000) D e c li n a t i o n ( J ) S N R Fig. 11.—
SZ observation of RCS2327. The CLEANed image is8 (cid:48) × (cid:48) in size. The image is in units of SNR and made from theSZA uv -data with a Gaussian uv -taper of 0.1 at 4 kλ . The FWHMof the synthesized beam for the image is shown in the bottom leftcorner. In this image, SNR of 1 corresponds to 0.21 mJy / bm. scatter due to the assumption on average gas fractionvalue and other model assumptions.Our mass estimates are consistent with Hasselfieldet al. (2013), who measure M = 9 . ± . × h − M (cid:12) from the UPP Y parameter quoted above.In addition to the UPP mass, Hasselfield et al. (2013)report a range of higher M estimates based on differ-ent scaling relations, M = 12 . − . × h − M (cid:12) ,somewhat higher than our measurement. However, theinconsistency between the higher-mass Hasselfield et al.(2013) values and our measurement is not significantlyworse than the inconsistency with their own UPP mass. Wide Field Imaging and Weak-Lensing MassEstimates
We obtained deep wide-field imaging data for RCS2327in the i (cid:48) filter using Megacam on CFHT with the aim ofdetermining the mass using weak gravitational lensing.The observing strategy and weak lensing analysis fol-lows that of the Canadian Cluster Comparison Project(CCCP; Hoekstra et al. 2012), with the only differencethat we use the i (cid:48) for the weak lensing analysis. The i (cid:48) data consist of 8 exposures of 650 s each, which are com-bined into two sets (each with a total integration time of2600 s). The pointings in each set are taken with smalloffsets, such that we can analyse the data on a chip-by-chip basis.The various steps in the analysis, from object detec-tion to unbiased shape measurements and cluster mass,are described in detail in Hoekstra (2007), with updatedprocedures in Hoekstra et al. (2015) and we refer thereader to those papers for more details. We measuregalaxy shapes as described in Hoekstra et al. (2015),which includes a correction for multiplicative bias basedon simulated images. The resulting shapes are estimatedto be accurate to 1 − Fig. 12.—
Mean tangential shear as a function of radius from theBCG is shown in the top panel, along with the best fitting isother-mal sphere model for reference. The model was fit only to thedata at r > (cid:48)(cid:48) (solid line). The dashed line is the extrapolationof the model to smaller projected radii. The bottom panels showsthe ’B’-mode lensing signal, which should be consistent with zeroif systematic distortions have been correctly removed. log which is used to derive the weak lensing mass. Toreduce contamination by cluster members, we also ob-tained four 720 s exposures in r (cid:48) , which are combinedinto a single image. Galaxies that are located on thecluster red-sequence are removed from the object cata-log, which reduces the level of contamination by a factorof two. However, many faint cluster members are blue,and we correct the lensing signal for this residual con-tamination, as described in Hoekstra (2007).To quantify the lensing signal, we compute the meantangential shear as a function of distance from the clus-ter center using galaxies with 22 < i (cid:48) < .
5. Figure 12shows the resulting signal, which indicates that the clus-ter is clearly detected. The bottom panel shows a mea-sure of the lensing ‘B’-mode, which is consistent withzero, indicating that the various corrections for system-atic distortions have been properly applied.As discussed in Hoekstra (2007), the weak lensing masscan be derived in a number of ways. However, to re-late the lensing signal to a physical mass requires knowl-edge of the redshift distribution of the galaxies used inthe lensing analysis. We use the results from Hoek-stra et al. (2015) and find that the mean ratio of an-gular distances between lens-source and observer-sourceis D ls /D s = 0 . E = 10 . (cid:48)(cid:48) ± . (cid:48)(cid:48)
9, which yields a velocitydispersion of σ = 1345 +122 − km s − for the adopted sourceredshift distribution. This value is in excellent agreementwith the dynamics inferred from the galaxy redshifts. Wealso fit an NFW model to the data, adopting the mass- concentration relation suggested by Duffy et al. (2008),which yields a mass M = 2 . +0 . − . × h − M (cid:12) . Wecompare the weak lensing mass to other mass estimatesand in other radii in § Strong Lensing Mass Estimates
RCS2327 was observed by
HST +ACS (Cycle 15 pro-gram GO-10846; PI Gladders) as part of a larger effortusing both ACS and NICMOS to acquire deep multi-band imaging of this cluster. Unfortunately, the fail-ure of ACS in early 2007 truncated this program, andthe only complete image which was acquired is a 3-orbit F435W image of the cluster core taken using theACS Wide Field Channel . Additional available obser-vations of the cluster core relevant for the strong lens-ing analysis include a deep ( ∼ HST +NICMOS; we have reconstructed thislast image from the useable portions of a nominally failed
HST observation which nevertheless yielded some usefulframes in a single orbit before guiding issues truncatedthe remainder of the observations. A color compositeimage of the cluster core, made from the F435W image,the deep LDSS-3 i -band image (see § s -band image, is shown in Figure 13.Using these various imaging data, we identify two setsof multiply-imaged galaxies that are lensed by RCS2327for which we have acquired spectroscopic redshifts aspart of the overall spectroscopic program described in § − z = 2 . ± . α emission line present in the early LDSS-3 spectroscopydescribed above. This lensed source was apparent in theRCS2 discovery imaging data, with a remarkably largeseparation from the cluster center, R=56 . (cid:48)(cid:48)
8, as measuredfrom the BCG. The arc does not appear to be caused bylocal substructure in the cluster, as there are no nearbysignificant cluster galaxies.Source B was observed spectroscopically in queue modein semester 2007B using the Gemini South telescopewith the GMOS instrument. We observed RCS2327 for8 × × × spectral axes),resulting in wavelength coverage of ∼ ∼
240 km sec − . The grat-ing tilt was optimized to record a wavelength range of ∼ − z = 1 . ± . λλ § HST and The field of RCS2327 was recently imaged by
HST in Cycle20 program GO 13177 (PI Bradaˇc). These data are not used inthis paper. A forthcoming lensing analysis of the Cycle 20 datawill be presented in Hoag et al. (2015). ass Measurements of RCS2 J232727.6-020437 13
Fig. 13.—
A 2’ ×
2’ color composite image of the core of RCS2327 composed of images from
HST in the F435W filter (blue channel),and from Magellan in the i − band (green channel) and K s -band (red channel). The point spread functions have been matched to the worstimage; the effective resolution is ∼ . (cid:48)(cid:48)
6. The merging pair image of source A at z =2.9834 is indicated. The greyscale cutouts are 2 (cid:48)(cid:48) indiameter and show the full-resolution images of source B, at z =1.4155, in the F435W filter. The critical curves from the best fit lens modelare overplotted, in red for a source at z =1.415, and in orange for a source at z =2.9834. IR imaging since it has a unique color and internal mor-phology. These properties also allow us to robustly elim-inate the presence of a fourth counter image; source Bis lensed as a naked cusp configuration (e.g., Oguri &Keeton 2004). A close inspection of the F435W imagereveals that two of the images (B1 and B2) have twoemission knots at their center; overall source B appearsto be a compact galaxy with a primarily redder stellarpopulation, but with two well confined regions of activestar formation in the galaxy’s core. The detailed positionof these bright knots indicates a larger magnification inthe tangential direction than in the radial direction forthis source. The two knots in the third image are not resolved, but the image is elongated in the tangential di-rection. Source B also has a significant Einstein radius,with separations for the three images from the clusterBCG of 36 . (cid:48)(cid:48)
8, 36 . (cid:48)(cid:48)
6, and 35 . (cid:48)(cid:48)
8. Further lensed featuresare also apparent, but we do not yet have redshift in-formation for them and they are not used in the initiallensing model discussed below.A strong lensing model for RCS2327 was constructedusing the publicly available software LENSTOOL (Julloet al. 2007). The mass model is composed of multi-ple mass clumps. The cluster halo is represented bya generalized NFW distribution (Navarro et al. 1997),parametrized with position, x , y ; ellipticity e ; position4 Sharon et al.angle θ ; central slope α ; and concentration c . The 50brightest red-sequence-selected cluster-member galaxiesare represented by Pseudo-Isothermal Ellipsoidal MassDistributions (PIEMD; see Jullo et al. 2007, for details)parametrized with positional parameters ( x , y , e , θ ) thatfollow their observed measurements, r core fixed at 0.15pc, and r cut and σ scaled with their luminosity (seeLimousin et al. 2005 for a description of the scaling re-lations). The parameters of an L* galaxies were fixed at r cut = 40 kpc and σ = 160 km s − . The model consistsof 13 free parameters. All the parameters of the clusterhalo are allowed to vary (R.A., Decl. of the mass clump,ellipticity, position angle, scale radius, concentration andcentral radial mass profile).The constraints are the positions of the lensed featuresand their redshifts. Each component of Arc A was repre-sented by three positions, and the two cores of source Bwere used in each of its images. The best fit model is de-termined through Monte Carlo Markov Chain (MCMC)analysis through minimization in the source plane, witha resulting image-plane RMS of 0 . (cid:48)(cid:48)
17. The best fit pa-rameters and their 68% percentile uncertainties are pre-sented in Table 1. Some of the model parameters are notwell-constrained by the lensing evidence. In particular,a large range of values is allowed for r s and α , and themodel can converge on any value of the concentrationparameter c . The latter is not surprising, since in orderto determine the concentration parameter one needs toconstrain the slope of the mass profile on small and largeradii, beyond the range of the strong lensing constraints.Thus the concentration uncertainty given in Table 1 rep-resents the range of priors assumed in the lens modelingprocess. We find strong correlations between, α , r s , and c , which we fit to find r s = 575 . − . α + 583 . α and c = 16 . − . α .The Einstein radius of a lens is often used as a mea-sure of its lensing cross section, or strength. We mea-sure the effective Einstein radius as R E = (cid:112) A/π , where A is the area enclosed by the tangential critical curve, R E ( z = 1 . . (cid:48)(cid:48) R E ( z =2 . . (cid:48)(cid:48) M cyl ( < R A ) =5 . +0 . − . × M (cid:12) , M cyl ( < R B ) =3 . +0 . − . × M (cid:12) . Statistical uncertain-ties are computed by sampling models described by theMCMC outputs, considering only models with values of χ within two of the best fit, representing 1- σ uncer-tainty in the parameter space. The resulting masses are ameasure of the projected (i.e., cylindrical) masses withinthe quoted radii. These statistical uncertainties may failto reflect some systematics due to the small number oflensing constraints in this system. In particular, sincethe lens is only constrained by arcs on one side of thecluster, we see correlations in the parameter space be- tween the mass, ellipticity, and position of the lens. Thesuperior data expected from HST
Cycle 20 program GO-13177, will enable a better constrained lens model (Hoaget al. 2015). We adopt a 15% systematic uncertaintyfrom Zitrin et al. (2015) for clusters with similar stronglensing signal.A notable further result from the strong lens modelis that the cluster halo is offset from the BCG by1 . +0 . − . and 7 . +1 . − . arcseconds in right ascensionand declination, respectively. This corresponds to anoffset of 54 kpc at the cluster redshift. Figure 5 showsthe positional relationship between the cluster galaxies– as demarcated by red-sequence members – and boththe X-ray data and the strong lensing model. The peakof the X-ray emission is coincident with the position ofthe BCG as is typically seen in lower redshift relaxedclusters (Sanderson et al. 2009; Bildfell et al. 2008). Thecenter of the overall distribution of the red sequence lightis coincident with the strong lensing mass peak, both ofwhich are hence offset from the BCG and the X-ray cen-troid by ∼
60 kpc. Disagreements between the mass peakas traced by lensing and the X-ray centroid are seen inmajor clusters mergers (e.g. Bradaˇc et al. 2008; Mahdaviet al. 2007; Clowe et al. 2004) although the magnitude ofthe disagreement in RCS2327 is not nearly as large andis similar to that observed in intermediate cooling flowclusters in the sample of clusters in Allen (1998). How-ever, the differing positions indicated by various masstracers is arguably the strongest evidence that RCS2327is anything but a single relaxed halo; we explore the im-plications of this further in § DISCUSSION
The various mass proxies detailed in § ∼ R and conversion of the X-ray spectrum and radialluminosity profile to a spherical mass estimate requiresthe assumption of hydrostatic equilibrium. The stronglensing data are sensitive to mass at similar or smallerradii than the X-ray data, but fundamentally measures acylindrical mass in projection. The galaxy dynamics aresensitive to mass at the virial scale and rely on externalscaling relations to provide a mass estimate, which, asdetailed in § Comparison to Other Clusters
The left and middle panels of Figure 14 compare thevelocity dispersion, X-ray temperature and richness ofRCS2327 to the global correlations of these properties inan intermediate X-ray selected cluster sample from Yee& Ellingson (2003). The right panel of Figure 14 plotsthe measured velocity dispersion and X-ray temperatureof RCS2327 against the cluster data and fitted relationfrom Xue & Wu (2000). We plot both the total and red-sequence richnesses, and the velocity dispersion from allgalaxies, and only early-type galaxies. Which of each ofthese properties is best compared to the correlations inass Measurements of RCS2 J232727.6-020437 15
TABLE 1Best fit Strong Lensing Model Parameters
Halo Model RA Dec e θ r s α c ( (cid:48)(cid:48) ) ( (cid:48)(cid:48) ) (deg) (kpc)Halo 1 gNFW 1 . +0 . − . . +1 . − . . +0 . − . . +0 . − . +62 − . +0 . − . . +5 . − . Note . — Coordinates are measured in arcseconds East and North of the center of the BCG, at [RA, Dec]=[351.865026, − e = ( a − b ) / ( a + b ). θ is measured North of West. Error bars correspond to 1- σ confidence level asinferred from the MCMC optimization. Log Richness B gc Log V e l o c i t y D i s pe r s i on ( k m s (cid:239) ) Log Richness B gc Log T x ( k e V ) Log Tx (keV)
Log V e l o c i t y D i s pe r s i on ( k m s (cid:239) ) Fig. 14.—
The comparison of richness, velocity dispersion, and X-ray temperature for RCS2327 (green squares) against relations forthese quantities from the literature. The left and middle panels compare to the data and fitted relations in Yee & Ellingson (2003) forvelocity dispersion - richness (left) and X-ray temperature - richness (middle) and the right panel compares to the data and fitted relationin Xue & Wu (2000) for velocity dispersion - X-ray temperature. Both the total and early-type-only richnesses are shown, as well asvelocity dispersions from both the early-type-only and all galaxies. The X-ray temperature and velocity dispersions (for all galaxies andearly-type-only) of ACT-CL J0102–4915 ( z = 0 .
87) from Menanteau et al. (2013) are plotted in orange circles.
Yee & Ellingson (2003) or Xue & Wu (2000) is not ob-vious (e.g., see § M versus the redshift of RCS2327,compared to clusters from large X-ray and SZ cluster sur-veys. The figure illustrates that RCS2327 is among themost massive clusters at all redshifts, and in particularat z ≥ . Comparison of Mass Proxies
Though each of the mass proxies discussed above mea-sure the mass most naturally at differing radii, it is stillinstructive to compare the results directly. To do so weconsider several additions to the main analyses in § Cylindrical Masses from X-ray, Strong and WeakLensing
As noted above, weak and strong lensing are both sen-sitive to projected mass density. However, they probedifferent regimes of the mass distribution: strong lensing
Redshift M [ M s un h (cid:239) ] RCS2327
Fig. 15.—
Reproduced from Bleem et al. (2015). Estimatedmass versus redshift for clusters from four large X-ray and SZ sur-veys: SPT-SZ 2500 deg (Bleem et al. 2015), ROSAT all sky sur-vey (Piffaretti et al. 2011), Planck-DR1 (Planck Collaboration etal. 2013), and ACT (Marriage et al. 2011). The X-ray mass ofRCS2327 ( M = 1 . +0 . − . × M (cid:12) ) is overplotted as a ma-genta triangle, placing it among the most massive clusters acrossall redshifts, and comparable to only few other clusters at z ≥ . z = 0 .
87. Other notable high-mass clusters are SPT-CLJ2337-5942 at z = 0 .
77, SPT-CLJ0615-5746 at z = 0 .
972 andSPT-CLJ2106-5844 at z = 1 .
132 (Bleem et al. 2015; Foley et al.2011; Planck Collaboration et al. 2011). is insensitive to the mass at the outskirts of the clus-ter, where no strong-lensing evidence exists. Weak lens-ing lacks the resolution at the cluster core. To com-pare the weak and strong lensing mass estimates, wefirst compute the projected enclosed mass (also knownas the aperture mass) as a function of radius directly6 Sharon et al.from the weak lensing data. We use the ζ c statis-tic (Clowe et al. 1998; Hoekstra 2007) and convert themeasurements into projected masses, using the best fitNFW to estimate the large scale mean surface density(see Hoekstra 2007, for details). The dependence of theresulting projected mass estimate on the assumed den-sity profile is minimal (Hoekstra et al. 2015). At a radiusof 500 h − kpc this yields a projected enclosed mass of M WL , cyl ( < h − kpc) = 5 . ± . × h − M (cid:12) .We can similarly extend the mass estimate from thestrong lensing model to larger radii. However, since thelens model is only constrained by lensing evidence in theinnermost 400 kpc (measured from the BCG) we in-crease the systematic uncertainty of the strong lensingmass estimate by ∼ § h − kpc radius of M SL , cyl ( < h − kpc) = 8 . ± . × h − M (cid:12) . Thesetwo values are in fair agreement. We refrain from extrap-olating the strong lensing mass to larger radii, where thestrong lensing model is not constrained.The X-ray masses can be converted to cylindrical mass,by integrating along the line of sight out to 10 Mpc onboth sides of the cluster center. We note that this mayintroduce some uncertainty as this is model-dependent.The projected enclosed X-ray masses at the radii ofthe lensed galaxies (see Table 2) are 2 . +0 . − . , 4 . +1 . − . ,6 . +2 . − . × h − M (cid:12) for 271, 352, 500 kpc, respectively.These values are in fair agreement with the projectedenclosed masses derived from strong lensing, 3 . +0 . − . ,5 . +0 . − . , 8 . +0 . − . × h − M (cid:12) , respectively. The differ-ences are in line with expected uncertainties and biases(see, e.g., Mahdavi et al. 2013) for hydrostatic masses,as overall we find that the lensing masses are somewhathigher than the X-ray and SZ masses. Nevertheless, itmay also indicate that structure along the line of sight orelongation of the cluster halo may be significant. For ex-ample, the structure that is indicated by a concentrationof galaxies at z ∼ .
73 (Figure 7) may be contributingto the lensing signal, and should be accounted for in fu-ture lensing analysis (D’Aloisio et al. 2014; McCully etal. 2014; Bayliss et al. 2014a).
Spherical Masses
To compare the weak lensing, X-ray, and SZ masseswe deproject the aperture masses following Hoekstra(2007), assuming the mass-concentration from Duffy etal. (2008). Although the deprojection is somewhat modeldependent, it is less sensitive to deviations from the NFWprofile. At the cluster core, we compute the correspond-ing deprojected weak lensing mass within 500 h − kpc(approximately R ). We obtain a value of M WL ( < h − kpc) = 4 . +1 . − . × h − M (cid:12) within this ra-dius, in agreement with the X-ray estimate of M X , =3 . +0 . − . × h − M (cid:12) , and SZ mass of M SZ , = 4 . ± . × h − M (cid:12) .At large radii, we use the extrapolated X-ray massas described in § R from each of theseanalyses agree within the uncertainties. The X-ray massis M X , = 1 . +1 . − . × h − M (cid:12) and the weak lens-ing mass from the NFW fit is M WL , ( < . . ± . × h − M (cid:12) . Hence at large radii the extrapo-lated X-ray mass and weak lensing data also agree withinthe uncertainties. Mass Profile
Figure 16 presents the enclosed masses measured inthis paper as a function of cluster-centric radius, aswell as SZ masses from the literature. As demon-strated above, these measurements are consistent witheach other within errors, and trace the mass profile fromthe very core out to R .We fit a set of spherical NFW profiles (Eq. 7) to thespherical masses measured in this paper. To estimatethe range of fits that are consistent with the measure-ments, we fit the profile 1000 times, each time to a setof measurements that were randomly sampled from their1- σ uncertainties, and weighted by their uncertainties.We did not include in the fit the extrapolated estimatesand constraints from the literature. These masses areshown in Figure 16 for reference, extrapolated measure-ments with in dashed error bars, and the Hasselfield etal. (2013) mass estimates in thin lines. A large rangeof scale radii is consistent with the measured masses,and the resulting range of NFW profiles is shown as thesolid shaded area in Figure 16. The striped area in theright panel of Figure 16 traces the cylindrical mass fromthe same NFW profiles that were fit to the sphericalmasses. While we could simultaneously fit the profile tothe cylindrical and spherical masses, we choose not to,because the cylindrical strong lensing measurements donot assume spherical symmetry and thus should not beexpected to be described by a spherical NFW profile. Wefind that the strong lensing masses are somewhat higherthan the predicted cylindrical masses, which could be dueto the triaxiality that is not taken into account in thissimplified fit. As expected, the projected X-ray massesdo agree with the spherical profile, since they were com-puted by integration of the X-ray best fit spherical profilealong the line of sight.The simplistic NFW fit to all the non-extrapolatedcylindrical mass measurements yields r s = 0 . +1 . − . Mpc.However, while a fit of a spherical NFW profile to themass measurements is possible (though a large range ofscale radii is consistent with the results), we caution thatsuch a fit is not meaningful at this point. The differentmeasurements were conducted completely independentlyof each other, and rely on different assumptions as de-scribed in the previous sections (e.g., mass-concentrationrelations, spherical symmetry, hydrostatic equilibrium,various scaling relations). In particular, some of themass proxies already assume a certain mass profile slope.A self-consistent combined multi-wavelength analysis iscalled for. Such an analysis would ideally allow triaxialsymmetry, and fit the mass distribution simultaneouslyto constraints derived directly from all the observables:strong lensing constraints, weak lensing shear, galaxyvelocity distribution, and X-ray and SZ measurements.This sort of analysis is left for future work, and is notwithin the scope of this paper. SUMMARY AND CONCLUSIONS
We present a multi-wavelength analysis of RCS2327,a massive cluster at z = 0 . TABLE 2Estimated Masses
Mass proxy Projected Mass [10 h − M (cid:12) ] Spherical Mass † R = 217kpc R = 352kpc R = 500kpc r M / r M / r M / [kpc] [ h − M (cid:12) ] [Mpc] [ h − M (cid:12) ] [Mpc] [ h − M (cid:12) ]Strong Lensing 3 . +0 . − . ± . . +0 . − . ± . . +0 . − . ± . · · · · · · · · · · · · · · · · · · X-ray 2 . +0 . − . . +1 . − . . +2 . − . +54 − . +0 . − . [1 . +0 . − . ] [11 +9 − ] [1 . +1 . − . ] [18 +18 − ]Weak Lensing · · · · · · . ± . . ± . +2 . − . · · · +9 − SZ · · · · · · · · · · · · · · · . ± .
02 8 . ± . · · · · · · SZ (M11 ‡ ) · · · · · · · · · ± . +0 . − . . ± .
02 8 . ± . · · · · · · Velocity dispersion · · · · · · · · · · · · · · · · · · · · · . +14 − . Caustics · · · · · · · · · · · · · · · · · · · · · +10 − Richness · · · · · · · · · · · · · · · · · · · · · +9 − Note . — Summary of the mass estimates from the different mass proxies considered in this work. Square brackets indicate extrapolatedvalues. Projected X-ray mass was computed by integrating the mass model along the line of sight out to 10 Mpc on both sides of thecluster. † The different mass proxies were estimated within different radii, as indicated. ‡ SZ measurments using the method of Mroczkowski (2011). r [kpc] M s ph ( < r) [ M s un ] SLXrayWLSZvdispcausticsrichness
Spherical mass R [kpc] M cy l ( < R ) [ M s un ] Cylindrical mass
Fig. 16.—
The mass estimates from the different mass proxies considered in this work (see Table 2) are plotted as a function of radius,color-coded by mass proxy as indicated in the legend. Points with dashed error bars are from extrapolated results (see text). The SZ massestimates from Hasselfield et al. (2013) are plotted at R = 1 . r , and in the right panel are cylindrical (projected) masses enclosed within projected radius R . 1- σ uncertainties are shown; wenote that when r ∆ and M ∆ are determined jointly their uncertainties are correlated. The shaded area in the left panel is the 1- σ rangeof spherical NFW mass profiles that were fit to the spherical masses measured in this work. The measurements that were included in thefit are indicated with thick circles and errorbars. The cylindrical masses in the right panel were not included in the fit, nevertheless, weshow the projected mass density of the same fits as striped area in the right panel. As discussed in Section 4.3, this simple fit does notrepresent a true joint analysis of the data, since various assumptions on the slope of the mass profile are already folded into some of thesemeasurements. proxies. At the core of the cluster, we measure the pro-jected mass from a strong lensing model; at intermedi-ate radii, ∼ . ∼ r ∆ ) thatare not necessarily uniform among these proxies. Thisunavoidably contributes to the scatter among the derivedmasses. Nevertheless, the simple internal comparisons in § § z ≥ . HST observations that have already been exe-8 Sharon et al.cuted. Further observations will provide constraints for aself-consistent modeling of the three-dimensional clustermass distribution (e.g., Umetsu et al. 2015; Limousin etal. 2013; Sereno et al. 2013), that takes into account theeffects of triaxiality and orientation on the mass observ-ables.We wish to thank the anonymous referee for a construc-tive review that improved the quality of this manuscript.Support for program number GO-10846 was provided byNASA through a grant from the Space Telescope ScienceInstitute, which is operated by the Association of Uni-versities for Research in Astronomy, Inc., under NASAcontract NAS5-26555. Support for this work was pro-vided by the National Aeronautics and Space Adminis-tration through
Chandra award GO2-13158X issued bythe
Chandra
X-ray Observatory Center, which is oper-ated by the Smithsonian Astrophysical Observatory forand on behalf of the National Aeronautics Space Ad-ministration under contract NAS8-03060. Based on ob-servations obtained at the Gemini Observatory, whichis operated by the Association of Universities for Re-search in Astronomy, Inc., under a cooperative agree-ment with the NSF on behalf of the Gemini partner-ship: the National Science Foundation (United States),the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia),Minist´erio da Ciˆencia, Tecnologia e Inova¸c˜ao (Brazil) andMinisterio de Ciencia, Tecnolog´ıa e Innovaci´on Produc-tiva (Argentina). Based on observations obtained withMegaPrime/MegaCam, a joint project of CFHT andCEA/DAPNIA, at the Canada-France-Hawaii Telescope(CFHT) which is operated by the National ResearchCouncil (NRC) of Canada, the Institute National des Sci-ences de l’Univers of the Centre National de la RechercheScientifique of France, and the University of Hawaii. Wealso present observation taken at the Magellan telescopesat Las Campanas Observatory, Chile, using LDSS-3 andGISMO. CARMA/SZA operations and science supportis provided by the National Science Foundation undera cooperative agreement and by the CARMA partneruniversities; the CARMA/SZA work presented here wassupported by NSF grant AST- 1140019 to the Universityof Chicago. ER acknowledges support from the NationalScience Foundation AST-1210973, SAO TM3-14008X(issued under NASA Contract No. NAS8- 03060). LFBresearch is funded by proyecto FONDECYT 1120676 andCentro BASAL CATA. ER acknowledges support fromFP7-PEOPLE-2013-IIF under Grant Agreement PIIF-GA-2013-627474.
Facilities:
Magellan, HST (ACS), CXO (ASIS),CFHT, Gemini.
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