Toward Solving the Puzzle: Dissecting the Complex Merger A521 with Multi-wavelength Data
Mijin Yoon, Wonki Lee, M. James Jee, Kyle Finner, Rory Smith, Jae-woo Kim
DDraft version June 25, 2020
Preprint typeset using L A TEX style emulateapj v. 12/16/11
TOWARD SOLVING THE PUZZLE: DISSECTING THE COMPLEX MERGER A521 WITHMULTI-WAVELENGTH DATA
MIJIN YOON , WONKI LEE , M. JAMES JEE , KYLE FINNER , RORY SMITH , AND JAE-WOO KIM Draft version June 25, 2020
ABSTRACTA521 has been a subject of extensive panchromatic studies from X-ray to radio. The cluster possessesa number of remarkable features including a bright radio relic with a steep spectrum, more than threedistinct galaxy groups forming a filament, and two disturbed X-ray peaks at odds with the distantposition and tilted orientation of the radio relic. These several lines of evidence indicate a complexmerger. In this paper, we present a multi-wavelength study of A521 based on Subaru optical,
HubbleSpace Telescope infrared,
Chandra
X-ray, GMRT radio, and MMT optical spectroscopic observations.Our weak-lensing (WL) analysis with improved systematics control reveals that A521 is composed ofthree substructures aligned in the northwest to southeast orientation. These WL mass substructuresare remarkably well-aligned with the cluster optical luminosity distribution constructed from ournew enhanced cluster member catalog. These individual substructure masses are determined bysimultaneously fitting three NFW profiles. We find that the total mass of A521 modeled by thesuperposition of the three halos is 13 . +1 . − . × M (cid:12) , a factor of two higher than the previous WLmeasurement. With these WL mass constraints combined with X-ray and radio features, we considertwo merging scenarios, carry out the corresponding numerical simulations, and discuss strengths andweaknesses of each case. Keywords: galaxy cluster — gravitational lensing: weak — dark matter — astrophysics: observations— large-scale structure of the Universe INTRODUCTION
Cluster collisions happen at the end of the mergerchains in the hierarchical structure formation paradigm.In-depth studies of these cosmic events provide uniqueopportunities to understand the growth of the large scalestructure of the universe. In addition, more recently,these merging clusters have been regarded as useful lab-oratories, enabling particle experiments beyond the en-ergy scale executable on Earth. One of the most out-standing questions that the experiments can address isthe nature of dark matter. However, obviously, we do nothave any control over the setup of the experiments (i.e.,initial conditions prior to collision). Moreover, only asingle snapshot of the long merger history is available tous. Therefore, careful characterization of the current sta-tus of the merging clusters and robust reconstruction ofmerger scenarios must be carried out in order to fully uti-lize these tremendous opportunities to address the fun-damental questions in physics.Radio relic clusters are a rare class of merging clustersthat exhibit large-scale ( (cid:38) Ruhr-University Bochum, Astronomical Institute, GermanCentre for Cosmological Lensing, Universittsstr. 150, 44801Bochum, Germany; [email protected] Department of Astronomy, Yonsei University, Yonsei-ro 50,Seoul, Korea; [email protected], [email protected] Department of Physics, University of California, Davis, Cali-fornia, USA Korea Astronomy and Space Science Institute, Daedeokdae-ro776, Yuseong-gu, Daejeon 34055, Republic of Korea since the impact and the orientation of the merger axis,which is an invaluable piece of information in our recon-struction of the merger scenario.We, Merging Cluster Collaboration (MC ) , are con-ducting a series of studies to investigate radio relic clus-ters. Our short-term scientific goals are to robustly mea-sure the distributions of the three cluster constituents(i.e., gas, dark matter, and galaxies) for our sample of ra-dio relic clusters based on multi-wavelength observationsand constrain most probable merger scenarios throughiterative numerical simulations. The long-term goals areto address the particle acceleration inefficiency problemsand measure the cross section of dark matter as a stepto reveal its fundamental properties.In this paper, we present our multi-wavelength studyof the complex cluster merger A521 at z = 0 . ∼ . a r X i v : . [ a s t r o - ph . GA ] J un number of the spectroscopic members (from 41 to 113)and confirmed that the A521 galaxy distribution indeedpossesses a sophisticated structure. The authors identi-fied seven groups forming the NW-SE filament and oneperpendicular (NE-SW) ridge in the cluster galaxy distri-bution. In addition, their velocity analysis indicates thatA521 is complex in the line-of-sight (LOS) direction, too.If these substructures are real as claimed by the authors,we may be witnessing multiple merging events in A521.Studies with improved X-ray observations (Ferrariet al. 2006; Bourdin et al. 2013) using Chandra andXMM-
Newton indicate that perhaps the X-ray data toomay support the complexity of the cluster substructuresproposed by optical studies. In particular, Bourdin et al.(2013) showed that A521 possesses interesting brightnessand temperature features including two cold fronts andtwo shock fronts.The A521 radio relic image was first presented by Ar-naud et al. (2000) with the archival NVSS data. Evenwith the broad beam ( ∼ (cid:48)(cid:48) ), the arc-like radio feature isclear in the NVSS image, although this radio morphol-ogy was neither explicitly mentioned nor referred to asa “relic” in Arnaud et al. (2000). Ferrari et al. (2003)and Giacintucci et al. (2008) confirmed the presence ofthe relic with higher-resolution Very Large Array (VLA)1.4 GHz and Giant Metrewave Radio Telescope (GMRT)610MHz observations, respectively.Despite the above wealth of information available forA521, no convincing merging scenario that explainsthe current multi-wavelength observations has been pre-sented. Given the large number of substructures seen inthe A521 cluster galaxy distribution map (Ferrari et al.2003), we believe that it is futile to attempt to suggestplausible merging scenarios that account for the entirecomplex galaxy distribution.We argue that one powerful method to reduce the di-mension of the complexity in the A521 puzzle is weak-lensing (WL) analysis. WL studies enable us to iden-tify the most significant cluster substructures in mass.This in turn allows us to identify apparent galaxy over-densities, that are not real, and simply due to projectioneffect. Because the mass-to-light ratio (M/L) values inbona fide galaxy groups and clusters are at least an or-der of magnitude higher than in individual galaxies, ingeneral a chance projection of multiple isolated galaxiesalong the LOS direction does not lead to a significantWL detection.Therefore, the primary goal of our current study is toconstrain the detailed mass distribution in A521 with acareful WL analysis. Although A521 is one of the 30 Lo-CuSS clusters (Mulroy et al. 2019) studied with WL inOkabe et al. (2010), the authors do not discuss its sub-structures. In our study, we characterize the substruc-ture properties with WL and provide detailed compari-son with our multi-wavelength data. In particular, we en-hance our knowledge on the galaxy distribution with ournew spectroscopic observations using MMT/Hectospec,which adds 67 new cluster members. Finally, we discussthe A521 merging scenario with our hydrodynamic sim-ulations.We present our paper as follows. In §
2, we in-troduce the data from Subaru/Suprime-Cam,
HubbleSpace Telescope /Wide Field Camera 3 (
HST /WFC3),MMT/Hectospec,
Chandra , and GMRT observations. In §
3, we explain detailed steps in our WL analysis, whichinclude member and source selections, point-spread-function (PSF) modeling, shape measurement, and thecluster mass estimation. Discussions including our merg-ing scenarios are presented in § § M ( M ) corresponds tothe total mass enclosed within a radius, inside which themean density is equal to 500 (200) times the critical den-sity of the universe at the cluster redshift z = 0 .
247 inthe adopted cosmology. We assume a flat ΛCDM uni-verse with Ω m = 0 . H = 70 km s − Mpc − , forwhich the plate scale is ∼
232 kpc arcmin − at the clusterredshift. All quoted uncertainties are at the 1 σ ( ∼ . OBSERVATION
Subaru/Suprime-Cam
Subaru/SuprimeCam observations on A521 were con-ducted with V , R , and i (cid:48) on 2001 October 15, withNB816 (narrow band) on 2002 February 15, with z (cid:48) on2002 February 16, and with B and U on 2003 February4. We retrieved the datasets for the V , R , and i (cid:48) filtersfrom SMOKA . The V , R , and i (cid:48) exposure times are 1,800 s,1,620 s, and 2,040 s with the seeings 0 . (cid:48)(cid:48)
59, 0 . (cid:48)(cid:48)
65, and 0 . (cid:48)(cid:48)
59, respectively (hereafter, we refer to i (cid:48) as I for readabil-ity). We note that the previous WL analysis of Okabeet al. (2010) used the I and V images whose exposuretimes are 1,320 s each.We used SDFRED1 (Yagi et al. 2002; Ouchi et al.2004) to perform the initial CCD-level data reduction(i.e. overscan & bias subtraction, bad-pixel masking,flat fielding, distortion correction, and AG probe mask-ing). The next data reduction steps including astromet-ric calibration and image stacking are crucial for con-trolling WL systematics. While Okabe et al. (2010) re-lied on
SDFRED1 for these tasks, we used
SCAMP (Bertin2006) and SWARP (Bertin et al. 2002). Image processingthrough the combination both software tools has beenextensively tested in the WL community (e.g., Jee et al.2013; Finner et al. 2017; Schrabback et al. 2018; Kuijkenet al. 2019). SWARP provides individual
RESAMP images,which we utilize to model the PSF variation for eachCCD and epoch. Since the Subaru/Suprime-Cam PSFis epoch- and CCD-dependent, as is true with all othertelescopes, this per-epoch CCD-level PSF modeling isimportant to address the PSF-induced galaxy shape dis-tortion.Objects were detected by running
SExtractor (Bertin& Arnouts 1996) in dual-image mode and finding at leastfive connected pixels whose rms values are 1.5 times thebackground rms. Since the I image is deepest, we used itas the detection image. Using the same detection imagefor every filter allows us to maintain consistent isophotalareas and object IDs across different filters, which is im-portant for robust color measurement. Throughout thepaper, we use SExtractor ’s MAG ISO to compute objectcolors while
MAG AUTO is employed for the rest.
HST/WFC3 https://smoka.nao.ac.jp Figure 1.
A521 observations with Subaru, GMRT, and
Chandra . We use the Subaru/SuprimeCam I , R , and V images to represent theintensities in red, green, and blue, respectively. Diffuse red and green emissions show the adaptively smoothed Chandra
X-ray and the153 MHz GMRT radio images, respectively. North is up and east is west. We show the central 13 . arcmin region (corresponding to the3 . Mpc physical area at the cluster redshift for the adopted cosmology). The ∼ ∼ A small ( ∼ . (cid:48) × . (cid:48)
1) region of the A521 field was ob-served with
HST /WFC3 during the 2018 April 10-13 pe-riod in F390W, F105W, and F160W with integrationsof 2468 s, 2612 s, and 5223 s, respectively (PROP ID:15435). The observation was done with a single point-ing covering the first and third BCGs (see Figure 1 forthe BCG locations). We retrieved the IR channel data(F105W and F160W) from the MAST and processedthe FLT images following the procedures described in Jeeet al. (2017) and Finner et al. (2020). In brief, we esti-mate shifts between exposures using common astronomi-cal sources while applying the time-dependent geometricdistortion correction. The final mosaic images were cre-ated with an output pixel scale of 0 . (cid:48)(cid:48)
05, the Gaussian“drizzle” kernel, and the pixfrac=0.7 parameter set-ting. We measure galaxy shapes from the F160W imagesince its exposure time is twice as long as that of F105W,which we use only to create a color-composite image.
MMT/Hectospec https://mast.stsci.edu Fiber spectrograph imaging of A521 was completed aspart of a merging cluster program (PI: Finner) with theMMT Hectospec. The observations were conducted onthe nights of 22 and 23 October 2019 under clear skieswith seeing of 0 . (cid:48)(cid:48) . (cid:48)(cid:48)
7, respectively. Hectospec con-sists of 300 fibers within its 1 ◦ diameter field of view. Weutilized the 270 grating (spectral range 3650 - 9200 ˚A)and performed two configurations of three 1200 s inte-grations.Target selection was done with the Subaru data within ∼ (cid:48) of the first BCG and the Pan-STARRS (Tonry et al.2012) DR2 data for the outer region using a V − I colorversus I magnitude diagram. A linear fit was performedto the existing spectroscopically confirmed cluster mem-bers and a region ± .
12 in color and I BCG < I < . xfitfibs softwareto create the two configurations while using caution toavoid fiber collisions. Raw spectra were processed withthe hs pipeline wrap command in HSRED 2.0 to pro-duce sky-subtracted and variance-weighted spectra. Theoutput spectra were then passed through the IDL task hs reduce1d where spectral template comparison was Table 1
MMT Hectospec spectroscopic redshift catalog of the A521 fieldRA Dec z σ z Note . — The catalog is available in its entirety in the electronicversion of this paper. performed and redshifts were determined. To finalizethe catalog, we applied the goodness of fit flag from theMMT pipeline, ‘zwarning’ = 0. Also, we applied a cutto exclude the objects outside of the redshift window,0 . < z <
1. Our spectroscopic redshift catalog fromour MMT/Hectospec observation is shown in Table 1.
Chandra
A521 is one of the clusters that
Chandra observed dur-ing the first cycle (PI: M. Arnaud) with ACIS-I andACIS-S. The exposure time for each instrument is ∼
40 ks.The cluster was re-observed with a total exposure of ∼
90 ks in Cycle 12 using ACIS-I (PI: M. Markevitch).We retrieved both datasets from the
Chandra archive and created a deep (a total exposure of ∼
130 ks) stackfor ACIS-I. We used the csmooth package to adaptivelysmooth (with the minimum and maximum significancesof 3 and 5, respectively) the exposure-uncorrected imageoutput by the merge obs script. The resulting smooth-ing scale map was utilized to apply the same adaptivesmoothing scheme once again to the exposure map. Thefinal adaptive smoothing map was obtained by dividingthe first csmooth output by the second csmooth output.In this paper, we use the
Chandra data only to comparethe spatial distribution of the X-ray emission with thecluster galaxy and mass distributions and perform no in-dependent spectral analysis. Where necessary, we quotespectral measurements found from the literature.
Giant Metrewave Radio Telescope
GMRT observed A521 at 153 MHz in August 2009 withintegration of 10 hours. The reduction and analysis ofthe data were presented in Macario et al. (2013), whokindly provided the final reduced image to us. Read-ers are referred to their paper for details. The authorsreported that after rigorous cleaning the total data losswas ∼ V , R , and I filters representing intensi-ties in blue, green, and red, respectively. Diffuse red and https://cda.harvard.edu green emissions show the adaptively smoothed Chandra
X-ray and the 153 MHz GMRT radio images, respec-tively. ANALYSIS
Spectroscopic Member Selection
We merge the two publicly available spectroscopic cat-alogs of Maurogordato et al. (2000) and Ferrari et al.(2003) with ours obtained from the MMT Hectospec ob-servation of the A521 field. We retrieved 47 objects inthe Maurogordato et al. (2000) study from the SIMBADastronomical database (we find that the column labelsof the SIMBAD catalog are in error at the time of thiswriting and use the column incorrectly labeled as “ra-dial velocity” for cz ). Ferrari et al. (2003) add 191 newobjects, which we downloaded from the VizieR Astro-nomical Server . With MMT/Hectospec, we obtaineda total of 398 spectra whose redshift errors were lessthan 10 − in the A521 field. Out of these 398 spec-tra, 15 objects are in the aforementioned public catalogsand used for cross-checking. The comparison shows thatonly one object has a large discrepancy ( ∼ .
1) and ourMMT/Hectospec measurement reveals that this objectis in fact a cluster member. For these 15 objects, we useour MMT/Hectospec values.MMT/Hectospec covers a large ( ∼ ◦ × ∼ ◦ ) area. Welimit our analysis to the objects located within the r = 2Mpc radius (this roughly corresponds to the virial ra-dius of A521, see § z = 0 . ± . σ D = 1587 ±
176 kms − ,respectively, where the uncertainties are measured frombootstrap resampling. We select 183 objects within∆ z = 0 .
02 (corresponding to ∼ σ D ) from the centralredshift as the A521 member galaxies. Figure 2 displaysthe redshift distribution of galaxies in the A521 field fromthe previous and our observations. Photometric Cluster Member Selection
The spectroscopic members discussed in § I <
21) withreasonable magnitude measurement errors ( σ I < . r h > . V − I colors are requiredto be within 0.15 mag from the best-fit color-magnituderelation while their R − I colors should be within 0.2 magfrom the best-fit color-color relation. Using the criteria,we select 244 galaxies as member candidates, in additionto the spectroscopic members, within the 2 Mpc radiusfrom the first BCG. In Figure 4, we display the locationsof the cluster members and member candidates on theSubaru color-composite image. The luminosity-weighteddensity map shows that A521 consists of three distinc-tive clumps (we denote them as NW, C, and SE in theleft panel of Figure 4), which are approximately colinearalong the NW-SE direction. These substructures alsoappear in the number density map while the NW clumpis somewhat less concentrated. http://simbad.u-strasbg.fr/simbad vizier.u-strasbg.fr Figure 2.
Redshift distribution of galaxies in the A521 field. Wemerge the two publicly available spectroscopic catalogs of Mauro-gordato et al. (2000) and Ferrari et al. (2003) with ours obtainedfrom the MMT/Hectospec observation. The objects observed againare counted as new data. Top: We display the distribution of allsources in the A521 field covered by the large ( ∼ ◦ ) field of viewof the Hectospec instrument. Bottom: Same as the top exceptthat the histogram is constructed using the objects located withinthe 2 Mpc radius from the first BCG. The central vertical dashedline represents the cluster redshift determined by the biweight es-timator (see text). The other two vertical dashed lines mark the∆ z = 0 .
02 interval, with which we define the A521 membership.The total number of the spectroscopic members is 183, includingthe previously confirmed 116 members.
This simple linear structure is in contrast with the pre-vious claim of Ferrari et al. (2003), who identified sevengroups and one “ridge” (see the cyan rectangle in theright panel of Figure 4 for the approximate location ofthe ridge), which together form a cross-like structure. Al-though the “ridge” structure is hinted at by our numberdensity map, the feature is much weaker than the NW-SE linear structure. In § PSF Modeling
Robust PSF modeling is a crucial step for accurateshape measurement. We follow the principal-component-analysis (PCA) method (Jee et al. 2007), which has beenextensively tested in our previous studies. Readers are
Figure 3.
Color-magnitude and color-color relations in the A521field. Top: We display the V − I color versus I magnitude relation.The spectroscopic members occupy a narrow locus. The dashedline is the best-fit relation observed by these spectroscopic memberswith exclusion of some blue members: V − I = − . I + 1 . V − I versus R − I colors are shown. The spectroscopicmembers span a narrow range in V − I color as well. The best-fitrelation between the two colors is given by the equation: R − I =0 . V − I ) + 0 . Table 2
Photometric cluster member selection criteria
Magnitude
I < σ I < . | k − . | < . k < . r h > Note . — We define k and k as k ≡ V − I + 0 . I and k ≡ R − I − . V − I ) − . referred to Jee et al. (2007) for details of the generalalgorithm. Below, we provide a description of the specificprocedure relevant to our Subaru/SuprimeCam and HST analyses.When modeling the Subaru PSF in each CCD expo-sure frame, we use the
RESAMP images output by
SWARP (Bertin 2010). We first selected stars based on the bright-
Figure 4.
Cluster members identified by spectroscopic observation and photometric selection based on the color-magnitude diagram. Thecontours represent the luminosity-weighted (left) and number densities (right). The circles show the confirmed members (yellow), clustermember candidates (red), confirmed foreground galaxies (white), confirmed background galaxies (blue), and confirmed stars (orange). Thecyan rectangle in the right panel marks the approximate location and orientation of the “ridge” feature claimed by Ferrari et al. (2003).The galaxy distributions show that A521 is mainly comprised of the three substructures: NW, C, and SE, although the NW substructureis somewhat less clear in the number density. ness vs. size relation. Each frame contains ∼
100 highS/N stars on average, which are sufficient for modelingthe spatial variation of the PSF with 3rd order polyno-mials discussed below. Then, we combined the postagestamp images of the selected stars and derived the mostsignificant 20 principal components. Each star is decom-posed with these principal components and representedas a weighted sum of them. The weighting factor for the i th principal component ( C i ) is assumed to vary spatiallyas follows: C i ( x, y ) = a + a x + a y + a x + a xy + a y + ... (1)where a jk is the coefficient of the polynomial and we useit up to the 3rd order ( j + k ≤ RESAMP imageswere already calibrated for shifts and rotations, this PSFstacking procedure is straightforward. However, it is stillnecessary to assign proper weights to individual PSFmodels according to the contribution of each frame tothe final image stack.For modeling the
HST
PSF, the direct PCA samplingfrom the science image explained above is not applica-ble because of the small field of view, where we haveonly several high S/N stellar images. Instead, we use atemplate-based approach (Jee et al. 2007) to model thePSF. First, we constructed the PSF library with PCAutilizing archival stellar field data. Then, we selectedstars from the A521 images (individual exposures) basedon the size-magnitude relation. Because the
HST
PSFpattern is related to the telescope focus breathing andthus is repeated approximately following the thermal cy-cle of the instrument, we find the matching template fromthe PSF library based on the stars on the A521 frame.After finishing the exposure-level PSF modeling, we ap-plied shift and rotation so that its contribution to the final mosaic image is properly accounted for. The finalPSF on the mosaic image is the sum of all contributingPSFs from individual exposures.
Source Galaxy Selection
We select source galaxies in two steps, utilizing thecolor-magnitude and color-color diagrams (Figure 3).First, we selected faint (22 < I <
27) galaxies whose V − I colors are within 0 .
35 from the best-fit relation(see the dashed line in the top panel of Figure 3) andexcluded the red-sequence galaxies. Then, we examinedthe excluded objects using the color-color diagram andselected the objects whose colors do not overlap withthose of the cluster member candidates (see the bottompanel of Figure 3). These sources are further required topossess well-defined ellipticities ( σ e < .
25 and e < . b > . ∼
26 arcmin − for Subaru.Our source selection criteria are summarized in Table 3.For the HST data, the F105W and F160W colors arenot optimal to identify and remove cluster members.Therefore, we select sources based on the F160W magni-tude within the 22 < F140W <
27 interval while remov-ing the spectroscopic (Hectospec) and photometric (Sub-aru) members of A521. We also apply the same shapecriteria used for the Subaru WL. The
HST
WFC3-IRimaging data provide a source density of ∼
150 arcmin − ,which enables us to investigate the A521 substructure ingreat detail for the central ∼ . (cid:48) × . (cid:48) Source Shape Measurement
We convolve the elliptical Gaussian galaxy profile withthe model PSF and fit it to the galaxy image using the
MPFIT algorithm for source shape measurement. Theelliptical Gaussian model is composed of seven free pa- http://cars9.uchicago.edu/software/python/mpfit.html Table 3
Source selection criteriaMagnitude 22 < I < σ I < . σ V < V − I > − . | k − . | > . | k − . | < . k > . e < . σ e < . a <
30 pixelSemi-minor axis b > . r h > Note . — See the Table 1 note for the definitions of k and k .s1 criteria is applied to exclude the red sequence galaxies and s2criteria is applied to reexamine the ones excluded by s1. rameters: centroid (x and y), amplitude, background am-plitude, semi-major and -minor axes, and orientation an-gle. Galaxy ellipticities ( e ) are defined as follows: e = a − ba + b , (2) e = e cos 2 θ, (3) e = e sin 2 θ. (4)where θ is the orientation of the semi-major axis, and a and b are the semi-major and -minor axes, respectively.The reduced shear g is obtained by averaging theseindividual ellipticities e as follows: g = (cid:104) e (cid:105) , (5) g = (cid:104) e (cid:105) . (6)However, it has been known that the raw ellipticitymeasurement is a biased estimator of the true shear (e.g.,Mandelbaum et al. 2015). The bias is often characterizedas g true = g est (1+ m )+ c , where m and c are referred to asmultiplicative and additive biases, respectively. Throughour image simulation (Jee et al. 2013), we derived a mul-tiplicative bias of m = 0 .
23 for Subaru shapes and foundthat the additive bias is negligibly small. We conductedshape measurement in all three Subaru filter images ( I , V , and R ) and verified that the resulting lensing sig-nals are consistent. However, the final analysis is carriedout with the I -band image, which has the best qualitiesin both seeing and depth. A similar multiplicative bias m = 0 .
22 is obtained for
HST data (Jee et al. 2017).However, we do not use the
HST data for quantitativeanalysis.
Redshift Estimation of Source Galaxies
A quantitative interpretation of WL analysis requiresus to define critical surface mass density Σ c :Σ c = c πGD l β , (7)where β is the lensing efficiency, c is the speed of light, G is the gravitational constant, and D l is the angulardiameter distance of the cluster. The lensing efficiency β is given by β = (cid:28) max (cid:18) , D ls D s (cid:19)(cid:29) . (8) where D s is the angular diameter distance of sources and D ls is the angular diameter distance of source seen at thecluster redshift.As we cannot obtain reliable redshift information ofindividual source galaxies based on three filters, we esti-mate the β value for the source population by comparingour photometry with the one from a reference photomet-ric redshift catalog. We used the Great ObservatoriesOrigins Deep Survey (GOODS; Giavalisco et al. 2004)photometric redshift catalogs as the reference. By apply-ing the same magnitude and color cuts to the GOODScatalogs, we determine (cid:10) β (cid:11) = 0 .
576 and (cid:10) β (cid:11) = 0 . (cid:10) β (cid:11) = 0 .
577 and (cid:10) β (cid:11) = 0 .
381 from the GOODS north field. The esti-mates from both fields are in an excellent agreement. Thevalue reported in Okabe et al. (2010) is 0.668 and 0.667for their “red+blue” and “faint” objects, respectively,which implies that their sources are at higher redshift onaverage.Because in fact our sources are not located on a singleredshift plane, the reduced shear is biased. To accountfor this, Seitz & Schneider (1997) suggested a calibrationequation as the following: g (cid:48) = (cid:34) (cid:32) (cid:10) β (cid:11) (cid:104) β (cid:105) − (cid:33) κ (cid:35) g (9)where g (cid:48) , g , and κ are the uncorrected reduced shear,corrected reduced shear, and convergence, respectively.With our measurements of (cid:10) β (cid:11) = 0 .
576 and (cid:10) β (cid:11) =0 . g (cid:48) /g ratio becomes 1 + 0 . κ . We apply thiscorrection when estimating the cluster mass. Mass Reconstruction
The relation between convergence ( κ ) and shear ( γ ) isgiven by the following: κ ( x ) = 1 π (cid:90) d x D ∗ ( x − x (cid:48) ) γ ( x (cid:48) ) , (10)where D ∗ ( x ) is the complex conjugate of the kernal D ( x ) = − / ( x − ix ) when the shear γ is expressedby the complex notation γ = γ + iγ . While the pop-ular method of Kaiser & Squires (1993) implements thealgorithm in Fourier space, we use the FIATMAP code (Fis-cher & Tyson 1997), which performs the computation inreal space.The reconstructed mass distribution is overlaid ongalaxy distributions in Figures 5 and 6. Remarkably,the reconstructed mass map closely follows the galaxydistribution, detecting the three substructures discussedin § ∼ . (cid:48) HST
WL mass recon-struction result. Because it has much higher source den-sity ∼
150 arcmin − than the Subaru value ∼
26 arcmin − ,the significance is also much higher. The result showsthat only a single mass peak is present near the C clumpin-between the the first and third BCGs as seen in theSubaru result. Note that the mass distribution is some-what asymmetric. Mass Estimation
Mass Estimation from Tangential Shear
Under the assumption that a cluster consists of a sin-gle halo, one can estimate the total mass of the clusterby fitting an analytic profile to the tangential shear mea-surement. Although we find that A521 is comprised ofmultiple halos, we include the cluster mass obtained inthis way in our presentation of the results in order toenable comparisons with previous studies. However, weremind the reader that our main results are the multi-halo fitting results described in § ∼ . ∼ . r . Using the mass-concentrationrelation from Duffy et al. (2008), we estimate the totalmass of the cluster to be M = 1 . ± . × M (cid:12) .This mass estimate is more than a factor of two higherthan the one from Okabe et al. (2010), who quote M =6 . +1 . − . × M (cid:12) . Mass Estimation from Multi-halo Fitting In § M (cid:12) ≤ M ≤ M (cid:12) and 2 ≤ c ≤
5, respec-tively. The mass estimates ( M ) of the C, NW, and SEclumps are 4 . +0 . − . × M (cid:12) , 2 . +0 . − . × M (cid:12) , and2 . +0 . − . × M (cid:12) , respectively. Assuming the threeclumps are located at the same distance from us, we cansuperimpose the three halos’ density profiles to estimatethe total mass. We find that the r radius (inside which We use h = 0 . M value in Table 8 of Okabeet al. (2010). the mean density of the sphere is 200 times the criticaldensity at the cluster redshift) is r = 2 . +0 . − . Mpc.The resulting mass is M = 13 . +1 . − . × M (cid:12) . Wedid not achieve meaningful constraints on concentrationparameters.Traditionally, mass-concentration relations (e.g., Duffyet al. 2008; Dutton & Macci`o 2014) have been employedto reduce the number of free parameters when NFWhalos are used. The relation represents a mean be-havior for a population of clusters with large scattersin numerical simulations and thus may not be applica-ble to individual clusters. When we select the Duffyet al. (2008) relation, the mass estimates of the C,NW, and SE clumps are M = 5 . +1 . − . × M (cid:12) ,2 . +0 . − . × M (cid:12) , and 2 . +0 . − . × M (cid:12) , respectively,all of which are consistent with the ones derived withoutthe mass-concentration relation. We summarize the massestimates above in Table 4 and 5. DISCUSSION
Mass Comparison with Previous Studies
We determine the total mass of A521 to be M =1 . +0 . − . × M (cid:12) by modeling the system with threehalos. The error bars here only include statistical un-certainties. Considering the various systematic uncer-tainties discussed in Jee et al. (2014), we estimate thatthe total mass uncertainty of A521 would increase up to ∼
20% of the total mass. Nevertheless, our WL mass issignificantly (a factor of two) larger than the WL massestimate M = 6 . +1 . − . × M (cid:12) from Okabe et al.(2010). In their analysis, they treat the A521 system as asingle halo and use tangential shear measurements with-out excluding the shear signal at small radii ( (cid:46) ∼
34% lower than the dy-namical mass estimate M vir = 1 . × M (cid:12) of Ferrariet al. (2003). However, since the authors do not quotean uncertainty of their mass estimate, we cannot eval-uate the significance of the difference. The Planck SZ-based mass estimate (Planck Collaboration et al. 2015) is M yz, = 6 . +0 . − . × M (cid:12) , which is ∼
23 % lower thanour result . Since A521, departing from the dynami-cal equilibrium, consists of multiple clumps, these massestimates based on dynamical and SZ measurements arepotentially biased. Substructure
As mentioned in § Our conversion to M yields M = 8 . +0 . − . × M (cid:12) . Figure 5.
WL mass reconstruction of A521. White contours represent the projected mass density. In the left panel, color-coded is theluminosity-weighted density distribution while in the right panel, color-coded is the cluster galaxy number density. Overall, the massdistribution agrees well with the cluster galaxy distribution. In particular, WL detects the three substructures: C, SE, and NW discussedin Figure 4.
Figure 6.
WL mass map overlaid on color-composite image. Left: Same as Figure 4 except that the Subaru WL mass is overlaid on thecolor-composite image. The yellow square marks the approximate region, where we perform
HST mass reconstruction displayed in the rightpanel. Right: We overlay the
HST
WL mass on the
HST color-composite image. This high-resolution (a factor of six increase in sourcedensity) mass reconstruction shows that the mass distribution in the C clump region is somewhat asymmetric. In addition, the centroidaligns with neither the first nor the third BCGs and is located in-between.
Table 4
Mass estimation and velocity of substructuresClump spec- z number RA Dec ∆ v σ v M (w/o M − c ) M (w/ M − c )[km s − ] [km s − ] [10 M (cid:12) ] [10 M (cid:12) ]C 30 4 h m . s -10 ◦ (cid:48) . (cid:48)(cid:48) ±
258 1390 ±
183 5 . +1 . − . . +0 . − . NW 12 4 h m . s -10 ◦ (cid:48) . (cid:48)(cid:48) -588 ±
379 1256 ±
268 2 . +0 . − . . +0 . − . SE 10 4 h m . s -10 ◦ (cid:48) . (cid:48)(cid:48) -183 ±
265 794 ±
197 2 . +0 . − . . +0 . − . Figure 7.
Tangential shear (green) and cross shear (red) radialmeasurement around the cluster center (BCG 1). The cross shear isconsistent with zero at most of scales within 1 σ error range excepta bin around 3 Mpc. A single NFW profile is fitted to tangentialshear signal of the scale range from 1 Mpc to 3.3 Mpc. The best-fitmass is M = 1 . ± . × M (cid:12) . Table 5
Total mass estimation of A521Halo modeling M [10 M (cid:12) ]One halo with M − c relation 14.8 ± M − c relation 10.4 +0 . − . Multi halo without M − c relation 13 . +1 . − . substructure remains significant in our experiment withbootstrapping and different source selection, although itis difficult to interpret the feature. When we apply asmaller smoothing kernel to the luminosity map, the Cclump is further resolved into two smaller clumps withthe larger of the two centered on the first BCG and theother on the third BCG ( ∼
300 kpc southeast of the firstBCG). This bimodality is consistent with the X-ray fea-tures (see Figures 1 and 9). Our Subaru WL detectedonly a single mass clump between the two X-ray peaks,which is confirmed by our
HST analysis. The
HST
WLresolution is capable of resolving two mass clumps if theyare separated by ∼
300 kpc.We consider two possibilities to resolve this puzzle.One possibility is that there exist two mass clumps whoseseparation is much smaller than our WL resolution. Theother is that the C clump is associated with the north-ern X-ray peak while the southern X-ray peak is linkedto the SE clump. For these two cases, we discuss the cor-responding merging scenarios using our numerical simu-lations in § ± ± ±
197 km s − ,respectively. The velocity dispersions of the NW andSE substructures are difficult to interpret because of thesmall numbers of the used spectroscopic members. The C clump has a high velocity dispersion (based on 30 mem-bers), which corresponds to an extremely high dynam-ical mass estimate (cid:38) . × M (cid:12) (Saro et al. 2013).This value is much higher than our WL mass estimate ∼ × M (cid:12) . One interpretation of this large discrep-ancy is that the velocity dispersion is severely inflatedbecause of the merger. A similarly extreme differenceis reported in Kim et al. (2019), who study A115 withmulti-wavelength data. They find that the WL massesare significantly lower than what the velocity dispersionsimply, attributing the large differences to the on-goingmerger activities.Table 4 lists the relative line-of-sight velocity ∆ v ofeach clump with respect to the mean velocity of the entiresystem. The relative velocities of the three clumps areconsistent with our hypothesis that the merger might behappening nearly in the plane of the sky. Revision of Merging Scenario with NumericalSimulations
One of the crucial prerequisites for a merging sce-nario reconstruction is identification of the subclustersinvolved in the merger. The most common method isto examine the difference between the distributions inthe ICM and cluster galaxies. This approach, however,should be used with caution in A521, which show non-trivial complexity in both cluster constituents.Ferrari et al. (2006) interpreted the Chandra X-raydata as indicating at least two merger events: a pre-merger of the southern main and northern infalling com-ponents and a post-merger along the NE-SW ridge (seeFigure 4 for the location and orientation of the ridge).The post-merger argument is based on the high veloc-ity dispersion and temperature structure of the regionwhereas the pre-merger hypothesis is based on the X-raytail morphology of the northern component and the gascompression feature at the southern edge of the BCG.It is difficult to reconcile the pre-merger scenario ofFerrari et al. (2006) with the position and location of theradio relic. The reality of the radio relic is confirmed byGiacintucci et al. (2008), who with GMRT and VLA ob-servations find that the radio relic has a spectral steepen-ing toward the cluster, which indicates the shock prop-agation (thus the merger) direction. Giacintucci et al.(2008) also report that the
Chandra data show a surfacebrightness jump across the radio relic. Based on XMM-
Newton data, Bourdin et al. (2013) find two X-ray shockfeatures. One coincides with the location of the radiorelic and the other is located at the southwestern edge ofthe X-ray emission.In this study, we revisit the A521 merging scenariosusing our WL mass and galaxy distributions in additionto the previous X-ray and radio relic observations (Fig-ure 9). The comparison between galaxy and mass dis-tributions shows that A521 has the three distinct sub-structures referred to as the SE, C, and NW clumpsin Figure 4. A close inspection on the galaxy distri-bution indicates that the C clump may be further re-solved into two subclumps approximately aligned withthe two X-ray peaks. On the other hand, our WL massmap reveals only a single clump in-between the two X-ray peaks. If this mass clump solely corresponds to thenorthern X-ray peak, the only probable mass clump as-sociated with the southern X-ray peak is the SE clump.1 Figure 8.
Luminosity weighted galaxy contours and spectroscopic members belonging to the NW, C, SE clumps. Left: the color representsrelative velocity of each spectroscopic member with respect to the mean cluster velocity. Right: the NW, C, SE clump members are depictedin orange, green, and blue respectively with each clump’s mean relative velocity (∆ v ) and velocity dispersion ( σ v ). No statistically significantLOS velocity difference is found among the three galaxy groups. Of course, the challenge with this merger scenario is thelarge ( (cid:38) . .Each cluster consists of a dark matter halo and an ICMthat follow the NFW (Navarro et al. 1997) and betaprofiles (Cavaliere & Fusco-Femiano 1976), respectively.Our WL mass (Table 4) is used to setup each halo mass.The simulations are computed with the adaptive meshrefinement code RAMSES (Teyssier 2002) and the clustersare resolved by ∼
100 kpc at the outskirt and ∼ pyXSIM and the mock WL mass map using the projected massdistribution. The position of the merger shock is inferredby identifying a hot ( >
10 keV) region in the cluster out-skirt ( > . head-on collision triggers the merger shock and the mass-gas dissociation. The simulated X-ray map shows theepoch at the first apocenter where the simulated featureis analogous to that of the A521 observation. The re-sult reproduces the large separation between the masspeaks, asymmetric and elongated X-ray emission, andthe close distance between the merger shock and thesouthern mass peak. Nevertheless, the separation be-tween the mass clump and the X-ray peak becomes negli-gibly small at this epoch. This is because the dissociationoccurred during their first passage rapidly diminishes intime. Also, unlike the observation, the northern darkmatter halo leads the ICM peak.Having seen that it is impossible to create a gas-massdissociation as large as ∼ . HST
WL mass map (right panel ofFigure 6). The
HST
WL mass contours show that the Cclump mass distribution is asymmetric with its somewhatcompact mass peak offset relative to the large-scale cen-troid, indicative of the possibility that two halos may besuperposed. This requires an off-axis cluster merger andmodification of the main and sub cluster masses. We as-sume that the C clump is comprised of two halos with themasses of 3.5 × M (cid:12) and 1.5 × M (cid:12) for the mainand sub clusters, respectively. We display this scenario inthe bottom row of Figure 10. The interaction during theoff-axis passage is much weaker than in the case of theprevious head-on collision, and thus the dissociation alsoweakens. In the later phase, the ICM gains angular mo-mentum and overruns the dark halo when it reaches theapocenter (e.g. Sheardown et al. 2018; Lee et al. 2020).2 Figure 9.
GMRT radio at 153MHz (green) and
Chandra
X-ray (red) images overlaid with WL mass map contours (left) and luminositycontours (right). In the central region, while WL detects only one mass clump (the C clump), X-ray observations reveals two peaksbracketing the mass clump. The optical luminosity distribution hints at this bimodality seen in X-ray albeit less prominent. The locationof the radio relic is ∼ Figure 10.
Schematic diagrams and toy simulation results of our two A521 merging scenarios. The first column illustrates the substructureconfiguration of the A521 dark matter and gas at the first passage. Purple circles represent the halos without dark matter-ICM dissociation.In the second and third columns, blue and red circles represent the dark matter and ICM, respectively, while green arcs indicate the mergershocks (radio relics). In the last column, we display the mock
Chandra
ACIS-I X-ray map (red) of a cluster at z = 0 .
25 generated by pyXSIM with the assumption of 100 ks exposure. White contours indicate the projected mass (dark matter plus ICM) with linear spacing. Greencontours marks the locations of the hot outskirt region (
T >
10 keV , r > . CONCLUSION
The clumpy and dynamically active cluster, A521 hasbeen studied extensively in many astrophysical contextsbased on optical, X-ray, and radio observations. The ex-istence of the radio relic and halo in the cluster supportsits post-merger state and provides hints leading to deeperunderstanding of their formation mechanism during themerger. In this study, we revisit the merging scenarioof A521 based on the enhanced member catalog and im-proved WL analysis.Our enhanced cluster member catalog provides a muchhigher S/N galaxy distribution than the previous studyand reveals that A521 is composed of three distinct sub-structures that we refer to as C, NW, and SE. This A521structure is significantly simpler than the previous viewthat the system consists of more than seven substruc-tures. Our WL mass reconstruction is remarkably con-sistent with this simpler view of the system.We find that the total mass of A521 is M =13 . +1 . − . × M (cid:12) , which is twice larger than the pre-vious WL mass estimate. The large discrepancy is at-tributed to the difference in treatment of the substruc-ture. We also estimate the masses of the individualclumps, which are used as a crucial input to our numer-ical simulation.We run numerical simulations for two merging scenar-ios. In one scenario, the SE and C clumps experience ahead-on collision. The simulation reproduces the closedistance between the radio relic and the southeasternmass clump. However, with this scenario it is impossibleto explain the large separation between the SE clumpand the southern X-ray clump. In the other scenario, wehypothesize that the C clump seen in WL is comprisedof two subclumps, as suggested by the high-resolution HST
WL. Our off-axis collision simulation with this as-sumption reproduces the position and the direction ofthe radio relic, the X-ray morphology, and the gas-massoffset. In this case, we are witnessing the onset of thesecond pass-through.
Acknowledgments.
We thank Giulia Macario for shar-ing the reduced GMRT data. M. Yoon acknowledgessupport from the Max Planck Society and the Alexan- der von Humboldt Foundation in the framework of theMax Planck-Humboldt Research Award endowed by theFederal Ministry of Education and Research. M. Yoonalso acknowledges support from the National ResearchFoundation of Korea (NRF) grant funded by the Ko-rea government (MSIT) under no. 2019R1C1C1010942.M. J. Jee acknowledges support for the current re-search from the National Research Foundation of Ko-rea under the program nos. 2017R1A2B2004644 and2017R1A4A1015178. Hectospec observations reportedhere were obtained at the MMT Observatory, a jointfacility of the Smithsonian Institution and the Univer-sity of Arizona. This work was supported by K-GMTScience Program of Korea Astronomy and Space ScienceInstitute. REFERENCES
Arnaud, M., Maurogordato, S., Slezak, E., & Rho, J. 2000, A&A,355, 461Beers, T. C., Flynn, K., & Gebhardt, K. 1990, AJ, 100, 32Bertin, E. 2006, in Astronomical Society of the Pacific ConferenceSeries, Vol. 351, Astronomical Data Analysis Software andSystems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique,112Bertin, E. 2010, SWarp: Resampling and Co-adding FITS ImagesTogether, ascl:1010.068Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393Bertin, E., Mellier, Y., Radovich, M., et al. 2002, in AstronomicalSociety of the Pacific Conference Series, Vol. 281, AstronomicalData Analysis Software and Systems XI, ed. D. A. Bohlender,D. Durand, & T. H. Handley, 228Bourdin, H., Mazzotta, P., Markevitch, M., Giacintucci, S., &Brunetti, G. 2013, The Astrophysical Journal, 764, 82Cavaliere, A., & Fusco-Femiano, R. 1976, A&A, 500, 95Duffy, A. R., Schaye, J., Kay, S. T., & Dalla Vecchia, C. 2008,MNRAS, 390, L64Dutton, A. A., & Macci`o, A. V. 2014, MNRAS, 441, 3359Ferrari, C., Arnaud, M., Ettori, S., Maurogordato, S., & Rho, J.2006, A&A, 446, 417Ferrari, C., Maurogordato, S., Cappi, A., & Benoist, C. 2003,A&A, 399, 813Finner, K., Jee, M. J., Webb, T., et al. 2020, ApJ, 893, 10Finner, K., Jee, M. J., Golovich, N., et al. 2017, ApJ, 851, 46Giacintucci, S., Venturi, T., Macario, G., et al. 2008, A&A, 486,347Giavalisco, M., Ferguson, H. C., Koekemoer, A. M., et al. 2004,ApJ, 600, L93Jee, M. J., Blakeslee, J. P., Sirianni, M., et al. 2007, Publ. Astron.Soc. Pac., 119, 1403Jee, M. J., Hughes, J. P., Menanteau, F., et al. 2014, ApJ, 785, 20Jee, M. J., Ko, J., Perlmutter, S., et al. 2017, ApJ, 847, 117Jee, M. J., Tyson, J. A., Schneider, M. D., et al. 2013, ApJ, 765,74Kim, M., Jee, M. J., Finner, K., et al. 2019, The AstrophysicalJournal, 874, 143Kuijken, K., Heymans, C., Dvornik, A., et al. 2019, A&A, 625, A2Lee, W., Jee, M. J., Kang, H., et al. 2020, ApJ, 894, 60Macario, G., Venturi, T., Intema, H. T., et al. 2013, Astronomy &Astrophysics, 551, A141Mandelbaum, R., Rowe, B., Armstrong, R., et al. 2015, MNRAS,450, 2963Maurogordato, S., Proust, D., Beers, T. C., et al. 2000, A&A,355, 848Mulroy, S. L., Farahi, A., Evrard, A. E., et al. 2019, MNRAS,484, 60Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490,493Okabe, N., Takada, M., Umetsu, K., Futamase, T., & Smith,G. P. 2010, Publications of the Astronomical Society of Japan,62, 811870Ouchi, M., Shimasaku, K., Okamura, S., et al. 2004, ApJ, 611, 660Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2015,A&A, 581, A144