Planck Sunyaev-Zel'dovich Cluster Mass Calibration using Hyper Suprime-Cam Weak Lensing
Elinor Medezinski, Nicholas Battaglia, Keiichi Umetsu, Masamune Oguri, Hironao Miyatake, Atsushi J.Nishizawa, Cristóbal Sifón, David N. Spergel, I-Non Chiu, Yen-Ting Lin, Neta Bahcall, Yutaka Komiyama
PPubl. Astron. Soc. Japan (2014) 00(0), 1–12doi: 10.1093/pasj/xxx000 Planck
Sunyaev-Zel’dovich Cluster MassCalibration using Hyper Suprime-Cam WeakLensing
Elinor Medezinski , Nicholas Battaglia , Keiichi Umetsu , MasamuneOguri , Hironao Miyatake , Atsushi J. Nishizawa , Crist ´obal Sif ´on ,David N. Spergel , I-Non Chiu , Yen-Ting Lin , Neta Bahcall and YutakaKomiyama Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA Institute of Astronomy and Astrophysics, Academia Sinica, P. O. Box 23-141, Taipei 10617,Taiwan. Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI),TokyoInstitutes for Advanced Study, The University of Tokyo, Chiba 277-8582, Japan Research Center for the Early Universe, University of Tokyo, Tokyo 113-0033, Japan Department of Physics, University of Tokyo, Tokyo 113-0033, Japan Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Institute for Advanced Research, Nagoya University, Nagoya 464-8602, Aichi, Japan Center for Computational Astrophysics, Flatiron Institute, 162 5th Ave. New York, NY 10010 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Department of Astronomy, School of Science, SOKENDAI (The Graduate University forAdvanced Studies), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan ∗ E-mail: [email protected]
Received ; Accepted
Abstract
Using ∼
140 deg Subaru Hyper Suprime-Cam (HSC) survey data, we stack the weak lensing(WL) signal around five
Planck clusters found within the footprint. This yields a 15 σ detectionof the mean Planck cluster mass density profile. The five
Planck clusters span a relativelywide mass range, M WL , = (2 − × M (cid:12) with a mean mass of M WL , = (4 . ± . × M (cid:12) . The ratio of the stacked Planck
Sunyaev-Zel’dovich (SZ) mass to the stackedWL mass is (cid:104) M SZ (cid:105) / (cid:104) M WL (cid:105) = 1 − b = 0 . ± . . This mass bias is consistent with previousWL mass calibrations of Planck clusters within the errors. We discuss the implications of ourfindings for the calibration of SZ cluster counts and the much discussed tension between
Planck
SZ cluster counts and
Planck Λ CDM cosmology.
Key words: gravitational lensing: weak — cosmology: observations — dark matter — galaxies: clusters:general — large-scale structure of universe
The abundance of galaxy clusters, particularly at high redshifts,is sensitive to the cosmological parameters that describe struc-ture formation such as the matter density ( Ω M ) and the normal- ization of the matter power spectrum ( σ , e.g., Bahcall & Fan1998; Henry 2000; Henry et al. 2009; Reiprich & B¨ohringer2002; Voit 2005; Allen et al. 2011). Since Abell’s seminal work(Abell 1958), many ongoing efforts have yielded detections of c (cid:13) a r X i v : . [ a s t r o - ph . C O ] J a n Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
The abundance of galaxy clusters, particularly at high redshifts,is sensitive to the cosmological parameters that describe struc-ture formation such as the matter density ( Ω M ) and the normal- ization of the matter power spectrum ( σ , e.g., Bahcall & Fan1998; Henry 2000; Henry et al. 2009; Reiprich & B¨ohringer2002; Voit 2005; Allen et al. 2011). Since Abell’s seminal work(Abell 1958), many ongoing efforts have yielded detections of c (cid:13) a r X i v : . [ a s t r o - ph . C O ] J a n Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0 thousands of clusters (e.g., Gladders & Yee 2000; Wen et al.2012; Rykoff et al. 2014; Vikhlinin et al. 2009; Mantz et al.2010). In particular, the
Planck satellite has provided an im-portant catalog of over a thousand galaxy clusters to higher red-shift (Planck Collaboration et al. 2014, 2016) through the ther-mal Sunyaev-Zel’dovich (SZ; Sunyaev & Zeldovich 1972) se-lection. Two other ongoing SZ surveys, namely the AtacamaCosmology Telescope (ACT; Kosowsky 2003), the South PoleTelescope (SPT; Carlstrom et al. 2011) and their successors,keep pushing the detection limits to lower masses and higherredshifts (e.g., Staniszewski et al. 2009; Marriage et al. 2011;Reichardt et al. 2013; Hasselfield et al. 2013; Bleem et al. 2015).The mass observable in all these SZ experiments is thevolume-integrated Intra-Cluster Medium (ICM) pressure, re-ferred to as the Compton- Y parameter. Since this SZ proxyis not a direct probe of mass, scaling relations are typically in-voked to translate it to a total cluster mass. In particular, Planck adopted a method that relies on X-ray observations of clustersto calibrate the Y parameter (e.g., Planck Collaboration et al.2014). The initial X-ray determination of the total cluster mass,on the other hand, assumes the clusters are in hydrostatic equi-librium (HSE, Pointecouteau et al. 2005; Arnaud et al. 2007).The cosmological constraints placed by Planck
SZ clustercounts have unveiled a modest tension between σ comparedto constraints derived by combining the primary cosmic mi-crowave background (CMB) anisotropies with non-cluster data(Planck Collaboration et al. 2014, 2016). If exacerbated by fu-ture data, this tension could be a signature of new physics, suchas a larger non-minimal sum of neutrino masses, or more likelycould point to systematics in the cluster mass calibration. The Planck
SZ mass calibration relied on X-ray observations fromXMM-Newton. There are a number of potential biases in thiscalibration. Clusters undergo mergers which would violate theassumption of HSE and result in few tens of percent bias (Rasiaet al. 2006; Nagai et al. 2007; Lau et al. 2009; Battaglia et al.2012; Nelson et al. 2014; Henson et al. 2017). In addition, sev-eral papers (Mahdavi et al. 2013; Donahue et al. 2014; Rozoet al. 2014) argue there are instrument calibration issues withXMM-Newton.Weak lensing (WL) offers an independent method for mea-suring and calibrating cluster masses, as it probes the totalmass, regardless of the nature or dynamical state of this mass.Cluster weak lensing has matured significantly in the last twodecades (see reviews by Bartelmann et al. 2001; Refregier 2003;Hoekstra & Jain 2008). Dedicated cluster simulations haveexplored different aspects of systematics in the cluster massderivation, including the triaxiality of clusters (Oguri et al.2005; Corless & King 2007; Becker & Kravtsov 2011), the in-clusion of line-of-sight structures (Hoekstra et al. 2013), the de-viations of clusters from commonly adopted spherical (Navarroet al. 1997) halos in the model extraction of total mass, and the impact of baryonic effects (Henson et al. 2017). Proper sourceselection and photometric redshift biases have been exploredin several pointed cluster WL studies (Medezinski et al. 2010;Okabe et al. 2010; Applegate et al. 2014; Gruen & Brimioulle2017). In parallel, image simulations have been utilized to ro-bustly calibrate biases in galaxy shape measurements (Heymanset al. 2006; Massey et al. 2007; Bridle et al. 2010; Kitching et al.2012; Mandelbaum et al. 2015; Fenech Conti et al. 2017).Several recent studies have used WL to recalibrate
Planck
SZ cluster masses, e.g., Weighing the Giants (WtG, von derLinden et al. 2014), the Canadian Cluster Cosmology Project(CCCP, Hoekstra et al. 2015), the Cluster Lensing And super-novae Survey with Hubble (CLASH, ? ; see also Umetsu et al.2014; Merten et al. 2015), and the Local Cluster SubstructureSurvey (LoCuSS; Smith et al. 2016). These papers introduced abias parameter to calibrate the measured SZ mass estimate withthe true mass, − b ≡ M SZ /M True . (1)where M SZ is the SZ mass estimate and M True is the true mass.The best estimator for the true mass is assumed to come fromweak lensing, M WL (for caveats, see Becker & Kravtsov 2011).If the bias were zero ( b = 0 ), the Planck primary CMB wouldpredict far more clusters than observed. Reconciling the
Planck
SZ cluster counts requires − b = 0 . , about σ away from Planck adopted value, − b = 0 . (Planck Collaboration et al.2016). The WL mass calibrations differ in their conclusion asto what the bias level is, with some studies agreeing with the Planck value ( b = 0 . – . ; von der Linden et al. 2014; Hoekstraet al. 2015; ? ; Sereno et al. 2017), and some finding little to nobias ( b = 0 . – . ; Smith et al. 2016). We note that the samplesof clusters used in these studies have marginal overlap in red-shift and mass ranges. It is not clear whether these differencesare the result of systematics in the WL observations or that − b has a mass or redshift dependence (Andreon 2014; Smith et al.2016; Sereno & Ettori 2017).In this paper, we address this important issue by calibrat-ing the SZ masses of Planck clusters located within the latestWL observations of the Hyper Suprime-Cam Subaru StrategicProgram (HSC-SSP; see Aihara et al. 2017a, 2017b). The HSC-SSP is an ongoing wide-field optical imaging survey with theHSC camera which is installed on the Subaru 8.2m telescope.Its Wide layer will observe the total sky area of ∼ deg to i (cid:46) . With its unique combination of area and depth, the HSCWide layer will both detect and provide accurate WL measure-ments of thousands of clusters to z ∼ . . In its current stage, ∼ deg have been observed, out of which we use ∼ deg of full-depth and full-color (FDFC) data to characterize the fiveoverlapping Planck clusters and provide an independent mea-sure of the SZ-WL mass ratio.This paper is organized as follows. In Section 2 we presentthe HSC survey and the
Planck clusters found within HSC. In ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 Table 1.
Planck clusters within HSC-Wide
Planck
Name NED Name R.A. Dec. z [deg] [deg]PSZ2 G068.61-46.60 Abell2457 338.91999 1.48489 0.0594PSZ2 G167.98-59.95 Abell0329 33.67122 − − − BCG center (J2000).
Section 3 we describe the WL methodology. In Section 4 wepresent the WL analysis and results, describing the source selec-tion, the stacked and individual cluster WL analysis, the model-ing, and the WL-SZ mass calibration. We summarize and con-clude in Section 5. Throughout this paper we adopt a
WilkinsonMicrowave Anisotropy Probe nine-year cosmology (
WMAP9 )(Hinshaw et al. 2013), where Ω M = 0 . , Ω Λ = 0 . , and h = H / km s − Mpc − . The HSC-SSP (Aihara et al. 2017b) is an optical imaging sur-vey with the new HSC camera (Miyazaki et al., in prep) in-stalled on the Subaru 8m telescope. The HSC-SSP survey con-sists of three layers: Wide, Deep and Ultradeep. The surveyhas been allocated 300 nights spanning five years (2014–2019).The Wide survey, when complete, will observe ∼ .In this study, we use the current internal data release (S16A).It contains ∼
140 deg of FDFC area. Aihara et al. (2017a,2017b) give an overview of the survey and its public data re-lease (S15B). The HSC Pipeline, hscPipe (Bosch et al. 2017),based on the Large Synoptic Survey Telescope (LSST) pipeline(Ivezic et al. 2008; Axelrod et al. 2010; Juri´c et al. 2015), isused to reduce HSC data.HSC-Wide consists of observations in five board-band fil-ters, grizy , reaching a typical limiting magnitude of i (cid:39) .So far it has reached exceptional seeing with a median ofFWHM = 0 . (cid:48)(cid:48) in the i band. Seven different codes have beenemployed by the team to produce photometric redshift (photo-z) catalogs from the multi-band data (Tanaka et al. 2017). Herewe make use of the MLZ photo-z code. Each galaxy is assigneda probability distribution function (PDF), from which variousphoto-z point estimates are derived (e.g., mean, median, etc.).We make use of the full PDF to avoid any potential biases ofpoint estimators.The WL shapes are estimated on the coadded i -band imagesusing the re-Gaussianization method (Hirata & Seljak 2003),and are fully described in Mandelbaum et al. (2017a). Basiccuts have been applied to these catalogs to ensure galaxies withrobust photometry and shapes. Further photo-z quality cuts (Tanaka et al. 2017) are applied to the catalogs so that onlygalaxies with measured photo-z’s remain. Cuts needed to ob-tain the source catalog are described in Section 4.1. Planck
Cluster Sample in HSC
We make use of the
Planck
Planck algorithms (
MMF1, MMF3, PwS ). Wecross-match the
Planck catalog with HSC FDFC footprint andfind that five clusters are contained within the it. We attemptto maximize the lensing signal by stacking around the bright-est cluster galaxy (BCG) center, which provides a better traceof the center of potential than the SZ peak (George et al. 2012)given the large
Planck beam size. We visually inspect the HSCimages of these five clusters in order to identify the BCG ofeach cluster. The five clusters, their BCG positions and red-shifts are listed in Table 1. In Figure 1, we show the sky distri-bution of all
Planck clusters (gray points), the HSC-Wide FDFCfields that have been so far observed (gray regions), the plannedHSC-Wide fields (black outline) and the
Planck clusters de-tected within the current HSC S16A fields (circles colored bycluster redshift). In Figure 2, we show color images of the fiveobserved
Planck cluster, acquired from the HSC imaging skyserver tool, scMap . This figure indicates the clusters are of-ten complex, non-relaxed and sometimes merging with othernearby groups. Weak lensing distorts the images of source galaxy shapes. Theamplitude of this distortion is proportional to all matter con-tained in the lensing cluster and along the line of sight to thelens. The tangential distortion profile is related to the projectedsurface-mass density profile of the average mass distributionaround the cluster, γ T ( R ) = ∆Σ( R )Σ cr = ¯Σ( < R ) − Σ( R )Σ cr , (2)where R is the comoving transverse separation between thesource and the lens, Σ( R ) is the projected surface mass den-sity, ¯Σ( < R ) is the mean density within R , and https://hsc-release.mtk.nao.ac.jp/hscMap/ Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
Planck cluster, acquired from the HSC imaging skyserver tool, scMap . This figure indicates the clusters are of-ten complex, non-relaxed and sometimes merging with othernearby groups. Weak lensing distorts the images of source galaxy shapes. Theamplitude of this distortion is proportional to all matter con-tained in the lensing cluster and along the line of sight to thelens. The tangential distortion profile is related to the projectedsurface-mass density profile of the average mass distributionaround the cluster, γ T ( R ) = ∆Σ( R )Σ cr = ¯Σ( < R ) − Σ( R )Σ cr , (2)where R is the comoving transverse separation between thesource and the lens, Σ( R ) is the projected surface mass den-sity, ¯Σ( < R ) is the mean density within R , and https://hsc-release.mtk.nao.ac.jp/hscMap/ Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
RA [deg] D ec [ d e g ] R e d s h i f t Fig. 1.
Sky distribution of the HSC-SSP Wide fields (black outline) and the area observed thus far in FDFC (gray regions). Black circles are
Planck -detectedclusters, colored circles are the five
Planck clusters within the HSC FDFC footprint. Color represents redshift, and circle size represents SZ mass. Σ cr = c πG D A ( z s ) D A ( z l ) D A ( z l , z s )(1 + z l ) , (3)is the critical surface mass density, where G is the gravitationalconstant, c is the speed of light, z l and z s are the lens and sourceredshifts, respectively, and D A ( z l ) , D A ( z s ) , and D A ( z l ,z s ) arethe angular diameter distances to the lens, source, and betweenthe lens and the source, respectively, and the extra factor of (1+ z l ) comes from our use of comoving coordinates (Bartelmann& Schneider 2001).We estimate the mean projected density contrast profile ∆Σ( R ) from Equation 2 by stacking the shear over a popula-tion of source galaxies s (over multiple clusters l ) that lie withina given cluster-centric radial annulus R (in comoving units), ∆Σ( R ) = 12 R ( R ) (cid:80) l,s w ls e t,ls (cid:2) (cid:104) Σ cr − (cid:105) ls (cid:3) − (1 + K ( R )) (cid:80) l,s w ls , (4)where the double summation is over all clusters and over allsources associated with each cluster (i.e., lens-source pairs), and e t = − e cos 2 φ − e sin 2 φ, (5)is the tangential shape distortion of a source galaxy, φ is theangle measured in sky coordinates from the right ascension di-rection to a line connecting the lens and source galaxy, and e , e are the shear components in sky coordinates obtainedfrom the pipeline (Mandelbaum et al. 2017a; Bosch et al. 2017).The mean critical density (cid:104) Σ − (cid:105) − ls is averaged with the sourcephoto-z PDF, P ( z ) , for each lens-source pair, such that (cid:104) Σ cr − (cid:105) ls = (cid:82) ∞ z l Σ cr − ( z l , z ) P ( z ) d z (cid:82) ∞ P ( z ) d z . (6)As long as the mean P ( z ) correctly describes the sample red-shift distribution, the above equation corrects for dilution bycluster or foreground source galaxies. However, obtaining real-istic photo-z P ( z ) is one of the biggest observational challengesin WL analyses. The weight in Equation 4, w ls , is given by w ls = ( (cid:104) Σ cr − (cid:105) ls ) σ e,s + e ,s , (7)where σ e is the per-component shape measurement uncertainty,and e rms ≈ . is the root mean square (RMS) ellipticity esti-mate per component. The factor (1 + K ( R )) corrects for a mul-tiplicative shear bias m as determined from the GREAT3-likesimulations (Mandelbaum et al. 2014, 2015) and is described inMandelbaum et al. (2017b). The factor is computed as K ( R ) = (cid:80) l,s m s w ls (cid:80) l,s w ls . (8)The ‘shear responsivity’ factor in Equation 4, R ( R ) = 1 − (cid:80) l,s e , s w ls (cid:80) l,s w ls ≈ . , (9)represents the response of the ellipticity, e , to a small shear(Kaiser 1995; Bernstein & Jarvis 2002). A full description andclarification of this procedure is given in Mandelbaum et al.(2017a).Finally, the bin-to-bin covariance matrix includes the sta-tistical uncertainty due to shape noise, the intrinsic varianceof the projected cluster lensing signal due to halo triaxialityand the presence of correlated halos (Gruen et al. 2015), andcosmic-noise covariance due to uncorrelated large-scale struc-tures along the line-of-sight (Hoekstra 2003), C = C stat + C int + C lss (10)where C stat ( R ) = 14 R ( R ) (cid:80) l,s w ls ( e ,s + σ e,s ) (cid:10) Σ − (cid:11) − ls [1 + K ( R )] (cid:104)(cid:80) l,s w ls (cid:105) . (11)The fractional intrinsic scatter is estimated to be 20% of the pro-jected cluster lensing signal, per cluster, from semi-analyticalcalculations calibrated by cosmological numerical simulations(Gruen et al. 2015; Umetsu et al. 2016; Becker & Kravtsov2011). Following the prescription of Umetsu et al. (2016), weassume the diagonal form of the C int matrix, diag [ C int ( R )] = ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 Fig. 2.
Color ( riz ) images of
Planck clusters observed by HSC Wide (top left to bottom left): Abell 2457 ( z = 0 . ), Abell 329 ( z = 0 . ), Abell 362 ( z = 0 . ),MaxBCGJ140.53188+03.76632 ( z = 0 . ) and Abell 776 ( z = 0 . ). Green circle marks the location of the BCG selected as the cluster center. The imagesare roughly (cid:48) × . (cid:48) in scale. [ α int ∆Σ( R )] , with α int = 0 . . We do not expect signifi-cant bin-to-bin covariance for the current binning scheme. Wecompute the cosmic-noise covariance C lss following Hoekstra(2003). We compute the elements of the C lss matrix using thenonlinear matter power spectrum of Smith et al. (2003) for theWMAP9 cosmology (Hinshaw et al. 2013), with a source planeat z = 1 . , the mean redshift of our source galaxies (M17). Forthe five Planck clusters, we simply scale the respective covari-ance matrices linearly according to the number of independent clusters: C → C /N with N = 5 . In this section, we present the WL analysis of the five
Planck clusters. We show both the individual and stacked mass profilesof the
Planck clusters. We fit the cluster density profile with amodel to obtain their total WL mass. Finally, we compare theirWL masses with their measured
Planck
SZ mass and obtain thefinal SZ-WL mass calibration.
Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0 ∆ Σ + [ h M fl p c − ] all, S/N=15.6P-cut, S/N=14.5CC, S/N=14.9 ∆ Σ × R [Mpc/ h ] n g / [ h M p c − ] Fig. 3.
Stacked surface mass density as a function of cluster-centric comov-ing radius (top panel). We compare between profiles derived using all galax-ies (black circles), using only sources where their (cid:80) P ( z > z cl + 0 . > . (P-cut; cyan squares), and selecting only sources within color-color-magnitude cuts (CC-cuts; blue triangles). The mass density profile that usesall galaxies appears diluted inside the cluster < ∼ . /h relative to themore conservative P-cut/CC-cut profiles, mostly due to contamination fromcluster members. The middle panels shows the ◦ -rotated shear, consis-tent with zero as expected. The bottom panel shows the effective numberdensity profile. We follow the methodology of Medezinski et al. (2010), furtherexplored and applied to HSC clusters in (Medezinski et al. 2017,hereafter M17), in selecting background galaxies from the fullgalaxy sample. Two methods have been explored in M17 –“CC-cuts” (Medezinski et al. 2010) and “P-cut” (Oguri 2014).CC-cuts relies on selection background galaxies in color-color(CC) space; specifically, for HSC the g − i vs r − z space hasbeen used, where the cluster red-sequence can be well isolatedin color from the background and foreground galaxies. TheP-cut method relies on selecting galaxies whose photo-z PDF( P ( z ) ) lie mostly beyond the cluster redshift plus some thresh-old, i.e. ∞ (cid:82) z l +∆ z P ( z )d z > . . An optimized threshold is foundto be ∆ z = 0 . . M17 show that, with the above chosen lim-its, these selections provide consistent, undiluted WL profiles.Without these cuts the lensing signal is severely diluted for low-redshift clusters, as are the Planck-HSC clusters. We repeat thistest here by utilizing the CC-cuts and P-cut source selections,and compare their profiles in the next section. We compute the mean lensing surface mass density profile, ∆Σ( R ) , given by Equation 4, stacked over the five Planck clus-ter. We present the profiles in the top panel of Figure 3 for thethree selection methods: using the full sample (‘all’; black cir-cles), using the P-cut source sample (cyan squares), and using the CC-cut source sample (blue triangles). As can be seen fromthis comparison, the black points are systematically below theprofiles of the other selection methods. However, as opposedto the overall consistency between P-cut and CC-cuts found inM17, here the P-cut signal is systematically below the CC-cutscurve, though in agreement within the errors. We explore theimpact of this dilution by comparing the fitted masses for theP-cut and CC-cut profiles next (Section 4.3).
To estimate the total mean mass of the clusters, we fit thestacked lensing profiles obtained in Section 4.2 with a univer-sal Navarro, Frenk, & White (1996, NFW) mass density profile,given by the form ρ NFW ( r ) = ρ s ( r/r s )(1 + r/r s ) , (12)where ρ s is the characteristic density, and r s is the charac-teristic scale radius at which the logarithmic density slope isisothermal. The halo mass M ∆ is given by integrating theNFW profile (Equation 12) out to a radius r ∆ , at which themean density is ∆ × ρ crit ( z l ) , the critical mass density ofthe universe at the cluster redshift, expressed as M ∆ ≡ M (
04 Mpc /h , and the frac-tion of miscentered clusters is P mis = 0 . ± . . We set flatprior around those parameters the size of the errors. We find R [Mpc/ h ] ¢ § + [ h M ¯ M p c ¡ ] P-cut, M =(2 : § : £ M ¯ =h CC, M =(3 : § : £ M ¯ =h Fig. 4.
NFW fit to the stacked surface mass density profile. Cyan squaresand curve show the profile and its fit using P-cut galaxies behind the lens,and blue triangles and curve show the same for source galaxies selectedwith the CC-cut. The best-fit mass is given in the legend. Over 30% bias iscaused by contamination of cluster/foreground galaxies when not applyingthe CC-cuts. M = (4 . ± . × M (cid:12) /h and c = 7 . ± . .Considering the mass difference between the models with andwithout miscentering, the systematic uncertainty is of the order | . − . | / . ∼ . Following the same procedure as above, we fit the ∆Σ( R ) in-dividually for each cluster. Since we have lower S/N for eachprofile, we treat the concentration as a nuisance parameter inthe range, ≤ c ≤ , and allow for a broader range ofmasses, ≤ M / (10 M (cid:12) /h ) ≤ . We preset the profilesand their fitted NFW models (see Section 4.3) in Figure 5. Thefitted mass, along with the redshift, is given above each pro-file. We also translate the mass to an overdensity of ∆ = 500 to compare with the SZ values. We summarize the fitted WLmasses and concentrations M , c , M , the SZ masses,and the SZ-to-WL mass ratio in Table 2 . All of our clustershave high S/N WL profiles, above S/N > ∼ . Here we defineS/N= (cid:112)(cid:80) i (∆Σ( R i ) / d∆Σ( R i )) , where our binning schemeensures ∆Σ( R i ) / d∆Σ( R i ) > in each radial bin per cluster,so that the noise contribution to our S/N estimator is negligible.The highest S/N cluster is Abell 362 at z = 0 . , with S/N=10.4.This cluster is also present in the ACTPol SZ cluster catalogthat is being used in an independent HSC WL-SZ mass calibra-tion study (Miyatake et al., in prep.). It is also present in theXMM-MCXC catalog and is being analyzed in an X-ray-WLmass calibration study by (Miyaoka et al. 2017). We all findconsistent WL masses for this cluster. The most massive clus-ter, both in terms of SZ and WL mass (though with large errors),is MaxBCGJ140.53188+03.76632 at z = 0 . . It is a relatively Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
NFW fit to the stacked surface mass density profile. Cyan squaresand curve show the profile and its fit using P-cut galaxies behind the lens,and blue triangles and curve show the same for source galaxies selectedwith the CC-cut. The best-fit mass is given in the legend. Over 30% bias iscaused by contamination of cluster/foreground galaxies when not applyingthe CC-cuts. M = (4 . ± . × M (cid:12) /h and c = 7 . ± . .Considering the mass difference between the models with andwithout miscentering, the systematic uncertainty is of the order | . − . | / . ∼ . Following the same procedure as above, we fit the ∆Σ( R ) in-dividually for each cluster. Since we have lower S/N for eachprofile, we treat the concentration as a nuisance parameter inthe range, ≤ c ≤ , and allow for a broader range ofmasses, ≤ M / (10 M (cid:12) /h ) ≤ . We preset the profilesand their fitted NFW models (see Section 4.3) in Figure 5. Thefitted mass, along with the redshift, is given above each pro-file. We also translate the mass to an overdensity of ∆ = 500 to compare with the SZ values. We summarize the fitted WLmasses and concentrations M , c , M , the SZ masses,and the SZ-to-WL mass ratio in Table 2 . All of our clustershave high S/N WL profiles, above S/N > ∼ . Here we defineS/N= (cid:112)(cid:80) i (∆Σ( R i ) / d∆Σ( R i )) , where our binning schemeensures ∆Σ( R i ) / d∆Σ( R i ) > in each radial bin per cluster,so that the noise contribution to our S/N estimator is negligible.The highest S/N cluster is Abell 362 at z = 0 . , with S/N=10.4.This cluster is also present in the ACTPol SZ cluster catalogthat is being used in an independent HSC WL-SZ mass calibra-tion study (Miyatake et al., in prep.). It is also present in theXMM-MCXC catalog and is being analyzed in an X-ray-WLmass calibration study by (Miyaoka et al. 2017). We all findconsistent WL masses for this cluster. The most massive clus-ter, both in terms of SZ and WL mass (though with large errors),is MaxBCGJ140.53188+03.76632 at z = 0 . . It is a relatively Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
Table 2.
NFW fitted mass, concentration and bias Name M WL , c M WL , M , − b [ M (cid:12) /h ] [ M (cid:12) ] [ M (cid:12) ]Abell2457 . +0 . − . . +0 . − . . +0 . − . . +0 . − . Abell0329 . +1 . − . . +0 . − . . +0 . − . . +1 . − . Abell0362 . +1 . − . . +1 . − . . +0 . − . . +0 . − . MaxBCGJ140.53188+03.76632 . +21 . − . . +13 . − . . +0 . − . . +0 . − . MACSJ0916.1-0023/Abell0776 . +3 . − . . +2 . − . . +0 . − . . +0 . − . Stacked . ± .
69 6 . ± . . ± .
61 3 . ± .
27 0 . ± . Using the source sample defined by CC-cuts. Planck
SZ-derived masses, after 15% Eddington bias correction (see Section 4.6). unstudied cluster, with a double-BCG disturbed morphology.For this cluster it was hard to determine which BCG to use as acenter, so we selected the one closest to the X-ray center, basedon shallow (10 ksec) X-ray images from the
Chandra archive(PI Rykoff).Finally, we compare the SZ to WL mass by plotting the ratio M SZ /M WL as a function of SZ mass, color-coded by clusterredshift, in Figure 6. Although there may appear to be a de-creasing trend with increasing mass, our sample is small andthe errors are large. This will be an interesting point to inves-tigate with a future larger sample once the HSC completes thefull Wide survey area. Cluster WL analyses, and in particular when using observationsas deep as HSC, may suffer several sources of systematic un-certainties. As discussed here and thoroughly investigated inM17, one of the main sources of systematics is due to contam-ination from cluster members, and foreground galaxies whosephoto-z’s are not well represented by the PDF. Although we at-tempt to provide the most robust selection scheme to removethose from the source sample by applying the CC-cuts, somelevel of contamination may remain. To assess residual clustercontamination (if any), a boost factor is typically calculated.However, given the small sample of clusters studies here, thisestimate will be unreliable, without availability of simulations(see discussion in M17).To assess foreground contamination robustly, a large, spec-troscopic sample representative of HSC galaxies in terms ofmagnitude and colors is needed, which is not currently obtain-able. The residual level of contamination estimated in M17from a re-weighted spectroscopic redshift analysis appears min-imal, (cid:46) without any cuts, and (cid:46) with the CC methodused here.As discussed in Section 4.3, the miscentering of clusterscan lead to 9% differences in the fitted mass, and so we ex-pect the systematic error due to miscentering to be of that order.To estimate the systematic error due to choice of radial rangeused in the modeling , we set a more conservative inner radial cut, R = 0 . /h , similar to that used by WtG, and find M = (3 . ± . × M (cid:12) /h for the CC-cut sample.This translates to a 1.5% difference, which is small comparedto the other sources of error. In summary, combined in quadra-ture, all these errors result in a 9% systematic error, below ourstatistical uncertainty (18%). Finally, we address the level of bias between the
Planck mea-sured SZ cluster mass and that determined from the stackedlensing analysis presented in Section 4.3. To do so, we first es-timate the mean SZ mass of the five
Planck clusters. We use thetotal lens-source weights (Equation 7) for each lens to combinethe SZ masses, such that the mean SZ mass is, (cid:104) M SZ (cid:105) = 11 + c EB (cid:80) l M SZ ,l (cid:80) s w ls (cid:80) l,s w ls (14)where the index l runs over the five clusters, and the index s identifies sources behind each cluster within the fitting rangeused in the model. In Equation 14 we have applied an Eddingtonbias correction to the Planck
SZ masses, c EB = 0 . . The cor-rection here corresponds to the average difference in SZ massesfound between ACT and Planck (Battaglia et al. 2016), sinceACT applied an Eddington correction to their published SZmasses and
Planck did not. The resulting mean SZ clustermass is (cid:104) M SZ (cid:105) = (3 . ± . × M (cid:12) . To compare withthe SZ mass, we convert the lensing mass fitted in Section 4.3to the same overdensity, ∆ = 500 , and obtain (cid:104) M WL (cid:105) = (4 . ± . ± . × M (cid:12) . Dividing the two masses,we find the bias for the five HSC- Planck clusters to be − b = (cid:104) M SZ (cid:105) / (cid:104) M WL (cid:105) = 0 . ± . ± . .We compare this value with those derived for the individualclusters in section 4.4, by taking the unweighted mean of theensemble following von der Linden et al. (2014), so as not tobe biased by the correlation of uncertainties with the − b val-ues (lower − b values have lower errors). The mean ratio is (cid:104) M SZ /M WL (cid:105) = 0 . , which is in agreement with the stackedvalue above.We present the stacked ratio in Figure 7 (blue star) as afunction of the mean SZ mass, and compare with other results ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 ∆ Σ + [ h M fl M p c − ] z cl = 0 . ; M = (2 . ± . × M fl /h z cl = 0 . ; M = (2 . ± . × M fl /h ∆ Σ + [ h M fl M p c − ] z cl = 0 . ; M = (4 . ± . × M fl /h z cl = 0 . ; M = (31 . ± . × M fl /h R [Mpc/h] ∆ Σ + [ h M fl M p c − ] z cl = 0 . ; M = (8 . ± . × M fl /h Fig. 5.
Surface mass density profile for individual clusters. NFW profile fits are shown as black lines with 68% confidence bounds. The cluster redshift andfitted mass are given for each cluster. from the literature. In the comparison, we consider a range ofEddington bias corrections, 3–15% (dashed lines), for WL stud-ies of
Planck that did not apply this correction in their origi-nal analysis, namely WtG (green squares; von der Linden et al.2014) and CCCP (light-purple square; Hoekstra et al. 2015), asapplied in Battaglia et al. (2016) (orange squares). Our resultis consistent, within the reported errorbars, to previous resultsover the same mass range in M SZ (CS82 by Battaglia et al. 2016and PSZ2LenS by Sereno et al. 2017). The values of − b foundat higher M SZ differ by (cid:46) σ (CLASH, ? and CCCP, Hoekstraet al. 2015) to 2 σ (WtG, von der Linden et al. 2014), depend- ing on the WL study and if considering the highest Eddingtonbias correction, 15%. This reported difference as a function of M SZ further supports the hypothesis that − b is a function ofhalo mass (e.g., von der Linden et al. 2014; Hoekstra et al. 2015;Sereno et al. 2015), although we cannot statistically concludethat a M SZ dependence exists. With the five clusters all beingat low redshift ( z < . ) we also cannot address the claims inSmith et al. (2016) that − b is a function of redshift (see alsoSereno & Ettori 2017). Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0
Planck that did not apply this correction in their origi-nal analysis, namely WtG (green squares; von der Linden et al.2014) and CCCP (light-purple square; Hoekstra et al. 2015), asapplied in Battaglia et al. (2016) (orange squares). Our resultis consistent, within the reported errorbars, to previous resultsover the same mass range in M SZ (CS82 by Battaglia et al. 2016and PSZ2LenS by Sereno et al. 2017). The values of − b foundat higher M SZ differ by (cid:46) σ (CLASH, ? and CCCP, Hoekstraet al. 2015) to 2 σ (WtG, von der Linden et al. 2014), depend- ing on the WL study and if considering the highest Eddingtonbias correction, 15%. This reported difference as a function of M SZ further supports the hypothesis that − b is a function ofhalo mass (e.g., von der Linden et al. 2014; Hoekstra et al. 2015;Sereno et al. 2015), although we cannot statistically concludethat a M SZ dependence exists. With the five clusters all beingat low redshift ( z < . ) we also cannot address the claims inSmith et al. (2016) that − b is a function of redshift (see alsoSereno & Ettori 2017). Publications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0, (2014), Vol. 00, No. 0 M SZ [10 M ⊙ ] M S Z / M W L r e d s h i f t Fig. 6.
Ratio of the
Planck
SZ masses to WL masses, M SZ /M WL , whichdepicts the level of bias as − b , plotted as a function of M SZ , for individual Planck clusters. The color scale represents cluster redshift.
We have presented in this paper a WL analysis of five
Planck clusters using the latest ∼ deg deep multi-band HSC-SSPsurvey. We have taken steps to address different systematicsthat plague WL measurements. Using the HSC photometry andshape measurement pipeline we correct for shape multiplicativebias. We minimize foreground and cluster contamination of thesource sample by applying CC-cuts. We measure the surfacemass density profiles both for the individual clusters and furtherstack them together to obtain a mean mass profile of ∼ σ . Wefit the mass profiles with an NFW model, and find their massrange to be (2 – × M (cid:12) , and a mean mass of M WL , c =(4 . ± . × M (cid:12) . The level of mass bias with respectto the SZ mean mass is found to be − b = (cid:104) M SZ (cid:105) / (cid:104) M WL (cid:105) =0 . ± . . This low bias does not stand in tension to previoushigher bias measurements, nor with the level needed to explainthe high σ found from primary Planck
CMB, − b = 0 . ,since we probe to a lower mass limit than previous studies. Wenote that the bias may be a function of cluster mass, however,we cannot conclude so based on this initial sample of only fiveclusters. To make more robust conclusions, we hope to revisitthis analysis with a future larger sample of clusters.When the full HSC-Wide survey is complete in 2019, it willhave observed ∼ deg , with which we expect to have ob-serve 10 times more Planck clusters. The level of uncertainty onthe mass calibration, if assuming it is statistics dominated andscales as N − / , will be reduced from the current for thefive Planck -HSC clusters to reach ∼ using 50 clusters. Thislevel will be below what we currently find the systematic uncer-tainty to be, ∼ , and will therefore require an even more ro-bust treatment of cluster contamination, improvement to photo-z codes, and modeling. With such a high S/N measurement( ∼ σ expected), we will be able to provide a tighter mass cal- M SZ [ M ⊙ ] − b = M S Z / M W L PlanckCMBWtGCCCPCLASH LoCuSSPSZ2LenSCS82 , NFWThiswork , stacked Fig. 7.
Ratio of the
Planck
SZ masses to WL masses, M SZ /M WL , whichdepicts the level of bias as − b , as a function of M SZ . We compare the ratioinferred from the stacked lensing analysis done on the five Planck clusters inHSC (blue star) with different WL studies from the literature (squares) asindicated in the legend. All but the CS82 study are done for
Planck clusters,as targeted by pointed WL observations. For WtG and CCCP, a range ofEddington bias is considered, 3%–15% (empty squares to squares with errorbars, respectively). The comparison suggests that the level of bias, − b ,could be a function of cluster mass. ibration and re-derive cosmological constraints from Planck
SZcluster counts below the current level. We will further gaininsight on the mass bias due to the HSE assumption and studyits possible dependence on cluster mass and redshift, informingus about the evolution of clusters and their gas physics.
Acknowledgments
EM acknowledges fruitful discussions with Andy Goulding and PeterMelchior. The Hyper Suprime-Cam (HSC) collaboration includes the as-tronomical communities of Japan and Taiwan, and Princeton University.The HSC instrumentation and software were developed by the NationalAstronomical Observatory of Japan (NAOJ), the Kavli Institute for thePhysics and Mathematics of the Universe (Kavli IPMU), the Universityof Tokyo, the High Energy Accelerator Research Organization (KEK),the Academia Sinica Institute for Astronomy and Astrophysics in Taiwan(ASIAA), and Princeton University. Funding was contributed by theFIRST program from Japanese Cabinet Office, the Ministry of Education,Culture, Sports, Science and Technology (MEXT), the Japan Society forthe Promotion of Science (JSPS), Japan Science and Technology Agency(JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA,and Princeton University. This paper makes use of software developedfor the Large Synoptic Survey Telescope. We thank the LSST Projectfor making their code available as free software at http://dm.lsst.org. ThePan-STARRS1 Surveys (PS1) have been made possible through contribu-tions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating in-stitutes, the Max Planck Institute for Astronomy, Heidelberg and the MaxPlanck Institute for Extraterrestrial Physics, Garching, The Johns HopkinsUniversity, Durham University, the University of Edinburgh, Queen?sUniversity Belfast, the Harvard-Smithsonian Center for Astrophysics,the Las Cumbres Observatory Global Telescope Network Incorporated, ublications of the Astronomical Society of Japan , (2014), Vol. 00, No. 0 the National Central University of Taiwan, the Space Telescope ScienceInstitute, the National Aeronautics and Space Administration under GrantNo. NNX08AR22G issued through the Planetary Science Division of theNASA Science Mission Directorate, the National Science Foundation un-der Grant No. AST-1238877, the University of Maryland, and EotvosLorand University (ELTE) and the Los Alamos National Laboratory.Based (in part) on data collected at the Subaru Telescope and retrievedfrom the HSC data archive system, which is operated by Subaru Telescopeand Astronomy Data Center at National Astronomical Observatory ofJapan. This paper makes use of packages available in Python’s openscientific ecosystem, including NumPy (Walt et al. 2011), SciPy (Joneset al. 2001–), matplotlib (Hunter 2007), IPython (P´erez & Granger2007), AstroPy (Astropy Collaboration et al. 2013), and cluster-lensing(Ford 2016). The work reported on in this paper was substantially per-formed at the TIGRESS high performance computer center at PrincetonUniversity which is jointly supported by the Princeton Institute forComputational Science and Engineering and the Princeton UniversityOffice of Information Technology’s Research Computing department. NBacknowledges the support from the Lyman Spitzer Jr. Fellowship. HMis supported by the Jet Propulsion Laboratory, California Institute ofTechnology, under a contract with the National Aeronautics and SpaceAdministration. This work was supported in part by World PremierInternational Research Center Initiative (WPI Initiative), MEXT, Japan,and JSPS KAKENHI Grant Number 26800093 and 15H05892. KU ac-knowledges support from the Ministry of Science and Technology ofTaiwan through the grant MOST 103-2112-M-001-030-MY3. References
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