Multi-wavelength Analysis of the Merging Galaxy Cluster A115
Mincheol Kim, M. James Jee, Kyle Finner, Nathan Golovich, David M. Wittman, R. J. van Weeren, W. A. Dawson
DDraft version March 6, 2019
Preprint typeset using L A TEX style emulateapj v. 12/16/11
MULTI-WAVELENGTH ANALYSIS OF THE MERGING GALAXY CLUSTER A115
Mincheol Kim , M. James Jee , Kyle Finner ,Nathan Golovich , David M. Wittman , R. J. van Weeren , W. A. Dawson Draft version March 6, 2019
ABSTRACTA115 is a merging galaxy cluster at z ∼ . ∼ . Chandra , and spectroscopic data from the Keck/DEIMOS and MMT/Hectospecinstruments. Our weak-lensing analysis shows that the cluster is comprised of two subclusters whosemass centroids are in excellent agreement with the two BCG positions ( (cid:46) (cid:48)(cid:48) ). By modeling A115with a superposition of two Navarro-Frenk-White halos, we determine the masses of the northernand southern subclusters to be M = 1 . +0 . − . × M (cid:12) and 3 . +0 . − . × M (cid:12) , respectively.Combining the two halos, we estimate the total cluster mass to be M = 6 . +1 . − . × M (cid:12) at R = 1 . +0 . − . Mpc. These weak-lensing masses are significantly (a factor of 3–10) lower than whatis implied by the X-ray and optical spectroscopic data. We attribute the difference to the gravitationaland hydrodynamic disruption caused by the collision between the two subclusters.
Keywords: gravitational lensing — dark matter — cosmology: observations — galaxies: clusters:individual (A115) — galaxies: high-redshift INTRODUCTIONMerging galaxy clusters are rich in astrophysical pro-cesses. Gravitational interaction distorts the dynami-cal structure of the pre-merger halos. Coulomb inter-action leads, for example, to ram pressure stripping,plasma heating, and shock propagation. If dark mat-ter particles interact non-gravitationally, the merger mayproduce measurable offsets between galaxies and weak-lensing mass peaks (Markevitch et al. 2004; Randall etal. 2008). Therefore, studying merging galaxy clusters indetail with observations and numerical simulations en-ables us to refine our knowledge on these astrophysicalprocesses and possibly probe fundamental physics.However, interpretation of observations of mergingclusters is difficult. They provide only a single snap-shot in the long merger history, which does not providesufficient information to differentiate merging scenarios.Multi-wavelength observations aide in resolving the de-generacy. For example, a presence of radio relics is astrong indication that the intracluster medium (ICM)has already experienced significant Coulomb interactionsand developed shocks (Ferrari et al. 2008; Br¨uggen et al.2011; Vazza et al. 2012; Skillman et al. 2013). The ori-entation and location of the relics provide constraints onthe merger axis. In addition, measurements of the spec-tral index and its steepening enable us to obtain Machnumbers of the shock, which is crucial for inferring thecollision velocity (e.g. Bonafede et al. 2014; Stroe et al.2014; Urdampilleta et al. 2018; Di Gennaro et al. 2018; Yonsei University, Department of Astronomy, Seoul, Korea;[email protected], [email protected] Department of Physics, University of California, Davis, Cali-fornia, USA Lawrence Livermore National Laboratory, 7000 East Av-enue,Livermore, CA 94550, USA Leiden Observatory, Leiden University, P.O. Box 9513, 2300RA Leiden, the Netherlands
Hoang et al. 2018). The morphology of the X-ray emis-sion and its offset with respect to galaxies can help usto estimate the direction of motion of the substructurebecause ICM is subject to ram pressure while galaxiesare effectively collisionless. X-ray temperature maps pro-vide invaluable information on the dynamical state of theICM such as shock-induced heating. Optical and near-IR spectroscopic data reveal exclusive information onthe line-of-sight (LOS) velocity structure of the systemand aide in our estimation of the merger geometry whencombined with other velocity constraints (e.g., Monteiro-Oliveira et al. 2017). Finally, weak-lensing studies informus of the dark matter distribution of the merging systemand allow us to quantify the mass of each merging com-ponent (e.g., Ragozzine et al. 2012; Soucail 2012; Jee etal. 2015, 2016; Finner et al. 2017). Despite the consensusthat merging galaxy clusters are useful astrophysical lab-oratories, the numerical simulation of radio relics is in itsinfancy. The major difficulty is our lack of understand-ing on how merger shocks lead to such powerful accel-eration of electrons to relativistic speeds enabling lumi-nous synchrotron emission. Because shocks alone cannotachieve such high efficiency, currently the so-called re-acceleration model is receiving a growing attention (e.g.,Kang & Ryu 2011; Kang et al. 2012; Pinzke et al. 2013;Kang & Ryu 2015). That is, existing fossil electronsseeded by nearby active galactic nuclei or radio galaxiesare re-accelerated to relativistic speeds by ICM shockstriggered by cluster mergers. To date, there are only afew merging systems that show direct evidence for thisre-acceleration scenario (e.g. Bonafede et al. 2014; vanWeeren et al. 2017).In this paper, we present a multi-wavelength studyof Abell 115 (hereafter A115), one of the few systemsthat have been considered as a test case to constrainthe origin of the shock-relic connection with the re-acceleration model. In general, it is believed that a radio a r X i v : . [ a s t r o - ph . C O ] M a r Kim et al. (2018) relic becomes observable when a merger happens nearlyin the plane of the sky under the hypothesis that themerger shock propagates as a form of shallow sphericalshell along the merger axis (e.g., Golovich et al. 2017).A115 is an X-ray luminous cluster with a distinct binarymorphology (Forman et al. 1981). The northern X-raypeak (hereafter A115N) hosts a cool core and is muchbrighter in X-ray emission than the southern peak (here-after A115S). The asymmetric X-ray morphology and itstrailing feature indicate that A115N is moving south-west and the gas is being stripped. A115S, separated by ∼
900 kpc from A115N, is hotter but less bright in X-ray.Similarly to A115N, the disturbed X-ray morphology ofA115S has been attributed to its motion to the north-east. Thus, one quick interpretation of the X-ray obser-vation and the presence of the radio relic is that A115is a post-merger binary cluster with the two subclustersorbiting around each other nearly on the plane of thesky. However, many lines of evidence suggest that A115is a much more complex system than this simplistic pic-ture. Based on their 88 spectroscopic members, Barrenaet al. (2007) claim that the line of sight (LOS) veloc-ity difference between A115N and A115S is very large( ∼ − ), exceeding the system’s global velocitydispersion ( ∼ − ). This alone suggests that thehigh-speed bulk motion along the LOS direction mightbe an important factor to consider in our reconstructionof the merging scenario. Using the Very Large Array(VLA) telescope at 1.4 GHz, Govoni et al. (2001) con-firm the presence of the radio relic in A115, whose exis-tence was initially hinted at by the earlier all sky radiosurvey (Condon et al. 1998). If we accept the belief thatradio relics become detectable when the merger happensnearly in the plane of the sky, the reconciliation of thelarge LOS velocity with the presence of the radio relicwould require an unusually large transverse velocity.Another puzzling aspect of A115 is a large difference inthe mass measurements reported in the literature (e.g.,Govoni et al. 2001; Barrena et al. 2007; Okabe et al. 2010;Oguri et al. 2010; Lidman et al. 2012; Sif´on et al. 2015).Although in general it is challenging to determine exactmasses for merging clusters possessing complicated sub-structures, the A115 mass discrepancy is nearly an orderof magnitude in some extreme cases. Given the poten-tial of A115 to enhance our understanding of the plasmaphysics in cluster mergers, one high-priority task is toobtain the accurate mass of each substructure, as wellas the global mass of the system. This mass informationis essential when one attempts to perform a numericalsimulation of the cluster merger with high accuracy.Our multi-wavelength study of A115 has several ob-jectives. First, we determine the accurate mass of A115with weak lensing (WL). Although there are several WLstudies of the system in the literature, our analysis differsin several aspects. Pedersen & Dahle (2007),Okabe et al.(2010), and Oguri et al. (2010) present only a global massof A115 without addressing the substructures. The sub-structure mass estimate is a crucial input to numericalsimulations. In addition, the global mass estimate itselfis subject to bias when one regards the merging systemas a single halo. Hoekstra et al. (2012) treat A115N andA115S separately and estimate individual masses. How-ever, each mass estimate is obtained without subtracting the contribution from the other substructure. In gen-eral, this omission leads to overestimation of the mass.Second, we reconstruct an accurate WL mass map andprovide careful statistical analysis of the mass peak po-sitions with respect to the ICM and optical luminositypeaks. Among the previous WL studies of A115, onlyOkabe et al. (2010) present a WL mass map. Interest-ingly, their mass peaks possess large offsets with respectto the corresponding brightest cluster galaxies (BCGs).However, since no remark on the centroid uncertaintyis present, it is impossible to interpret the result quan-titatively. Third, we revisit the dynamical analysis ofA115 with our new spectroscopic catalog. Because ournew catalog (266) contains more than a factor of 3 timesthe spectroscopic cluster members of the one (88) usedby Barrena et al. (2007), the overall gain in statisticalpower is substantial. In particular, we re-examine thelarge LOS velocity difference between A115N and A115Sclaimed by Barrena et al. (2007). We also compare clus-ter mass estimates based on improved velocity disper-sion measurements. Fourth, we provide mass estimatesusing deep (360 ks) Chandra data. Early
Chandra stud-ies are mostly based on relatively short exposure data.The latest study (Hallman et al. 2018) utilized all ex-isting
Chandra data to provide a high-quality tempera-ture map. However, the study did not present a repre-sentative temperature measurement for each X-ray peakand no mass estimate was given. Finally, we present anew merging scenario of A115 consistent with our multi-wavelength data.Our paper is structured as follows. § § § § § H = 70 kms − Mpc − , Ω m = 0.3, and Ω Λ = 0.7. At the redshiftof A115, z = 0 . ∼ .
21 kpc (cid:48)(cid:48)− . M c is defined as the mass enclosed by a sphere insidewhich the average density equals to 200 times the criticaldensity at the cluster redshift. We use the AB magnitudesystem throughout. OBSERVATION AND DATA REDUCTION2.1.
Subaru/Suprime-Cam Data
A115 was observed using the Subaru/SuprimeCam on2003 September 25 and 2005 October 3. We retrievedthe V - and i (cid:48) -band archival data from SMOKA . The totalintegrations are 1,530 s and 2,100 s for the V and i (cid:48) filters, respectively. The seeings of the V and i (cid:48) filtersare FWHM = 0 . (cid:48)(cid:48) and 0 . (cid:48)(cid:48) , respectively. Note thatthe V -band dataset used in Okabe et al. (2010) is a subset(the total integration was 540 s) of the one used in thecurrent study whereas their i (cid:48) -band dataset is identicalto ours.The basic CCD processing (overscan subtraction, biascorrection, flat-fielding, initial geometric distortion cor-rection, etc.) was carried out with the SDFRED1 (Yagi https://smoka.nao.ac.jp/ eak-lensing Study of A115 h m s s m s s ◦ RA (J2000) D e c ( J ) RadioX-ray
500 kpc~2.5 arcmin
Figure 1.
Color composite image of A115. Subaru/Suprime-Cam V , V + i (cid:48) , and i (cid:48) filter images represent the intensities in blue, green, andred, respectively. Overlaid are the Chandra
X-ray emission reduced in the current paper and the VLA radio images provided by Botteonet al. (2016). The X-ray emission shows that A115 is comprised of two subclusters. The ∼ . et al. 2002; Ouchi et al. 2004) pipeline. We performedthe rest of the imaging data reduction using our WLpipeline, which incorporates the SCAMP , SExtractor ,and SWARP packages.We utilized the SDSS-DR9 (Ahn et al. 2012) catalog torefine astrometric accuracy with SCAMP . A deep mosaicstack was produced in two steps. A median mosaic imagewas generated with
SWARP using the alignment informa-tion output by
SCAMP . This median-stacking algorithmenables us to remove cosmic rays, some bleeding trails,and some CCD glitch features. However, in terms of S/N,this median-stacking result is not optimal. The final sci-ence image was created by weight-averaging individual frames, where we flagged the aforementioned, unwantedfeatures by performing 3 σ clipping based on the medianimage generated in the first step.We ran SExtractor in dual-image mode, which takestwo images as input and uses one for detection and theother for measurement. Our detection image was cre-ated by weight-averaging the V - and i (cid:48) -band mosaic im-ages. This dual-image mode allows us to obtain identicalisophotal apertures between the two filters based on thecommon detection image, which is deeper than either ofthe two images alone. These identical isophotal aper-tures are needed to obtain accurate object colors. Pho-tometric zeropoints were determined by using the SDSSData Release 13 catalog that overlaps the cluster field.Because the SDSS-DR13 does not include the Johnson V -band, we performed a photometric transformation us- Kim et al. (2018) ing the following relation (Jester et al. 2005): V Johnson = g SDSS − . g SDSS − r SDSS ) − . . (1)We employed isophotal magnitudes ( MAG ISO ) to esti-mate object colors, whereas total magnitude (
MAG AUTO )was used to compute object luminosities.2.2.
Chandra Data
We retrieved the
Chandra data (ObsID: 3233, 13458,13459, 15578, and 15581) for A115 from the
Chandra archive . The ObsID 3233 dataset was taken in 2002,while the other four were taken in 2012 November. Allobservations were carried out with the ACIS-I detectorin VFAINT mode with total exposure time ∼
360 ks. Wereduced the
Chandra data using the
CIAO
CALDB merge obs script.We created a broadband image by selecting the eventswithin the energy range 0.5-7 keV with a 2 pixel × to produce an exposure-correctedimage. In Figure 1 this exposure-corrected image is over-layed with the VLA radio emission on our Subaru color-composite image.In preparation for X-ray temperature measurement,we performed our initial data reduction using the chandra repro script. The chandra repro script auto-mates the instrument-dependent sensitivity corrections,Charge Transfer Inefficiency (CTI) corrections, and re-moval of bad pixels and cosmic rays. The reduced datawere reprojected to a common tangent plane using the reproject obs script. We masked out the point sourcesthat are detected by the wavdetect script. We then con-structed a lightcurve and identified background flares asdetections that are 3 σ outliers. The flares were removedusing the deflare script. WEAK-LENSING ANALYSIS3.1.
Shear Measurement
Our WL pipeline has been applied to a number ofground- and space-based imaging data (e.g., Jee et al.2013; Finner et al. 2017) and its variant has been vali-dated in the most recent public shear testing program(Mandelbaum et al. 2015). Readers are referred toFinner et al. (2017) for details. Here we present a briefsummary of our PSF model and ellipticity measurement.3.1.1.
PSF Modeling
Point spread function (PSF) modeling is a crucial stepin a WL study. Unless corrected for, the PSF not onlydilutes the lensing signal, but also induces a distortionmimicking WL. In this study, we use the principal com-ponent analysis (PCA) approach (Jee et al. 2007; Jee &Tyson 2011).The observed PSF at a specific location on the mo-saic is a combination of the PSFs from all contributingframes. Thus, to properly consider each component, we http://cxc.harvard.edu/cda/ The exposure map is an image of the effective area at eachsky position and accounts for the effects of dither motion. modeled the PSF for each contributing frame and thenstacked them to a final PSF model.One way to examine the fidelity of the PSF model isto compare the ellipticity pattern of the mosaic fieldsbetween observation and model as shown in Figure 2.The left panel shows the ellipticity pattern of the ob-served stars and the right panel shows the pattern re-constructed by our PSF model. For the V filter (top),both magnitude and direction of the PSFs across themosaic field are closely reproduced. The mean residualrms is (cid:10) δe (cid:11) / ∼ .
014 per ellipticity component. Thegood agreement demonstrates that the PCA-based PSFmodel is robust. Also, it demonstrates that the image co-adding alignment is performed with high fidelity; even asubpixel-level misalignment would manifest itself as a no-ticeable PSF ellipticity pattern in the co-add image (leftpanel), which however could not be reproduced by themodel (right panel) that assumes a perfect alignment.For the i (cid:48) filter (bottom), we could not make the modelPSF ellipticity pattern match the observed pattern as ac-curately as in the case of the V filter. The mean residualrms in this case is (cid:10) δe (cid:11) / ∼ . V -bandimage, for which our PSF model is more accurate. Anadditional merit from using the V -band data rather thanthe i (cid:48) -filter is its smaller PSF ( ∼
11% smaller on average).Given the same PSF model accuracy, smaller PSFs pro-vide more reliable shapes for fainter and smaller galaxies,which have higher chances of being background and thusdominate WL signals.3.1.2.
Ellipticity Measurement
We fit a PSF-convolved elliptical Gaussian to a galaxyimage to determine its two ellipticity components e and e , which we define as e = e cos 2 θ,e = e sin 2 θ,e = a − ba + b (2)where a and b are the semi-major and semi-minor axes ofthe best-fit elliptical Gaussian, respectively, and θ is theposition angle of the semi-major axis. Since the ellipticalGaussian is convolved with a model PSF when fitted tothe galaxy image, the resulting ellipticity is corrected forPSF systematics.The elliptical Gaussian profile contains seven free pa-rameters: normalization, two parameters for centroid,semi-major axis, semi-minor axis, position angle, andbackground level. We fixed the centroid and backgroundlevel using the SExtractor outputs
X IMAGE , Y IMAGE ,and
BACKGROUND , respectively. This reduces the numberof free parameters to four, which improves convergencefor faint sources. We used the χ minimization code MPFIT to fit the model to the galaxy image and esti-mate the ellipticity uncertainty.In general, this raw ellipticity is a biased measure ofthe true shear for a number of reasons (e.g., Mandelbaum ∼ craigm/idl/fitting.html eak-lensing Study of A115 Figure 2.
Comparison between the observed and model PSFs. The length of the stick represents the magnitude of the star/PSF ellipticitywhile the orientation shows the direction of elongation. The observed PSF ellipticities are measured from the star images in our coaddimage. The model PSFs are created by stacking all contributing PSFs (modeled with PCA) from individual exposures. Top: For the V -filter, the position-dependent ellipticity variation of the model PSFs closely matches that of the observed stars, which indicates that ourmodel is a robust representation of the observed PSF ( (cid:10) δe (cid:11) / ∼ . i (cid:48) -filter, the agreement between model andobservation is not as accurate as the one for the V -filter ( (cid:10) δe (cid:11) / ∼ . et al. 2015). The bias is often expressed as γ = (1 + m γ ) e + m β , where m γ and m β are often referred to as“multiplicative” and “additive” biases, respectively. Wefind that although the additive bias is negligible for ourWL pipeline, the multiplicative bias is not (Jee et al.2013). From our image simulation, we determine m γ =0 .
15 for our source population. This multiplicative factoris applied to our ellipticity catalog. 3.2.
Source Selection
Only light from galaxies located at a greater distancethan the cluster is lensed by the gravitational potentialof the cluster. Ideally, one can use a photometric red-shift technique to enable efficient selection of backgroundgalaxies. However, this is not feasible in our case, whereonly two broadband filters are available. Therefore, inthe current study we used a color-magnitude relation to
Kim et al. (2018) select source galaxies.Figure 3 shows the color-magnitude diagram (CMD)of the A115 field. It is clear that a majority of the early-type galaxies of A115 show a tight color-magnitude rela-tion. We selected galaxies that are bluer and fainter thanthis red-sequence to minimize the contamination of oursource catalog by cluster galaxies. This selection schemeis based on the general trend that more distant galaxiesare bluer and fainter than the cluster red sequence at z ∼ .
2. Obviously, this trend is only roughly true andthus some fraction of the sources defined in this way arenot behind the cluster. We estimated this fraction in oursource redshift estimation ( § b is smaller than 0.3 pixels were discarded be-cause they are usually indistinguishable from stars. Werequire that the ellipticity error is below 0.25. This re-moves not only low S/N objects, but also point sources,which tend to have large ellipticity errors (in principle,stars should have no shape after PSF deconvolution).Many spurious sources are removed by the above ellip-ticity error and size conditions. As a further measure, wediscarded sources whose ellipticities are greater than 0.9because they are in general too elongated to be a galaxy.The last selection criteria that we applied is an MPFITSTATUS = 1 (a good fit).After all selection criteria were applied, some spuriousobjects still survived. These objects mostly appear ondiffraction spikes and reflection rings from bright stars.We removed the spurious objects by visual inspection.These spurious features are particularly important nearA115N where a bright star with diffraction spikes is lo-cated ∼ (cid:48) west. Our final source catalog has ∼ ∼
600 arcmin area. The resulting sourcedensity ∼
24 arcmin − is a factor of two larger than theone used in Okabe et al. (2010). We summarize oursource selection criteria in Table 1. Table 1
Source Selection CriteriaMagnitude 21 . < V < . − < V − i < . e < . σ e < . a < b > . f < s = 1 Redshift Estimation of Source Population
Quantitative interpretation of a lensing signal requiresinformation on the redshift distribution of the sourcepopulation. The observed shears that are extracted fromthe source galaxies are expressed in units of the criticalsurface density Σ c defined asΣ c = c πGD l β , (3)where c is the speed of light, G is the gravitational con-stant, D l is the angular diameter distance of the lens, Figure 3.
Color-magnitude relation in the A115 field. Galacticdust reddening has been corrected for using Schlegel et al. (1998).Red-sequence galaxies show a tight color-magnitude relation. Redcircles are spectroscopically confirmed cluster members and greencircles are photometric member candidates based on the color-magnitude relation and our visual inspection of the galaxy mor-phology of each object. The green parallelogram depicts the colorand magnitude selection criteria for the selection of photometricmember candidates. Blue circles are the galaxies that populateour source catalog, as selected by the criteria in Table 1. Bothspectroscopic members and photometric candidates are utilized toestimate the number and luminosity density of the cluster. Onlyspectroscopic members are used for the dynamical mass estimation. and β is the lensing efficiency. The lensing efficiency isgiven by β = (cid:28) max (cid:18) , D ls D s (cid:19)(cid:29) , (4)where D s and D ls are the angular diameter distancesto the cluster and from cluster to source galaxy, respec-tively. Note that objects with negative β values are as-signed a zero value because foreground sources do notcontribute to the lensing signal regardless of their red-shifts. Since we do not have photometric redshifts forindividual galaxies, we evaluated β for the source popu-lation statistically using a control field. This requires theassumption that the statistical properties of the controlfield are similar to those of the A115 field. One may beconcerned that this assumption might be invalid when wecompare two small fields because of the sample variance.Jee et al. (2014) investigated the issue in their mass esti-mation of the galaxy cluster ACT-CL J01024915. Theyfound that even for their 6 (cid:48) × (cid:48) field the effect of the sam-ple variance is small, responsible for only ∼
4% shift inmass. This is mainly because the image is deep and thusproduces a large redshift baseline for the source galaxydistribution. In the current study, where the field is muchlarger with a comparable depth, we expect that the sam-ple variance is also sub-dominant.We chose the Great Observations Origins Deep SurveySouth (GOODS-S; Giavalisco et al. 2004) data as ourcontrol field and utilized the photometric redshift cat-alog of Dahlen et al. (2010). After applying the samecolor and magnitude selection criteria (Table 1) on theGOODS-S catalog, we compared its magnitude distribu-tion (red bins) with that in the source population (bluebins), as shown in the top panel of Figure 4. Since theGOODS-S images are deeper, and its galaxies are better eak-lensing Study of A115 i (cid:48) (cid:38)
25. Toaccount for this difference, we weighted the redshift dis-tribution of the GOODS-S catalog for each magnitudebin by the number density ratio of our source catalog tothe GOODS-S catalog (see the bottom panel of Figure 4).With the GOODS-S conformed to our source catalog, wemeasured the average lensing efficiency by Equation 4.The lensing efficiency obtained in this way is β = 0 . z eff = 0 . β value is similar to the estimate β = 0 .
701 reportedin Okabe et al. (2010), whose source shape measurementis based on a 1500s i (cid:48) -band image. The assumption thatall sources are located at this single redshift causes bias incluster mass estimation (as discussed in Seitz & Schnei-der 1997; Hoekstra et al. 2000). To correct for this bias,we applied the following correction to the observed shear: g (cid:48) = (cid:34) (cid:32) (cid:10) β (cid:11) (cid:104) β (cid:105) − (cid:33) κ (cid:35) g = (1 + 0 . κ ) g, (5)where (cid:104) β (cid:105) ∼ . Hubble Space Telescope
WLanalysis, Jee et al. (2014) compared the magnitude dis-tribution of the sources in A520 at z (cid:39) . RESULTS4.1.
Mass Reconstruction
The shapes of lensed galaxy images are sheared by asmall amount, which is typically a tiny fraction of theintrinsic shape noise. Thus, measurement of these shearsrequires averaging over a large sample of backgroundgalaxies. The “whisker plot” in Figure 6 shows the shearin the A115 field obtained by averaging over the back-ground galaxy ellipticities. Each whisker in the 20 × r = 80 (cid:48)(cid:48) .
21 22 23 24 25 26 27
Magnitude N / a r c m i n GOODS-SAbell115
Redshift N / a r c m i n <β> = 0.72 <β > = 0.57
Estimation of the effective redshift for our source pop-ulation. We utilized the GOODS-S photometric redshift catalog(Dahlen et al. 2010) as our control field. The top panel comparesthe magnitude distributions between our sources and the GOODS-S galaxies after application of the same source selection criteria.The density of the GOODS-S galaxies is higher because of thedifference in depth and de-blending resolution. The GOODS-Sgalaxies were weighted by the ratio of our source density to thecontrol field density when we estimate the effective redshift of oursource population. The bottom panel shows the resulting redshiftdistribution before (blue) and after (red) this weighting.
Radius (kpc) S o u r c e D e n s i t y ( / a r c m i n ) Global CenterNorthern CenterSouthern Center
Figure 5.
Source density profile as a function of projected dis-tance from each cluster center. The profiles are centered on theglobal center (black), northern cluster (blue), and southern cluster(red). Dashed line indicates the mean source density of the clusterfield. No significant excess at small radii is found.
The shear γ can be converted to the surface mass den-sity κ (convergence) map using the following relation(Kaiser & Squires 1993, hereafter KS93): κ ( x ) = 1 π (cid:90) D ∗ ( x − x (cid:48) ) γ ( x (cid:48) ) d x , (6)where D ( x ) = − / ( x − ix ) is the transformation ker-nel. A number of algorithms exist for this γ -to- κ conver-sion in the literature.In this study, we used the maximum entropy maxi-mum likelihood method (MAXENT) described in Jee etal. (2007) for our mass reconstruction. The MAXENTmethod utilizes the “entropy” of the pixels to regularizethe mass map. This enables us to reveal high-resolutionfeatures where the S/N is high while it reduces the noise Kim et al. (2018) by applying large smoothing kernels in the low S/N re-gion such as field boundaries. Color-coded in Figure 6is the resulting κ map, which presents two prominentmass peaks. When we used the traditional KS93 inver-sion method, we recovered similar features near the masspeaks with a FWHM ∼ (cid:48)(cid:48) Gaussian kernel. The κ con-tours are overlayed on the Subaru color-composite imagein Figure 7, where we see an excellent spatial agreementbetween both the two BCGs and the mass peaks ( (cid:46) (cid:48)(cid:48) ,32 kpc); the two mass peaks also coincide with the two X-ray peaks (Figure 8). Our bootstrapping analysis basedon the KS93 reconstruction (see § σ and 3.6 σ , respectively, and the twomass centroids are highly consistent with the BCGs. h m s s m s s ◦ RA (J2000) D e c ( J ) Figure 6. “Whisker” plot over convergence map. Each whiskeris the reduced shear determined by averaging over the backgroundgalaxy ellipticity within an r = 80” circle. Green star markersindicate the position of each BCG. The length and orientation ofeach whisker indicate the magnitude and direction of the reducedshear, respectively. The reduced shear tends to be tangentiallyaligned around the mass peak and decreases with the distance fromthe mass center. The convergence (color-coded) was reconstructedusing the maximum-entropy-maximum-likelihood method (Jee etal. 2007). The mass map clearly reveals the bimodal structure ofA115. Weak-lensing Mass Estimation
Many WL studies estimate galaxy cluster masses,based on the assumption that they are comprised of asingle halo. However, this assumption can lead to non-negligible mass bias if substructures’ masses are com-parable, as in the case of A115. In this study, ourmain results were obtained by simultaneously fitting twoNavarro Frenk-White (NFW; Navarro et al. 1997) haloprofiles to A115N and A115S. The NFW shear modelderived in Wright & Brainerd (2000) was adopted. How-ever, we also present the results from one-dimensional(azimuthally averaged) profile fitting centered on eachsubstructure for comparison. This enables us to assessthe amount of bias that would have been introduced ifonly the one-halo fitting method had been used. Also,the comparison provides a sanity check for the two halo fitting method, which is numerically less stable and re-quires more complicated procedure.4.2.1.
One-dimensional Profile Fitting
The first step in one-dimensional profile fitting isthe construction of the azimuthally-averaged tangentialshear profile as a function of radius. Tangential shear isdefined as g T = − g cos 2 φ − g sin 2 φ, (7)where φ is the position angle of the source with respectto the subcluster center, and g and g are the two com-ponents of the calibrated ellipticity. Figure 9 shows thethree tangential shear profiles when the center is placedat the global, A115N, and A115S centers. For the twosubclusters, we chose the BCG locations as their cen-ters since the centroids of the three cluster constituents(BCG, X-ray emission, and WL mass) agree nicely. Weadopted the mean of the two subcluster peaks as theglobal center. If our weak-lensing resolution had beenpoorer (e.g., if the number density of sources had beenless than 10 arcmin − ), we would have detected only asingle mass clump centered near this middle point.In Figure 9, weak-lensing signals are clearly detectedin all three cases nearly out to the field boundary ( r ∼ (cid:48)(cid:48) ). The consistency of the cross shears (obtained byrotating the position angle by 45 ◦ ) with zero indicatesthat no significant B-modes are present in our analysis.It is a common practice to discard signals at small radiiin model fitting because of a number of issues. First, theweak-lensing assumption is violated near the cluster cen-ter. Since galaxy images are sheared non-linearly, themeasurement performed without any correction can leadto cluster mass bias. Second, cluster member contami-nation is highest near the center, which can suppress thelensing signal. Third, the shape of the profile at smallradii is sensitive to the choice of the center and the truecenter is unknown. Fourth, we expect baryonic effects tobe non-negligible in the central region, which can makethe actual profile differ from the NFW one. Currently,no consensus exists for the choice of a cuttoff radius ex-cept that it should increase with halo mass. We chose r cut = 50 (cid:48)(cid:48) when the center was placed on each subclus-ter while this threshold was increased to r cut = 200 (cid:48)(cid:48) for the global mass estimation. This increase is neededto reduce the impact of the cluster substructures on thetangential shear profile; the projected distance from theglobal center to a subcluster is ∼ (cid:48)(cid:48) . We also excludethe tangential shears at large radii if the measurementscome from incomplete annuli.We used the mass-concentration relation from Dutton& Macci`o (2014) to characterize our NFW halo. Fromour one-dimensional NFW fitting, we determine themasses of A115N and A115S to be M c = 1 . +0 . − . × M (cid:12) and 3 . +0 . − . × M (cid:12) , respectively. The globalmass is estimated to be 6 . +2 . − . × M (cid:12) (Table 2).Consistent masses are obtained when we assume a singu-lar isothermal sphere (SIS) instead (Table 3). We usedthese SIS fitting results to evaluate inferred velocity dis-persions. The reduced χ values show that both modelsdescribe the observed profiles reasonably well and thereis no significant indication that one model is preferredover the other. eak-lensing Study of A115 h m s s m s s
26 27 RA (J2000) D e c ( J ) . . . . . . . . . . . . Luminosity PeakNumber Density Peak
Figure 7.
Mass reconstruction over color composite. The northern and southern mass clumps are detected at a significance of 3.8 σ and3.6 σ , respectively. The two mass centroids are in excellent agreement with the locations of the two BCGs. Table 2
1D NFW Profile Fitting Result R c (Mpc) M c ( × M (cid:12) ) χ red Global 1 . +0 . − . . +2 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . Table 3
1D SIS Profile Fitting Result σ v (km s − ) R c (Mpc) M c ( × M (cid:12) ) χ red Global 922 +72 − . +0 . − . . +1 . − . +54 − . +0 . − . . +0 . − . +42 − . +0 . − . . +0 . − . Two-dimensional Simultaneous Profile Fitting withTwo Halos
The results presented in § § Chandra
X-ray peaks, and the BCGpositions agree excellently, it is unlikely that this cen-troid choice leads to any significant mass estimate bias.We model both halos with NFW profiles using the mass-0
Kim et al. (2018) h m s s m s s ◦ RA (J2000) D e c ( J )
500 kpc~2.5 arcmin . . . . . . . . . . . . Figure 8.
Exposure-corrected
Chandra
X-ray image overlaid with convergence contours. The image was adaptively smoothed and pointsources are removed. Each mass peak agrees nicely with the corresponding X-ray peak. concentration of Dutton & Macci`o (2014) and determinethe expected shear at every source galaxy position basedon the combined contribution from the halos. Our log-likelihood is given as L = (cid:88) i (cid:88) s =1 , [ g ms ( M A N , M A S , x i , y i ) − g os ( x i , y i )] σ SN + σ e , (8)where g ms ( g os ) is the s th component of the predicted (ob-served) reduced shear at the i th galaxy position ( x i , y i )as a function of the two clusters’ masses M A N and M A S . The ellipticity dispersion (shape noise) is σ SN = 0 .
25 whereas σ e is the ellipticity measurementnoise of each object. Note that the evaluation of thislikelihood function does not require source galaxy bin-ning.We used the Markov-Chain-Monte-Carlo (MCMC)method to sample this likelihood. We display the result- ing parameter contours in Figure 10 and list the best-fitparameters in Table 4. One may expect a degeneracybetween the two parameters to exist to some extent be-cause the two masses can trade with each other with-out significantly affecting the global goodness-of-the-fit.However, we find that the degeneracy is weak, which isattributed to the large distance ( ∼
900 kpc) between thetwo subclusters. The masses for A115N and A115S are M c = 1 . +0 . − . × M (cid:12) and 3 . +0 . − . × M (cid:12) ,respectively. These masses are consistent with our one-dimensional fitting results, although the decrease in thecentral value is in line with our expectation.The total mass of A115 is not a simple sum of the twomasses of A115N and A115S if we maintain a consistentscheme in defining halo masses (i.e., a mass containedwithin a spherical volume as defined in § M c mass, we need to determine R c for the total system, which requires the two following as- eak-lensing Study of A115 R e d u c e d t a n g e n t i a l s h e a r Inferred velocity dispersion (SIS) = +72 − km s − Global
SIS, χ red =0 . , R =1 . +0 . − . Mpc, M =5 . +1 . − . × M fl NFW, χ red =0 . , R =1 . +0 . − . Mpc, M =6 . +2 . − . × M fl Radius (arcsec) N u m b e r R e d u c e d t a n g e n t i a l s h e a r Inferred velocity dispersion (SIS) = +54 − km s − North
SIS, χ red =0 . , R =0 . +0 . − . Mpc, M =1 . +0 . − . × M fl NFW, χ red =0 . , R =1 . +0 . − . Mpc, M =1 . +0 . − . × M fl Radius (arcsec) N u m b e r R e d u c e d t a n g e n t i a l s h e a r Inferred velocity dispersion (SIS) = +42 − km s − South
SIS, χ red =0 . , R =1 . +0 . − . Mpc, M =2 . +0 . − . × M fl NFW, χ red =0 . , R =1 . +0 . − . Mpc, M =3 . +0 . − . × M fl Radius (arcsec) N u m b e r Figure 9.
Reduced tangential shear profiles of A115. Black circles represent the azimuthally averaged tangential shear in each annulus.Gray circles show the cross shear and should be consistent with zero, as shown, when WL systematics are negligible. Solid and dashed linesindicate the best-fit NFW and SIS models, respectively. Vertical dotted lines denote the minimum and maximum radii between which weinclude the data for fitting. See text for descriptions on our center choices and criteria for the minimum and maximum radii. Kim et al. (2018) sumptions. First, we assume that the two subclustersare merging on the plane of the sky. This allows us toadopt the projected distance as the physical separationbetween A115N and A115S. Since our analysis ( §
5) favorsthe scenario wherein the merger is happening nearly inthe plane of the sky, we believe that this assumption doesnot greatly depart from the truth. Second, we assumethat the system’s global center is located at the geometricmean of the two subclusters. One may argue that a bet-ter choice would be the barycenter. However, our anal-ysis shows that this change causes a less than 10% shiftin the total mass. We populate a three-dimensional gridwith the sum of two densities based on the NFW param-eters of both clusters. The R c value is determined bylocating the radius of the spherical volume, inside whichthe mean density becomes 200 times the critical densityof the universe at the cluster redshift. The total massobtained in this way is M c = 6 . +1 . − . × M (cid:12) at R c = 1 . +0 . − . Mpc. Comparison of these WL masseswith our X-ray and spectroscopic results and the valuesin the literature are discussed in § Figure 10.
Mass determination of A115N and A115S from our si-multaneous two-dimensional fitting with two NFW halos. We usedthe MCMC sampling method to explore the parameter space. Theresult shown here is derived from one million chains. Since we as-sume the mass-concentration relation of Dutton & Macci`o (2014),the total number of free parameters is two. The dashed lines indi-cate the 1 σ uncertainties while the inner and outer contours showthe 1 σ and 2 σ regions, respectively. The degeneracy between thetwo subcluster masses is weak (the Pearson correlation coefficientis ρ = − . X-ray Mass Estimation
Our first step toward X-ray-based mass estimation isthe measurement of the ICM temperature. We used theX-ray spectra within a 1-5 keV energy band and theMEKAL plasma model (Kaastra & Mewe 1993; Liedahlet al. 1995). Exclusion of the energy band less than 1 keVis our conservative measure to minimize the impact fromthe well-known low-energy calibration issue of the ACIS
Table 4
2D Two Halo NFW Fitting Result R c (Mpc) M c ( × M (cid:12) )Global 1 . +0 . − . . +1 . − . North 1 . +0 . − . . +0 . − . South 1 . +0 . − . . +0 . − . detector (e.g., Chartas & Getman 2002). The Galactichydrogen density, metallicity abundance, and redshift ofthe cluster were fixed to N H = 5 . × cm − (Stark etal. 1992), Z (cid:12) = 0 .
3, and z = 0 . T X = 7 . ± .
21 keV ( χ red = 0 .
88) and 6 . ± .
21 keV ( χ red = 0 . T X = 5 . ± . T X = 6 . ± .
19 keV for A115N and A115S,respectively. The decrease in A115N is significant andshows that the core temperature of A115N is indeed low.As shown by previous studies, we also confirm that us-ing a smaller circular aperture leads to lower tempera-tures for both X-ray peaks. For example, choosing an r = 47 kpc aperture gives T X = 3 . ± .
06 keV forA115N and 5 . ± .
51 keV for A115S. These measure-ments are consistent with the measurements in Gutierrez& Krawczynski (2005).One popular method for X-ray-based mass estimationis to determine the mass using both X-ray and surfacebrightness measurements with the assumption that thehalo follows a certain analytic profile such as NFW. Wedo not employ this method here, however, because thedisturbed morphology prevents us from obtaining a reli-able surface brightness profile. Instead, we estimate thecluster mass from a mass-temperature ( M − T ) relationbased on the temperature measurements extracted fromthe aforementioned annuli.Using the scaling relations of Mantz et al. (2016) gives M c = 6 . +1 . − . × M (cid:12) and 5 . +1 . − . × M (cid:12) forA115N and A115S, respectively. For comparison withweak-lensing masses, we converted these M c massesto M c masses by extrapolation. Using the mass-concentration relation of Dutton & Macci`o (2014), weobtained M c = 9 . +2 . − . × M (cid:12) ( R c = 1 . +0 . − . Mpc) for A115N and 8 . +1 . − . × M (cid:12) ( R c =1 . +0 . − . Mpc) for A115S. As mentioned in § § M c = 20 . +3 . − . × M (cid:12) or eak-lensing Study of A115 M c = 14 . +2 . − . × M (cid:12) .4.4. Dynamical Mass Estimation
We compiled our spectroscopic redshift galaxy cata-log of the A115 field by combining the Golovich et al.(2017) and Rines et al. (2018) data. The Golovich et al.(2017) catalog contains 198 spectroscopic members fromour own DEIMOS survey and NASA/IPAC Extragalac-tic Database (NED) . The NED catalog has contribu-tions from Beers et al. (1990), Zabludoff et al. (1990),Barrena et al. (2007), Skrutskie et al. (2006), and Alamet al. (2015). From their HeCS-red survey, Rines et al.(2018) provided 512 objects in the A115 field, of which95 are A115 members. Out of these 95 objects, 27 are re-dundant with those in the Golovich et al. (2017) catalog.We verified that the spectroscopic redshifts of these 27common objects agree excellently to the fourth decimalpoint. The total number of A115 cluster members in ourcombined catalog is 266.We applied the bi-weight estimator (Beers et al. 1990)and determined the redshift and LOS velocity dispersionof A115 to be z = 0 . ± . σ v = 1356 ±
67 km s − , respectively; we use bootstrapping to evaluatethe uncertainties. Both values are consistent with theBarrena et al. (2007) measurements ( z = 0 . ± . σ v = 1362 +126 − km s − ) and also with the Golovichet al. (2018) results ( z = 0 . ± . σ v =1439 ±
79 km s − ). The top panel of Figure 12 showsthe redshift distribution of the 266 members of A115. Weagree with Golovich et al. (2017) that the overall redshiftdistribution of the A115 galaxies is well-described witha single Gaussian profile.Assigning a galaxy to one of the two subclusters isnon-trivial because their virial radii overlap. We used aGaussian Mixture Model (GMM) analysis to determinethe membership between A115N and A115S. The analy-sis assigned 134 and 132 galaxies to A115N and A115S,respectively. After σ -clipping, the number of membersreduced to 115 (120) for A115N (A115S). The second andthird panels (light shade) of Figure 12 display the redshiftdistributions of A115N and A115S, respectively. TheLOS difference in velocity between the two subsystemsis 244 ±
144 km s − (see the bottom panel of Figure 12).The individual velocity dispersions of A115N and A115Sare σ v = 1019 ±
57 km s − and σ v = 1101 ±
64 km s − ,respectively.We converted the above velocity dispersions to dynam-ical masses using the M − σ v scaling relation of Saroet al. (2013). The dynamical mass of the entire sys-tem was estimated to be M c = 37 . +5 . − . × M (cid:12) while we obtained M c = 16 . +2 . − . × M (cid:12) and M c = 20 . +3 . − . × M (cid:12) for A115N and A115S, re-spectively.Barrena et al. (2007) quoted a very large( ∼ − ) velocity difference between A115Nand A115S from their analysis of 88 cluster members.This claim is based on measurement of only the mem-bers within ∼ .
25 Mpc of the BCG. However, thismeasurement lacks statistical significance because only https://ned.ipac.caltech.edu We used the scikit-learn implementation available athttps://scikit-learn.org/stable/modules/mixture.html. ±
551 km s − . The central value is higher than thecase where we use the GMM method to determine thesubcluster membership (244 ±
144 km s − ). However,the two measurements are different only by ∼ σ becauseof the large uncertainty attached to the measurementfrom the members in the subcluster core. Nevertheless,it is interesting to note that the LOS velocity differencebetween the two BCGs is ∼
853 km s − , which is close tothe central value of the measurement 838 ±
551 km s − based on the members in the core ( r < .
25 Mpc). Thechange in the LOS velocity happens mostly becausethe galaxies located in the A115N center on averagehave higher redshifts than the rest (see the solid versusdashed lines in the second panel of Figure 12). We donot observe this trend for A115S (the third panel ofFigure 12). This radial dependence is also mentioned byBarrena et al. (2007) in Figure 13 and 14 of their paper.We defer our interpretation of the above results to § M/L
Ratio Estimation
Mass-to-light ratios (
M/L ) of galaxy clusters havebeen used to estimate the matter density of the universeunder the assumption that clusters are representative ofour universe (e.g., Carlberg et al. 1997). Also, the evo-lution of cluster
M/L values with redshift provide usefulconstraints on the stellar mass assembly history. Herewe present our estimation of the
M/L value of A115.One of the motivations of this investigation is to examinethe consistency of the resulting
M/L values with resultsfor other clusters. Although the
M/L dispersion amongclusters is quite large in the literature (for example, the
M/L value spans the range 50 ∼ − M (cid:12) clusters according to Girardi et al. 2002), the order-of-magnitude difference between our WL and other massestimates makes this comparison still statistically inter-esting. To measure the M/L value, we evaluated theA115 mass and luminosity within a cylindrical volumerather than a spherical volume. We used the best-fitNFW parameters presented in our two-halo simultaneousfitting ( § z members and selectedthe candidate galaxies whose V − i (cid:48) colors are within 0.05magnitude from the fitted line and V -band magnitudesare brighter than V = 22 (see photometric candidate inFigure 3). Our final member catalog contains 377 ob-jects. We estimated B -band luminosity L B (cid:12) from our V and i (cid:48) magnitudes using the photometric transformationobtained by performing synthetic photometry (Sirianni4 Kim et al. (2018)
Table 5
X-ray MassX-ray R c (Mpc) R c (Mpc) M c ( × M (cid:12) ) M c ( × M (cid:12) )Global 1 . +0 . − . . +0 . − . . +2 . − . . +3 . − . North 1 . +0 . − . . +0 . − . . +1 . − . . +2 . − . South 1 . +0 . − . . +0 . − . . +1 . − . . +1 . − . Figure 11.
Core-excised
Chandra
X-ray spectra of A115N and A115S. The upper boxes show the spectra whereas the lower boxes displaythe residuals. The red solid lines represent the best-fit results based on the MEKAL model. et al. 2005) with a spectral energy distribution (SED)template of elliptical galaxies.Figure 13 shows the cumulative
M/L profile for ourthree chosen centers (two BCGs and one global). Whenthe centers are placed at the BCGs, the
M/L value islow at small radii because of the BCG’s contribution tothe luminosity. The
M/L value is estimated high nearthe global center because no bright galaxies are presentin this region. We find that the
M/L ratio of A115Nand A115S are ∼
400 and ∼ ∼ ∼ . M/L values are higher than the mean value of theΛCDM prediction, but can be accommodated within thedistribution of the sample of 89 clusters studied in Gi-rardi et al. (2002). This comparison shows that our WLmasses, although substantially lower than the X-ray ordynamical estimates, give the most physical
M/L val-ues for A115. If dynamical masses are used instead, theimplied
M/L value would increase by an order of magni-tude, which is difficult to accommodate within the cur-rent ΛCDM paradigm. In general, dynamics of galaxiesare known to be biased in a merger (Pinkney et al. 1996;Takizawa et al. 2010). DISCUSSION5.1.
Comparison with Previous Mass Estimates
A115 is one of the most studied galaxy clusters. Here,we compare our WL mass estimates with those from theliterature.
Global Mass.
Figure 14 shows the global M c esti-mates from various studies. Note that most past studiesdid not report separate masses for A115N and A115S.For studies that only quote M c values, we converted them to M c values using an NFW profile and the mass-concentration relation of Dutton & Macci`o (2014). Thisconversion was also applied to our WL results.The most significant outlier in Figure 14 is the dynam-ical mass estimate from Barrena et al. (2007). Becauseour velocity dispersions from improved statistics yielda similarly high mass, we attribute the large differencenot to any errors in measurement, but to a significantdeparture of A115 from dynamical equilibrium due tothe merger. In general, velocity dispersion is believed tobe boosted in epochs close to pericentric passages (e.g.,Pinkney et al. 1996; Monteiro-Oliveira et al. 2017). How-ever, it remains to be investigated by future numericalsimulations whether or not the merger alone can inflatethe velocity dispersion measurement to this extent. Thedynamical mass estimate from Sif´on et al. (2015) is sub-stantially lower than the Barrena et al. (2007) result.This is because Sif´on et al. (2015) treated A115 as a sin-gle halo whereas Barrena et al. (2007) took into accountthe multiplicity.The X-ray and WL mass estimates presented in Fig-ure 14 seem to be consistent with our weak lensing result.However, the caveat is that these values are obtained un-der the single-halo assumption. Substructure Mass.
Hoekstra et al. (2012) pre-sented WL masses for A115N and A115S separately us-ing Canada-France-Hawaii Telescope (CFHT) imagingdata. They quoted M c = 3 . +1 . − . × M (cid:12) and5 . +1 . − . × M (cid:12) for A115N and A115S, respectively.These masses were derived by de-projecting their aper-ture masses. When they directly fit an NFW profile, theyobtain M c = 3 . +1 . − . × M (cid:12) (3 . +1 . − . × M (cid:12) )for A115N (A115S). The de-projected values are higher eak-lensing Study of A115 A115 z =0 . ± . v r =57607 ± km s − σ v =1356 ± km s − N = 266
Total membersA115 z
A115N z =0 . ± . v r =57774 ± km s − σ v =1019 ± km s − N (Core) = 115 (15)
A115NA115N (Core)A115N zN-Core zN-BCG z
A115S z =0 . ± . v r =57483 ± km s − σ v =1101 ± km s − N (Core) = 120 (15)
A115SA115S (Core)A115S zS-Core zS-BCG z .
175 0 .
177 0 .
179 0 .
181 0 .
183 0 .
185 0 .
187 0 .
189 0 .
191 0 .
193 0 .
195 0 .
197 0 .
199 0 .
201 0 .
203 0 .
205 0 .
207 0 . Redshift
Radial velocity difference v r,N − v r,S =244 ± kms − v r,N − v r,S =838 ± kms − v r,N − v r,S =853 ± kms − A115NN-Core zN-BCG zA115SS-Core zS-BCG z . . . . . . . . . . . . . . . . . . Velocity ( × km s − ) Figure 12.
Redshift distribution of 266 cluster member galaxiesand velocity dispersion estimation. The top panel shows the globalredshift distribution. The second and third panels represent theredshift distribution of the northern and southern subclusters, re-spectively. The bottom panel shows the radial velocity differencesof the subclusters, core regions, and BCGs. The membership wasdetermined by the Gaussian Mixture Model (GMM). The memberswithin the core region of 0.25 h − Mpc radius are represented bydark shades. We performed σ -clipping on both subcluster membersto remove the outliers. The means and standard deviations of over-laid Gaussians are from the biweight statistics (Beers et al. 1990).The radial velocity v r is measured from the classical Doppler ef-fect relation v r = cz , where c is the speed of light. The velocitydispersion is measured in the rest frame of the cluster. The solid,dashed, and dotted lines on each panel are the mean redshift of thecluster, core region, and the redshift of BCG, respectively. than our results by a factor of 2-3; when converted to M c , our Subaru-base WL masses become M c =1 . +0 . − . × M (cid:12) and 2 . +0 . − . × M (cid:12) for A115Nand A115S, respectively. When the two masses (A115Nand A115S) from Hoekstra et al. (2012) are combined,the resulting global mass of A115 would be also 2-3times higher than our WL result. In order to investi-gate the source of the discrepancy with the Hoekstra etal. (2012) results, we analyzed their CFHT data with ourWL pipeline. The difference in depth and seeing resultsin a slight ( ∼ ∼
19 arcmin − vs ∼
24 arcmin − ).Nevertheless, we find that our masses derived from theCFHT data are in agreement with our Subaru-based val-ues within ∼ Radius (kpc) M a ss t o L i g h t R a t i o ( M / L B ) GlobalNorthSouth
Figure 13.
Cumulative
M/L profile of A115. Black, red, and blueopen markers represent the
M/L ratios of the global, northern, andsouthern clusters, respectively. The vertical dashed lines indicatethe virial radius of each cluster. In this plot, we use projectedmasses derived from our NFW model and galaxy luminosity froma photometrically selected red sequence.
Table 6
Mass Comparison M c ( × M (cid:12) ) Global North SouthWeak Lensing 6 . +1 . − . . +0 . − . . +0 . − . X-ray 20 . +3 . − . . +2 . − . . +1 . − . Velocity Dispersion 37 . +5 . − . . +2 . − . . +3 . − . crepancy between Hoekstra et al. (2012) and ours maybe attributed to the difference in the WL pipeline andmass estimation method. Mass distribution.
Among the few WL studies inthe literature, only Okabe et al. (2010) presented a two-dimensional mass distribution for A115, which shows twomass peaks similar to ours. However, both of their massclumps are offset toward the northeast with respect totheir nearest BCGs. As mentioned in §
3, our mass peakscoincide with the corresponding BCGs. Okabe et al.(2010) performed their WL analysis using the i (cid:48) -bandimage, which was significantly deeper than the V -bandimage at the time of the analysis. Because our WL shapeis derived from the V -band data, we think that the differ-ence may be due to different systematics. To address theissue, we repeated the measurement with the i (cid:48) imagingdata. We find that the position-dependent PSF elliptic-ity pattern of the i (cid:48) image is much more complex than thepattern in the V image and our PCA-based PSF modelcould not reproduce the observed PSF pattern with thesame fidelity (Figure 2), as mentioned in § i (cid:48) -bandanalysis resembles the one in Okabe et al. (2010), pos-sessing similar offsets. Therefore, it is possible that themass-galaxy offsets in Okabe et al. (2010) may be dueto large residual PSF systematics in the i (cid:48) -band imagingdata. However, we can only be speculative regarding thisissue because we do not have access to their WL catalog.5.2. Significance of Weak-lensing Mass Centroid Kim et al. (2018)
Figure 14.
Global mass estimations of A115 from previous re-search. Global M c of the cluster is compared on the plot with1 σ uncertainty error bars. In the case that the previous researchonly measured M c , we converted M c to M c assuming thecluster follows the NFW halo model. The gray shaded region isthe error region of our mass estimation. The results are sortedin chronological order. Our mass estimation is 1 σ -consistent withother weak-lensing masses. Dynamical and X-ray masses tend tobe higher than the weak-lensing masses, which we attribute to theirassumption of the cluster being in hydrostatic equilibrium. As shown in Figure 7, our mass centroids agree nicelywith the BCG positions. If the BCG represents thetrue center of each halo, one can interpret the agree-ment as evidence for dark matter with negligible self-interacting cross-section. However, it is still unclear ingeneral whether or not a BCG can serve as the proxyfor a halo center. Alternatively, one can use smoothedgalaxy distributions to define halo centers. In Figure15, we display mass contours over galaxy number andluminosity density maps. Interestingly, the centroids ofthe smoothed galaxy distributions possess offsets withrespect to the BCGs. For A115S, both number and lu-minosity density centroids are displaced south by ∼ (cid:48)(cid:48) .Similar offsets are found for A115N except that the num-ber density peak is at a greater distance from the BCGthan the luminosity peak. Here we present our investi-gation of the statistical significance of the mass centroidwith respect to various definitions of subcluster centers.We used bootstrap analysis to measure the significanceof the centroids for both mass and galaxy distributions.To estimate the WL mass distribution centroid uncer-tainty, we bootstrapped the final source catalog and gen-erated 5000 convergence maps using the KS93 method.From each convergence map realization, we identifiedpeaks by determining the first moment. Then, the distri-bution of the resulting peak locations was processed witha Kernel Density Estimation (KDE) to define the signif-icance regions. We also generated 5000 bootstrap real-izations of the galaxy distribution by sampling the pho-tometrically and spectroscopically selected cluster mem-bers (presented in Figure 3). Again, we identified peaksusing the first moment and used KDE to define the sig-nificance regions. While we believe that the resultingcentroid uncertainty of the galaxy number density is afair measure of the significance, we argue that the cen-troid uncertainty of the luminosity density obtained inthis way corresponds to an upper limit because the peaklocation in each realization is dominated by several brightgalaxies. Figure 16 compares the 1 σ contours among the mass, luminosity, and number density results. We findthat the three centroids are highly consistent with oneanother (well within 1 σ contours).5.3. Merging Scenario
A115 is a merging galaxy cluster with a number ofintriguing features summarized as follows.1. A giant ( ∼ . ∼ . ∼ M = 1 . − . M c = 6 . +1 . − . × M (cid:12) .7. The analysis with our enhanced spectroscopic cat-alog with 266 members shows that the LOS veloc-ity difference between A115N and A115S is small(244 ±
144 km s − ).Point 1 is strong evidence that the system is postmerger. Although Hallman et al. (2018) suggests a pos-sibility that the radio relic might be a pre-merger shock,our numerical simulation with our WL masses as inputshows that this shock would be too weak to generate sucha giant radio relic even if there exists a rich populationof so-called fossil electrons (Lee et al. in prep). The lastpoint supports the possibility that the merger is takingplace nearly in the plane of the sky. Future radio observa-tions can provide further insights into this viewing angleissue from polarization fraction measurements. Points 2and 3 indicate that A115N and A115S might have col-lided in the north-south direction with a non-negligibleimpact parameter. Point 4 can be interpreted as suggest-ing that the shock velocity is as high as ∼ − .Finally, we can infer from the morphology (Point 5) ofthe X-ray peak that A115N (A115S) might be headingsouthwest (northeast).Based on the subset of the points above, we can carryout some consistency checks for the progression of themerger. If the impact happened near the global center,the shock traveled ∼ ∼ − derived from the Mach num-ber, we estimate that it takes about 0.5 Gyr for the shockto reach the current location. Some simulations suggestthat a shock traveling speed is a good proxy for the colli-sion speed at the time of impact (e.g., Springel & Farrar eak-lensing Study of A115 h m s s m s s ◦ RA (J2000) D e c ( J )
500 kpc~2.5 arcmin . . . . . . . . . . . . . Number Density
X-ray PeakBCGLuminosity PeakNumber Density Peak h m s s m s s ◦ RA (J2000) D e c ( J )
500 kpc~2.5 arcmin . . . . . . . . . . . . . Luminosity Density
X-ray PeakBCGLuminosity PeakNumber Density Peak
Figure 15.
Convergence overlaid on the number and luminosity density maps of the cluster members. A total of 377 cluster members(266 spectroscopic members and 111 photometric members) are used to create these number and luminosity maps. The displayed resultsare obtained after smoothing with a FWHM = 188 (cid:48)(cid:48)
Gaussian kernel. Our bootstrapping analysis (see text) shows that the five centroids(mass, X-ray, galaxy number, galaxy luminosity, and BCG location) are statistically consistent. v ∼ (cid:18) M + M M (cid:12) (cid:19) / × (cid:18) − d/d − ( b/d ) (cid:19) / (cid:18) d (cid:19) − / km s − , (9)where the initial separation is d ∼ . (cid:18) M + M M (cid:12) (cid:19) / (cid:18) t impact
10 Gyr (cid:19) / Mpc . (10)We assume that M + M = 4 . × M (cid:12) is the sum ofthe individual WL cluster masses, t impact = 11 Gyr is thetime from rest to impact, b = 0 is the impact parameter,and the current separation d = 1 Mpc. Setting b =0 is justified in this approximation because Equation 9varies quite slowly in b/d when d is large. The resultingrelative velocity of the clusters at impact is ∼ − . This agrees with the velocity derived from the Machnumber of the shock. Furthermore, since the radio relicis close to A115N, it is unlikely that the subclusters haveturned around and we are witnessing a returning phase.This is in contrast to the scenario that one might derivefrom the X-ray morphology.More specific merger scenarios can be inferred when wesearch for merging cluster analogs in cosmological nu-merical simulations. Using the Wittman et al. (2018)method, we sampled cluster mergers by matching thecluster redshift, projected distance, radial velocity dif-ference, and cluster masses. As explained in Wittman etal. (2018), this method has several advantages over theMonte Carlo Merger Analysis Code (MCMAC; Dawson2013) method. One important advantage is that findingmerger analogs in cosmological simulations allows us toconsider the cases where the subcluster velocity vectors are not entirely parallel to the separation vector whilethe MCMAC method always assumes that the collisionis head-on. This head-on collision assumption leads to onaverage a larger deviation between the separation vectorsand the plane of the sky. As A115 is believed to be anoff-axis merger, this issue cannot be neglected.Figure 17 shows the trajectories of each analog (top)and constraints of time since pericenter (TSP; bottomleft), maximum colliding velocity (bottom middle), andvelocity direction (bottom right). TSP is a useful quan-tity because the information helps us to distinguish be-tween in-bound and out-bound cases. The maximumcolliding velocity is the impact velocity, which can beapproximated to be the shock propagation velocity. In-vestigation of the velocity direction allows us to infer theviewing angle of the merger. The time since pericenteris most likely to be ∼
600 Myr with a maximum collisionvelocity of ∼ − . These values are consistentwith the above estimates based on the Mach number,position of the radio relic, and timing argument. Thevelocity direction (the angle between the relative veloc-ity vector and the separation vector) is centered at ∼ ◦ .Although not shown here, we also found that about 68%of analogs have their separation vector axis less than 19 ◦ from the plane of the sky. Therefore, our LOS velocitydifference constraint 244 ±
144 km s − only marginallyfavors mergers near the plane of the sky. This weak con-straint is not surprising because the velocity vectors ofthe analogs are not perfectly aligned with the separa-tion vectors. The trajectory plot (top) shows that themajority of the analogs are in the outgoing phase at thecluster redshift. This can also be inferred by either theshort TSP or the relative velocity vector being less than90 ◦ ; the relative velocity vector is (mostly) parallel to theseparation vector, rather than anti-parallel. Since we donot use the radio relic in our analog search, it is inter-esting that this analog-based result also favors the sameoutgoing case. However, note that the small bump near8 Kim et al. (2018)
250 200 150 100 50 0 -50 -100 -150 -200 -250 ∆ RA (arcsec) -250-200-150-100-50050100150200250 ∆ D e c ( a r c s e c ) Mass NumberLuminosityNorthern Cluster
250 200 150 100 50 0 -50 -100 -150 -200 -250 ∆ RA (arcsec) -250-200-150-100-50050100150200250 ∆ D e c ( a r c s e c ) Mass NumberLuminositySouthern Cluster
Figure 16.
Centroid uncertainty estimation from 5000 bootstrapresampling runs. The coordinate (0,0) represents the peak of themass centroid distribution. Black, red, and blue dots representmass, number density, and luminosity peaks, respectively, from asingle realization. The contours show the 1 σ confidence regions. ◦ in the velocity direction panel (or near ∼ . CONCLUSIONSA115 is a merging galaxy cluster with a number ofremarkable features including a giant ( ∼ . Chandra , spectroscopic data from theKeck/DEIMOS and MMT/Hectospec instruments, wesummarize our conclusions as follows: • Our WL study confirms the finding of Okabe et al.
Figure 17.
Trajectories of each cluster analog (top) and con-straints of time since pericenter (TSP), maximum colliding velocity,and relative velocity direction with respect to the separation vec-tor (bottom). Bottom panels present the likelihood and cumulativelikelihood distributions. TSP is most likely to be ∼
600 Myrs witha maximum colliding velocity of ∼ − and the relativevelocity direction of ∼ ◦ from the separation vector. This analy-sis prefers outgoing phase of subclusters, which is contradictory towhat we would expect intuitively from the X-ray morphology. Notethat the small bump near 160 ◦ in the velocity direction panel (ornear ∼ (2010) that the mass structure of A115 is bimodaland resembles the X-ray map. • Both mass clumps are in good spatial agreementwith the distributions of galaxies and plasma. • We determine the masses of A115N and A115Sto be M c = 1 . +0 . − . × M (cid:12) and M c =3 . +0 . − . × M (cid:12) , respectively. The total massof the system is M c = 6 . +1 . − . × M (cid:12) . • The mass estimates made with our X-ray and spec-troscopic data analysis are 3-10 times higher thanthe WL values. We attribute the difference to se-vere disruption of the gravitational and hydrostaticstructure due to the merger. When we adopt non-WL masses, the