Hubble Space Telescope/Advanced Camera for Surveys Confirmation of the Dark Substructure in A520
aa r X i v : . [ a s t r o - ph . C O ] J a n Draft version February 14, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
HUBBLE SPACE TELESCOPE /ADVANCED CAMERA FOR SURVEYS CONFIRMATION OF THE DARKSUBSTRUCTURE IN A520 M. J. JEE , H.. HOEKSTRA , A. MAHDAVI , AND A. BABUL Draft version February 14, 2018
ABSTRACTWe present the results from a weak gravitational lensing study of the merging cluster A520 based onthe analysis of
Hubble Space Telescope /Advanced Camera for Surveys (ACS) data. The excellent dataquality allows us to reach a mean number density of source galaxies of ∼
109 per sq. arcmin, whichimproves both resolution and significance of the mass reconstruction compared to a previous studybased on Wide Field Planetary Camera 2 (WFPC2) images. We take care in removing instrumentaleffects such as the trailing of charge due to radiation damage of the ACS detector and the position-dependent point spread function (PSF). This new ACS analysis confirms the previous claims thata substantial amount of dark mass is present between two luminous subclusters. We examine thedistribution of cluster galaxies and observe very little light at this location. We find that the centroidof the dark peak in the current ACS analysis is offset to the southwest by ∼ ′ with respect to thecentroid from the WFPC2 analysis. Interestingly, this new centroid is in better spatial agreementwith the location where the X-ray emission is strongest, and the mass-to-light ratio estimated withthis centroid is much higher (813 ± M ⊙ /L R ⊙ ) than the previous value; the aperture mass basedon the WFPC2 centroid provides a slightly lower, but consistent mass. Although we cannot providea definite explanation for the presence of the dark peak, we discuss a revised scenario, wherein darkmatter with a more conventional range ( σ DM /m DM < g − ) of self-interacting cross-section canlead to the detection of this dark substructure. If supported by detailed numerical simulations, thishypothesis opens up the possibility that the A520 system can be used to establish a lower limit of theself-interacting cross-section of dark matter. Subject headings: gravitational lensing — dark matter — cosmology: observations — X-rays: galaxies:clusters — galaxies: clusters: individual (Abell 520) — galaxies: high-redshift INTRODUCTION
Galaxy clusters are comprised of dark matter, clustergalaxies, and hot plasma. When two clusters collide, itis believed that the galaxies and dark matter temporar-ily dissociate from the hot plasma because the latter iscollisional and subject to ram pressure. Eventually, thedark matter of the cluster, the gravitationally dominantcomponent, pulls the hot plasma back into its potentialwell, and the dissociation disappears. Therefore, in gen-eral we have a narrow time-window (a few Gyrs after thecore pass-through) to witness observationally significantoffsets between collisional and collisionless constituentsof the clusters.Detailed studies of these “dissociative” mergers (Daw-son 2012) provide unique opportunities to enhance notonly our astrophysical understanding of the cluster for-mation and evolution, but also our understanding of fun-damental physics on the nature of dark matter. Because Based on observations made with the NASA/ESA
HubbleSpace Telescope , obtained at the Space Telescope Science Insti-tute, which is operated by the Association of Universities forResearch in Astronomy, Inc. Department of Physics, University of California, Davis, OneShields Avenue, Davis, CA 95616, USA Leiden Observatory, Leiden University, Leiden, The Nether-lands Department of Physics and Astronomy, San Francisco StateUniversity, San Francisco, CA 94131, USA Department of Physics and Astronomy, University of Victo-ria, Victoria, BC, Canada Kavli Institute for Theoretical Physics, Kohn Hall, Univer-sity of California, Santa Barbara, CA 93106, USA a direct lab detection of dark matter particles may nothappen within the current decade, these merging clusterswith large offsets among the different cluster constituentsare receiving growing attention (e.g., Springel & Farrar2007; Randall et al. 2008; Dawson 2012).To date, only a few merging systems are known to pos-sess such large dissociative features (e.g., Dawson et al.2012, Merten et al. 2011, Bradac et al. 2008; Okabe& Umetsu 2008; Soucail 2012), and only two systems,namely 1E0657-56 at z = 0 . z = 0 . Hubble Space Telescope (HST)
Wide Field Plan-etary Camera 2 (WFPC2) weak lensing analysis of A520and confirmed the results of M07 and Okabe & Umetsu(2008). Both the two-dimensional mass map and theaperture mass results of J12 are consistent with M07,except for the detection of two additional mass peaks,which were not reported in M07. One of the two newpeaks (labeled as P5 in J12) resolves one of the questionsraised in M07, who considered the absence of any signifi-cant mass peak around this location also discordant withour common light-traces-mass hypothesis along with thepresence of the significant mass in the dark core region.The other new peak (labeled as P6 in J12) is detected ∼
200 kpc south of the dark core and coincides with thespatial distribution of the cluster galaxies. As for thedark core both J12 and M07 discuss a number of pos-sibilities that may lead to the observation, but neitherstudy could exclusively single out one definite scenarioresponsible for these observations.The scenarios considered in J12 and M07 are: 1) apossible presence of a background high-redshift ( z > z > z ∼
1. Sce-nario 2 is discarded because no numerical simulationshave shown that brightest cluster galaxies are ejectedduring three-body encounter, although it can happento faint satellite galaxies. The third possibility is un-likely because the filament must be very thin in such away that most of the projected mass is confined to thecentral r < § §
3. The mass reconstruction is discussed in § §
5. We compare our re-sults to those of C12 in § §
6. Throughout this paperwe use (Ω M , Ω Λ , h ) = (0 . , . , .
7) for cosmology unlessexplicitly stated otherwise. This gives a plate scale of ∼ . ′′ at the redshift ( z = 0 .
2) of Abell 520. All thequoted uncertainties are at the 1- σ ( ∼ DATA
We retrieved the
HST /ACS images of A520 (PI:Clowe) from the Mikulski Archive for Space Telescopes(MAST) in 2012 July after the new charge transfer inef-ficiency (CTI) correction of Ubeda and Anderson (2012)had become available. The cluster was observed in theCycle 18 (2011 February and April) and the raw data areseverely affected by CTI. The images are comprised offour pointings in F435W, F606W, and F814W to coverthe approximately 7 ′ × ′ central region of the cluster.The exposure time per pointing is 4,600 s for F814Wwhereas it is a factor of two smaller for both F435W andF606W. A similar exposure time per pointing (4,400 s)was used for the WFPC2 observation (PI: Dalcanton) ofA520, although the ACS image is in general ∼ http://archive.stsci.edu CTI causes systematic elongation of object shapes along thereadout direction. Readers are referred to 3.1 for details.
ST Study of Dark Core in Abell 520 3We combine the four ACS pointings into a single mo-saic image, which is used to measure the galaxy shapes(note that we keep track of the combined PSF). As dis-cussed in more detail in §
2, a careful treatment of theimpact of the CTI is critical. To investigate this, we cre-ated three different versions of mosaic images. The firstmosaic was generated with the
FLT files processed by theCALACS pipeline (Hack et al. 2003). These images arecorrected for the bias stripping noise with no CTI cor-rection applied. The second mosaic is made from the FLC files also processed by the CALACS pipeline, which re-moves both bias stripping noise and CTI trails using thelatest 2012 CTI model of Ubeda and Anderson (2012).This latest model was not available to C12. Finally, forour third mosaic image, we use the
PixCteCorr scriptto correct the CTI effects as per the 2009 CTI model(Anderson & Bedin 2010). This old model is consideredinferior to the latest model for the accuracy of the cor-rection in the low-flux regime. We defer the detailedcomparison to § . .
01 pixels.However, the offsets between different pointings are dif-ficult to determine reliably using automated algorithmsbecause the small overlapping areas ( ∼
200 pixels) and thedense distribution of cosmic rays make only a few objectsavailable for shift estimation. Therefore, we choose tocreate a separate stack for each pointing as an interme-diate step and to use the catalog from the resulting image(where cosmic rays are removed and fainter sources areavailable) to determine accurate offsets between differ-ent pointings ( ∼ .
02 pixel). The final full 2 × MultiDrizzle software (Koekemoeret al. 2002) with the
Lanczos3 drizzling kernel and anoutput pixel scale of 0 . ′′
05. The
Lanczos3 kernel closelyapproximates the theoretically ideal sinc (sin x/x ) inter-polation kernel by truncating the oscillation beyond thethird pixel from the center. In Jee et al. (2007a), wedemonstrate that this
Lanczos3 drizzling kernel is supe-rior to the “square” kernels in minimizing both aliasingand noise correlation and gives the sharpest PSF. Wenote that C12 used a square kernel with an output pixelscale of 0 . ′′
05 to drizzle the ACS images, which may notbe optimal for measuring accurate shapes of small galax-ies. ANALYSIS
The key ingredient in any weak lensing analysis is theaccurate measurement of the shapes of the source galax-ies. A number of observational effects prevent us fromsimply using the observed shapes. Instead we need tocharacterize these instrumental distortions and correctfor them. In addition to the usual correction for thePSF (both size and anisotropy), the analysis of ACSdata needs to account for the trailing of charge due toCTI. Since charge trapping happens every time chargesare transferred from one pixel to another, CTI is greaterfor pixels farther from the readout register. After thetrapped charges in one transfer are released, a fractionof them remain trapped during the next transfer. This cascading effect leads to trails, leading to a change in theshapes of galaxies. Both photometry and shape measure-ments are affected by CTI, although both are sensitiveto different species of traps.Although this undesirable artifact happens in everyCCD, it is an especially serious concern for space tele-scopes where the CCDs are subject to constant spaceradiation and the sky background is very low. The num-ber of defects increases roughly linearly with time, andthe A520 data taken in the Cycle 18 (2011 February andApril) are severely affected by this CTI problem.J12 discussed the potential impact of uncorrected CTIin the WFPC2 analysis. Although WFPC2 at the timeof the observation of A520 was in orbit longer than ACSat the time of the current observation, the much smallersize of the readout distance (800 pixels vs. 2048 pixels)makes the overall impact less severe. In addition, thedirection of the CTI trails differs for the three CCDs ofWFPC2, which results in a more effective mixing of anyresidual CTI pattern. Correction for CTI
We measure the CTI utilizing warm pixels and com-pact cosmic rays present in the same science data (Jee etal. 2009; Jee et al. 2011; J12). These sub-PSF features(hereafter SPFs) suffer from the charge transfer efficiencydegradation but are not affected by the anisotropic PSFof the instrument. Hence we can single out CTI and per-form a statistical analysis of their ellipticity as a functionof charge transfer distance and flux.We quantify the elongation of SPFs due to CTI usingthe ellipticity defined as e = a − ba + b (1) e + = e cos(2 θ ) (2) e × = e sin(2 θ ) (3)where a and b are the semi-major and -minor axis, re-spectively. θ is the orientation of the ellipse. For thecurrent CTI measurement, we choose the serial readoutdirection as our x -axis and the parallel readout directionas our y -axsis.The plot on the left panel of Figure 1 shows the e + component of the SPF ellipticity as a function of a chargetransfer distance; because the x -axis is defined to be or-thogonal to the readout direction, the sign of e + becomesnegative for CTI trails. Different colors represent differ-ent ranges of flux counts (after background being sub-tracted). Several features are worth noting in compari-son with previous work. First, the CTI is still linear withtransfer distance, as was observed in our previous studies(Jee et al. 2009; Jee et al. 2011; Hoekstra et al. 2011).Second, even the brightest SPFs are severely affected byCTI. Compared to our 2009 data, the slope of the SPFsat the flux range 2500-4000 e − has increased by morethan a factor of two, showing that the farthest ( ∼ δe ∼ . ∼ e − Jee et al.
Figure 1.
CTI effects in the A520 ACS data measured from the ellipticity of sub-PSF features (SPFs) such as cosmic rays and warm pixels.The counts are calculated with the background subtracted. The left plot shows the result from the uncorrected ACS images. Without anycorrection, severe charge trailings are present, and thus weak lensing based on the raw images will be non-negligibly biased. The middlepanel displays the result when the old (Anderson & Bedin 2010) pixel-based method is applied, which reduces the CTI artifacts. However,the residual ellipticities indicate that the results are not yet satisfactory. The right panel shows the result when the latest (Ubeda andAnderson 2012) correction is used. The latest correction method successfully takes care of these residual CTI effects for the SPFs withcounts greater than ∼ ∼ (see Figure 31 of Jee et al. 2011), which would affectobjects fainter than F W ∼
27. However, the A520images show that the slope becomes less negative for de-creasing flux initially and then suddenly turns around at ∼ e − . At the faintest limit, it turns around again,and the CTI is mitigatied once more.Anderson & Bedin (2010) developed a so-called pixel-based CTI correction method, and their standalonescript PixCteCorr is publicly available and can be ap-plied to regular
FLT files. The results shown in themiddle panel of Figure 1 are obtained from these im-ages (hereafter we refer to this method as the Y2009model) when we repeat the above experiment. TheY2009 model reduces the CTI effects substantially, andthe performance is excellent especially in the brightestregime (700 − e − ). Nevertheless, the model doesunder-correct the CTI in the intermediate flux range(300 − e − ). However, the most interesting feature isthe behavior of the SPFs at the faintest end (50 − e − ).The CTI slopes are positive in this flux range becausethe model overcorrects the CTI. This also serves as proofof the CTI mitigation at the faint limit first reported inJee et al. (2009) and later supported by Schrabback etal. (2010).A new CTI correction method has been proposed byUbeda and Anderson (2012) and it is now part of the de-fault STScI pipeline. This method (hereafter the Y2012model) is an important improvement over the earliermethod in that it includes both time and temperature de-pendence. In addition, Ubeda and Anderson (2012) statethat the performance in the low flux regime has beensignificantly improved. We display the results obtainedfrom this new correction in the right panel of Figure 1.It is clear that the undercorrection problems (e.g., seethe slope for the range 300 − e − in the middle panel)seen in the old model nicely disappear in this case. How-ever, unfortunately, the overcorrection problem at thefaint limit still remains (perhaps becoming even slightlyworse). Nonetheless the performance of this correction isthe best and we use the Y2012 CTI-correction algorithmfor our actual weak lensing analysis.The remaining concern is the treatment of the over- correction problems at the faint limit. The flux range50 − e − corresponds roughly to F W = 27 − . PSF Model
Although the PSF of ACS is small, a careful effort mustbe made to model and remove the smearing effect of thePSF. In particular, when one desires to utilize sourcesnear the 5 σ detection limit and the size of the PSF, thecomplex spatial variation of the ACS PSF should be fullyconsidered to avoid bias due to the PSF anisotropy (thesizes of these faint sources are comparable to that of thePSF).About 10-20 high S/N ( >
20) stars are found in the in-dividual exposures of the A520 data. Since the ACS PSFis both time- and position-dependent, it is impossible touse this small number of stars to derive a reliable PSFmodel at the location of galaxies across the field. There-fore, we utilize the PSF library of Jee et al. (2007a)ST Study of Dark Core in Abell 520 5
Figure 2.
PSF reconstruction in the F814W images. The left panel shows the observed ellipticity pattern of the stars whereas in the middlepanel we display the ellipticity of the model PSF derived from globular cluster fields. The sticks illustrate the direction and magnitude ofthe ellipticity of the PSFs. The solid lines represent the observation footprints. The plot in the right panel displays the residual ellipticityof the stars. constructed from dense stellar fields. The PSF patternof ACS is repeatable (Jee et al. 2007a), and thus canbe estimated for each exposure by measuring the shapeproperties of the stars in the A520 data and comparingthem with those from the PSF library. We keep track ofthe model PSFs at the locations of source galaxies in in-dividual exposures to compute the final PSF on the stackimage. This requires a rigorous propagation of the im-age stacking history including offset, rotation, and weightapplied to individual exposures. We refer readers to ourprevious publication (e.g., Jee et al. 2011) for details.Figure 2 compares the PSF ellipticity pattern of thestars and the model PSFs in the A520 F814W images,where we measure shears. The comparison shows thatour PSF model reasonably mimics the observed PSF pat-tern. Any significant registration error is supposed tocreate spurious stellar ellipticities not observed in themodel. We do not find any hints of such a large discrep-ancy. The residual PSF ellipticity rms per componentis small ( ∼ . Shape Measurement and Cluster/Source GalaxySeparation
Our ellipticity is defined by ( a − b ) / ( a + b ), where a and b are the semi-major and minor axes, respectively . Wedetermine the ellipticity of an object by fitting a PSF-convolved elliptical Gaussian.Because the elliptical Gaussian is not the best repre-sentation of real galaxies, it is important to correct forthis “underfitting” (Bernstein 2010) together with othershear calibration issues such as the dilution of the signalby noise and spurious sources. Our internal shear cali-bration utilizing the Hubble Ultra Deep Field (Beckwithet al. 2006; HUDF) data shows that the average correc-tion factor is ∼ F W > An alternative definition of shape using ( a − b ) / ( a + b )is often used in the literature. One should remember that this so-called polarisation needs to be divided by 2 to obtain an estimateof the shear. which require a slightly larger ( ∼
14% on average) cor-rection factor, but still contain a useful lensing signal.This S/N-dependent correction is often called noise bias(Melchior & Voila 2012; Refregier et al. 2012), and isan important factor affecting cosmic shear results. Inthis paper, we multiply a S/N-independent average cor-rection factor 1.11 to our galaxy ellipticity. However,we verify that analysis using a S/N-dependent correctionscheme yields virtually indistinguishable weak-lensing re-sults. Note that this multiplicative bias affects the ampli-tude of the lensing signal, but should not affect featuresin the mass map. To maximize the S/N of the lens-ing signal, the ellipticity of galaxies must be properlyweighted by taking into account both the source elliptic-ity distribution and measurement errors. We employ thefollowing simple inverse-variance weighting scheme: µ i = 1 σ SN + ( δe i ) , (4)where σ SN is the dispersion of the source ellipticity dis-tribution ( ∼ .
25 per component for the A520 data), and δe i is the i th galaxy’s ellipticity measurement error percomponent.For bright galaxies (F814W < < F W < . <
24) cluster members. We do notattempt to remove cluster members at F814W >
24 be-cause the above color-based selection is not efficient inthis regime (in § > Figure 3.
Magnitude distribution of source galaxies in the A520field. We apply the identical selection (after due color transforma-tion) criteria to the UDF and GOODS data and show the result-ing magnitude distributions for comparison. For relatively brightsource galaxies ( F W . . F W & .
5. Nevertheless, whenwe degrade these control fields in such a way that the noise lev-els become comparable, we observe a good agreement in this faintregime, too, up to the sample variance. The displayed error barsinclude only Poissonian noise. ponent is set to 0.25. The total number of sources afterthese cuts is 4,932, giving us a source density of ∼ ∼
56 galaxies per sq.arcmin in their ACS weak lensing analysis of A520.According to Equation 4, the uncertainty of the shearis given by σ γ = r µ i . (5)On the other hand, if no weighting scheme is used, theshear uncertainty is simply: σ γ = σ SN √ n . (6)We define the effective number by equating the last twoequations and obtain n eff = X σ SN σ SN + ( δe i ) . (7)Therefore, the effective number is always smaller thanthe actual number of sources. We estimate the effectivesource density to be ∼
96 per sq. arcmin. The corre-sponding rms shear is ∼ .
026 per sq. arcmin, which is ∼
28% smaller than the value quoted by C12 ( ∼ .
036 persq. arcmin).
Redshift Estimation of Source Population
Since we do not apply any color cut for galaxies fainterthan F814W ∼
24, it is important to estimate the level of potential contamination in our source catalog carefullyand to propagate it to our redshift estimation. To ad-dress this issue, we utilize the Coe et al. (2006) HUDFphoto-z catalog, the 2004 STScI release of the HUDFimages (Beckwith et al. 2006), and the 2008 STScI re-lease of the Great Observatories Origins Deep Survey(GOODS; Giavalisco et al. 2004) images. We apply thesame source selection criteria to our galaxy catalog of theHUDF and GOODS data and compare their magnitudedistributions with those from the source population inFigure 3.The comparison shows no excess of galaxies in the A520source catalog with respect to the magnitude distributioncomputed from the above reference fields. At the faintend, the number densities of the galaxies in the referencefields are somewhat higher than those in the A520 fieldsimply because of their increased depth. To enable a faircomparison, we degrade the reference images to matchthe noise level of the A520 images. The resulting distri-bution from the UDF is in good agreement with that ofthe A520 source galaxies. Our test with the GOODS im-ages also confirms that the cluster galaxy contaminationis negligible.In order to scale our lensing signal properly, we mustestimate the β parameter defined as: β = (cid:28) max (cid:18) , D ls D s (cid:19)(cid:29) , (8)where D ls and D s are the angular diameter distances be-tween the lens and the source, and between the observerand the source, respectively. This β parameter deter-mines the critical surface mass density Σ c of the clustergiven by Σ crit = c πGD l β , (9)where c is the speed of light, G is the gravitational con-stant, and D l is the angular diameter distance to thelens. Compared to high-redshift clusters, the weak lens-ing mass of A520 at z = 0 . β =0 .
75, which corresponds to an effective source plane at z eff ∼
1. This value is slightly biased high because thereare fewer galaxies at the faint limit in the A520 data thanin the UDF image. In addition, the ellipticities of thesefaint galaxies are down-weighted when we estimate shear.Considering both effects, the revised estimate becomes β = 0 .
73 or z eff ∼ .
85. The resulting critical massdensity Σ crit is 3 . × M ⊙ pc − .C12 quote Σ crit = 3 . × M ⊙ pc − for their weaklensing analysis. This higher surface mass density impliesthat their source redshift is lower than ours, which isconsistent with the fact that our source catalog containsmore faint galaxies than theirs . We note that C12 estimate the critical surface mass densityof J12 to be Σ crit ≃ . × M ⊙ pc − using β = 0 .
64 quotedin J12. However, substituting this β value into equation 9 yieldsΣ crit ≃ . × M ⊙ pc − ; the difference in the assumed cosmo-logical parameters between J12 and C12 makes only a negligiblechange in the conversion of β to Σ crit . ST Study of Dark Core in Abell 520 7
Figure 4.
Smoothed ellipticity distribution of source galaxies.The “whisker” plot is produced by convolving the ellipticities witha Gaussian kernel. The diameter of the circle represents theFWHM (30 ′′ ) of the convolution kernel while the stick inside thiscircle shows a 10% horizontal shear. Clear correlation of sourcegalaxy ellipticity is seen. The approximate locations of the sub-structures reported in J12 are annotated with P1-P6. MASS RECONSTRUCTION
An important application of weak gravitational lens-ing is that the observed shear signal can be used toreconstruct the projected mass density. The smoothedshear field presented in Figure 4 shows a coherent patternaround the main galaxy overdensities. This can be re-lated directly to the convergence map κ ( x ) = Σ( x ) / Σ crit through κ ( x ) = 1 π Z D ∗ ( x − x ′ ) γ ( x ′ ) d x . (10)where D ∗ ( x ) is the complex conjugate of the convolutionkernel D ( x ) = − / ( x − i x ) and γ ( x ) is the complexrepresentation of gravitational shear.A better result is produced if we do not pre-smooththe ellipticities, but instead let the strength of the shearsignal determine the local smoothing scale. One suchmethod is the maximum-entropy-regularized mass recon-struction first introduced by Seitz et al. (1998). In thisstudy, we use the Jee et al. (2007b) implementation ofthe method. Figure 5 shows the result. A similar resultis obtained when we use equation 10, although the mapbecomes noisier near the edges.The substructures seen in this ACS analysis are in gen-eral similar to those in the WFPC2 results of J12 andtheir locations are denoted as P1-P6; their coordinatesare listed in Table 1. However, one of the important dif-ferences is the location of the dark peak. The currentcentroid (P3 ′ ) is about 1 ′ shifted to the southwest com- pared to the one in J12 (P3). Although mass reconstruc-tions using different imaging data can sometimes resultin small offsets in the positions of the mass peaks, it isunusual to observe a shift as large as ∼ ′ .Another noteworthy difference between our ACS andWFPC2 results is the strength of the substructure P4.In our ACS result, P4 is the strongest mass peak in theA520 field whereas it appears as a minor (much weakerthan P3) clump in our WFPC2 analysis. However, thisdifference can arise from the incomplete coverage of theregion by the WFPC2 observation. In addition, we findthat the ACS images reveal many new arclets aroundP4, which all contribute to the significance of the peak inmass reconstruction. We note that the inferred projectedmass of P4 is consistent with the value reported in J12. Centroid and Significance of the Dark Peak inA520
We perform a bootstrapping analysis to measure boththe significance and the positional uncertainty of the sub-structures. Utilizing the fast Fischer & Tyson (1997)implementation
FIATMAP of the KS93 algorithm, we gen-erate 1000 realizations. In Figure 6, we display nine ran-dom samples of the bootstrapped mass reconstructions.The circle denotes the approximate location of the darkpeakWe measure the centroids using the first momentsweighted by a circular Gaussian, whose FWHM matchesthe size of the substructure. The results are displayed inTable 1. The mean positional uncertainty is small ( ∼ ′′ ),and thus we conclude that the large shift of the darkpeak centroid between the current study and J12 is notcaused by noise in the mass reconstruction. We discuss anumber of possible explanations in § r =150 kpc centeredon P3 (old centroid) is still consistent with the WFPC2value (see § ′ substructurerequires us to determine a reasonable baseline in the ab-sence of the dark peak. We make a conservative esti-mate of this baseline by (1) taking the luminosities ofall the galaxies in the P3 ′ region (see § dark matter mass assuming a fidu-cial M/L of 300 M ⊙ /L B ⊙ (higher than the M07 valueof 232, and so more conservative), and (3) adding tothis dark matter mass the maximum gas mass alongthe column. For the X-ray gas mass, we adopt the up-per limit M gas = 0 . × M ⊙ . The resulting meanconvergence (adding both dark matter and gas masses)within the r <
150 kpc aperture is ∼ .
04. Because theFIATMAP convergence maps are subject to mass-sheetdegeneracy, we rescale the maps in such a way that thesubstructure masses agree with those derived from aper-ture mass statistics. The significance is computed by firstsubtracting the baseline value from the rescaled conver-gence within the r = 150kpc aperture and then dividingthe result by the rms obtained from the 1000 runs. Thedistribution in the significance of the P3 ′ is shown inFigure 7. The mean of the distribution is ∼ . σ , and thelow-end tail is > σ . This mean value ∼ . σ is similarto the significance estimate based on our aperture massdensitometry ( § Figure 5.
Maximum-entropy-regularized mass reconstruction of A520. The left panel shows the density distribution using the colorscheme shown at the bottom. We annotate the location of the substructures reported in J12 as P1-P6. On the right panel, we overlay themass contours on the ACS color composite image. The intensity of the X-ray emission observed by Chandra is represented in red.
Table 1
Mass Properties of Substructure ( r <
150 kpc)Substructure α, δ ∆ α, ∆ δ Projected Mass Gas Mass( h m s , ◦ ′ ′′ ) ( ′′ , ′′ ) ( h − M ⊙ ) ( h − / M ⊙ )P1 (04 54 20.76, +02 57 38.4) (5.3,4.1) 2 . ± . < . . ± . < . . ± . < . . ± . < . . ± . < . . ± . < . Note . — The positional uncertainty is estimated from bootstrapping. The mass uncertainties are evaluated from 1000 Monte-Carlo realizations.The gas mass is derived using Cauchy-Schwartz method in M07 based on the data set ObsID 9426 (110 ks) for P3 ′ and ObsId 528 (38 ks) for theother peaks. The Cauchy-Schwarz method is a model-independent means of deriving an upper limit on the gas mass column in a given region ofthe sky. The method requires an estimate of the maximum length of the cluster gas along the line of sight that contributes 99% of the emission.We refer to M07 for details; here we use an updated maximum column length of 4 Mpc (instead of 2), which is a more conservative estimate giventhe total mass of Abell 520. As a result, our gas mass upper limits are more conservative, being higher than M07 by √
2. The given values are 90%confidence level upper limits. with the C12 weak-lensing catalog. The dark peak is stillpresent in C12, although the significance in C12 is sys-tematically lower. The reason is two-fold. C12 used afactor of two fewer source galaxies, and the convergencein the P3 ′ slightly lower. This catalog-based comparisonis detailed in § Impact of the CTI correction model
As discussed in §
2, CTI is an important instrumentaleffect and although the Y2012 method (Ubeda & An-derson 2012) that we use in our analysis is not perfect,our tests on SPFs presented in Figure 1 shows it per-forms better than the Y2009 correction (Anderson &Bedin 2010) down to fluxes of 300 e − . One commonmisconception regarding the CTI effect on weak lens-ing mass reconstruction is that it affects only the region where the readout distance is the largest. However, thisis not an accurate statement especially in the case oftwo-dimensional mass reconstructions, which are relatedto shear fields non-locally. It is therefore interesting toexamine whether or not the residual CTI features affectour weak lensing analysis.In Figure 8 we compare the Kaiser & Squires (1993;hereafter KS93) mass reconstruction results when we donot correct for CTI (left panel), use the Y2009 method(middle panel) or the most recent approach (Y2012; rightpanel). Note that C12 used the Y2009 method as well asan updated model from Massey et al. (2010) and claimedconsistent results in both cases. We assume the equality g = γ because an iterative nonlinear reconstruction usingthe relation g = γ/ (1 − κ ) may exaggerate the differenceST Study of Dark Core in Abell 520 9 Figure 6.
Bootstrapping test of the A520 mass reconstruction. Mass reconstruction is performed with bootstrap-resampled source galaxies.The test provides a measure to examine the statistical significance of the A520 substructures. We use the
FIATMAP code to generate 1000results. Here we display nine random results. The circle denotes the approximate location of the dark peak. among the different versions.The overall distributions of the three convergence fieldsare similar to one another without any conspicuous sub-structure only seen in any particular version. However,it is important to note that the relative strengths of themass peaks are significantly different. The most criticalsubstructure in A520 is the overdensity P3’ (indicated bythe white arrow) between the two dominant mass peaks,where there are no luminous cluster members. It is re-markable that the overdensity in this region is strongestwhen we apply the best-performing Y2012 CTI correc-tion method (right panel). The feature is still seen, butweakest when no CTI correction is applied (left panel).The Y2009 correction gives an intermediate significance. As shown in Figure 8, the assessment of the substruc-ture significance relative to another is influenced by im-perfect CTI correction. Therefore, we conclude thatthe impact of the fidelity of the CTI correction is non-negligible in weak lensing analysis with the current A520data. We revisit this issue when we discuss our actualmass determinations in § Comparison with the WFPC2 analysis
The most noteworthy difference in the weak lensingresults between our current ACS and the WFPC2 studyis the large shift of the centroid of the dark peak fromP3 to P3 ′ by ∼ ′ . Since this shift is much larger than thecentroid uncertainty determined from the bootstrapping0 Jee et al. Figure 7.
Significance of the dark peak measured from our 1000bootstrap runs. The signficance is measured using a r = 150kpcaperture against the background, which is determined within eachmass reconstruction field. See text for details. experiment (Table 1), it is difficult to attribute the shiftto mere shot noise. Here we examine whether the shiftoriginates from a systematic difference between the twosource catalogs of ACS and WFPC2.We first carry out a galaxy-by-galaxy comparison ofthe two catalogs. Figure 9 shows that the raw elliptic-ities (prior to the application of shear calibration) be-tween ACS and WFPC2 agree nicely. The average slopeof the two ellipticity components is ∼ .
05. This smalldeparture from unity disappears when we apply the ap-propriate shear calibration factor to each dataset. Hencethis comparison does not indicate a systematic differencein ellipticity.To examine whether any systematic shape error mightbe localized near the dark peak we perform a weak lens-ing mass reconstruction using the shapes of the ACS databut based on the source selection in J12. In our WFPC2catalog there are more (less) source galaxies in the P3(P3 ′ ) region than in our ACS catalog. Thus, the numberdensity distribution of the common source galaxies doesnot exactly match the source density distribution of theWFPC2 data. We return to the issue of source densitybelow.Figure 10 shows the convergence field obtained fromthis source catalog using the KS93 method. Interestingly,the location of the dark core now coincides with that ofP3 in J12 in this mass reconstruction. This demonstratesthat the shape catalogs based on either WFPC2 or ACSdata give consistent results when a similar source selec-tion is made. Origin of the shift in peak location
While matching objects between the WFPC2 and ACScatalogs, we found that there is a systematic differencein source galaxy density distribution. Figure 11 com-pares the source galaxy distribution between the ACSand WFPC2 data. It is clear that in the WFPC2 cata-log the density in the P3 region is much higher than thesurrounding area. This is mainly because the WFPC2observation was planned in such a way that much deeper imaging is performed in this region (see also Figure 2 ofJ12). Although we still hold to the claim of J12 thatthe spatial variation of the source galaxy number den-sity does not cause any spurious substructure, it appearsthat the centroid of the dark peak is influenced by thislarge inhomogeneity of the source galaxy distribution.We suspect that the elongation of the substructure inthe dark peak region along the merger axis also facilitatesthe centroid shift. This particular shape of the substruc-ture should make its centroid more uncertain along theP3-P3 ′ orientation and sensitive to the source densityfluctuation near the dark peak region. The CFHT loca-tion of the dark peak in M07 is similar to that of J12,although it is closer to P3 ′ by ∼ ′′ than in J12. However,given the large smoothing scale (because of the relativelysmall number of source galaxies) of the CFHT mass re-construction, we do not consider the centroid differencebetween M07 and the current study very significant (seethe centroid variation in Figure 7 of M07 for differentimages).Finally, we discuss the effect of cluster galaxy contam-ination. In J12, the cluster member selection is basedon the CFHT g − r color, mainly identifying the red-sequence galaxies of A520 except for some blue galaxieswhose spectroscopic redshifts are known. The currentACS selection based on three filters approximately in-creases the number of the cluster member candidates by ∼
60% (295 vs. 474 candidates). Most of this increasecomes from increasing the number of relatively faint bluecluster member candidates whose F435W-F606W colorsare less than ∼ .
3. However, this improvement in thecluster member removal has a negligible impact on theweak lensing analysis for the following reasons. First,the blue cluster member selection is still unreliable evenwhen one uses three broadband photometry. Second, wefind that the spatial distribution of these additional bluecluster candidates does not correlate with the substruc-tures. Third, most importantly, our mass reconstructionusing the source galaxy catalog where we only removethe red-sequence is very similar to the results presentedin Figure 5. MASS ESTIMATES
It is possible to use the two-dimensional mass map tomeasure substructure masses, but the results are sensi-tive to the algorithm used. More importantly, on smallscales the result depends on details such as smoothingscheme, treatment of non-linearity, etc. Also, one canconsider fitting halo models (e.g., NFW) to all massclumps simultaneously. This is feasible when the sub-structures are simple and sufficiently massive such asthose of the “El Gordo” cluster (Jee et al. 2013). Wefind that this simultaneous fit becomes unstable when ap-plied to A520, which consists of at least five mass clumpswithin the r ∼ . Figure 8.
Influence of CTI on the A520 mass reconstruction. We present mass reconstruction results based on the KS93 method fordifferent CTI-correction schemes. The left, middle, and right panels correspond to the cases of the left, middle, and right panels in Figure 1,respectively. Although the CTI effect alone does not introduce any artificial substructures. Incomplete corrections will cause inaccuraterepresentation of the relative strengths among different substructures. The arrow indicates the location which we identify as a new centroidof the dark core. It is clear that the significance of this substructure will be underestimated if the CTI correction is less than optimal. Weuse the same intensity-to-color mapping scheme for the representation of the three mass maps after normalizing the result by the maximumconvergence value of each map.
Figure 9.
Ellipticity comparison between ACS and WFPC2. We compare the raw ellipticities that are directly obtained from ellipticalGaussian fitting. A total of 1764 source galaxies are common to both shape catalogs. PSF and CTI effects are corrected, but no shearcalibration is applied. The J12 ellipticities from the WFPC2 image agree nicely with those from the current ACS data. The average slopeof the two panels is ∼ .
05. This small departure from unity disappears when we apply the due shear calibration factor to each dataset.
Figure 10.
Mass reconstruction test using the source selectionin J12. The galaxy shapes are measured from the current ACSdata. We use the KS93 method to compute the convergence fieldby assuming g = γ . Interpretation requires caution because thefield boundary defined by the overlapping region between the ACSand WFPC2 images is complicated. Nevertheless, we confirm thatin this mass reconstruction the location of the dark core agreeswith that in J12. mass-sheet degeneracy. C12 combined ACS and Magel-lan data in their aperture densitometry to overcome thesmall field of view of ACS. Although both this study andC12 supplement the ACS data with ground-based im-ages, we believe that the main differences arise from thedifferent treatments of the ACS data.As is done in J12, we combine the shape catalogs fromthe CFHT and ACS images by preferring ACS shapeswherever available. The difference in the effective sourceplane redshift between ACS and CFHT is accounted forby scaling up the CFHT shears by the amount requiredfor the difference in the redshift. We verify that theamount of correction due the mean source redshift dif-ference is consistent with the difference in the amplitudeof the raw tangential shear profiles in the overlappingregion.The tangential shear is defined as g T ( r ) = − g + ( r ) cos 2 φ − g × ( r ) sin 2 φ, (11)where φ is the position angle of the object with respectto the reference point. We use the symbol “ g ” to remindreaders that the measured quantities are in fact reducedshears.In Figure 12, we present the tangential shear profilesderived from this combined shape catalog around P3 (left) and P3 ′ (right). The open circles represent theresults from our “null” (45-deg rotation) test and showthat this so-called B-mode signal is statistically consis-tent with zero. The best-fit isothermal profiles usingthe data at r > ′′ (dashed) predict a velocity dis-persion of 1077 ±
44 km/s. The best-fit NFW profileusing the Duffy et al. (2008) mass-concentration rela-tion gives M = 9 . +1 . − . × M ⊙ ( r = 1 . ± . c = 3 . ± . . Although we quote these val-ues based on the tangential shears around P3, little dif-ference is observed as to the total mass of the clusterwhen we select P3 ′ as a reference point. C12 report M = (9 . ± . × M ⊙ by assuming c = 3 .
5. Their M mass is consistent with ours.A good agreement in terms of the global mass is alsoseen when we compare projected masses. C12 estimatethat within r = 700 kpc the aperture mass is (5 . ± . × M ⊙ , which is close to our estimate (5 . ± . × M ⊙ .The aperture mass statistics can be evaluated by per-forming the following integral: ζ c ( r , r , r max ) = ¯ κ ( r ≤ r ) − ¯ κ ( r < r ≤ r max ) (12)= 2 Z r r h γ T i r dr + 21 − r /r max Z r max r h γ T i r dr, (13)where h γ T i is the azimuthally averaged tangential shear, r is the aperture radius, and r and r max are the inner-and the outer radii of the annulus. It is important toiteratively update γ using γ = (1 − κ ) g where κ is non-negligible. Because ζ c ( r , r , r max ) provides a densitycontrast of the region inside r < r with respect to thecontrol annulus ( r , r max ), one desires to choose r and r max to be large so that the mean density in the controlannulus becomes small and mostly limited by the largescale structure (i.e., cosmic shear) of the field. In thispaper, we choose the annulus defined by r = 600 ′′ and r max = 800 ′′ . When P3 is selected as the reference, themean density of this region is estimated to be ¯ κ = 0 . κ = 0 . ∼
5% differ-ence in the substructure masses within the r = 150 kpcradius. In this paper, we adopt the SIS fitting values forconsistency with J12.As for error propagation in aperture mass densitom-etry, we perform 1000 Monte Carlo simulations by ran-domizing the tangential shear profiles. Neither the differ-ence in the background density estimation nor the effectof the cosmic shear (Hoekstra 2001, 2003) is included inour error propagation. We note that the latter is notimportant on small scales.Table 1 lists the substructure masses obtained from thecurrent aperture mass densitometry. We leave out thesubstructure P6 because its r = 150kpc circle substan-tially overlaps with that for P3 ′ . We do list the resultsfor P3 to enable a comparison with the results from J12and C12.The aperture mass centered on P3 ′ is (3 . ± . × M ⊙ , whereas for P3 we find (3 . ± . × M ⊙ . By M , we define the total within the radius for which themean internal density is 200 times the critical density. ST Study of Dark Core in Abell 520 13
Figure 11.
Difference in the source galaxy distribution between ACS (left) and WFPC2 (right) data. We smooth the source galaxydistribution using a Gaussian with FWHM=30 ′′ . Overlaid are the convergence contours derived from the ACS data. We argue that thedifference in the source density fluctuation might have caused the centroid shift of the substructure P3 in J12. One of the largest differencebetween the two source density maps is seen near P3 (red circle), where the WFPC2 shows a strong concentration relative to the neighboringregion whereas this contrast is not clear in the ACS data. The latter value is lower than that of J12 by ∼ . ± . × M ⊙ from theiraperture mass densitometry. This estimate is statisti-cally consistent with our current result, mainly becauseof their larger errors. When we use the ACS shape cat-alog matched to the WFPC2 observations, we obtain(3 . ± . × M ⊙ , in better agreement with theJ12 value.As both this study and C12 analyze the same ACSdata, perhaps this 16% discrepancy in the central valueis an indicator of a systematic difference between thetwo studies. The C12 mass of P3 is in slight tensionwith the J12 and M07 values at the ∼ σ level. A similarlevel of variations exists for other substructures as well.For example, the current aperture mass of P4 is (4 . ± . × M ⊙ , whose central value is about 16% higherthan the J12 result, although again the two results arestatistically consistent. C12 estimated the mass of P4to be 5 . ± .
68. This result is ∼
32% higher than theresult estimated in this study, and the discrepancy islarger than in the case of the P3 comparison.The ratio of the aperture mass of P3 ′ to that of P3 inour ACS analysis is ∼ .
17, which may appear discordantwith the visual impression of a larger difference that onereceives from the mass reconstruction (Figure 5). We at-tribute this difference to the different range of tangential shears affecting each result: the aperture mass densit-ometry uses only the information outside the apertureradius ( r > r ) whereas the mass reconstruction is influ-enced by the shear signal inside the aperture, as well asthe information outside the aperture. Therefore, the fac-tor of two higher amplitude of the tangential shear (Fig-ure 12) at the inner most bin, which is not included inthe aperture mass statistics, is responsible for the largercontrast between P3 and P3 ′ in our ACS mass recon-struction.In § M ap ( r <
150 kpc) = (3 . ± . × M ⊙ for P3, ∼
8% lower thanthe above (3 . ± . × M ⊙ . When no CTI cor-rection is applied, the resulting aperture mass becomes M ap ( r <
150 kpc) = (2 . ± . × M ⊙ , ∼
14% lowerthan the result that we obtain with the latest CTI model.On the other hand, we find that the aperture mass of P4increases by ∼ Figure 12.
Tangential shear profile around P3 (a) and P3 ′ (b). We combine the shape catalogs from the ACS and CFHT images,and applied the due redshift scaling to the CFHT shears. The relevant critical surface mass density for the plots shown here is Σ c =3 . × M ⊙ pc − . The filled circles represent the tangential shears around the reference points. The open circles represent our null textresults obtained by rotating galaxies by 45 ◦ . The latter result (being consistent with zero) shows that the residual systematics in ouranalysis is negligible. The dotted line denotes the lower limit of the radial bin used for fitting the two model (NFW and SIS) profiles. Table 2
Optical Luminosity of Substructure ( r <
150 kpc)Substructure L B L R L F W M/L B M/L R M/L F W ( h − L B ⊙ ) ( h − L R ⊙ ) ( h − L F W ⊙ ) ( h M ⊙ /L B ⊙ ) ( h M ⊙ /L R ⊙ ) ( h M ⊙ /L F W ⊙ )P1 1.35 1.52 2.18 139 ±
32 123 ±
28 86 ± ± ± ± ±
43 266 ±
34 186 ± ±
97 813 ±
78 572 ± ± ± ± ±
19 107 ±
15 92 ± Note . — We subtract the gas mass (the upper limit in Table 1) in the estimation of the M/L values. For the estimation of L F W , no colortransformation is performed in order to ease the comparison with the C12 results. We compare the substructure masses in Figure 13 withthose obtained by J12 and C12. Our ACS weak lens-ing analysis of A520 provides results that are generallyconsistent with those from our previous WFPC2 study(J12). The central values of the masses of P1, P3, and P5are lower in our ACS study by ∼ ∼ ∼ ∼
5% and ∼ Luminosity and
M/L
Estimation
M07 and J12 estimated the rest-frame B -band lumi-nosity by selecting cluster galaxies using the CFHT g − r color in conjunction with the spectroscopic catalogs. Inthis paper, we update the luminosities of A520 using theACS data. The availability of three filters and the im-proved photometry thanks to high-resolution imaging are Figure 13.
Mass comparison among four different studies. Wecompare aperture masses from M07, J12, C12, and this study. Thetwo largest differences between this study and C12 are found forthe mass estimates of P3 and P4. C12 give a lower value for P3and a higher value for P4. We are able to reproduce this trendwhen we repeat our weak lensing analysis without performing anyCTI correction (see also Figure 8). Not compared in this plot isthe substructure mass of P3 ′ , which is not identified by C12. ST Study of Dark Core in Abell 520 15
Figure 14.
Mass-to-light ratio comparison among the differentsubstructures in A520. The M/L values of the “normal” peaks (P1,P2, P4, and P5) are consistent with one another with small scattersaround their mean ∼ M ⊙ /L R ⊙ . However, the dark peaks (P3and P3 ′ ) have considerably higher M/L values. expected to improve the accuracy in the A520 luminos-ity estimation. We define the cluster galaxies as the ob-jects whose F606W-F814W and F435W-F606W colorsare consistent with those of the spectroscopic members.For easy comparison, we adopt the same quadrilateralboundary shown in Figure 1 of C12. We discard theobject if the spectroscopic redshift is known and is notwithin the cluster redshift range. Also, stars are identi-fied by comparing the light profile with that of the modelPSF. The F814W filter is close to the rest frame R filterat z = 0 .
2, and we establish the photometric transfor-mation by performing synthetic photometry using thespectral energy distribution (SED) templates of Kinneyet al. (1996) and the filter throughput curves of ACSand Johnson R; we verify that the elliptical template ofKinney et al. (1996) yields F606W-F814W ≃ .
78 andF435W-F606W ≃ .
73, consistent with the observed val-ues of the A520 spectroscopic members (see Figure 1 ofC12).The linear best-fit result is: R rest = F W − . F W − F W )+0 . − DM, (14)where DM is the distance modulus for the cluster red-shift. We summarize the rest-frame luminosity and theresulting M/L value of the cluster substructure in Ta-ble 2. We update the B rest luminosity of J12 based onthe current new cluster member selection, and the resultsare also displayed in Table 2.C12 did not perform any k -correction and convertedtheir observed F814W magnitude into the rest-frame lu-minosity by simply applying the distance modulus (D. We use the SEDs of the elliptical, S0, Sa, Sb, SB1, and SB2galaxies from the Kinney-Calzetti spectral atlas.
Clowe, in private communication). We refer to this lu-minosity as L F W and list our estimate also in Ta-ble 2. Our estimate of the luminosity for P3 whenwe ignore the color-dependence of the k -correction is ∼ . h − L F W ⊙ , in agreement with the C12 es-timate. The luminosities for the other peaks agree to ∼ ∼
17% when the center on the peak of the light dis-tribution, in line with the variation we see for the otherpeaks. Furthermore, to facilitate the comparison withthe mass reconstruction, C12 measure luminosities fromthe smoothed light map. Although this does not biastheir mass-to-light ratios, it does reduce the luminositymeasured within a fixed aperture by ∼ − k -correction.The Kinney et al. (1996) SED of the elliptical galaxygives more flux in R than B by ∼
35% when normalizedwith the SED of the Sun. In fact, as discussed above, wecan reproduce the C12 results.C12 argue that their selection criteria (we adopt thesame criteria also in our current study) are more inclusiveof blue cluster galaxy candidates than those of J12. Thecomparison of L B ⊙ between this study and J12 showsthat the difference is small, and our our updated rest-frame B -band luminosity for P3 is only 18% higher thanthe J12 value. This is in part because the g − r color selec-tion window in J12 was broad enough to include most ofthe bright galaxies selected in the current study. Accord-ing to the current selection, the B -band luminosities ofP3 and P4 increase by ∼
18% and ∼ B -band luminosities of P1, P2, andP5 are reduced by ∼ ∼ ∼ R -band of ∼ M ⊙ /L R ⊙ .For the B -band we find a value of ∼ M ⊙ /L B ⊙ .For sample of 4 clusters Hoekstra et al. (2002) foundan average mass-to-light ratio of 279 ± M ⊙ /L B ⊙ (eval-uated at z=0.2, assuming passive evolution). Sheldon etal. (2009) examined a large sample of clusters observedin the Sloan Digital Sky Survey. Figure 8 in Sheldon etal. (2009) shows that on small scales the central galaxiesdominate the light, resulting the mass-to-light to increasewith radius, before leveling off beyond ∼ ± M ⊙ /L i ⊙ forthe cluster. The average asymptotic value for the rangein richness is 293 ± M ⊙ /L i ⊙ .Sheldon et al. (2009) examine the M/L as a functionof distance from the BCG and their results suggest thatwithin the inner 150 kpc, the mean M/L is about 40-50%of the asymptotic value. The values listed in Table 2 forthe luminous substructures are in good agreement with6 Jee et al.this finding if we consider the M/L values from Hoekstraet al. (2002). On the other hand, the M/L values of P3and P3 ′ are much higher. Compared to the global value232 ± M ⊙ /L B ⊙ in M07 , the M/L in P3 is higherby 2 . σ , but value for P3 ′ is more than 7 σ higher. OurACS weak lensing analysis therefore supports the claimof M07 and J12 for the presence of substantial dark massin this region. In Figure 14, we compare the M/L valuesof the substructures in A520. DETAILED COMPARISON WITH C12
We have compared the results from our weak lens-ing analysis of ACS data to the results from J12 whichwas based on WFPC2 observations. In this section wepresent a more detailed comparison with the results pre-sented in C12. We start by noting that the overall large-scale distribution of the C12 mass map is similar to ourACS result. However, there are a few differences worthyof further discussion.The C12 mass map shows some indication of overden-sity at the location of P3 ′ , but it appears more as anextension of P4, rather than a definite peak as seen inour mass reconstruction (Figure 5). However, our testsof the CTI correction suggest that this may be the maincause of this difference. C12 also noticed a substructureabout 2 ′ north of P4 and labeled it as ”Peak 7” (Figure 2of C12). However, this mass peak does not appear in ourmass reconstruction, although there is a weak indicationof an overdensity around the location in our mass map.The M/L values of the substructures are slightlydifferent. The M/L value of the P3 region (150 ± M ⊙ /L F W ⊙ ) from C12 is lower than the currentvalue (200 ± M ⊙ /L F W ⊙ ) by ∼ ∼
15% and 2) their gas mass estimate 0 . × M ⊙ is higher than our value 0 . × M ⊙ by ∼ § k -correction. Using the C12 selectioncriteria, we estimate 0 . × L B ⊙ in the rest-frame B ,which is only ∼
18% higher than the estimate of J12. Ig-noring the k -correction, we obtain 1 . × L F W ⊙ inthe rest-frame F814W, which is in good agreement withthe estimate of C12.C12 presented their bootstrap resampling experimentsand claimed that any substructure resembling the darkpeak only happens in ∼
2% of the total realizations. C12speculated on the possibility that some chance alignment We cannot estimate the global M/L with the current ACSdata because of the field limit. of the sources might have led to the detection in previ-ous studies. However, the source number density in J12data is significantly higher than that of M07 and Okabe& Umetsu (2008). Furthermore, our ACS study is basedon a higher source density compared to C12 and we con-firm the presence of an overdensity. A caveat is that C12focused on the location of the dark peak defined in J12,which is ∼ ′ offset from the current centroid. C12 mighthave obtained different results if they had examined theregion near P3 ′ . As stated in §
4, our bootstrapping testshows that the dark peak P4 ′ appears ∼
99% of the ran-dom realizations at the > σ significance.We note that similar levels of M/L and mass discrep-ancy are present in other substructures as well. For in-stance, C12 quotes an aperture mass of (5 . ± . × M ⊙ for P4 whereas we estimate (4 . ± . × M ⊙ . This 32% difference for P4 is in fact largerthan the contrast in P3. Figure 13 shows the compari-son for the rest of the substructures.The error bars of C12 are on average a factor of twolarger than ours, and here we provide detailed analysisof the discrepancy. C12 present analytic expression forestimating the ζ statistic as follows: σ ζ = (cid:18) d ln r ) σ SN − r /r max (cid:19) Σ n − bin , (15)where n bin is the effective number of sources per logarith-mic bin. The summation is carried out over these loga-rithmic bins. Note that we correct for the typographicalerror in C12, where the exponent of the (1 − r /r max )term should have been two (as above) not one. The equa-tion is an approximation because 1) the integral in the ζ statistic is treated as summation, 2) the aperture massis estimated using ζ c rather than ζ , and 3) the nonlin-earity g = γ/ (1 − κ ) is ignored. We compare the resultsof this analytic error propagation with those obtainedfrom our direct Monte-Carlo analysis and find that theapproximation overestimates the errors by 70 ∼
90% forthe r = 150 kpc aperture mass given the same sourcedensity. The remaining discrepancy comes from the dif-ference in the number density of source galaxies. Thenumber density in C12 is 56 per sq. arcmin whereas it is109 per sq. arcmin in this study. De-weighting low S/Ngalaxies being considered, the rms shear of C12 is ∼ § ∼
100 per sq. arcmin whenever thenumber of orbits per pointing is two or higher as in thecurrent A520 data (Jee et al. 2005a; 2005b; 2006; 2007;2011; Dawson et al. 2012). Also, even for ACS imageswith the depth of a single orbit, our typical number den-sity of usable galaxies is above ∼
70 per sq. arcmin (Jeeet al. 2011). The source number density also depends onshape measurement and image reduction method. It ispossible that the C12 implementation of KSB togetherwith the use of the square drizzling kernel gives a smallernumber of usable galaxies. Nevertheless, Schrabback etal. (2010), who also use a KSB technique, still quote ∼
76 galaxies per sq. arcmin from their analysis of theCOSMOS data, where the mean number of orbits perpointing is about one.ST Study of Dark Core in Abell 520 17Finally, we carry out a catalog-level comparison be-tween this study and C12. C12 kindly agreed to exchangeeach team’s shape catalogs to enable a detailed compari-son. The total number of sources in C12 is 2,507 whereasit is 4,788 in this study. By looking for pairs within thedistance of 0 . ′′
5, we identify 2,148 common objects be-tween the two source catalogs.One of the most basic sanity checks is to compare ellip-ticities of identical sources, and we display the results inFigure 15. Because the shape catalog provided by C12 al-ready includes their shear calibration, we also apply ourindependent (determined from image simulation) shearcalibration to our source ellipticity to enable a fair com-parison. Figure 15 shows that there is no major shearcalibration difference. The mean slope is consistent withunity.Having found no major systematic difference at leastin global shear calibration between the two studies, wecompare mass reconstruction results obtained from thecommon 2,148 sources. We use the
FIATMAP code with-out the nonlinear updating g = γ/ (1 − κ ) because thismay amplify the difference and hamper a fair assessmentof the difference. Figure 16 shows the comparison. Itis clear that our mass map created with the C12 shape(middle) shows the mass overdensity at P3 ′ . This re-sult is slightly different from Figure 2 of C12, where theauthors perform the mass reconstruction using the com-bined shapes from HST and Magellan. Their HST onlymass reconstruction is presented in the right panel of Fig-ure 6 in C12, which shows more mass in the dark peakregion and hence is more similar to our mass map createdwith the C12 shapes (middle panel of Figure 16). Ourbootstrap experiment with the C12 weak-lensing cata-log shows that a significance mass is found in the darkpeak region for their weak-lensing data (Figure 7). Weconclude that the C12 mass map supports the presenceof the significant mass in the dark peak region in A520,although the slightly weaker significance might make theoverdensity appear as an extension of P4 rather than aseparate peak.Remember that the above comparison is limited to thecommon sources found in both the current and C12 stud-ies. Thus, an important question is how much the sourcegalaxies not used by C12 (but included in our study)affect the results. In Figure 17, we present the massreconstruction from these sources. Note that this is acompletely independent mass map. The result is sim-ilar to the one presented in Figure 16. We can see thesame substructures (including the dark peak) in this ver-sion. This illustrates that the faint galaxies discarded byC12 but included in the current study contains signifi-cant lensing signals. In addition, the comparison verifiesthat the dark peak in A520 is not caused by any potentialsystematic shape errors in the low S/N galaxies. INTERPRETATION OF THE DARK PEAK
Our ACS weak lensing analysis supports the finding ofM07 and J12 of a significant amount of dark matter inA520 at a location where there are few luminous clustergalaxies. As in J12 we identify a peak, but its positionhas shifted (as explained in § ± M ⊙ /L R ⊙ after the gas mass is subtracted. This value is much larger than what is typ-ically observed in clusters and either points to a pile-upof dark matter or a reduction in cluster galaxies in thatregion. M07 and J12 discussed a number of scenarios,and readers are referred to these two papers for details.Here we revisit the subject of collisional dark matteras a potential origin of this dark substructure. Our moti-vation is not that the current ACS analysis result favorsthis scenario, but that it is worth investigating it giventhe updated centroid and substructure properties. Wedo note that the new location of the dark peak is in bet-ter agreement with the densest part of the X-ray emis-sion and the morphology of this substructure is extendedalong the merger axis toward P2, which may support thecollisional dark-matter hypothesis for the nature of thesubstructure.M07 assumed a toy model, where peaks 1, 2, 4, and 5each contributed ∼
25% of the total mass observed in thecentral dark peak. Thus, the model assumes that thechance of dark matter scatter per particle during thisencounter is 1 in 4 or τ = σ DM m DM Σ M ≈ . , (16)where Σ M is the effective scattering depth viewed by aparticle moving along the merger axis. M07 used themass of P3 to estimate this effective depth, and obtained σ DM /m DM ∼ . ± . g − , which is about 4 σ higherthan the σ DM /m DM < g − constraint from theBullet Cluster (Markevitch et al. 2003; Randall et al.2008).In this paper, we revise the M07 model as follows. Wedecompose the mass of the dark peak into the contribu-tions from the P2 and P4 halos, the gas mass, the darkmatter associated with the cluster galaxies found withinthe r = 150kpc aperture, and the excess dark matterdue to self-interaction. On the other hand, M07 consid-ered the possibility that the entire mass of the dark peakoriginates from self-interaction.Our ACS mass reconstruction indicates that the overallpre-merger cluster mass distribution might be approxi-mately bimodal, dominated by two massive halos (P2and P4) when we hypothesize that the dark peak in thecenter is produced after the collision. We estimate thecontribution from the wings of these two halos by assum-ing an NFW profile with a scale radius of 100 kpc. Thesecond parameters of the NFW model are determinedby the lensing masses within the r = 150 kpc aperturecentered on each halo. The total contribution to theP3 ′ mass is determined to be ∼ . × M ⊙ with P2and P4 providing ∼ . × M ⊙ and ∼ . × M ⊙ ,respectively. Using the Cauchy-Schwarts inequality, weobtain a generous upper limit of 0 . × M ⊙ for theplasma mass within the r = 150kpc radius of P3 ′ . The R -band luminosity of 0 . × L R ⊙ is converted to0 . × M ⊙ using the average M/L of the rest ofthe subclusters, and we assume this to represent thedark matter mass associated with the few cluster galaxiesaround the region. Then, the net excess mass attributedto the collisional deposit becomes ∼ . × M ⊙ .Now the most uncertain part of this scenario is how thisexcess dark matter is contributed by the subclusters ofA520, and this dominates our uncertainty in the estima-8 Jee et al. Figure 15.
Shear measurement comparison between this study and C12. Shear calibration is applied. A total of 2,148 sources are commonto both shape catalogs. The comparison provides basic sanity checks (e.g., systematic difference in shear calibration). The red solid line isa fit to the data, and we found that the mean slope is consistent with unity.
Figure 16.
Direct comparison of our mass reconstruction with the C12 result. The mass reconstruction is performed with
FIATMAP usingthe common 2,148 sources. Note that this number is more than a factor of two smaller than the total number of sources 4,788 in our study.The mass overdensity at P3 ′ is seen in both mass maps. tion of the collisional cross-section. If we assume P2 andP4 contribute equally to this excess mass through darkmatter self-interaction, the mass loss fraction for eachsubstructure is ∼ M is the surface mass density of P2 or P4 beforethe mass loss (we assume spherical symmetry). In thiscase, we obtain Σ M = 0 . ± . − by averagingthe surface mass density of P2 and P4 and multiplyingthe result by 1.13. Then, from the scattering probabil-ity of ∼
13% we estimate σ DM /m DM ≈ . / (0 . ± . g − ≈ . ± .
06 cm g − . This value doesnot violate the Bullet Cluster estimate σ DM /m DM ≤ g − of Markevitch et al. (2003). Of course, therequired cross-section decreases if we assume that thescattering depth is higher than the adopted value. Thiswould happen if the dark matter particles in P4 havepassed through more than P2 before it arrived at thecurrent observed location. In fact, the location of thebow-shock feature indicates that P4 may correspond tothe “bullet” of the Bullet Cluster and have experiencedST Study of Dark Core in Abell 520 19 Figure 17.
Mass reconstructing using the faint galaxies presentin the catalog of this study but excluded by C12. We use
FIATMAP with the remaining 2640 sources. The resulting mass map is similarto our full mass reconstruction obtained from all 4788 sources. Thisillustrates that the faint galaxies discarded by C12 but included inthe current study contains significant lensing signals. In addition,the results verifies that the dark peak in A520 is not caused bypotential systematic shape errors in the low S/N galaxies. the most acceleration, which implies that the other grav-itational potential may have been deeper than that ofP2. If we assume that P4 passed through P1, P2, and P5on its way to the current location, the scattering depthincreases to Σ M = 0 . ± . − , which gives across-section σ DM /m DM ≈ . ± .
12 cm g − .Although the above constraint on the dark mattercross-section is based on simplistic assumptions of theunobserved pre-merger configuration, the result is inter-esting because it shows that the current observation ofA520 may be explained by self-interaction of dark mat-ter without creating any serious tension with previousvalues. Tighter constraints may become possible if thecluster is followed up with detailed numerical studies. CONCLUSIONS
We have presented a re-analysis of HST/ACS images ofA520. Our ACS weak lensing study confirm the presenceof a region of very high mass-to-light ratio, first reportedin M07 with CFHT data and subsequently supportedby Obake & Umetsu (2008) and J12 with Subaru andWFPC2 data, respectively. We are able to reproduce theresults from J12 when we match the selection of our ACSweak lensing catalog to that of the WFPC2 analysis, butfind no clear peak at the location where they reportedone. Our detailed comparison suggest that this is caused by a variation in the source number density, which leadsto additional systematic noise in the mass map. TheACS analysis shows less variation, owing in part to theoverall higher number density, and thus should be morereliable.The analysis presented here indicates a peak that isshifted by ∼ ′ compared to J12. Its position now co-incides well with the location of the peak of the X-rayemission. Our mass reconstruction compares well withthat of C12, although we identify a number of differences.In particular, C12 do not identify such a clear peak, al-though we note an extension of P4 in their map towardsP3 ′ . A comparison of CTI correction algorithms, includ-ing one used by C12, suggest that the density contrast atthe location of P3 ′ is affected by CTI (see Figure 8). Weuse the latest algorithm from Ubeda & Anderson (2012)which performs best as demonstrated in Figure 1. Notethat this CTI correction method was not available toC12.Our shape measurement analysis is able to reach asource number density of ∼
109 arcmin − , which is con-siderably higher than the ∼
56 arcmin − used by C12.This may be explained by differences in the reductionof ACS data and how measurements in the different fil-ters are combined. The three-filter ACS data allow foran improved membership determination which increasesthe luminosity by ∼
16% compared to J12. We find thatour luminosity estimates are consistent with C12 whenwe compare to the same band. The mass-to-light ratios(after subtracting the X-ray gas mass) of the dark peakusing the old and new centroids are 285 ± M ⊙ /L R ⊙ and 813 ± M ⊙ /L R ⊙ , respectively (in the rest-frame B -band, 349 ± M ⊙ /L B ⊙ and 966 ± M ⊙ /L B ⊙ , re-spectively). Our χ test shows that the constant mass-to-light ratio hypothesis is rejected at least at the ∼ σ level. The mass-to-light ratio is therefore much higherthan is typically observed in clusters and could be dueto a reduction in cluster galaxies or an increase in theamount of dark matter in that region. Although westill cannot single out a scenario that explains the ob-servations, we revisit the case of collisional dark matter.With the updated substructure properties and consid-eration of other physical factors for the contribution tothe dark peak mass, we find that the net excess massof the dark peak region can be explained with a moreconventional range of dark matter self-interacting cross-section σ DM /m DM ≈ . − .
94 cm g − , where theuncertainty is dominated by unknown scattering depthalong the merger axis. This range is consistent with theresults obtained from the Bullet Cluster. Detailed nu-merical simulations must be carried out to draw morephysically meaningful constraints from the current A520observation. Nevertheless, our analytic study hints atthe possibility that A520 can be used to investigate thelower limit of the self-interacting dark matter.We thank D. Clowe for some useful discussions andagreeing to exchange weak-lensing catalogs. M. J. ac-knowledges support from the National Science Founda-tion under Grant No. PHYS-1066293 and the hospitalityof the Aspen Center for Physics. H. H. ackowledges sup-port from NWO VIDI grant number 639.042.814. Thisresearch was supported in part by the National Science0 Jee et al.Foundation under Grant No. NSF PHY05-51164 andNSF PHY11-25915 to KITP. AB acknowledge supportfrom NSERC Canada through the Discovery Grant pro-gram., where theuncertainty is dominated by unknown scattering depthalong the merger axis. This range is consistent with theresults obtained from the Bullet Cluster. Detailed nu-merical simulations must be carried out to draw morephysically meaningful constraints from the current A520observation. Nevertheless, our analytic study hints atthe possibility that A520 can be used to investigate thelower limit of the self-interacting dark matter.We thank D. Clowe for some useful discussions andagreeing to exchange weak-lensing catalogs. M. J. ac-knowledges support from the National Science Founda-tion under Grant No. PHYS-1066293 and the hospitalityof the Aspen Center for Physics. H. H. ackowledges sup-port from NWO VIDI grant number 639.042.814. Thisresearch was supported in part by the National Science0 Jee et al.Foundation under Grant No. NSF PHY05-51164 andNSF PHY11-25915 to KITP. AB acknowledge supportfrom NSERC Canada through the Discovery Grant pro-gram.