Cluster-Cluster Lensing and the Case of Abell 383
Adi Zitrin, Yoel Rephaeli, Sharon Sadeh, Elinor Medezinski, Keiichi Umetsu, Jack Sayers, Mario Nonino, Andrea Morandi, Alberto Molino, Nicole Czakon, Sunil R. Golwala
MMon. Not. R. Astron. Soc. , 1–9 (2011) Printed 15 October 2018 (MN L A TEX style file v2.2)
Cluster-Cluster Lensing and the Case of Abell 383
Adi Zitrin (cid:63) , Yoel Rephaeli , Sharon Sadeh , Elinor Medezinski , Keiichi Umetsu ,Jack Sayers , Mario Nonino , Andrea Morandi , Alberto Molino , Nicole Czakon ,Sunil R. Golwala School of Physics and Astronomy, the Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University,Tel Aviv 69978, Israel Department of Physics and Astronomy, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218 Institute of Astronomy and Astrophysics, Academia Sinica, P. O. Box 23-141, Taipei 10617, Taiwan Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125 INAF-Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34131 Trieste, Italy Instituto de Astrof´ısica de Andaluc´ıa (CSIC), C/Camino Bajo de Hu´etor, 24, Granada, 18008, Spain
15 October 2018
ABSTRACT
Extensive surveys of galaxy clusters motivate us to assess the likelihood of cluster-cluster lensing (CCL), namely, gravitational-lensing of a background cluster by a fore-ground cluster. We briefly describe the characteristics of CCLs in optical, X-ray andSZ measurements, and calculate their predicted numbers for ΛCDM parameters and aviable range of cluster mass functions and their uncertainties. The predicted numberof CCLs in the strong-lensing regime varies from several ( <
10) to as high as a fewdozen, depending mainly on whether lensing triaxiality bias is accounted for, throughthe c-M relation. A much larger number is predicted when taking into account alsoCCL in the weak-lensing regime. In addition to few previously suggested CCLs, wereport a detection of a possible CCL in A383, where background candidate high- z structures are magnified, as seen in deep Subaru observations. Key words: cosmology: observations; dark matter; galaxies: clusters: individuals:Abell 383; galaxies: clusters: general; gravitational lensing
The mass density in the central regions of galaxy clusterstypically exceeds the critical value required for lensing, gen-erating multiple-images of background objects. This phe-nomenon is known as strong-lensing (SL) and the back-ground sources are usually very distant field galaxies, lensedinto magnified and often multiple arcs on the lens plane. Re-cent analyses have shown that many sets of multiply-lensedimages can be uncovered with high-quality space imag-ing measurements and improved modelling techniques (e.g.,Broadhurst et al. 2005; Liesenborgs et al. 2007; Limousinet al. 2008; Newman et al. 2009; Zitrin et al. 2009; Coeet al. 2010; Deb et al. 2010; Richard et al. 2010; Mertenet al. 2011).With more precise knowledge of the global and large- (cid:63)
E-mail: [email protected] scale parameters, and extensive ongoing surveys of galaxyclusters in several spectral regions, the possibility of a fore-ground cluster lensing a background cluster is of practicalinterest.An initial estimate of the possibility of observingcluster-cluster lensing (CCL) was made by Cooray, Holder& Quashnock (1999), who predicted that a few dozen CCLsmay be observed over the full sky. Soon thereafter, two suchlenses were discovered. Blakeslee (2001) and Blakeslee et al.(2001) found that the nearby supercluster A2152 ( z = 0 . z = 0 .
134 (which wasthen designated A2152-B). The centres of these two clustersare separated by 2.4 (cid:48) , and some background cluster galaxiesof the more distant cluster seem magnified and distorted inthe image-plane of A2152. Athreya et al. (2002) have shownthat an excess of distant galaxies in the South-West area ofMS 1008-1224 is most likely also a weaker lensing effect of a c (cid:13) a r X i v : . [ a s t r o - ph . C O ] A ug Zitrin et al. background cluster near the line of sight. There seem to beno other explicit cases of CCLs reported to date.Bertin & Lombardi (2001) have also investigated theproperties of a “double lens” configuration, and mainly itseffect on WL analyses. In this context, the effect of interestis the lensing of a background source by two (at least par-tially) aligned lenses, where several such configurations weresuggested or theoretically discussed before (e.g., Crawford,Fabian & Rees 1986; Seitz & Schneider 1994; Molinari, Buz-zoni & Chincarini 1996; Wang & Ulmer 1997; Gavazzi et al.2008).Major advances in the capability of detecting weak low-brightness emission in the optical and X-ray regions, andmore recently also in SZ mapping of many clusters, togetherwith increased precision in the values of the cosmological pa-rameters, make the (strong) CCL phenomenon of practicalinterest as a probe of cluster properties. Additionally, thestatistics of CCLs enhances the use of clusters as probes ofthe evolution of the large scale structure (LSS). The man-ifestation of SL in different bands of the electromagneticspectrum secures the identification of CCLs. Contrasting theresults from a search of CCLs with theoretical predictionsmay yield important new insight, especially on the late evo-lution of the LSS.We briefly describe the possible observational signaturesof CCLs in the optical, X-ray and SZ, and carry out a de-tailed calculation of the expected numbers of CCLs in sev-eral cosmological models using current values of the globaland cluster parameters. Our updated treatment here (forprevious calculation see Cooray, Holder & Quashnock 1999)yields a wide range of values for the predicted numbers ofCCLs, reflecting modelling and observational uncertainties.Additionally, we report a (possible) discovery of anothermoderately-lensed (magnified by 14 ± § z background cluster at z ∼ . +0 . − . behind A383 ( z = 0 . ∼ . (cid:48) from its centre, as seen in Figure 2.The paper is organised as follows: In § § §
4. Our main results are summarized in § Lensing of a background cluster results in magnified opti-cal images of the background cluster galaxies, and in hith-erto undetected signatures in the X-ray and microwave re-gions. In the image plane, a clear local overdensity of mag-nified, distorted, and stretched optical images would gener-ally be expected when the galaxies of a background clusterare lensed. The higher redshift of the background clustershould result in images fainter by the luminosity distanceratio (relative to the lensing cluster), but boosted by themagnification effect which though preserves surface bright-ness, will magnify the total flux (due to the increased areaoccupied by each source in the image-plane). Also, whenhaving multi-band imaging, the higher redshift of the back-ground cluster will cause the background galaxies to lookredder relative to the lens red-sequence galaxies (see Fig-ure 2), though this effect might not be prominent in a sim-ple RGB colour-composite image when redshift differences are relatively small (and further weakened by the Butcher-Oemler effect; e.g., Butcher & Oemler 1978), and in sucha case are more likely to be revealed by producing photo-metric catalogues which may exhibit a different, secondaryred-sequence corresponding to the background cluster.The steep dependence of the X-ray surface brightnesson redshift would generally mean that, even though magni-fied by the foreground cluster, the background cluster will atbest look as a faint part of the foreground cluster emission.If the background cluster lies further away from the line ofsight, there might be a traceable signature, as the magnifiedbackground flux will be seen far enough from the foregroundcluster centre, where the foreground flux is lower and thusmight enable a clear detection, but only if the backgroundcluster is sufficiently luminous. We note, however, that in thestrong regime this may resemble X-ray images of a substruc-ture, merger, or related shocks, and thus without additionalinformation, even if such a signal is detected it could wellbe miss-interpreted. In addition (as was noted previously byCooray, Holder & Quashnock 1999), X-ray spectra can beused to determine the background cluster redshift, particu-larly by the measurement of the relatively strong Fe lines.Current measurement capabilities (e.g, with
Chandra ) en-able determining the cluster redshift up to z ∼
1. Still, itmight not be feasible to detect a CCL based solely on X-rayimaging measurements.The SZ effect is the change in the CMB intensity dueto Compton scattering of CMB photons as they traverseintracluster gas (e.g., Rephaeli 1995; Carlstrom, Holder &Reese 2002). The result is a redshift-independent distortionof the CMB spectrum, whose thermal component constitutesa decrement of CMB spectrum below (cid:39)
218 GHz, and anincrement of the spectrum above (cid:39)
218 GHz.The SZ effect is measured with respect to the unscat-tered CMB at the location of the cluster, so lensing affectsthe SZ signal similarly at all observed frequencies. The to-tal observed SZ signal is therefore a sum of the intrinsic SZsignal from the lensed cluster, which is then magnified bythe foreground cluster, plus the SZ signal due to scatteringin the foreground cluster.The fact that the SZ effect is independent of redshiftmay help in making the identification of a CCL more fea-sible in SZ surveys than in X-ray surveys. However, it maystill be hard to disentangle the signals of the foreground andbackground structures, as the SZ signal usually stretches outto large (projected) distances and may thus cover-up lensedfeatures. The net result from such a trade-off will depend onthe lens and source redshifts, and on the projected distanceof the lensed feature from the line-of-sight of the lensingcluster, so that generally, structures closer to the line-of-sight will be more strongly lensed and magnified, but therelative flux from the foreground cluster will also be higher.As in the X-ray, also here strong CCL may resemble imagesof merger, or related shocks. Obviously, a CCL identificationcan be more secure if lensing features are revealed in bothX-ray and SZ measurements, or if clearly detected in opticalimaging measurements. With photometric and/or spectro-scopic data, such a detection could yield precise informationon both clusters.In § c (cid:13) , 1–9 luster-Cluster Lensing: A383 In order to assess the probability for CCLs we integrate themass function over two cluster populations, namely thoseof the lenses and sources. We do so for both the Press &Schechter (1974) mass function (hereafter PS), and that of(Sheth & Tormen 1999, hereafter ST). For each cluster of thelens population we integrate the mass function of sources ly-ing behind the lens, and included within the Einstein radius,as (properly) determined by the source and lens redshifts.The volume element over which the source integration is car-ried out is computed in terms of the solid angle defined bythe Einstein ring in the plane of the lens, projected onto thesource redshift, by means of the ratio of the squared lens-source angular diameter distances. Integrating over the lenspopulation then yields the desired number of CCLs.Note that we include in this estimate only sources thatare fully enclosed within the respective Einstein radius, ig-noring a partial alignment of the source within this radius.In this regard our estimate constitutes a lower limit on thenumber of CCLs.
The equation governing the relation between the concentra-tion parameter and the Einstein radius assuming an NFWprofile (Broadhurst & Barkana 2008) is, (cid:16) R v ρ zc ∆ c cr (cid:17) c v ln (1 + c v ) − c v / (1 + c v ) g ( x ) x = 1 , (1)where ∆ c and ρ zc are the overdensity at virialisation andcritical density at redshift z , respectively,Σ cr = c πG D OS D OL D LS (2)is the critical surface density, D OS , D OL , and D LS are theobserver-source, observer-lens, and lens-source distances, re-spectively, and R v = 1 .
691 + z (cid:20) MM π Ω m ∆ c (Ω m , z ) (cid:21) / Mpc · h − , (3)is the virial radius. Also, x ≡ R E c v R v , where R E is the Einsteinradius, and g ( x ) = ln x , x = 1 √ x − tan − (cid:113) x − x +1 , x > √ − x tanh − (cid:113) − x x , x < . (4)The concentration parameter c v scales with mass andredshift according to the following relation: c v = A ( M/M ∗ ) B (1 + z ) C , (5)where the parameters A, B, C and M ∗ are taken from variousc-M relations as we discuss below.The solution of Eq. (1) provides the Einstein radius asa function of c v , from which the angular Einstein radius θ E = R E /D A ( z l ), the ratio between the (physical) Einsteinradius and the angular diameter distance to the lens, can bereadily determined.Having solved for the angular Einstein radius at thelens, we can now estimate the number of source clusters that Figure 1.
The lens-source configuration. The grey area repre-sents the section of the lens plane which is included within theEinstein radius, as calculated from the lens and source redshifts.Integration of the source population is performed along the coneextending to the right of the lens, with an angular cross sec-tion corresponding to the projected Einstein radius at the sourceredshift, z S . The corresponding source-plane volume element isdenoted in purple. Note that by virtue of the low angular scalesinvolved, one can safely use the flat sky approximation to calcu-late the volume element at the source redshift. would undergo lensing, i.e. the ones lying behind the lensand included within the angular area subtended by the Ein-stein radius. For this purpose we set the lens mass and red-shift, and integrate the mass function over the relevant massrange, a volume element defined by the source-cluster red-shift, z L < z S < ∞ , and the angular diameter element spec-ified by the Einstein radius of the lens-source system, pro-jected onto the source redshift by means of the squared lens-source angular diameter distance ratio, ( d A L /d A S ) (Fig. 1).This result provides the number of lensed sources behind alens lying at redshift z L , and having a mass m L . The totalnumber of CCL occurrences is likewise estimated by inte-grating the mass function over the mass-redshift space ofthe lens: Ncc = (cid:82) mL (cid:82) VL (cid:82) ms (cid:82) VS n ( mL, zL ) n ( mS, zS ) dmLdVLdmSdVS (6)= 4 π (cid:82) mL (cid:82) zL n ( mL, zL ) r LdmL drLdzL dzL...... (cid:82) mS (cid:82) zS (cid:82) Ω θE n ( mS, zS ) dmSdzSd Ω θE . As is obvious, results depend significantly on the mass func-tion, and quite strongly on the c-M relation. This relation isonly roughly estimated from numerical simulations of clus-ters; therefore, it introduces a large uncertainty in the pre-dicted numbers of CCLs. We have used the PS and ST massfunctions and various c-M relations, each specified in termsof a different set of A,B,C and M ∗ parameters (in eq. 5).We first use the notation and parameters given in Komatsu& Seljak (2002), based on the work of Seljak (2000) andBullock et al. (2001). In this notation M ∗ = 5 . × M (cid:12) (as calculated by us according to WMAP7 parameters) isthe solution to σ ( M ) = δ c , where σ ( M ) is the present dayrms mass fluctuations, and δ c the threshold overdensity for c (cid:13)000
The lens-source configuration. The grey area repre-sents the section of the lens plane which is included within theEinstein radius, as calculated from the lens and source redshifts.Integration of the source population is performed along the coneextending to the right of the lens, with an angular cross sec-tion corresponding to the projected Einstein radius at the sourceredshift, z S . The corresponding source-plane volume element isdenoted in purple. Note that by virtue of the low angular scalesinvolved, one can safely use the flat sky approximation to calcu-late the volume element at the source redshift. would undergo lensing, i.e. the ones lying behind the lensand included within the angular area subtended by the Ein-stein radius. For this purpose we set the lens mass and red-shift, and integrate the mass function over the relevant massrange, a volume element defined by the source-cluster red-shift, z L < z S < ∞ , and the angular diameter element spec-ified by the Einstein radius of the lens-source system, pro-jected onto the source redshift by means of the squared lens-source angular diameter distance ratio, ( d A L /d A S ) (Fig. 1).This result provides the number of lensed sources behind alens lying at redshift z L , and having a mass m L . The totalnumber of CCL occurrences is likewise estimated by inte-grating the mass function over the mass-redshift space ofthe lens: Ncc = (cid:82) mL (cid:82) VL (cid:82) ms (cid:82) VS n ( mL, zL ) n ( mS, zS ) dmLdVLdmSdVS (6)= 4 π (cid:82) mL (cid:82) zL n ( mL, zL ) r LdmL drLdzL dzL...... (cid:82) mS (cid:82) zS (cid:82) Ω θE n ( mS, zS ) dmSdzSd Ω θE . As is obvious, results depend significantly on the mass func-tion, and quite strongly on the c-M relation. This relation isonly roughly estimated from numerical simulations of clus-ters; therefore, it introduces a large uncertainty in the pre-dicted numbers of CCLs. We have used the PS and ST massfunctions and various c-M relations, each specified in termsof a different set of A,B,C and M ∗ parameters (in eq. 5).We first use the notation and parameters given in Komatsu& Seljak (2002), based on the work of Seljak (2000) andBullock et al. (2001). In this notation M ∗ = 5 . × M (cid:12) (as calculated by us according to WMAP7 parameters) isthe solution to σ ( M ) = δ c , where σ ( M ) is the present dayrms mass fluctuations, and δ c the threshold overdensity for c (cid:13)000 , 1–9 Zitrin et al. spherical collapse at z = 0, with A = 10, B = − .
2, and C = − m , Ω Λ , n, h, σ ) = (0 . , . , . , . , . × M (cid:12) - 1 × M (cid:12) our calculations yield ∼ .
03 CCLs witha PS mass function, and ∼ . × M (cid:12) , we obtain ∼ . ∼ . M ∗ = 2 × h − M (cid:12) , A = 7 . B = − . C = − .
71. With these values, for a ΛCDM model with(Ω m , Ω Λ , n, h, σ ) = (0 . , . , . , . , . × M (cid:12) - 1 × M (cid:12) , our calculationsyield ∼ ∼ × M (cid:12) , our cal-culations yield ∼ ∼ M ∗ = 1 . × h − M (cid:12) , A = 12 . B = − .
13, and C = − m , Ω Λ , n, h, σ ) = (0 . , . , . , . , . × M (cid:12) - 1 × M (cid:12) , our calculations yield ∼ ∼
17 CCLs with a ST mass function.When taking into account also background groups ofgalaxies down to 5 × M (cid:12) , we predict ∼
38 CCLs with aPS mass function, and ∼
68 CCLs with a ST mass function.Thus, taking into account the lensing projection bias boostsCCL numbers by about an order of magnitude.We compare these results to the observed c-M relationfrom a small sample of 10 clusters derived by Oguri et al.(2009), in which M ∗ = 1 × M (cid:12) , A = 12 . B = − . C = −
1. This relation yields concentrations higher thanpredicted by ΛCDM simulations, and even higher than thosederived observationally by previous work (e.g., Comerford &Natarajan 2007), and are likely to be extreme results thatare perhaps less relevant for our purposes.Assuming these values, in ΛCDM with(Ω m , Ω Λ , n, h, σ ) = (0 . , . , . , . , . × M (cid:12) - 1 × M (cid:12) , our calculations yield ∼
165 CCLs witha PS mass function, and ∼
260 CCLs with a ST massfunction. When taking into account also background groupsof galaxies down to 5 × M (cid:12) , our calculations yield ∼
660 CCLs with a PS mass function, and ∼
940 CCLswith a ST mass function. Thus, according to the observedrelation (which is known to produce higher concentrationthan ΛCDM simulations) the predicted total numbers ofCCLs are quite large.It should be noted that taking into account the weaklensing regime, in which the background cluster does nothave to be within the Einstein radius as projected onto the source plane, but can be further out up to several Einsteinradii, the likelihood of a CCL increases significantly. Specif-ically, still assuming the flat sky approximation, the likeli-hood of a CCL increases simply as the square of the ratioof the projected distance of the background cluster and theEinstein radius of the foreground cluster.Moreover, extending the calculations to the 1 σ ranges ofthe ΛCDM parameters broadens the ranges of our predictednumbers of CCLs by up to a factor of ∼
2. Finally, the use ofother mass functions - such as Jenkins et al. (2001) or Tinkeret al. (2008) - can introduce another ∼
20% variation.
In the course of this work we inspected (among other clus-ters) deep archival multiband images of A383 obtained withthe SuprimeCam on the Subaru telescope (Miyazaki et al.2002) in 2002,2005,2007,2008 and new data collected in 2010dedicated to the CLASH sample (Postman et al. 2011; seealso below), with total integration times of at least ∼ ∼ mscred task in IRAF , while coadded im-ages were created following Nonino et al. (2009). Zero-pointswere estimated from standard stars observations.In these wide-field ( ≈ (cid:48) × (cid:48) ) Subaru images of thefield of A383, the multiwavelength coverage uncovers sev-eral higher- z structures. Among these, two large structuresare seen; one is located ∼ . (cid:48) East and ∼ . (cid:48) North ofA383, around RA=02:48:24.96 DEC=-03:29:31.8, and thesecond ∼ (cid:48) East and ∼ . (cid:48) North of A383, aroundRA=02:48:56.03 DEC=-03:29:06.6, and extends Northwardstowards a third (possibly different) substructure of similarcolours (and redshift), but these structures are too far fromthe centre of A383 to be relevant for this work. Our BPZ(Ben´ıtez 2000; Ben´ıtez et al. 2004; Coe et al. 2006) pho-tometric catalogue, based on the 6 Subaru imaging bandsmentioned above, suggests redshifts of z ∼ . z ∼ . (cid:39) ∼ . (cid:48) North-East of the cen-tre of A383, around RA=02:48:09.57 DEC=-03:29:41.6 (seeFigure 2). The background structure is clearly seen as a redoverdensity of galaxies very faint in the B-band (see Fig-ure 2 for an RGB colour image), implying a higher redshiftthan A383, further confirmed by a photometric redshift of z ∼ . +0 . − . for all 40 member galaxies. The average pho-tometric redshift for these galaxies is z = 0 .
96, though weadopt the photo- z of the brightest member, z (cid:39) .
9, as theredshift of this structure.We have downloaded
Chandra
X-ray images and ob-tained Bolocam 140 GHz SZ images of A383 to examine Valdes (1998). IRAF is distributed by the National Optical As-tronomy Observatories, which are operated by the Association ofUniversities for Research in Astronomy, Inc., under cooperativeagreement with the National Science Foundation.c (cid:13) , 1–9 luster-Cluster Lensing: A383 Figure 2.
The central field of A383 with the high- z background cluster marked on the image. Note the much redder colours of thegalaxies in the background cluster with respect to A383. According to our WL analysis, A383 magnifies the background cluster by14 ±
3% (see § whether this background cluster is seen also in these spec-tral regions. As may be expected (see § ± ∼
10 Einsteinradii away from the centre of A383, therefore the SL modelcannot be used for the magnification estimate, but only tocheck consistency with our WL analysis of A383 in the re-gion of overlap (around 0.7-1 arcminute in radius; see Figure5 in Zitrin et al. 2011b).It should be noted, that these higher- z structures arededuced in both 1D and 2D WL analyses, even though dif-ferent approaches are employed in these. In the 1D analysis(e.g., Umetsu et al. 2011), such background structures areseen in the shape of “dips” in the tangential shear profile,and translate to local mass excess in the lens convergence c (cid:13)000
10 Einsteinradii away from the centre of A383, therefore the SL modelcannot be used for the magnification estimate, but only tocheck consistency with our WL analysis of A383 in the re-gion of overlap (around 0.7-1 arcminute in radius; see Figure5 in Zitrin et al. 2011b).It should be noted, that these higher- z structures arededuced in both 1D and 2D WL analyses, even though dif-ferent approaches are employed in these. In the 1D analysis(e.g., Umetsu et al. 2011), such background structures areseen in the shape of “dips” in the tangential shear profile,and translate to local mass excess in the lens convergence c (cid:13)000 , 1–9 Zitrin et al.
Figure 3.
Smoothed X-ray image of A383. The location of the z ∼ . § ( κ ) profile (see Okabe et al. 2010; see also Zitrin et al. 2011b,Figure 5). In the 2D WL analysis presented here, these willsimply be seen as 2D structures in the mass distribution, ascan be seen in Figure 4.Note also that the detection here is based on the opticaldata, meaning that the lensed cluster is clearly seen, and notby other means which later need further verification.In order to calculate, or put limits on the backgroundcluster mass, we first examine the total light by this cluster.The photometry of the 40 detected z ∼ . . +0 . − . × L (cid:12) (using the LRG templates from Ben´ıtez et al. 2009; errorsinclude conversion from different bands), in roughly the ∼ ± . +0 . − . × L (cid:12) .Adopting a typical M/L B ratio (e.g., Zitrin et al. 2011a),of 250 ± M/L B , this translates into a total mass of (cid:39) . +0 . − . × M (cid:12) for the lensed cluster, which constitutesa lower limit on its mass, since we did not account for mem-ber galaxies lying below the detection threshold ( (cid:39) R c -band; 5 σ ).Next, we perform a 2D gravitational shear analysis ofSubaru multiband ( BV R c I c i (cid:48) z (cid:48) ) data (see Zitrin et al. 2011bon A383) to constrain the mass distribution of the z = 0 . z ph ) selected sample of background galaxies ( z ph > .
9, 21 < z (cid:48) <
26 AB mag), we construct a spin-2 reduced-shear field on a regular grid of 0 . (cid:48) × . (cid:48) independent pixels,covering a 20 (cid:48) × (cid:48) region centred on A383. We model theprojected mass distribution around the z = 0 . z = 0 . M vir ), concentration ( c v ), and centroid position( x c , y c ). We use the Markov Chain Monte Carlo techniquewith Metropolis-Hastings sampling to constrain the massmodel with 8 parameters.From a simultaneous 2-component fitting to the 2D shear data, we find M vir = 1 . +1 . − . × M (cid:12) (68 .
3% con-fidence limits) for the z = 0 . R = 1 Mpc is M (cid:39) . × M (cid:12) . This result is in good agreement withour optically-based estimation (although the latter consti-tutes a lower limit).Additionally, we use SZ measurements to deduce thegas mass, from which we estimate the total mass. Althoughthe z = 0 . χ /DOF = 1223/1117) .Using the transfer function computed for this model, wethen deconvolved the effects of noise filtering of our data toobtain an unbiased SZ image of A383. Since the filtering issomewhat non-linear, our deconvolved image of the z = 0 . < z = 0 . z = 0 . z = 0 . Y Mpc =0 . × − ster, with a statistical error of σ Y,stat =1 . × − ster. Restricting to physically allowed posi-tive values of Y Mpc , this results in a 95% confidence levelupper limit of Y Mpc < . × − ster. Note that themodel-subtracted A383 SZ flux within our 1 Mpc apertureis Y A ,model = 1 . × − ster.Using three published Y − M gas scaling relations basedon projected Y (Sayers et al. 2011, Plagge et al. 2010, andBonamente et al. 2008), we estimate the 95% confidencelevel upper limit for the gas mass of the z = 0 . . × M (cid:12) , respectively. All three of these scaling re-lations were constrained largely (or entirely) using clusterswith much higher masses, which is the likely cause of thelarge scatter in the derived masses. We adopt the gas masslimit derived from the Sayers et al. (2011) scaling relation,since it was calibrated using Bolocam data analysed iden-tically to our A383 data. We note that the spread in mass Note that we simultaneously fit, and subtracted, a point sourcefrom the NVSS catalogue at 02:48:22.09, -03:34:30.5, which wefound, had a flux density of 12.8 mJy (Condon et al. 1998). Thispoint source is approximately 5 arcmin from the centres of bothA383, and the z = 0 . (cid:13) , 1–9 luster-Cluster Lensing: A383 limits from the three scaling relations provides an estimateof the uncertainties in the Y /M scaling.By assuming a typical gas mass fraction of 13% (e.g.,Umetsu et al. 2009), we derive a 95% confidence level upperlimit on the total mass of the z = 0 . M SZ < . × M (cid:12) , in agreement with our previous estimatesbased on the luminosity and our WL analysis.For general completeness, we repeat a similar procedurealso for the X-ray data, although only a rough upper masslimit can be expected. In order to estimate the X-ray surfacebrightness from the z ∼ . z = 0 . Z = 0 . Chandra spectra, where theemissivity model (MEKAL model, Kaastra 1992; Liedahlet al. 1995) is folded through response curves (ARF andRMF) of the ACIS–I CCD imaging spectrometer in order togenerate theoretical counts for the surface brightness. Theluminosity value is obtained by rescaling the fake Chandraspectrum in order to reproduce the observed number of dif-ferential counts.Given that the X-ray luminosity mildly depends alsoon the value of the IC gas temperature of the backgroundcluster, which is unknown a priori, we start by assuminga guessed value of the temperature and derive the corre-sponding luminosity. This luminosity is then translated viathe L − T relation (Morandi et al. 2007) into a global temper-ature, which has been used iteratively in order to estimatethe X-ray luminosity and then the same global temperaturefor the background cluster. This process is repeated untilconvergence of the temperature is achieved. The luminos-ity is finally converted into a total mass via standard X-rayscaling relations (e.g., Morandi et al. 2007), and errors onthe physical parameters were calculated via Montecarlo ran-domisation. We derive a 95% confidence level upper limit onthe total mass of background cluster of M X < . × M (cid:12) ,in agreement with our previous estimates. We have calculated the predicted numbers of CCLs in theΛCDM model for different mass functions and cluster prop-erties. According to our rather conservative estimates, onlyfew ( ∼
3) CCLs are predicted over the full sky based onWMAP7 parameters, using either a PS or a ST mass func-tion, for clusters in the mass range 1 × − × M (cid:12) (forboth the lens and the source). The number increases some-what to ∼
10 when taking into account also backgroundgroups of galaxies (down to 5 × M (cid:12) ), and consideringdifferent mass functions, but rises substantially to ∼ a fewdozen when taking into account possible lensing triaxiality Figure 4.
Contours of the dimensionless surface mass density κ smoothed with a Gaussian of FWHM 1 . (cid:48) , superposed on the BRz (cid:48) pseudocolour image of A383. The lowest contour and thecontour interval are ∆ κ = 0 .
03, corresponding to the 1 σ recon-struction error. As can be seen, the WL analysis is sufficiently sen-sitive to detect a clear extension around the location of the lensedbackground cluster detected in the optical deep RGB colour inFigure 2. biases, and to hundreds when considering also the weak lens-ing regime.Two CCLs were claimed a decade ago - A2152, andless significantly, MS 1008-1224, where background galax-ies are obviously magnified or create a local over-densityin the image-plane. In addition, several “double lens” con-figurations were suggested or theoretically discussed before(e.g., Crawford, Fabian & Rees 1986; Seitz & Schneider 1994;Molinari, Buzzoni & Chincarini 1996; Wang & Ulmer 1997;Bertin & Lombardi 2001; Gavazzi et al. 2008). Comparisonof the number of observed CCLs with theoretical predic-tions (see also Cooray, Holder & Quashnock 1999) is clearlyimportant and may add significant new insight on the evo-lution of the LSS in ΛCDM. This could be quite useful inlight of claimed discrepancies, such as larger than predictedEinstein radii, and high concentration or disparities in theabundance of giant arcs (e.g., Hennawi et al. 2007; Broad-hurst & Barkana 2008; Broadhurst et al. 2008; Sadeh &Rephaeli 2008; Puchwein & Hilbert 2009; Horesh et al. 2010;Meneghetti et al. 2010; Sereno, Jetzer & Lubini 2010; Zitrinet al. 2011a).While inspecting lensing measurements of a sampleof clusters we have noticed a lensed background cluster-ing structure behind A383 ( z = 0 . z ∼ . +0 . − . , and is clearly seen redder in an RGB colourimage, and very faint in the B band. Our WL modelling ofA383 implies a magnification of 14 ± . +0 . − . × L (cid:12) summed over all 40 mem-bers, which is translated into a lower-limit mass estimate of c (cid:13)000
03, corresponding to the 1 σ recon-struction error. As can be seen, the WL analysis is sufficiently sen-sitive to detect a clear extension around the location of the lensedbackground cluster detected in the optical deep RGB colour inFigure 2. biases, and to hundreds when considering also the weak lens-ing regime.Two CCLs were claimed a decade ago - A2152, andless significantly, MS 1008-1224, where background galax-ies are obviously magnified or create a local over-densityin the image-plane. In addition, several “double lens” con-figurations were suggested or theoretically discussed before(e.g., Crawford, Fabian & Rees 1986; Seitz & Schneider 1994;Molinari, Buzzoni & Chincarini 1996; Wang & Ulmer 1997;Bertin & Lombardi 2001; Gavazzi et al. 2008). Comparisonof the number of observed CCLs with theoretical predic-tions (see also Cooray, Holder & Quashnock 1999) is clearlyimportant and may add significant new insight on the evo-lution of the LSS in ΛCDM. This could be quite useful inlight of claimed discrepancies, such as larger than predictedEinstein radii, and high concentration or disparities in theabundance of giant arcs (e.g., Hennawi et al. 2007; Broad-hurst & Barkana 2008; Broadhurst et al. 2008; Sadeh &Rephaeli 2008; Puchwein & Hilbert 2009; Horesh et al. 2010;Meneghetti et al. 2010; Sereno, Jetzer & Lubini 2010; Zitrinet al. 2011a).While inspecting lensing measurements of a sampleof clusters we have noticed a lensed background cluster-ing structure behind A383 ( z = 0 . z ∼ . +0 . − . , and is clearly seen redder in an RGB colourimage, and very faint in the B band. Our WL modelling ofA383 implies a magnification of 14 ± . +0 . − . × L (cid:12) summed over all 40 mem-bers, which is translated into a lower-limit mass estimate of c (cid:13)000 , 1–9 Zitrin et al.
Figure 5.
Bolocam SZ images of A383. From top to bottomthe thumbnails show the high-pass filtered (processed) image,the deconvolved image, and the model-subtracted deconvolvedimage. The solid white contours in the processed image repre-sent S/N= − , − , − , .. , and the dashed white contours repre-sent S/N= +1 , +2 , +3 , .. . We do not include S/N contours inthe deconvolved images due to the significant amount of large-angular-scale noise. The white plus sign denotes the centre of the z = 0 . z = 0 . . × M (cid:12) , see § . +0 . − . × M (cid:12) , using a typical M/L ratio of M/L B =250 ±
50. We have also analysed SZ and X-ray data, andindependent WL measurements, to obtain mass estimatesof M SZ < . × M (cid:12) , M X < . × M (cid:12) (95% CLupper limits) and M vir , WL = 1 . +1 . − . × M (cid:12) (or a pro-jected mass M ( < Mpc ) (cid:39) . × M (cid:12) ), respectively.These are commensurate with our prior estimate based onthe luminosity. These are also in agreement with the factthat no excess emission is seen in the SZ or X-ray images ofA383 at the location of the background cluster (see Figure3), reflecting its probable low mass.Deeper images in the different spectral regions would beof interest to examine further the possibility that this clus-ter is a CCL, along with spectroscopic data for measuringthe exact background cluster redshift. In addition, futuredetections of CCLs are important, as their overall numbercould probe the LSS parameters, the cluster (and group)mass function, and the c-M relation. ACKNOWLEDGMENTS
AZ is grateful for the John Bahcall excellence prize whichfurther encouraged this work, and to Piero Rosati and mem-bers of the CLASH team for useful comments. Work at TelAviv University was partly supported by the US-IL Bina-tional Science foundation grant 2008452, and by a grantfrom the British Council. A.M. acknowledges support by Is-rael Science Foundation grant 823/09. JS was partially sup-ported by a NASA Graduate Student Research Fellowship,a NASA Post- doctoral Program fellowship, NSF/AST-0838261, and NASA/NNX11AB07G; NC was partially sup-ported by NASA Graduate Student Research Fellowship.Bolocam observations and analysis were also supported bythe Gordon and Betty Moore Foundation. Part of this workis based on data collected at the Subaru Telescope, whichis operated by the National Astronomical Society of Japan.The
Chandra
X-ray Observatory Center is operated by theSmithsonian Astrophysical Observatory on behalf of NASA.Bolocam was constructed and commissioned using fundsfrom NSF/AST-9618798, NSF/AST-0098737, NSF/AST-9980846, NSF/AST-0229008, and NSF/AST-0206158.
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