Precise Strong Lensing Mass Modeling of Four Hubble Frontier Fields Clusters and a Sample of Magnified High-Redshift Galaxies
Ryota Kawamata, Masamune Oguri, Masafumi Ishigaki, Kazuhiro Shimasaku, Masami Ouchi
aa r X i v : . [ a s t r o - ph . GA ] J a n Accepted for publication in ApJ
Preprint typeset using L A TEX style emulateapj v. 5/2/11
PRECISE STRONG LENSING MASS MODELING OF FOUR HUBBLE FRONTIER FIELDS CLUSTERS ANDA SAMPLE OF MAGNIFIED HIGH-REDSHIFT GALAXIES
Ryota Kawamata , Masamune Oguri , Masafumi Ishigaki , Kazuhiro Shimasaku , and Masami Ouchi Accepted for publication in ApJ
ABSTRACTWe conduct precise strong lensing mass modeling of four
Hubble
Frontier Fields (HFF) clusters,Abell 2744, MACS J0416.1 − glafic software, which assumes simply parametrized mass distributions. Our mass modelingalso exploits a magnification constraint from the lensed Type Ia supernova HFF14Tom for Abell 2744and positional constraints from the multiple images S1–S4 of the lensed supernova SN Refsdal forMACS J1149.6+2223. We find that our best-fitting mass models reproduce the observed image posi-tions with RMS errors of ∼ . ′′
4, which are smaller than RMS errors in previous mass modeling thatadopted similar numbers of multiple images. Our model predicts a new image of SN Refsdal with arelative time delay and magnification that are fully consistent with a recent detection of reappearance.We then construct catalogs of z ∼ − ∼
120 galaxies at z &
6, about 20 of which are predicted to bemagnified by a factor of more than 10. Some of the high-redshift galaxies detected in the HFF havelensing-corrected magnitudes of M UV ∼ −
15 to −
14. Our analysis demonstrates that the HFF dataindeed offer an ideal opportunity to study faint high-redshift galaxies. All lensing maps producedfrom our mass modeling will be made available on the STScI website a . Subject headings: galaxies: clusters: individual (Abell 2744, MACS J0416.1 − INTRODUCTION
Studies of faint high-redshift galaxies can be signifi-cantly improved by utilizing massive clusters of galaxiesas natural telescopes. This is made possible by the so-called gravitational lensing effect, in which the propaga-tion of a light ray is deflected by an intervening matterdistribution (Schneider et al. 1992). Although rare, ex-tremely strong lensing events provide an opportunity tostudy very distant galaxies using their highly magnifiedimages that otherwise cannot even be detected.The
Hubble
Frontier Fields (HFF; PI: J. Lotz) is anon-going public
Hubble Space Telescope (HST) surveyto image six massive clusters. The main purpose ofthe HFF is to study properties and populations of fainthigh-redshift galaxies behind the cores of these clus-ters with help of lensing magnifications. Analyses ofearly HFF data have already produced useful results on
Email: [email protected] Department of Astronomy, Graduate School of Science, TheUniversity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,Japan Department of Physics, Graduate School of Science, TheUniversity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,Japan Research Center for the Early Universe, The University ofTokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Uni-verse (Kavli IPMU, WPI), The University of Tokyo, 5-1-5 Kashi-wanoha, Kashiwa, Chiba 277-8583, Japan Institute for Cosmic Ray Research, The University of Tokyo,5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582, Japan a https://archive.stsci.edu/prepds/frontier/lensmodels/ faint-end luminosity functions of high-redshift galaxies(Coe et al. 2015; Atek et al. 2014, 2015a,b; Ishigaki et al.2015; Oesch et al. 2015; McLeod et al. 2015), size evolu-tion of galaxies (Kawamata et al. 2015), and deep spec-troscopy of faint high-redshift galaxies (Vanzella et al.2014; Zitrin et al. 2015a).A key ingredient for the analysis of the HFF data isprecise mass modeling of the lensing clusters. This isbecause we need to convert observed quantities, suchas apparent magnitudes and angular sizes of galaxies,to physical quantities such as intrinsic luminosities andphysical sizes which require corrections of gravitationallensing effects. The mass distribution of the core of acluster is usually constrained so that it can reproducethe positions of multiple images behind the cluster. A lotof efforts had been made for mass modeling before theHFF observations started, using pre-HFF data, in orderto allow prompt analyses of the HFF data by the com-munity (e.g., Richard et al. 2014; Johnson et al. 2014;Zitrin et al. 2015b).The accuracy of mass modeling relies on the numberof multiply imaged background galaxies. Much deeper HST images obtained by the HFF in fact allow oneto identify many more multiply imaged galaxies andtherefore improve strong lensing mass modeling (e.g.,Jauzac et al. 2014, 2015a; Lam et al. 2014; Diego et al.2015a,b; Limousin et al. 2015). In addition, spectroscopyof these multiple images is crucial for robust identifi-cation of multiple images as well as constraining themass distribution, particularly the radial density pro- Kawamata et al.file. Significant efforts are being made to collect spec-troscopic redshifts of galaxies detected in the HFF (e.g.,Schmidt et al. 2014; Grillo et al. 2015a; Karman et al.2015; Wang et al. 2015; Treu et al. 2015b; Sebesta et al.2015).In this paper, we present our mass modeling re-sults of the first four HFF clusters, Abell 2744 (Abell1958), MACS J0416.1 − z ∼ − HST data used in the paper, as wellas the construction of photometric catalogs. Our massmodeling procedure is described in detail in Section 3,and the results of the mass modeling are given in Sec-tion 4. We construct z ∼ − M = 0 .
3, thecosmological constant Ω Λ = 0 .
7, and the Hubble con-stant H = 70 km s − Mpc − . Magnitudes are given inthe AB system (Oke & Gunn 1983) and coordinates aregiven in J2000. HST
DATA
HST Images
We use the public HFF data for our analysis. TheHFF targets six massive clusters, Abell 2744 ( z = 0 . − z = 0 . z = 0 . z = 0 . z = 0 . z = 0 . HST observations for the first four clusters, Abell 2744,MACS J0416.1 − . ′′
03 pixel − provided by Space Telescope Science Institute (STScI).The images for each cluster consist of F435W ( B ),F606W ( V ), and F814W ( i ) images from ACS,and F105W ( Y ), F125W ( J ), F140W ( JH ), andF160W ( H ) images from WFC3/IR. While we usestandard correction mosaics for the ACS images, wechoose mosaics corrected for time-variable backgroundsky emission for the WFC3/IR images when available.In order to take account of the inhomogeneity of the lim-iting magnitude due to, e.g., intracluster light, we divide Figure 1.
Measured 5 σ limiting magnitudes in 4 × H limiting magnitudes are shown on the HST H band imagefor Abell 2744 ( upper left ), MACS J0416.1 − upper right ),MACS J0717.5+3745 ( lower left ), and MACS J1149.6+2223 ( lowerright ). Each number shows the limiting magnitude in each cell.We use only the regions within the white lines to search for high-redshift galaxies. the WFC3/IR field of view of each cluster into 4 × σ limiting magnitudes on a0 . ′′
35 diameter aperture of these images are ∼
29 mag.Three out of the four clusters have also been observedwith
HST in the CLASH project (see Postman et al.2012, for more details). Although the CLASH imaginguses many additional bands (F225W, F275W, F336W,F390W, F475W, F625W, F775W, F850LP, and F110W),we do not use these images because they are considerablyshallower than the HFF images.
Photometric Catalogs
We construct two different photometric catalogs spec-ified for the following two purposes, (1) selection of clus-ter member galaxies and (2) detection of faint high-redshift galaxies, using the method similar to the oneused in Ishigaki et al. (2015). Here we briefly describethe method to construct the photometric catalogs.Member galaxies are selected utilizing both the red se-quence and photometric redshift techniques. For accu-rate estimates of galaxy colors, we convolve
HST im-ages with a Gaussian kernel in order to match thepoint-spread function (PSF) sizes of all images of in-terest to the largest one. Then, we run
SExtractor (Bertin & Arnouts 1996) in dual-image mode using the i image as the detection image setting the parameters DEBLEND MINCONT = 0.00005 , DEBLEND NTHRESH = 50 , DETECT MINAREA = 5 , and
DETECT THRESH = 2.5 . Weestimate photometric redshifts of the galaxies in this cat-alog using
BPZ (Ben´ıtez 2000). We use the B − V color-magnitude diagram to identify the red sequence,and extract cluster members with V -band magnitudesrecise mass modeling of four HFF clusters 3brighter than ∼ −
25 mag (see Ishigaki et al. 2015,for more details). We then select galaxies in the vicinityof the red sequence whose photometric redshifts coincidewith the cluster redshift as cluster members. After apply-ing these criteria, we refine the member galaxy catalog byadding and removing some galaxies based on their colors,morphologies, and spectroscopic redshifts (Owers et al.2011; Ebeling et al. 2014).In the construction of a photometric catalog of high-redshift galaxies, we co-add three bands ( J , JH ,and H ) for the i - and Y -dropout selection and twobands ( JH and H ) for the YJ -dropout selection us-ing SWarp (Bertin et al. 2002). Weight images of theseco-added images are also produced from public weightimages. Before running
SExtractor to build photo-metric catalogs, we again match PSF sizes for reliablecolor measurements. For the i -dropout selection, imagesfor all the bands are PSF-matched except for B and V , and for the other selections all except for B , V ,and i are PSF-matched. Then, we run SExtractor in dual-image mode using the co-added images as the de-tection image with the parameters of
DEBLEND MINCONT= 0.0005 , DEBLEND NTHRESH = 16 , DETECT MINAREA =4 , and
DETECT THRESH = 3.0 . For measuring colors ofgalaxies, we use aperture magnitudes (
MAG APER ) m AP with a aperture diameter of 0 . ′′
35 for the convolved im-ages and 0 . ′′
20 ( B ), 0 . ′′
19 ( V ), and 0 . ′′
19 ( i ) for thenon-convolved images. Total magnitudes of galaxies arealso derived from MAG APER magnitudes with the aperturecorrection derived in Ishigaki et al. (2015). Specifically,the aperture correction factor c AP is c AP = 0 .
82, whichis defined such that the total magnitude m tot is given by m tot = m AP − c AP .We also derive photometric redshifts for the high-redshift galaxies detected in the second photometric cata-log using BPZ . For reliable color measurements, we PSF-match all the band images. The photometric redshiftsare used to both identify multiple images (see Section 3)and select high-redshift galaxies (see Section 5). MASS MODELING PROCEDURE
Here we describe the method to model the mass distri-butions of the four HFF clusters in detail. We adopt theso-called “parametric lens modeling” approach, in whicha simply parametrized mass model consisting of severalmass components is assumed and the model parame-ters are optimized to reproduce observed multiple imageproperties. Throughout the paper mass modeling andanalysis are performed using the public software glafic (Oguri 2010), which has extensively been used for stronglensing mass modeling of clusters (e.g., Oguri et al. 2012,2013; K¨ohlinger & Schmidt 2014; Ishigaki et al. 2015;Newman et al. 2015).
Mass Components
In this paper we adopt the following mass components.Details of each mass component are described in Oguri(2010). We give a brief summary below.A cluster-scale dark halo is modeled by an ellipticalextension of the NFW (Navarro et al. 1997) density pro-file. We introduce an elliptical symmetry in the pro-jected mass density, and compute its lensing proper-ties by numerical integrals (Schramm 1990). The modelparameters include virial mass M , positions, ellipticity e ≡ − a/b ( a and b being minor and major axis lengths,respectively) and its position angle θ e , and concentrationparameter c .Member galaxies are modeled by pseudo-Jaffe ellip-soids (Keeton 2001). To reduce the number of param-eters, in most cases we introduce scaling relations ofmodel parameters with luminosity L , such that veloc-ity dispersion is given by σ/σ ∗ ∝ L / and truncationradius r trun /r trun , ∗ ∝ L η . The ellipticity and positionangle of each galaxy are fixed to the values measuredby SExtractor . All the input quantities for the mem-ber galaxies are measured in the i band. Luminositiesare computed from total magnitudes ( MAG AUTO ) given by
SExtractor . The model parameters are the normaliza-tion of velocity dispersion σ ∗ , truncation radius r trun , ∗ ,and dimensionless parameter η . We call this model of aset of member galaxies GALS.Member galaxies that are located adjacent to multipleimages can have significant contributions to the imageproperties of the multiple images including their loca-tions. For some of these member galaxies we do notapply the scaling relations mentioned above but insteadmodel them independently by pseudo-Jaffe ellipsoid com-ponents, to which we refer as PJE. The model parame-ters are velocity dispersion σ , ellipticity e and its positionangle θ e , and truncation radius r trun .It has been shown that adding an external perturbationon the lens potential and an internal perturbation de-scribing a possible asymmetry of the cluster mass distri-bution sometimes improves the mass model significantly(e.g., Oguri 2010; Oguri et al. 2013). Both perturbationsare described by a multipole Taylor expansion at the po-sition of the BCG of the form φ = ( C/m ) r n cos m ( θ − θ ∗ ),where r is the distance from the BCG, θ is angular co-ordinate, θ ∗ is position angle, and C is expansion co-efficient. In the case of the external perturbation, thezeroth ( n = 0, m = 0) and the first ( n = 1, m = 1)orders of the Taylor expansion are unobservable. Wecall the second order term of the external perturbation( n = 2, m = 2), which is equivalent to the so-called exter-nal shear, PERT. We also include higher multipole terms( m ≥
3) to approximately model higher-order terms ofthe external perturbation as well as a possible asymme-try of the cluster mass distribution, which we refer toas MPOLE. Note that a term inducing constant conver-gence κ ( n = 2, m = 0) is not included in our massmodeling.The amplitudes of the perturbations are defined for agiven fiducial source redshift z s, fid , and are scaled withthe source redshift assuming that the perturbation orig-inates from the structure at the cluster redshift. Themodel parameters for PERT are external shear γ and itsposition angle θ γ , and those for MPOLE are expansioncoefficient ǫ , position angle θ ǫ , m , and n . The values of γ and ǫ are assumed to be constant over the entire field. Modeling Strategy
We adopt the following unified strategy for conductingour mass modeling. We place several NFW componentson the positions of bright cluster member galaxies. Whenan NFW component has a sufficient number of multi-ple images around it to constrain the model parameterswell, all the NFW model parameters are treated as freeparameters. On the other hand, for NFW components Kawamata et al.located at the edge or outside the strong lensing regions,we fix some model parameters such as positions, elliptic-ities, and position angles, to observed values. For NFWcomponents lacking strong observational constraints, itis also difficult to reliably constrain the concentrationparameter c . In this case we simply assume c = 10.We start with a small number of NFW components,and increase the number of components until we find theleast reduced χ . We stop adding an NFW componentwhen it begins to increase the reduced χ , which is causedbecause a decrease in the degree of freedom surpasses animprovement in the raw χ . Perturbations (PERT andMPOLE) are also added as long as they improve the massmodel significantly. In parallel with building the massmodel, we iteratively refine multiple images used as con-straints, by validating known multiple image candidatesand searching for new multiple image candidates. Newmultiple image candidates are identified based on consis-tency with the mass model and on colors, morphologies,and photometric redshifts. Our selection of multiple im-ages is conservative in the sense that we remove any un-reliable or suspicious candidates. A final set of multipleimages for each cluster is given in Section 3.4.About one fifth of the multiple images have spectro-scopic redshifts. The source redshifts are fixed to thespectroscopic redshifts when available. The redshifts ofthe other multiple images are treated as model param-eters and are optimized together with source positions.Some multiple images have a precise photometric red-shift estimate. For them, we include this information inthe optimization by adding a Gaussian prior centered atthe estimated redshift and a conservative standard de-viation of σ z = 0 . Optimizations and Error Estimates
All the model parameters are simultaneously optimizedto reproduce the positions and photometric redshifts ofthe multiple images. Specifically, the optimization is per-formed to minimize χ χ = χ + χ z , (1) χ = X i | x i, obs − x i | σ x i , (2) χ z = X j ( z j, obs − z j ) σ z , (3)where x i is the position of the i -th image and z j is thesource redshift of the j -th system. The positional uncer-tainties σ x,i can be different for different images and aregiven in Section 3.4. For Abell 2744, we include an addi-tional term χ µ = ( µ obs − µ ) /σ µ from the observation ofa Type Ia supernova behind this cluster (see Section 3.4for more details).Formally we need to solve a non-linear lens equationto estimate the position χ (Equation 2), which is time-consuming. We adopt the so-called source plane min-imization which evaluates Equation (2) in the sourceplane. Once a distance in the source plane is converted toa corresponding distance in the image plane using the full magnification tensor, this provides a very good approxi-mation for the image plane position χ (see Appendix 2of Oguri 2010).We derive the best-fitting mass model for each clusterthat minimizes the total χ (Equation 1) by a standarddownhill simplex method. In addition, we run MarkovChain Monte Carlo (MCMC) to estimate errors in themass models. When deriving the best-fitting mass modeland running MCMC, the parameter ranges of ellipticity,concentration parameter, and index η for GALS are re-stricted to [0, 0.8], [1, 40], and [0.2, 1.5], respectively. Input Data for Each Cluster
Abell 2744
Multiple images for this cluster have been iden-tified in Merten et al. (2011), Atek et al. (2014),Richard et al. (2014), Zitrin et al. (2014), Lam et al.(2014), Ishigaki et al. (2015), and Jauzac et al. (2015a).Spectroscopic redshifts of multiple images have been pre-sented in Richard et al. (2014), Johnson et al. (2014),and Wang et al. (2015). Lam et al. (2014) andWang et al. (2015) regarded systems 55 and 56 as a partof systems 1 and 2, respectively, and assigned their red-shifts accordingly. To avoid introducing biases, we donot fix the redshifts but treat them as model param-eters. While Wang et al. (2015) reported the redshiftof system 56 to be z = 1 . z = 2 . z = 1 . +0 . − . , which is closer tothat of Johnson et al. (2014). Due to a controversy overthe position of the counter image of system 3 (see e.g.Lam et al. 2014; Jauzac et al. 2015a, for more details),we do not use its position as a constraint in our massmodeling. For system 5, we find one new counter image.Although Wang et al. (2015) recently reported the red-shift of system 22 to be z = 4 .
84, we do not adopt thisvalue because it is not very secure. We identify a new setof multiple images (system 62) in the northwest part ofthis cluster. As noted above, we conservatively excludesome multiple images in the literature. As a result, wehave 37 multiple image systems from the literature andone new system for our mass modeling. The total num-ber of multiple images is 111. The positional uncertaintyof σ x = 0 . ′′ z = 1 . µ = 2 . ± .
29. We use thisconstraint by adding a term to the total χ (Equation 1). MACS J0416.1 − Multiple images for this cluster have been identi-fied in Zitrin et al. (2013), Jauzac et al. (2014), andDiego et al. (2015a). Spectroscopic redshifts of multipleimages have been presented in Christensen et al. (2012)and Grillo et al. (2015a). We also use new spectroscopicredshifts from GLASS (Hoag et al. in prep.; see alsoSchmidt et al. 2014 and Treu et al. 2015b) and Rodneyet al. (in prep.). While Jauzac et al. (2014) estimatedrecise mass modeling of four HFF clusters 5 -0.0005 0.0002 0.0023 0.0058 0.0107 0.0170 0.0247 0.0338 0.0444 0.0563 0.0696
20 arcsec
YJ3Y10 Y9Y8 Y7Y6 Y5Y4 Y3Y2Y1 i22 i21i20 i19i18i17 i16i15 i14i13i12i11 i10i9 i8i7i6i5 i4i3 i2i1
20 arcsec
Y5 Y4Y3 Y2Y1 i23 i22i21 i20i19 i18 i17i16 i15i14 i13 i12i11i10 i9i8i7 i6 i5 i4i3i2 i1
20 arcsec i20i19 i18i17 i16i15i14i13i12 i11 i10i9 i8i7i6 i5i4i3i2 i1
20 arcsec
Image 1.3 Image 1.2Image 1.1YJ4 YJ3YJ1Y2 i35 i34i33i32 i31 i30i29i28 i27i26 i25i24 i23 i22i21 i20 i19i18i17 i16 i15i14 i13i12 i11i10i9i8 i7i6 i5 i4i3i2i1
Image 1.1
Image 1.2
Image 1.3
Figure 2.
Multiple image systems used for mass modeling, dropout galaxies, and critical curves of the best-fitting models for Abell 2744( upper left ), MACS J0416.1 − upper right ), MACS J0717.5+3745 ( middle left ), and MACS J1149.6+2223 ( middle right ). Underlyingcolor-composite images are created from the HST B + V , i + Y , J + JH + H band images. Small yellow squares showthe positions of multiple images (see Appendix A for the coordinates). High-redshift dropout galaxies are marked with large squares (seeSection 5 for details). Critical curves for a source redshift of z = 8 are shown with the solid lines. Bottom panels show zoomed in HST i -band images of the system 1 in the MACS J1149.6+2223 field. Small yellow squares represent the positions of multiply imaged knotsthat are used as constraints in mass modeling. Kawamata et al.
Table 1
Summary of mass modelingCluster χ /dof Image plane RMSsystems (with spec- z ) ( ′′ )Abell 2744 38 (5) 111 98.2/100 0.37MACS J0416.1 − Table 2
Mass Model Parameters for Abell 2744Component Model Mass e θ e c ∆ x a ∆ y a (10 h − M ⊙ ) (deg) (arcsec) (arcsec)Cluster halo 1 NFW 4 . +2 . − . . +0 . − . . +2 . − . . +0 . − . − . +0 . − . . +0 . − . Cluster halo 2 NFW 1 . +0 . − . . +0 . − . . +1 . − . . +0 . − . − . +0 . − . − . +0 . − . Cluster halo 3 NFW 0 . +0 . − . . +0 . − . . +2 . − . [10 .
00] [ − .
97] [30 . σ ∗ b r trun , ∗ η (km s − ) ( ′′ )Member galaxies GALS 208 . +7 . − . . +29 . − . . +0 . − . z s, fid γ θ γ (deg)External perturbation PERT [2 .
00] 0 . +0 . − . . +4 . − . z s, fid ǫ θ ǫ m n (deg)Multipole perturbation MPOLE [2 .
00] 0 . +0 . − . . +3 . − . [3 .
00] [2 . a Coordinates are relative to the brightest cluster galaxy position in the Abell 2744 field (R.A. = 3.58611, Decl. = − . b The normalization luminosity L ∗ corresponds to i = 18 . * Numbers in square brackets are fixed during the model optimization.
Table 3
Mass Model Parameters for MACS J0416.1 − e θ e c ∆ x a ∆ y a (10 h − M ⊙ ) (deg) (arcsec) (arcsec)Cluster halo 1 NFW 3 . +1 . − . . +0 . − . . +1 . − . . +0 . − . − . +0 . − . . +0 . − . Cluster halo 2 NFW 1 . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +0 . − . − . +0 . − . Cluster halo 3 NFW 0 . +0 . − . . +0 . − . . +3 . − . . +1 . − . . +0 . − . − . +1 . − . σ ∗ b r trun , ∗ η (km s − ) ( ′′ )Member galaxies GALS 261 . +21 . − . . +10 . − . . +0 . − . σ e θ e r trun ∆ x a ∆ y a (km s − ) (deg) ( ′′ ) (arcsec) (arcsec)Member galaxy PJE 125 . +50 . − . [0 .
27] [166 .
70] 0 . +1 . − . [ − .
56] [15 . z s, fid γ θ γ (deg)External perturbation PERT [2 .
00] 0 . +0 . − . . +3 . − . z s, fid ǫ θ ǫ m n (deg)Multipole perturbation MPOLE [2 .
00] 0 . +0 . − . . +5 . − . [3 .
00] [2 . a Coordinates are relative to the brightest cluster galaxy position in the MACS J0416.1 − − . b The normalization luminosity L ∗ corresponds to i = 18 . * Numbers in square brackets are fixed during the model optimization. recise mass modeling of four HFF clusters 7
Table 4
Mass Model Parameters for MACS J0717.5+3745Component Model Mass e θ e c ∆ x a ∆ y a (10 h − M ⊙ ) (deg) (arcsec) (arcsec)Cluster halo 1 NFW 4 . +1 . − . . +0 . − . . +1 . − . . +0 . − . . +1 . − . . +1 . − . Cluster halo 2 NFW 2 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . − . +0 . − . Cluster halo 3 NFW 2 . +0 . − . . +0 . − . . +0 . − . . +1 . − . − . +0 . − . . +1 . − . Cluster halo 4 NFW 3 . +0 . − . . +0 . − . . +2 . − . . +0 . − . . +0 . − . . +0 . − . Cluster halo 5 NFW 1 . +0 . − . [0 .
32] [174 .
30] [10 .
00] [129 .
13] [77 . . +0 . − . . +0 . − . . +1 . − . . +0 . − . [ − .
33] [ − . . +0 . − . . +0 . − . . +1 . − . . +0 . − . [108 .
64] [45 . . +0 . − . . +0 . − . . +4 . − . . +0 . − . [ − .
32] [ − . . +0 . − . . +0 . − . . +4 . − . . +5 . − . . +2 . − . − . +1 . − . σ ∗ b r trun , ∗ η (km s − ) ( ′′ )Member galaxies GALS 518 . +35 . − . . +2 . − . . +0 . − . z s, fid γ θ γ (deg)External perturbation PERT [2 .
00] 0 . +0 . − . . +1 . − . z s, fid ǫ θ ǫ m n (deg)Multipole perturbation 1 MPOLE [2 .
00] 0 . +0 . − . . +2 . − . [3 .
00] [2 . .
00] 0 . +0 . − . . +2 . − . [4 .
00] [2 . .
00] 0 . +0 . − . . +1 . − . [5 .
00] [2 . a Coordinates are relative to the brightest cluster galaxy position in the MACS J0717.5+3745 field (R.A. = 109.3982391,Decl. = +37 . b The normalization luminosity L ∗ corresponds to i = 17 . * Numbers in square brackets are fixed during the model optimization.
Table 5
Mass Model Parameters for MACS J1149.6+2223Component Model Mass e θ e c ∆ x a ∆ y a (10 h − M ⊙ ) (deg) (arcsec) (arcsec)Cluster halo 1 NFW 8 . +1 . − . . +0 . − . . +1 . − . . +0 . − . − . +0 . − . − . +0 . − . Cluster halo 2 NFW 1 . +0 . − . . +0 . − . . +7 . − . . +2 . − . [16 .
38] [47 . . +0 . − . . +0 . − . . +3 . − . . +1 . − . − . +1 . − . − . +1 . − . Cluster halo 4 NFW 0 . +0 . − . . +0 . − . . +2 . − . [10 .
00] [ − .
77] [ − . σ ∗ b r trun , ∗ η (km s − ) ( ′′ )Member galaxies GALS 233 . +21 . − . . +1 . − . . +0 . − . σ e θ e r trun ∆ x a ∆ y a (km s − ) (deg) ( ′′ ) (arcsec) (arcsec)Member galaxy c PJE 232 . +25 . − . [0 .
30] [47 .
50] 1 . +0 . − . [3 .
22] [ − . z s, fid γ θ γ (deg)External perturbation PERT [2 .
00] 0 . +0 . − . . +9 . − . z s, fid ǫ θ ǫ m n (deg)Multipole perturbation MPOLE [2 .
00] 0 . +0 . − . . +4 . − . [3 .
00] [2 . a Coordinates are relative to the brightest cluster galaxy position in the MACS J1149.6+2223 field (R.A. = 177.3987491,Decl. = +22 . b The normalization luminosity L ∗ corresponds to i = 18 . c This component corresponds to the member galaxy that produces four multiple images S1–S4 of SN Refsdal. * Numbers in square brackets are fixed during the model optimization.
Kawamata et al.the redshift of system 14 to be z = 2 . z = 1 . σ x = 0 . ′′ MACS J0717.5+3745
Multiple images for this cluster have been iden-tified in Zitrin et al. (2009), Limousin et al. (2012),Vanzella et al. (2014), Richard et al. (2014), andDiego et al. (2015b). Spectroscopic redshifts of mul-tiple images have been presented in Limousin et al.(2012), Schmidt et al. (2014), Vanzella et al. (2014), andTreu et al. (2015b). The redshift of system 5 wasnewly confirmed and those of systems 12 and 13 wereupdated by GLASS (Schmidt et al. 2014; Treu et al.2015b). While we use the updated redshift of system12, we do not use that of system 5 as it is significantlydifferent from our model prediction and that of system 13as it is less precise than that estimated in Limousin et al.(2012). We assign image 25.4 to system 25, which was re-garded as a part of system 5 in Diego et al. (2015b). Weadd six new counter images, 25.4, 55.3, 64.3, 64.4, 65.3,and 65.4, and 20 new systems, 66 −
85. As a result, wehave 40 multiple image systems from the literature and20 new systems for our mass modeling. The total numberof multiple images is 173. As a foreground galaxy locatedat (R . A . = 109 . , Decl . = +37 . glafic does not sup-port multiple lens planes. We assume a positional un-certainty of σ x = 0 . ′′
6, which is larger than those for theother HFF clusters, for all multiple images. The largerpositional uncertainty and the large number of mass com-ponents are due to the fact that the mass distribution ofthis cluster appears to be considerably more complicatedthan the other clusters, presumably due to ongoing mul-tiple mergers (see, e.g., Limousin et al. 2012).
MACS J1149.6+2223
Multiple images for this cluster have been identi-fied in Zitrin & Broadhurst (2009), Smith et al. (2009),Zheng et al. (2012), Rau et al. (2014), Richard et al.(2014), Jauzac et al. (2015b), and Treu et al. (2015a).Spectroscopic redshifts of multiple images have beenpresented in Smith et al. (2009), Jauzac et al. (2015b),Grillo et al. (2015b), and Brammer et al. (in prep.).While Smith et al. (2009) estimated the redshift of sys-tem 3 to be z = 2 . z = 3 . −
40, for our mass modeling. We also include additional positional constraints from multi-ple images of seven knots in a lensed face-on spiral galaxyat z = 1 .
488 as well as four supernova images of SN Refs-dal in the lensed spiral galaxy (Kelly et al. 2015b). Thetotal number of multiple images is 108 from 36 systems.In order to accurately predict the reappearance ofSN Refsdal image (Oguri 2015; Sharon & Johnson 2015;Diego et al. 2015c; Jauzac et al. 2015b; Grillo et al.2015b) and its magnification, we follow Oguri (2015)to adopt different positional errors for different multi-ple images. Specifically, we assume the standard posi-tional error of σ x = 0 . ′′ σ x = 0 . ′′ σ x = 0 . ′′
05 for the four SN images. A member galaxy lo-cated at R.A. = 177 . . MASS MODELING RESULTS
The best-fitting mass models
The numbers of input multiple images and mass mod-eling results of the four HFF clusters are summarized inTable 1, and the critical curves of the best-fitting mod-els are shown in Figure 2. Figure 3 shows magnificationmaps for sources at z = 9 and the positions of the NFWand PJE components. We provide lists of all multipleimages used as constraints in Appendix A. Model param-eters and errors from the MCMC for individual clustersare shown in Tables 2 −
5. Parameters in square bracketsare fixed during the model optimization. Maps of mag-nification factor, lens potential, kappa, and shear fromour mass modeling will be made available on the STScIwebsite .Table 1 indicates that all of our best-fitting modelshave reduced chi-square values, χ /dof, close to unity. Infact this is expected, because we have chosen the posi-tional errors of multiple images to reproduce χ / dof ∼ ∼ . ′′ . ′′
68 for MACSJ0416.1 − . ′′
79 for Abell2744 (Jauzac et al. 2015a) by the CATS team, both ofwhich used more than 100 multiple images as constraints.Grillo et al. (2015a) modeled MACS J0416.1 − . ′′
36, but only 30 multiple images wereused as constraints. Our mass modeling satisfies both alarge number of multiple images and a good accuracy intheir reproduced positions. https://archive.stsci.edu/prepds/frontier/lensmodels/ recise mass modeling of four HFF clusters 9 Cluster Halo 3Cluster Halo 2Cluster Halo 1
PJE Cluster Halo 3Cluster Halo 2Cluster Halo 1
Cluster Halo 9Cluster Halo 8 Cluster Halo 7Cluster Halo 6 Cluster Halo 5Cluster Halo 4Cluster Halo 3 Cluster Halo 2Cluster Halo 1
PJECluster Halo 4 Cluster Halo 3 Cluster Halo 2Cluster Halo 1
Figure 3.
Positions of model components are shown on a magnification map for z = 9 sources for Abell 2744 ( upper left ), MACSJ0416.1 − upper right ), MACS J0717.5+3745 ( lower left ), and MACS J1149.6+2223 ( lower right ). To illustrate this point further, in Figure 4 we plot thedistributions of ∆ x ≡ | x obs − x model | , the distance be-tween the observed and model-predicted image positionsfor each multiple image. We find that for any cluster ∆ x is indeed small for most of the multiple images, with adistribution peaking around 0 . ′′ x < . ′′
6, which again indicates the successof our mass modeling.The accuracy of our mass models may be tested furtherby observations of other than image positions. For Abell2744, our model yields a magnification µ = 2 . ± .
12 at the position of the lensed Type Ia supernova HFF14Tom(Rodney et al. 2015a). This is fully consistent with theobserved magnification µ = 2 . ± .
29, although wenote that this may not be a fair comparison as we haveexplicitly included the observed magnification as a con-straint in mass modeling. On the other hand, the timedelays and flux ratios of the lensed supernova SN Refsdal(Kelly et al. 2015b) in MACS J1149.6+2223 can providea useful blind test of our mass model. We will discussthis blind test in Section 4.3.As shown in Tables 2 −
5, some NFW components have0 Kawamata et al. ∆ x / arcsec N This Work Jauzac+15aJohnson+14
Abell 2744 ∆ x / arcsec N This Work Jauzac+14Johnson+14Grillo+15
MACS J0416.1−2403 ∆ x / arcsec N This WorkJohnson+14
MACS J0717.5+3745 ∆ x / arcsec N This Work Johnson+14Smith+14Rau+14
MACS J1149.6+2223
Figure 4.
The distribution of the distances between observed and model-predicted image positions, ∆ x ≡ | x obs − x model | , for all themultiple images used for mass modeling for Abell 2744 ( upper left ), MACS J0416.1 − upper right ), MACS J0717.5+3745 ( lower left ),and MACS J1149.6+2223 ( lower right ). See Appendix A for lists of multiple images for individual clusters. The red solid, black long-dashed, and black dash-dotted vertical lines show RMSs of ∆ x calculated from our models, previous mass models that used more than 100multiple images, and previous mass models that used less than 100 multiple images, respectively. The RMSs of ∆ x for all the clusters aresummarized in Table 1. high ellipticities ( e > . Model comparison
Some teams have also constructed precise mass modelsexploiting the full-depth HFF data and more than 100multiple images. We here compare our best-fitting massmodels with those obtained in previous work.
Abell 2744 — We place three cluster-scale NFW com-ponents to model the cluster mass distribution. The po-sitions of Cluster halos 1 and 2 are consistent with thosein Jauzac et al. (2015a). Wang et al. (2015), who adopta free-form modeling method, also predict mass peaks atthese positions. In addition, we assume a third NFWcomponent, Cluster halo 3, as described above, wherethere is also a mass peak in Wang et al.’s (2015) model.
MACS J0416.1 − — We place three cluster-scaleNFW components and one PJE component. The PJEcomponent is for better modeling of the member galaxynear systems 1, 2, 6, 89, and 90, as this member has asignificant effect on these multiple image systems. Thepositions of Cluster halos 1 and 2 are consistent withthose in Jauzac et al. (2014) and Diego et al. (2015a),but the PJE component is included only in our model.While Jauzac et al. (2014) and Diego et al. (2015a) as-sume only two halo components, there is a “soft compo-recise mass modeling of four HFF clusters 11nent” in the model of Diego et al. (2015a) at the positionof our Cluster halo 3. MACS J0717.5+3745 — Limousin et al. (2015) usefour halo-scale profiles. Diego et al. (2015b) also identifyfour mass peaks in their free-form model. While we placenine cluster-scale NFW components, only four, Clusterhalos 1+3, 2, 4, and 5, have a significant mass peak. Thisis consistent with their results. Limousin et al. (2015) re-port very shallow mass profiles for this cluster, which isconsistent with our NFW components having relativelysmaller concentration parameters. We note that the posi-tion of Cluster halo 9 is consistent with an X-ray emissionpeak from
Chandra (see Figure 4 in Diego et al. 2015b).
MACS J1149.6+2223 — We place four cluster-scaleNFW components and one PJE component. The po-sitions of Cluster halos 1, 2, and 3 are consistent withthose in Jauzac et al. (2015b). They do not place a com-ponent at the position of Cluster halo 4. On the otherhand, they place a halo component at the position of abright member galaxy located ∼
100 arcsec north fromthe BCG and is out of the region of the HFF WFC3/IRobservation.
Predictions for SN Refsdal
In our mass modeling of MACS J1149.6+2223, we onlyuse positions of the multiple images S1–S4 of SN Refs-dal as observational constraints. Importantly, when ourmass modeling was completed, any relative time delaysand magnifications had not been measured yet, which in-dicates that observations of relative time delays and mag-nifications serve as an important blind test of our massmodel. Treu et al. (2015a) made a detailed comparisonof predictions of our best-fitting model (corresponding tothe short name “Ogu-a” in Treu et al. 2015a) with thosefrom other mass modeling teams. Treu et al. (2015a)also compared predictions of relative magnifications andtime delays between images S1–S4 with preliminary mea-surements, finding a good agreement between our best-fit model predictions and observations. Updated mea-surements and comparisons are available in Rodney et al.(2015b).Most mass models of MACS J1149.6+2223 predict twoadditional images of SN Refsdal around images 1.2 and1.3, which we call SX and SY following Oguri (2015). SXis predicted to appear approximately one year after S1–S4, whereas SY is predicted to have appeared a decadeago. Our refined model predictions for the time delay, po-sition, and magnification factor of SX are ∆ t SX = 336 +22 − days, x SX = − . +0 . − . arcsec, y SX = − . +0 . − . arcsec,and µ SX = 4 . +0 . − . , where ∆ t SX is the relative timedelay from the image S1, x SX and y SX are coordinatesrelative to the BCG. The predicted time delay, position,and magnification factor of SY are ∆ t SY = − +209 − days, x SY = − . +0 . − . arcsec, y SY = 12 . +0 . − . arcsec,and µ SY = 3 . +0 . − . .While this paper is under review, a new SN imagewas discovered in HST images taken on 11 December(Kelly et al. 2015a). The observed position of the imageis x = − .
43 arcsec and y = − .
62 arcsec, which is fullyconsistent with the predicted position of SX with offsetsfrom the predicted position only 0 .
27 arcsec to the eastand 0 .
12 arcsec to the south. Furthermore, as can be seen in Figure 2 in Kelly et al. (2015a), our time delayand magnification predictions on SX are fully consistentwith the observed values. We again emphasize that thesepredictions are made before the reappearance of the newimage. These blind test results support the validity andaccuracy of our mass modeling method. DROPOUT GALAXY SAMPLE
Lyman Break Galaxy Selection
Galaxies at z ∼ − i band. We adopt the selection criteria used inAtek et al. (2015a) i − Y > . , (4) Y − J < . , (5) i − Y > Y − J ) + 0 . . (6)Objects which show 2 σ level signals in both the B and V band images or in the B + V stacked image areexcluded. We require that objects need to be detectedat the 5 σ level both in the Y and J bands. For anobject not detected in the i band, we calculate the i − Y color assigning the 2 σ limiting magnitude tothe i band magnitude.To select galaxies at z ∼
8, we adopt the selectioncriteria presented in Atek et al. (2014) Y − J > . , (7) J − JH < . , (8) Y − J > . . J − JH ) . (9)Objects which show a 2 σ level signal in at least one ofthe B , V , or i band image are excluded. Again,objects also need to be detected at the 5 σ level in all the J , JH , and H band images.To select galaxies at z ∼
9, we adopt the selection cri-teria similar to those presented in Ishigaki et al. (2015)( Y + J ) / − JH > . , (10)( Y + J ) / − JH > .
75 + 0 . JH − H ) , (11) J − H < . , (12) JH − H < . . (13)Objects which show a 2 σ level signal in at least one of the B , V , or i band image are excluded. We requirethat objects need to be detected at the 3 σ level in boththe JH and H band images and at the 3 . σ levelin at least one of these two bands. If an object is fainterthan the 0.9 σ level magnitude in the Y or J band,we assign the 0.9 σ level magnitude to the photometry ofthat band.In addition, we adopt a pseudo- χ constraint to reducethe contamination rate. This constraint is defined as χ < .
8, where χ = P i SGN( f i )( f i /σ i ) . Here, f i is the flux density in the i -th band and SGN( x ) is the signfunction defined by SGN( x ) = 1 if x > x ) = − x <
0. The summation runs over all the opticalbands. Finally, we visually inspect all the dropout galaxycandidates and remove seven obvious spurious sources.
Dropout galaxy sample −0.5 0.0 0.5 1.0 Y −J i − Y −0.5 0.0 0.5 1.0 J −JH Y − J −0.5 0.0 0.5 1.0 JH − H ( Y + J ) /2 − J H Figure 5.
Two-color diagrams for i -dropout ( top ), Y -dropout( middle ), and YJ -dropout ( bottom ) galaxy candidates, with ourcolor selections indicated with solid lines. Filled circles representdropout galaxy candidates. Tracks of expected galaxy colors com-puted assuming UV-slopes of β = − − −24 −20 −16 −12061218243036 N z ∼6−7
23 27 31 35 −23 −19 −15
Absolute Magnitude z ∼8
25 29 33
Corrected Apparent Magnitude −21 −19 −17 −1501234 z ∼9
27 29 31 33
Figure 6.
Histograms of dropout galaxies at z ∼ − left panel ), z ∼ middle panel ), and z ∼ right panel ) in the four HFF clus-ter fields as a function of the intrinsic (unlensed) absolute mag-nitude. Magnification factors of individual dropout galaxies arecorrected based on our best-fitting mass models. Most of the in-trinsically faint galaxies are highly magnified and their estimatedmagnitudes are affected by the uncertainty in the magnificationfactor. Nevertheless, magnitude errors propagated from errors inthe magnification factor in the z ∼ −
7, 8, and 9 samples are nolarger than only 0.87, 0.11, and 1.19 mag, respectively. Details ofthese dropout galaxies are given in Tables B1 − B3. Note that allof the dropout galaxy candidates are plotted here.
We list the i -dropout ( z ∼ − Y -dropout ( z ∼ YJ -dropout ( z ∼
9) galaxies from the four HFF clus-ter fields in Tables B1 − B3 respectively in Appendix B.We show the distribution of these dropout galaxies incolor-color spaces in Figure 5. For each galaxy, thefirst part of ID represents the field in which it is found;1C, 2C, 3C, and 4C indicate Abell 2744 cluster, MACSJ0416.1 − In theTables we also provide magnification factors at the posi-tions of galaxies predicted by our mass models presentedin Section 4.In summary, we select 100 i -dropout, 17 Y -dropout,and 10 YJ -dropout galaxies. Note that there are someoverlaps in the dropout samples. We find that one objectis identified by the Y - and i -dropout selections, and thatsix objects meet the criteria of the YJ - and Y -dropoutselections. Most of the dropout galaxies have a modestmagnification factor, µ .
5, while some are highly mag-nified. For instance, based on the magnification maps ofour best-fitting models, 14 and four galaxies at z ∼ − z ∼ − z ∼
9a have magnification factor larger than 50, albeit withlarge uncertainties.Some of these high-magnification galaxies may be in-trinsically faint. To examine this possibility, we plot thehistograms of all dropout galaxies as a function of in-trinsic magnitude corrected for magnification factor inFigure 6. We find that they typically have absolute mag-nitudes of M UV ∼ −
18, or intrinsic magnitude of ∼ M UV ∼ −
14, or intrinsicmagnitude of ∼
33 mag. For example, HFF1C-2251-4556 is found in Abell 2744 clusterfield and its coordinates are R.A.=00:14:22.51, Decl.= − recise mass modeling of four HFF clusters 13 YJ3 YJ1 Faint red galaxyYJ4
Figure 7.
Color-composite images of the multiple image candi-dates, HFF4C-YJ1 and HFF4C-YJ3 ( left panel ), and of HFF4C-YJ4 and its companion ( right panel ). Left : HFF4C-YJ1 andHFF4C-YJ3 may be distorted in the direction of the shear at thatposition.
Right : A faint red galaxy is located very close to HFF4C-YJ4, and its position is consistent with being a counter image ofHFF4C-YJ4.
Multiple image candidates
Our analysis suggests that some dropout galaxies aremultiply imaged. Among them, reliable ones have beenincluded in our mass modeling; systems 28, 46, and54 in Abell 2744 field; systems 6, 90, 91, and 92 inMACS J0416.1 − z ∼ HFF2C-i2, -i3, -i7, and -i16 — These are newlyidentified multiple images in MACS J0416.1 − HFF4C-YJ1 and HFF4C-YJ3 — HFF4C-YJ1 is abright z ∼ z ∼ z ∼ JH − H colors ofYJ1 and YJ3 are 0 . ± .
04 and 0 . ± .
23, respectively,and are consistent with being multiple images.
HFF4C-YJ4 — This is a z ∼ z ∼
9, but it is below the detection limit used for thedropout selection. The relative positions of these twogalaxies are fully consistent with being multiple imagesof a single z ∼ JH − H col-ors of YJ4 and the faint red galaxy are − . ± .
24 and0 . ± .
24, respectively. This is consistent with beingmultiple images.Even if these galaxy pairs are not real multiple imagesof single galaxies, the close separations are interesting interm of galaxy formation and evolution.
Future Analyses
We have presented a sample of high-redshift galaxiesselected in the cluster fields where lensing effects are sig-nificant. If those from the accompanied parallel fieldsare added, we will have a four times larger sample of z & M UV ≃ − . − .
8, and − . z ∼ −
7, 8, and 9,respectively, enabling us to study extremely faint galax-ies in the reionization era. These limiting magnitudes at z ∼ − M UV ≃ − .
25 at z ∼ − M UV ≃ − . z ∼ CONCLUSION
We have conducted precise mass modeling of four HFFclusters, exploiting the full depth HFF data and the lat-est spectroscopic follow-up results on multiple images.We have used the positions of 111, 182, 173, and 108multiple images to constrain the matter distributions ofAbell 2744, MACS J0416.1 − glafic (Oguri 2010). We have found that our best-fitting mass models reproduce the observed positions ofmultiple images quite well, with image plane RMS of ∼ . ′′ z ∼ − z ∼ −
7, 17galaxies at z ∼
8, and 10 galaxies at z ∼
9, althoughsome of them are detected in multiple dropout selections.While most of these galaxies have modest magnifications, µ .
5, there are several dropout galaxies with a magni-fication larger than 10. Specifically, 14 at z ∼ − z ∼ ∼ −
33 mag, which indicates that the HFF programindeed detects the faintest galaxies known to date.
ACKNOWLEDGMENTS
We thank the Frontier Fields mass modeling initiativeled by Dan Coe and participants of this initiative forsharing invaluable data before the publications. We are4 Kawamata et al.grateful to the authors of Treu et al. (2015a) for shar-ing the follow-up data of MACS J1149.6+2223 and forhelpful discussions. This work was supported in partby World Premier International Research Center Initia-tive (WPI Initiative), MEXT, Japan, and JSPS KAK-ENHI Grant Number 26800093, 23244025, 15H05892,and 15H02064.
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The list of multiple images we use for mass modeling is given in Tables A1 − A4.
Table A1
Abell 2744 Multiple Image SystemsID R.A. Decl. z spec z model Photo-z prior Reference a . − . · · · · · · JM, XW1.2 3 . − . · · · · · · JM1.3 3 . − . · · · · · · JM2.1 3 . − . · · · . +0 . − . · · · JM recise mass modeling of four HFF clusters 15 Table A1 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . − . · · · · · · JM2.3 3 . − . · · · · · · JM2.4 3 . − . · · · · · · JM3.1 3 . − . · · · · · · JM, TJ3.2 3 . − . · · · · · · JM4.1 3 . − . · · · · · · JM, JR4.2 3 . − . · · · · · · JM4.3 3 . − . · · · · · · JM4.4 3 . − . · · · · · · JR4.5 3 . − . · · · · · · JR5.1 3 . − . · · · . +0 . − . · · · JM5.2 3 . − . · · · · · · JM5.3 3 . − . · · · · · · JM5.4 3 . − . · · · · · · · · · . − . · · · · · · JM, JR6.2 3 . − . · · · · · · JM6.3 3 . − . · · · · · · JM7.1 3 . − . · · · . +0 . − . . ± . . − . · · · JM7.3 3 . − . · · · JM8.1 3 . − . · · · . +0 . − . · · · JM8.2 3 . − . · · · · · · JM8.3 3 . − . · · · · · · MJ9.1 3 . − . · · · . +0 . − . · · · JM9.2 3 . − . · · · · · · JM10.1 3 . − . · · · . +0 . − . . ± . . − . · · · JM11.1 3 . − . · · · . +0 . − . · · · JM11.2 3 . − . · · · · · · JM11.3 3 . − . · · · · · · JM11.4 3 . − . · · · · · · JR12.2 3 . − . · · · . +0 . − . . ± . . − . · · · JR13.1 3 . − . · · · . +0 . − . · · · JR13.2 3 . − . · · · · · · JR13.3 3 . − . · · · · · · JR14.1 3 . − . · · · . +0 . − . · · · JR14.2 3 . − . · · · · · · JR14.3 3 . − . · · · · · · MJ18.1 3 . − . · · · · · · JR, XW18.2 3 . − . · · · · · · JR18.3 3 . − . · · · · · · DL20.1 3 . − . · · · . +0 . − . · · · DL20.2 3 . − . · · · · · · DL20.3 3 . − . · · · · · · MJ21.1 3 . − . · · · . +0 . − . · · · DL21.2 3 . − . · · · · · · DL21.3 3 . − . · · · · · · MJ22.1 3 . − . · · · . +0 . − . · · · DL22.2 3 . − . · · · · · · HA1422.3 3 . − . · · · · · · HA1423.1 3 . − . · · · . +0 . − . · · · DL23.2 3 . − . · · · · · · HA1423.3 3 . − . · · · · · · HA1424.1 3 . − . · · · . +0 . − . · · · MJ24.2 3 . − . · · · · · · MJ24.3 3 . − . · · · · · · MJ25.1 3 . − . · · · . +0 . − . · · · MJ25.2 3 . − . · · · · · · MJ25.3 3 . − . · · · · · · MJ26.1 3 . − . · · · . +0 . − . · · · DL26.2 3 . − . · · · · · · DL26.3 3 . − . · · · · · · DL28.1 3 . − . · · · . +0 . − . . ± . . − . · · · HA1428.3 3 . − . · · · HA1428.4 3 . − . · · · DL29.1 3 . − . · · · . +0 . − . · · · MJ29.2 3 . − . · · · · · · MJ30.1 3 . − . · · · . +0 . − . . ± . . − . · · · MJ Table A1 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . − . · · · MJ31.1 3 . − . · · · . +1 . − . · · · DL31.2 3 . − . · · · · · · DL32.1 3 . − . · · · . +0 . − . · · · MJ32.2 3 . − . · · · · · · MJ32.3 3 . − . · · · · · · MJ33.1 3 . − . · · · . +0 . − . · · · HA1433.2 3 . − . · · · · · · HA1433.3 3 . − . · · · · · · MJ34.1 3 . − . · · · . +0 . − . · · · MJ34.2 3 . − . · · · · · · MJ34.3 3 . − . · · · · · · MJ41.1 3 . − . · · · . +0 . − . · · · MJ41.3 3 . − . · · · · · · MJ46.1 3 . − . · · · . +0 . − . . ± . . − . · · · AZ46.3 3 . − . · · · AZ53.1 3 . − . · · · . +0 . − . · · · DL53.2 3 . − . · · · · · · DL54.1 3 . − . · · · . +0 . − . · · · DL54.2 3 . − . · · · · · · DL54.5 3 . − . · · · · · · DL55.1 3 . − . · · · . +0 . − . · · · DL55.2 3 . − . · · · · · · DL55.3 3 . − . · · · · · · DL56.1 3 . − . · · · . +0 . − . · · · DL56.2 3 . − . · · · · · · DL56.3 3 . − . · · · · · · DL56.4 3 . − . · · · · · · DL59.1 3 . − . · · · . +0 . − . · · · MI59.2 3 . − . · · · · · · MI60.1 3 . − . · · · . +0 . − . . ± . . − . · · · DL60.3 3 . − . · · · DL62.1 3 . − . · · · . +0 . − . . ± . · · · . − . · · · · · · a JM = Merten et al. (2011), HA14 = Atek et al. (2014), JR = Richard et al. (2014), AZ = Zitrin et al. (2014), DL = Lam et al. (2014),TJ = Johnson et al. (2014), MI = Ishigaki et al. (2015), MJ = Jauzac et al. (2015a), XW = Wang et al. (2015). Table A2
MACS J0416.1 − z spec z model Photo-z prior Reference a . − . · · · · · · AZ, LC1.2 64 . − . · · · · · · AZ1.3 64 . − . · · · · · · AZ2.1 64 . − . · · · · · · AZ, CG2.2 64 . − . · · · · · · AZ2.3 64 . − . · · · · · · AZ3.1 64 . − . · · · · · · AZ, CG3.2 64 . − . · · · · · · AZ3.3 64 . − . · · · · · · AZ4.1 64 . − . · · · · · · AZ, CG4.2 64 . − . · · · · · · AZ4.3 64 . − . · · · · · · AZ5.2 64 . − . · · · · · · AZ, AH5.3 64 . − . · · · · · · AZ5.4 64 . − . · · · · · · AZ6.1 64 . − . · · · . +0 . − . . ± . . − . · · · AZ6.3 64 . − . · · · · · · . − . · · · · · · AZ, CG7.2 64 . − . · · · · · · AZ7.3 64 . − . · · · · · · AZ8.1 64 . − . · · · . +0 . − . · · · AZ8.2 64 . − . · · · · · · AZ8.3 64 . − . · · · · · · · · · . − . · · · . +0 . − . · · · AZ9.2 64 . − . · · · · · · AZ recise mass modeling of four HFF clusters 17 Table A2 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . − . · · · · · · MJ10.1 64 . − . · · · · · · AZ, CG10.2 64 . − . · · · · · · AZ10.3 64 . − . · · · · · · AZ11.1 64 . − . xx · · · · · · AZ, SR11.2 64 . − . · · · · · · AZ11.3 64 . − . · · · · · · AZ12.1 64 . − . · · · . +0 . − . · · · AZ12.2 64 . − . · · · · · · AZ13.1 64 . − . · · · · · · AZ, CG13.2 64 . − . · · · · · · AZ13.3 64 . − . · · · · · · AZ14.1 64 . − . · · · · · · AZ, CG14.2 64 . − . · · · · · · AZ14.3 64 . − . · · · · · · AZ15.1 64 . − . · · · · · · MJ, AH15.2 64 . − . · · · · · · AZ16.1 64 . − . · · · · · · AZ, AH16.2 64 . − . · · · · · · AZ16.3 64 . − . · · · · · · AZ17.1 64 . − . · · · · · · AZ, CG17.2 64 . − . · · · · · · AZ17.3 64 . − . · · · · · · AZ18.1 64 . − . · · · . +0 . − . · · · AZ18.2 64 . − . · · · · · · AZ23.1 64 . − . · · · · · · AZ, AH23.2 64 . − . · · · · · · AZ23.3 64 . − . · · · · · · AZ25.1 64 . − . · · · . +0 . − . · · · AZ25.2 64 . − . · · · · · · AZ25.3 64 . − . · · · · · · MJ25.4 64 . − . · · · · · · AZ27.1 64 . − . · · · · · · MJ, AH27.2 64 . − . · · · · · · MJ27.3 64 . − . · · · · · · MJ29.1 64 . − . · · · · · · MJ, AH29.2 64 . − . · · · · · · · · · . − . · · · · · · MJ30.1 64 . − . · · · . +3 . − . · · · MJ30.2 64 . − . · · · · · · MJ31.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ31.3 64 . − . · · · MJ33.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ33.3 64 . − . · · · MJ34.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ34.3 64 . − . · · · · · · . − . · · · . +0 . − . . ± . . − . · · · MJ35.3 64 . − . · · · MJ37.1 64 . − . · · · . +0 . − . · · · MJ37.2 64 . − . · · · · · · MJ37.3 64 . − . · · · · · · · · · . − . · · · . +0 . − . . ± . . − . · · · MJ38.3 64 . − . · · · MJ40.1 64 . − . · · · . +0 . − . · · · MJ40.2 64 . − . · · · · · · MJ40.3 64 . − . · · · · · · · · · . − . · · · . +0 . − . · · · MJ41.2 64 . − . · · · · · · MJ41.3 64 . − . · · · · · · · · · . − . · · · . +0 . − . · · · MJ42.2 64 . − . · · · · · · MJ42.3 64 . − . · · · · · · MJ43.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ44.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ44.3 64 . − . · · · MJ Table A2 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . − . · · · . +0 . − . · · · MJ46.2 64 . − . · · · · · · MJ46.3 64 . − . · · · · · · MJ47.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ48.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ48.3 64 . − . · · · MJ49.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ50.1 64 . − . · · · . +0 . − . · · · MJ50.2 64 . − . · · · · · · MJ50.3 64 . − . · · · · · · · · · . − . · · · . +0 . − . . ± . . − . · · · MJ51.3 64 . − . · · · MJ52.1 64 . − . · · · . +0 . − . · · · MJ52.2 64 . − . · · · · · · MJ52.3 64 . − . · · · · · · MJ53.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ53.3 64 . − . · · · MJ54.1 64 . − . · · · . +0 . − . · · · MJ54.2 64 . − . · · · · · · MJ54.3 64 . − . · · · · · · MJ55.1 64 . − . · · · . +0 . − . · · · MJ55.2 64 . − . · · · · · · · · · . − . · · · . +0 . − . · · · MJ56.2 64 . − . · · · · · · MJ56.3 64 . − . · · · · · · MJ57.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ59.1 64 . − . · · · . +0 . − . · · · MJ59.2 64 . − . · · · · · · MJ59.3 64 . − . · · · · · · MJ60.1 64 . − . · · · . +0 . − . · · · MJ60.2 64 . − . · · · · · · MJ61.1 64 . − . · · · . +0 . − . · · · MJ61.2 64 . − . · · · · · · MJ63.1 64 . − . · · · . +0 . − . . ± . . − . · · · MJ63.3 64 . − . · · · MJ65.1 64 . − . · · · . +0 . − . · · · MJ65.2 64 . − . · · · · · · MJ68.1 64 . − . · · · . +0 . − . · · · MJ68.2 64 . − . · · · · · · MJ68.3 64 . − . · · · · · · MJ69.1 64 . − . · · · . +0 . − . · · · MJ69.2 64 . − . · · · · · · MJ72.1 64 . − . · · · . +0 . − . · · · MJ72.2 64 . − . · · · · · · MJ74.1 64 . − . · · · . +0 . − . . ± . · · · . − . · · · · · · . − . · · · · · · . − . · · · . +0 . − . · · · · · · . − . · · · · · · · · · . − . · · · . +0 . − . · · · · · · . − . · · · · · · · · · . − . · · · · · · · · · . − . · · · . +0 . − . · · · · · · . − . · · · · · · · · · . − . · · · . +0 . − . · · · JD84.2 64 . − . · · · · · · JD85.1 64 . − . · · · . +0 . − . · · · JD85.2 64 . − . · · · · · · JD86.1 64 . − . · · · . +0 . − . · · · JD86.2 64 . − . · · · · · · JD87.1 64 . − . · · · . +0 . − . · · · JD recise mass modeling of four HFF clusters 19 Table A2 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . − . · · · · · · JD88.1 64 . − . · · · . +0 . − . · · · JD88.2 64 . − . · · · · · · JD89.1 64 . − . · · · . +0 . − . · · · · · · . − . · · · · · · · · · . − . · · · · · · · · · . − . · · · . +0 . − . . ± . · · · . − . · · · · · · . − . · · · · · · . − . · · · . +0 . − . . ± . · · · . − . · · · · · · . − . · · · · · · . − . · · · . +0 . − . . ± . · · · . − . · · · · · · . − . · · · . +0 . − . · · · · · · . − . · · · · · · · · · a LC = Christensen et al. (2012), AZ = Zitrin et al. (2013), MJ = Jauzac et al. (2014), CG = Grillo et al. (2015a), JD = Diego et al. (2015a),AH = Hoag et al. (in prep.), SR = Rodney et al. (in prep.). Table A3
MACS J0717.5+3745 Multiple Image SystemsID R.A. Decl. z spec z model Photo-z prior Reference a . . · · · · · · AZ, ML1.2 109 . . · · · · · · AZ1.3 109 . . · · · · · · AZ1.4 109 . . · · · · · · AZ1.5 109 . . · · · · · · EV2.1 109 . . · · · . +0 . − . · · · AZ2.2 109 . . · · · · · · AZ3.1 109 . . · · · · · · AZ, ML3.2 109 . . · · · · · · AZ3.3 109 . . · · · · · · ML4.1 109 . . · · · · · · AZ, KS4.2 109 . . · · · · · · AZ4.3 109 . . · · · · · · AZ5.1 109 . . · · · . +0 . − . . ± . . . · · · AZ5.3 109 . . · · · ML6.1 109 . . · · · . +0 . − . · · · AZ6.2 109 . . · · · · · · AZ6.3 109 . . · · · · · · AZ7.1 109 . . · · · . +0 . − . · · · AZ7.2 109 . . · · · · · · AZ7.3 109 . . · · · · · · AZ8.1 109 . . · · · . +0 . − . · · · AZ8.2 109 . . · · · · · · AZ8.3 109 . . · · · · · · AZ12.1 109 . . · · · · · · AZ, TT12.2 109 . . · · · · · · AZ12.3 109 . . · · · · · · AZ13.1 109 . . · · · · · · AZ, ML13.2 109 . . · · · · · · AZ13.3 109 . . · · · · · · AZ14.1 109 . . · · · · · · ML, ML14.2 109 . . · · · · · · ML14.3 109 . . · · · · · · ML15.1 109 . . · · · · · · ML, ML15.2 109 . . · · · · · · ML15.3 109 . . · · · · · · ML16.1 109 . . · · · . +0 . − . · · · ML16.2 109 . . · · · · · · ML16.3 109 . . · · · · · · ML17.1 109 . . · · · . +0 . − . · · · ML17.2 109 . . · · · · · · ML17.3 109 . . · · · · · · ML17.4 109 . . · · · · · · JD18.1 109 . . · · · . +0 . − . · · · ML18.2 109 . . · · · · · · ML Table A3 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . . · · · · · · EV19.2 109 . . · · · · · · EV19.3 109 . . · · · · · · JR20.1 109 . . · · · . +0 . − . · · · JD20.2 109 . . · · · · · · JD23.1 109 . . · · · . +0 . − . . ± . . . · · · JD25.1 109 . . · · · . +0 . − . . ± . . . · · · JD25.3 109 . . · · · JD25.4 109 . . · · · · · · . . · · · . +0 . − . · · · JD27.2 109 . . · · · · · · JD29.1 109 . . · · · . +0 . − . · · · JD29.2 109 . . · · · · · · JD29.3 109 . . · · · · · · JD31.1 109 . . · · · . +0 . − . · · · JD31.2 109 . . · · · · · · JD31.3 109 . . · · · · · · JD32.1 109 . . · · · . +0 . − . . ± . . . · · · JD32.3 109 . . · · · JD33.1 109 . . · · · . +0 . − . · · · JD33.2 109 . . · · · · · · JD33.3 109 . . · · · · · · JD36.1 109 . . · · · . +0 . − . · · · JD36.2 109 . . · · · · · · JD36.3 109 . . · · · · · · JD45.1 109 . . · · · . +0 . − . · · · JD45.2 109 . . · · · · · · JD49.1 109 . . · · · . +0 . − . · · · JD49.2 109 . . · · · · · · JD50.1 109 . . · · · . +0 . − . · · · JD50.2 109 . . · · · · · · JD50.3 109 . . · · · · · · JD52.2 109 . . · · · . +0 . − . · · · JD52.3 109 . . · · · · · · JD53.1 109 . . · · · . +0 . − . · · · JD53.2 109 . . · · · · · · JD53.3 109 . . · · · · · · JD55.1 109 . . · · · . +0 . − . . ± . . . · · · JD55.3 109 . . · · · · · · . . · · · . +0 . − . · · · JD56.2 109 . . · · · · · · JD56.3 109 . . · · · · · · JD57.1 109 . . · · · . +0 . − . · · · JD57.2 109 . . · · · · · · JD57.3 109 . . · · · · · · JD58.1 109 . . · · · . +0 . − . · · · JD58.2 109 . . · · · · · · JD58.3 109 . . · · · · · · JD60.1 109 . . · · · . +0 . − . . ± . . . · · · JD60.3 109 . . · · · JD60.4 109 . . · · · JD60.5 109 . . · · · JD61.1 109 . . · · · . +0 . − . . ± . . . · · · JD62.1 109 . . · · · . +0 . − . . ± . . . · · · JD63.1 109 . . · · · . +0 . − . . ± . . . · · · JD64.1 109 . . · · · . +0 . − . . ± . . . · · · JD64.3 109 . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . . . · · · JD recise mass modeling of four HFF clusters 21 Table A3 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · · · · a AZ = Zitrin et al. (2009), ML = Limousin et al. (2012), KS = Schmidt et al. (2014), EV = Vanzella et al. (2014), JR = Richard et al. (2014),JD = Diego et al. (2015b), TT = Treu et al. (2015b) Table A4
MACS J1149.6+2223 Multiple Image SystemsID R.A. Decl. z spec z model Photo-z prior Reference a . . · · · · · · AZ, GS1.2 177 . . · · · · · · AZ1.3 177 . . · · · · · · AZ Table A4 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . . · · · · · · AZ, GS2.2 177 . . · · · · · · AZ2.3 177 . . · · · · · · AZ3.1 177 . . · · · · · · AZ, MJ, CG3.2 177 . . · · · · · · AZ3.3 177 . . · · · · · · AZ4.1 177 . . · · · · · · AZ, CG4.2 177 . . · · · · · · AZ4.3 177 . . · · · · · · AZ5.1 177 . . · · · · · · AZ, GB5.2 177 . . · · · · · · AZ5.3 177 . . · · · · · · AZ6.1 177 . . · · · . +0 . − . · · · AZ6.2 177 . . · · · · · · AZ6.3 177 . . · · · · · · AZ7.1 177 . . · · · . +0 . − . · · · AZ7.2 177 . . · · · · · · AZ7.3 177 . . · · · · · · AZ8.1 177 . . · · · . +0 . − . · · · AZ8.2 177 . . · · · · · · AZ8.4 177 . . · · · · · · WZ13.1 177 . . · · · · · · WZ, GB13.2 177 . . · · · · · · WZ13.3 177 . . · · · · · · WZ14.1 177 . . · · · · · · JR, GB, CG14.2 177 . . · · · · · · JR21.1 177 . . · · · . +0 . − . · · · MJ21.2 177 . . · · · · · · MJ21.3 177 . . · · · · · · MJ23.1 177 . . · · · . +1 . − . · · · TT23.2 177 . . · · · · · · TT23.3 177 . . · · · · · · TT24.1 177 . . · · · . +0 . − . . ± . . . · · · GS24.3 177 . . · · · GS25.1 177 . . · · · . +2 . − . · · · TT25.2 177 . . · · · · · · TT26.1 177 . . · · · . +0 . − . . ± . . . · · · MJ26.3 177 . . · · · MJ28.1 177 . . · · · . +0 . − . . ± . . . · · · MJ28.3 177 . . · · · MJ29.1 177 . . · · · · · · MJ, CG29.2 177 . . · · · · · · MJ29.3 177 . . · · · · · · MJ30.1 177 . . · · · . +0 . − . · · · TT30.2 177 . . · · · · · · TT31.1 177 . . · · · . +0 . − . · · · TT31.2 177 . . · · · · · · TT31.3 177 . . · · · · · · TT32.1 177 . . · · · . +0 . − . . ± . . . · · · MJ32.3 177 . . · · · MJ33.1 177 . . · · · . +0 . − . . ± . . . · · · MJ33.3 177 . . · · · MJ34.1 177 . . · · · . +0 . − . · · · MJ34.2 177 . . · · · · · · MJ34.3 177 . . · · · · · · MJ35.1 177 . . · · · . +0 . − . · · · TT35.2 177 . . · · · · · · TT35.3 177 . . · · · · · · TT36.1 177 . . · · · . +0 . − . · · · TT36.2 177 . . · · · · · · TT37.1 177 . . · · · . +0 . − . · · · TT37.2 177 . . · · · · · · TT38.1 177 . . · · · . +0 . − . . ± . · · · . . · · · · · · . . · · · . +0 . − . . ± . · · · . . · · · · · · recise mass modeling of four HFF clusters 23 Table A4 — Continued
ID R.A. Decl. z spec z model Photo-z prior Reference a . . · · · . +0 . − . · · · · · · . . · · · · · · · · · . . · · · · · · · · · SN Refsdal
S1 177 . . · · · · · · PK, GSS2 177 . . · · · · · · PKS3 177 . . · · · · · · PKS4 177 . . · · · · · · PK Knot in System 1 . . · · · · · · GS, GS1.2.2 177 . . · · · · · · GS1.2.3 177 . . · · · · · · GS1.2.4 177 . . · · · · · · GS1.2.6 177 . . · · · · · · SR1.13.1 177 . . · · · · · · GS, GS1.13.2 177 . . · · · · · · GS1.13.3 177 . . · · · · · · GS1.13.4 177 . . · · · · · · GS1.16.1 177 . . · · · · · · GS1.16.2 177 . . · · · · · · GS1.16.3 177 . . · · · · · · GS1.17.1 177 . . · · · · · · GS, GS1.17.2 177 . . · · · · · · GS1.17.3 177 . . · · · · · · GS1.19.1 177 . . · · · · · · SR1.19.2 177 . . · · · · · · SR1.19.3 177 . . · · · · · · SR1.19.5 177 . . · · · · · · SR1.23.1 177 . . · · · · · · GS, GS1.23.2 177 . . · · · · · · GS1.23.3 177 . . · · · · · · GS1.23.5 177 . . · · · · · · SR1.30.1 177 . . · · · · · · SR, GS1.30.2 177 . . · · · · · · SR1.30.3 177 . . · · · · · · SR1.30.4 177 . . · · · · · · SR a AZ = Zitrin & Broadhurst (2009), GS = Smith et al. (2009), WZ = Zheng et al. (2012), SR = Rau et al. (2014), JR = Richard et al. (2014),PK = Kelly et al. (2015b), MJ = Jauzac et al. (2015b), TT = Treu et al. (2015a), CG = Grillo et al. (2015b), GB = Brammer et al. (in prep.).* We note that in the identification of the multiple images, we do not refer to Jauzac et al. (2015b), which was posted to arXiv very recently. Allof the multiple images labeled Jauzac et al. (2015b) in this table are also presented in Treu et al. (2015a). B. LISTS OF DROPOUT GALAXY CANDIDATES
The list of dropout galaxy candidates is given in Tables B1 − B3.
Table B1
Dropout galaxy candidates at z ∼ − a ID a,b R.A. Decl. i − Y Y − J J µ best µ c z photo Reference d HFF1C2251-4556 i1 3 . − . . ± .
31 0 . ± .
05 26 . ± .
03 3 .
64 3 . +0 . − . . +0 . − . A , I, A . − . . ± .
10 0 . ± .
05 26 . ± .
04 1 .
47 1 . +0 . − . . +0 . − . A , I, A . − . . ± .
08 0 . ± .
05 26 . ± .
04 1 .
55 1 . +0 . − . . +0 . − . A , I, A . − . > .
36 0 . ± .
09 26 . ± .
06 4 .
47 4 . +0 . − . . +0 . − . A , I, A . − . . ± .
13 0 . ± .
07 26 . ± .
06 2 .
84 3 . +0 . − . . +0 . − . · · · . − . > .
13 0 . ± .
10 26 . ± .
07 3 .
31 3 . +0 . − . . +0 . − . I, A . − . . ± . − . ± .
09 27 . ± .
08 1 .
68 1 . +0 . − . . +0 . − . I2047-3526 i8 3 . − . > .
83 0 . ± .
14 27 . ± .
11 3 .
23 3 . +0 . − . . +0 . − . WZ , I, A . − . . ± .
22 0 . ± .
12 27 . ± .
09 3 .
74 3 . +0 . − . . +0 . − . A , I, A . − . > . − . ± .
12 27 . ± .
10 11 .
88 12 . +2 . − . . +0 . − . I, A . − . . ± . − . ± .
11 27 . ± .
09 1 .
48 1 . +0 . − . . +0 . − . I, A , C2477-4372 i12 3 . − . > . − . ± .
13 27 . ± .
10 4 .
02 4 . +0 . − . . +0 . − . A , WZ , I, A . − . . ± . − . ± .
14 27 . ± .
11 6 .
81 7 . +0 . − . . +0 . − . I, A . − . > .
45 0 . ± .
18 27 . ± .
13 8 .
00 7 . +1 . − . . +0 . − . I, A . − . . ± . − . ± .
14 27 . ± .
12 2 .
95 3 . +0 . − . . +0 . − . I Table B1 — Continued ID a ID a,b R.A. Decl. i − Y Y − J J µ best µ c z photo Reference d . − . . ± .
33 0 . ± .
19 27 . ± .
15 3 .
45 3 . +0 . − . . +0 . − . · · · . − . . ± . − . ± .
14 27 . ± .
12 1 .
44 1 . +0 . − . . +0 . − . I, A . − . . ± .
45 0 . ± .
18 27 . ± .
13 3 .
12 3 . +0 . − . . +0 . − . I, A . − . . ± . − . ± .
17 27 . ± .
14 1 .
85 1 . +0 . − . . +3 . − . · · · . − . > .
18 0 . ± .
25 27 . ± .
18 15 .
56 17 . +6 . − . . +0 . − . · · · . − . > .
90 0 . ± .
26 27 . ± .
19 9 .
25 9 . +0 . − . . +5 . − . · · · . − . > . − . ± .
24 28 . ± .
19 1 .
73 1 . +0 . − . . +0 . − . I, A HFF2C0949-5187 i1 64 . − . . ± . − . ± .
05 26 . ± .
04 1 .
54 1 . +0 . − . . +0 . − . B1148-3434 i2 64 . − . . ± . − . ± .
06 26 . ± .
05 19 .
12 18 . +2 . − . . +0 . − . B, C1131-3400 i3 64 . − . . ± . − . ± .
08 26 . ± .
06 11 .
18 10 . +1 . − . . +0 . − . · · · . − . . ± . − . ± .
11 27 . ± .
09 3 .
38 3 . +0 . − . . +0 . − . C0960-3425 i5 64 . − . . ± .
36 0 . ± .
14 27 . ± .
11 11 .
10 10 . +1 . − . . +0 . − . B, C1147-4580 i6 64 . − . > .
85 0 . ± .
13 27 . ± .
09 1 .
40 1 . +0 . − . . +0 . − . C1220-3595 i7 64 . − . . ± . − . ± .
11 27 . ± .
09 3 .
55 3 . +0 . − . . +0 . − . C1156-3446 i8 64 . − . . ± . − . ± .
12 27 . ± .
10 31 .
58 31 . +9 . − . . +0 . − . · · · . − . . ± . − . ± .
19 27 . ± .
15 6 .
32 6 . +0 . − . . +0 . − . · · · . − . . ± . − . ± .
12 27 . ± .
10 68 .
19 76 . +55 . − . . +0 . − . · · · . − . . ± . − . ± .
16 27 . ± .
13 2 .
87 2 . +0 . − . . +0 . − . · · · . − . > .
49 0 . ± .
15 27 . ± .
11 1 .
80 1 . +0 . − . . +1 . − . · · · . − . . ± .
28 0 . ± .
14 27 . ± .
11 1 .
74 1 . +0 . − . . +0 . − . · · · . − . > .
71 0 . ± .
14 27 . ± .
11 1 .
23 1 . +0 . − . . +0 . − . · · · . − . . ± . − . ± .
19 27 . ± .
15 1 .
78 1 . +0 . − . . +0 . − . C1045-3324 i16 64 . − . . ± . − . ± .
16 27 . ± .
14 5 .
20 5 . +0 . − . . +0 . − . · · · . − . . ± .
37 0 . ± .
23 27 . ± .
16 16 .
04 15 . +2 . − . . +1 . − . · · · . − . > .
68 0 . ± .
18 27 . ± .
15 4 .
02 3 . +0 . − . . +0 . − . · · · . − . . ± .
24 0 . ± .
16 27 . ± .
13 2 .
24 2 . +0 . − . . +0 . − . · · · . − . . ± .
32 0 . ± .
16 27 . ± .
13 3 .
46 3 . +0 . − . . +0 . − . C1308-3431 i21 64 . − . . ± . − . ± .
18 27 . ± .
15 3 .
80 3 . +0 . − . . +0 . − . · · · . − . . ± . − . ± .
19 27 . ± .
16 1 .
77 1 . +0 . − . . +0 . − . · · · . − . > . − . ± .
21 28 . ± .
18 1 .
71 1 . +0 . − . . +0 . − . · · · HFF3C3377-4319 i1 109 . . . ± . − . ± .
04 25 . ± .
04 60 .
69 65 . +13 . − . . +0 . − . B3817-5168 i2 109 . . . ± . − . ± .
04 25 . ± .
04 4 .
96 4 . +0 . − . . +0 . − . B3785-4338 i3 109 . . . ± . − . ± .
05 26 . ± .
04 8 .
40 8 . +0 . − . . +0 . − . B3578-5538 i4 109 . . . ± . − . ± .
07 26 . ± .
06 6 .
59 6 . +0 . − . . +0 . − . B3269-5069 i5 109 . . . ± .
29 0 . ± .
09 26 . ± .
07 3 .
06 3 . +0 . − . . +0 . − . B3342-3294 i6 109 . . . ± .
24 0 . ± .
09 26 . ± .
07 2 .
35 2 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
09 26 . ± .
07 3 .
34 3 . +0 . − . . +0 . − . · · · . . . ± .
20 0 . ± .
09 26 . ± .
08 4 .
08 4 . +0 . − . . +0 . − . · · · . . . ± .
41 0 . ± .
20 27 . ± .
15 23 .
83 23 . +4 . − . . +0 . − . · · · . . . ± . − . ± .
16 27 . ± .
14 4 .
81 5 . +0 . − . . +0 . − . · · · . . . ± .
26 0 . ± .
17 27 . ± .
13 5 .
43 5 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
17 27 . ± .
14 8 .
18 8 . +1 . − . . +0 . − . · · · . . . ± . − . ± .
18 27 . ± .
14 95 .
69 53 . +86 . − . . +0 . − . · · · . . . ± .
39 0 . ± .
19 27 . ± .
15 7 .
21 6 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
19 27 . ± .
16 8 .
49 11 . +5 . − . . +0 . − . · · · . . > .
44 0 . ± .
22 27 . ± .
17 4 .
38 4 . +0 . − . . +0 . − . · · · . . > . − . ± .
20 27 . ± .
17 15 .
31 12 . +2 . − . . +0 . − . · · · . . . ± . − . ± .
17 27 . ± .
14 5 .
99 6 . +0 . − . . +0 . − . · · · . . > . − . ± .
23 27 . ± .
19 9 .
14 7 . +1 . − . . +0 . − . · · · . . > . − . ± .
22 28 . ± .
20 9 .
94 10 . +0 . − . . +0 . − . · · · HFF4C4025-5027 i1 177 . . > .
48 0 . ± .
03 25 . ± .
02 1 .
57 1 . +0 . − . . +0 . − . · · · . . . ± .
05 0 . ± .
03 25 . ± .
02 1 .
94 2 . +0 . − . . +0 . − . B3321-2566 i3 177 . . . ± . − . ± .
05 26 . ± .
04 1 .
74 1 . +0 . − . . +0 . − . B3180-3434 i4 177 . . . ± .
09 0 . ± .
06 26 . ± .
04 2 .
28 2 . +0 . − . . +0 . − . B recise mass modeling of four HFF clusters 25 Table B1 — Continued ID a ID a,b R.A. Decl. i − Y Y − J J µ best µ c z photo Reference d . . . ± . − . ± .
06 26 . ± .
05 3 .
68 4 . +1 . − . . +0 . − . B4042-4205 i6 177 . . . ± . − . ± .
06 26 . ± .
05 1 .
77 1 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
08 26 . ± .
07 1 .
87 1 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
07 26 . ± .
06 1 .
77 1 . +0 . − . . +0 . − . · · · . . . ± .
14 0 . ± .
08 26 . ± .
06 1 .
73 1 . +0 . − . . +0 . − . · · · . . > .
16 0 . ± .
11 27 . ± .
09 1 .
71 1 . +0 . − . . +0 . − . · · · . . > .
76 0 . ± .
12 27 . ± .
08 1 .
95 2 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
10 27 . ± .
08 1 .
73 1 . +0 . − . . +0 . − . · · · . . > .
88 0 . ± .
12 27 . ± .
09 3 .
50 4 . +4 . − . . +0 . − . · · · . . . ± .
38 0 . ± .
12 27 . ± .
09 6 .
21 5 . +0 . − . . +0 . − . · · · . . . ± .
22 0 . ± .
12 27 . ± .
09 5 .
15 4 . +1 . − . . +5 . − . · · · . . > .
97 0 . ± .
13 27 . ± .
10 8 .
54 8 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
13 27 . ± .
10 3 .
17 2 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
14 27 . ± .
12 1 .
68 1 . +0 . − . . +0 . − . · · · . . > .
59 0 . ± .
17 27 . ± .
11 6 .
95 8 . +15 . − . . +0 . − . · · · . . . ± . − . ± .
14 27 . ± .
11 5 .
10 5 . +2 . − . . +0 . − . · · · . . . ± .
40 0 . ± .
16 27 . ± .
11 2 .
08 2 . +0 . − . . +1 . − . · · · . . > .
73 0 . ± .
16 27 . ± .
12 6 .
51 5 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
15 27 . ± .
12 2 .
36 2 . +0 . − . . +0 . − . · · · . . > .
55 0 . ± .
17 27 . ± .
12 7 .
10 6 . +0 . − . . +0 . − . · · · . . . ± .
24 0 . ± .
16 27 . ± .
12 11 .
19 11 . +3 . − . . +0 . − . · · · . . > .
40 0 . ± .
19 27 . ± .
14 7 .
27 6 . +0 . − . . +0 . − . · · · . . > .
34 0 . ± .
20 27 . ± .
15 2 .
58 2 . +0 . − . . +0 . − . · · · . . . ± .
35 0 . ± .
21 27 . ± .
16 3 .
56 3 . +0 . − . . +1 . − . · · · . . . ± .
43 0 . ± .
20 27 . ± .
15 2 .
38 2 . +0 . − . . +5 . − . · · · . . . ± . − . ± .
19 27 . ± .
15 1 .
93 1 . +0 . − . . +0 . − . · · · . . . ± .
35 0 . ± .
24 27 . ± .
18 578 .
83 119 . +241 . − . . +4 . − . · · · . . . ± . − . ± .
20 27 . ± .
17 3 .
01 2 . +0 . − . . +0 . − . · · · . . > . − . ± .
23 27 . ± .
19 1 .
73 1 . +0 . − . . +0 . − . · · · . . . ± . − . ± .
20 28 . ± .
18 5 .
22 4 . +0 . − . . +0 . − . · · · . . > .
09 0 . ± .
26 28 . ± .
20 2 .
45 2 . +0 . − . . +0 . − . · · · a For simplicity, the part that represents the cluster name is omitted. Examples of full IDs are HFF1C-2251-4556 and HFF1C-i1.b Short ID used only in this paper for simplification and clarity.c Total magnitude.d Median value and 1 σ error of the magnification factor from the MCMC posterior distribution.e A = Atek et al. (2014), B = Bradley et al. (2014), WZ = Zheng et al. (2014), I = Ishigaki et al. (2015), A = Atek et al. (2015a),C = Coe et al. (2015). Table B2
Dropout galaxy candidates at z ∼ a ID a,b R.A. Decl. Y − J J − JH JH µ best µ d z photo Reference e HFF1C2508-2496 Y1 3 . − . . ± .
07 0 . ± .
04 25 . ± .
03 1 .
31 1 . +0 . − . . +0 . − . L , A , WZ , I, A , C2481-2561 Y2 3 . − . . ± .
15 0 . ± .
08 26 . ± .
05 1 .
40 1 . +0 . − . . +0 . − . WZ , I, A , C2306-3089 Y3 3 . − . . ± .
15 0 . ± .
08 26 . ± .
05 2 .
04 2 . +0 . − . . +0 . − . WZ , I, A , C2555-2515 Y4 3 . − . . ± . − . ± .
09 26 . ± .
06 1 .
33 1 . +0 . − . . +0 . − . WZ , I, A , C2492-2561 Y5 3 . − . . ± .
32 0 . ± .
10 26 . ± .
07 1 .
40 1 . +0 . − . . +0 . − . WZ , I, A , C2557-2513 Y6 3 . − . . ± .
22 0 . ± .
13 27 . ± .
08 1 .
32 1 . +0 . − . . +0 . − . WZ , I, A . − . . ± . − . ± .
12 27 . ± .
09 1 .
69 1 . +0 . − . . +0 . − . WZ , I, A , C2495-2562 Y8 3 . − . . ± .
28 0 . ± .
18 27 . ± .
11 1 .
40 1 . +0 . − . . +0 . − . WZ , I, C2216-4356 Y9 3 . − . . ± . − . ± .
23 28 . ± .
18 8 .
57 9 . +0 . − . . +0 . − . WZ , I, A . − . . ± . − . ± .
23 28 . ± .
17 1 .
35 1 . +0 . − . . +0 . − . I, A HFF2C1151-4540 Y1 64 . − . . ± .
18 0 . ± .
06 26 . ± .
04 1 .
43 1 . +0 . − . . +0 . − . L , C, M0939-5354 Y2 64 . − . . ± .
30 0 . ± .
07 26 . ± .
05 1 .
39 1 . +0 . − . . +0 . − . L , M1153-4531 Y3 64 . − . . ± .
46 0 . ± .
10 26 . ± .
06 1 .
43 1 . +0 . − . . +0 . − . L , C Table B2 — Continued ID a ID a,b R.A. Decl. Y − J J − JH JH µ best µ d z photo Reference e . − . . ± .
50 0 . ± .
17 27 . ± .
12 1 .
69 1 . +0 . − . . +0 . − . L , M1447-3538 Y5 64 . − . . ± . − . ± .
15 27 . ± .
12 1 .
76 1 . +0 . − . . +0 . − . HFF4C4025-5027 f i1 f . . . ± .
03 0 . ± .
02 25 . ± .
02 1 .
58 1 . +0 . − . . +0 . − . · · · . . . ± .
42 0 . ± .
18 27 . ± .
11 1 .
63 1 . +0 . − . . +1 . − . · · · a For simplicity, the part that represents the cluster name is omitted. Examples of full IDs are HFF1C-2508-2496 and HFF1C-Y1.b Short ID used only in this paper for simplification and clarity.c Total magnitude.d Median value and 1 σ error of the magnification factor from the MCMC posterior distribution.e L = Laporte et al. (2014), A = Atek et al. (2014), WZ = Zheng et al. (2014), I = Ishigaki et al. (2015), L = Laporte et al. (2015),A = Atek et al. (2015a), C = Coe et al. (2015), M = McLeod et al. (2015).f Selected by our two criteria for i -dropout and Y -dropout galaxies. Table B3
Dropout galaxy candidates at z ∼ a ID a,b R.A. Decl. YJ c − JH JH − H H µ best µ e z photo Reference f HFF1C2481-2561 g Y2 g . − . . ± . − . ± .
07 26 . ± .
05 1 .
40 1 . +0 . − . . +0 . − . WZ , I, A g Y5 g . − . . ± .
18 0 . ± .
09 26 . ± .
06 1 .
40 1 . +0 . − . . +0 . − . WZ , I, A , M2220-4053 YJ3 3 . − . > .
21 0 . ± .
27 27 . ± .
15 14 .
12 14 . +1 . − . . +1 . − . AZ, I, OHFF2C1151-4540 g Y1 g . − . . ± .
10 0 . ± .
06 26 . ± .
04 1 .
43 1 . +0 . − . . +0 . − . L , C, M0939-5354 g Y2 g . − . . ± .
16 0 . ± .
07 26 . ± .
05 1 .
39 1 . +0 . − . . +0 . − . L , M0901-5172 g Y3 g . − . . ± . − . ± .
19 27 . ± .
14 1 .
70 1 . +0 . − . . +1 . − . L , C, MHFF4C3358-4457 YJ1 177 . . > .
39 0 . ± .
05 25 . ± .
03 17 .
51 6 . +21 . − . . +1 . − . WZ g Y2 g . . . ± . − . ± .
16 27 . ± .
11 1 .
63 1 . +0 . − . . +0 . − . · · · . . > .
30 0 . ± .
26 27 . ± .
16 63 .
34 18 . +40 . − . . +0 . − . · · · . . > . − . ± .
28 27 . ± .
20 35 .
85 41 . +12 . − . . +0 . − . · · · a For simplicity, the part that represents the cluster name is omitted. Examples of full IDs are HFF1C-2481-2561 and HFF1C-Y2.b Short ID used only in this paper for simplification and clarity.c YJ ≡ ( Y + J ) /