Table Of ContentMon.Not.R.Astron.Soc.000,000–000 (0000) Printed12January2011 (MNLATEXstylefilev2.2)
A Weak Lensing Detection of the Cosmological
Distance-Redshift Relation Behind Three Massive
⋆
Clusters
Elinor Medezinski1, Tom Broadhurst2,3, Keiichi Umetsu4, Narciso Ben´ıtez5
& Andy Taylor6
1 1Department of Physics & Astronomy, The Johns Hopkins University,3400 N. Charles Street, Baltimore, MD 21218, USA
1 2Theoretical physics, Universityof the Basque Country, Bilbao 48080, Spain
0 3Ikerbasque, Basque Foundation for Science, Alameda Urquijo, 36-5 Plaza Bizkaia 48011, Bilbao, Spain
2 4Institute of Astronomy and Astrophysics, Academia Sinica, P. O. Box 23-141, Taipei 106, Taiwan, Republic of China
5Instituto de Astrof´ısica de Andaluc´ıa (CSIC), Granada, Spain
n
6Scottish UniversitiesPhysicsAlliance (SUPA), Institute for Astronomy, School of Physics, Universityof Edinburgh,
a
J Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, U.K.
0
1
12January2011
]
O
C ABSTRACT
The amplitude of weak lensing should increase with source distance, rising steeply
.
h behind a lens and saturating at high redshift, providing a model-independent means
p ofmeasuringcosmicgeometry.Wemeasuretheamplitudeofweaklensingwithredshift
- forthreemassiveclusters,A370(z =0.375),ZwCl0024+17(z =0.395)andRXJ1347-
o
r 11 (z = 0.451), using deep, three-colour Subaru imaging. We define the depth of
t lensed populations with reference to the COSMOS and GOODS fields, providing a
s
a consistency check of photo-z estimates over a wide range of redshift and magnitude.
[ Thepredicteddistance-redshiftrelationisfollowedwellforthedeepestdataset,A370,
for a wide range of cosmologies, and is consistent with less accurate data for the
1
other two clusters.Scaling this result to a new survey of ∼25 massiveclusters should
v
5 provide a useful cosmological constraint on w, complementing existing techniques,
5 with distance measurements covering the untested redshift range, 1<z <5.
9
Key words: cosmology: observations – gravitational lensing – galaxies: clusters:
1
. individual(Abell 370) – galaxies: clusters: individual(ZwCl 0024.0+1652) – galaxies:
1
clusters: individual(RX J1347.5-1145)
0
1
1
:
v
1 INTRODUCTION In principle, lensing can provide a complementary distance
i
X measurements in the range, z >1, from the purely geomet-
Constraining cosmological parameters has been the focus
r ric deflection of light, which increases with source distance
a of major surveys in the last decade, via precision cos-
behind a lens.
micmicrowavebackground(CMB)temperaturecorrelations
(Spergel et al. 2007; Brown et al. 2009) and SN-Ia light For lensing clusters, the bend-angle of light scales lin-
curves (Riess et al. 1998; Perlmutter et al. 1999). A stan- earlywithangulardiameterdistanceratio,dls/ds,thesepa-
dard, ΛCDM, cosmological model has been defined by this ration between thelensand thesource,divided bydistance
work,albeitatthepriceofacceptinganacceleratingexpan- to the source. This distance ratio has a characteristic geo-
sion driven by a cosmological constant, and non-baryonic metricdependenceonredshift,risingsteeplybehindthelens
dark matter (DM) of an unknown nature dominating the and then saturating at large source redshift (e.g., Fig. 1 of
mass density of the Universe. Measurements of the angular Broadhurst, Taylor & Peacock 1995). This effect has been
diameter distance of the CMB refer to z 1100, and lumi- detected behind massive lensing clusters, where the sepa-
∼
nosity distances are derived from SN-Iain the range z <1. ration in angle between multiple images of higher redshift
sources is noticeably larger than for lower redshift sources.
For example, for the well studied cluster SDSSJ1004+4112
⋆ BasedondatacollectedatSubaruTelescopeandobtainedfrom (z = 0.68), five images of a QSO at z = 1.734 are within
the SMOKA,whichis operated by the AstronomyData Center, an Einstein radius of about θE 7′′ (Inada et al. 2003;
∼
NationalAstronomicalObservatoryofJapan. Oguri et al. 2004), whereas a more distant multiply lensed
(cid:13)c 0000RAS
2 Medezinski et al. 2010
galaxy behind this cluster at z = 3.332 is at a much larger
Table 1.TheClusterSample:RedshiftandFilterInformation
Einstein radius of θE 16′′ (Sharon et al. 2005). Other
∼
sets of multiple images show this increasing angular scal- Cluster z Filtersused1 Seeing
ingwithsourceredshift,following welltheexpectedgeneral (exp’timeinsec) (arcsec)
form of the redshift-distance relation in careful strong lens-
ing analyses of deep Hubble data (Soucail, Kneib & Golse A370 0.375 BJ(7200),RC(8340),z′(14221) 0.6
2004; Broadhurst et al. 2005; Zitrin et al. 2009b; Zitrin & ZwCl0024+17 0.395 BJ(3600),RC(5280),z′(1680) 0.8
Broadhurst 2009; Zitrin et al. 2009a). RXJ1347-11 0.451 VJ(1800),RC(2880),z′(4860) 0.76
However, these studies are not able to distinguish be-
tween the relatively subtle changes between cosmologies in
1Detection bandmarkedinbold.
therangeofinterest,duetotheinherentinsensitivityofthe
distance ratio dls/ds to the cosmological parameters. More- backgrounddepthswithwhichtoexplorethedependenceof
over,thebend-angleisparticularlysensitivetothegradient
WL distortion on source redshift. With only three bands
of the mass profile, requiring many sets of multiple images
wecannotreliablydefinephotometricredshiftsforasizable
in the strong regime to simultaneously solve for both the
proportion of objects, but instead, by reference to the red-
cosmological model and the mass distribution. Instead in
shift disributions of the well studied deep field surveys, we
practice, strong lens modeling usually adopts the standard
may reliably define several galaxy populations of differing
cosmological relation inordertobetterderivethemass dis-
meandepthsintheCC-spacecoveredbythefiltersusedfor
tribution, with multiply lensed sources forced to lie on the
each cluster.
lensing distance-redshift relation. This helps eliminate the
Three colour selection has also been applied in a simi-
otherwise considerabledegeneracy in constrainingtheslope
lar context to simulations aimed at forecasting the capabil-
of the lensing mass profile of a galaxy cluster (Broadhurst
ities of WL tomograghy (Jain, Connolly & Takada 2007;
et al. 2005; Zitrin et al. 2009b; Zitrin & Broadhurst 2009;
Medezinski et al. 2010). These simulations convincingly
Zitrin et al. 2009a). The hope of constraining the cosmog-
demonstrate that greater efficiency is likely by using lim-
raphyfrom stronglensing dataisremotewith currenttools
ited3-bandimagingforWLtomography,ratherthanbyin-
(Gilmore & Natarajan 2009).
vestinggreaterimagingtimeinadditionalbandstoimprove
Weak lensing (WL), by contrast, offers a model inde-
photometricredshiftprecision.Forourpurposestooweshow
pendent way of constraining the cosmological parameters
herethatajudiciouschoiceofnon-orthogonalboundariesin
viathedistance-redshiftrelation(Tayloretal.2004).Image
CC-space allows the definition of several distinct redshift
distortionsandmagnificationdependongradientsofthede-
samples of differing mean depth, with relatively little over-
flectionfieldandintheWLlimit,thesearejustproportional
lap in redshift.
todls/ds.Themassprofileentersonlyinthestrongerregime Here we rely on well studied deep field surveys to esti-
as a second order correction (Medezinski et al. 2007). Here
matetheredshift distribution of thesedifferentbackground
we are concerned with the amplitude of cluster WL depen-
populations, using the wide-field COSMOS 30-band photo-
dence on source redshift, for which no mass reconstruction
metricredshiftsurvey(Ilbertetal.2009)andalsothedeeper
is required when evaluating the distance-redshift relation.
GOODS-MUSIC survey which has wide multi-wavelength
However,althoughthisobservedeffectisindependentofthe
coveragein 14 bands(from theUbandtotheSpitzer8µm
mass distribution in the weak limit, the sensitivity to cos-
band) (Grazian et al. 2006).
mological parameters is still inherently verysmall.
In 2 we present the cluster observations and data re-
The analogous effect in the field has been explored in §
duction and in 3 we explain the selection of background
termsofthecosmicshear, tomeasurethegeneral mass dis- §
galaxy samples and in 4wedescribe theWLanalysis and
tribution. Optimal formalisms have been developed which §
outline the formalism. In 5 we derive the WL amplitude
cross-correlate theforeground distribution of galaxies along §
and mean redshift information of the background samples,
a given line of sight with the distribution of background
presentingourresultsregardingthelensingdistance-redshift
images (Wittman et al. 2001; Jain & Taylor 2003; Bacon
relation. We discuss the requirements for constraining the
et al. 2003; Taylor et al. 2004, 2007) with clear detections
cosmological model with this method in 6. We summarize
of large scale structure, including the COMBO-17 fields
and conclude in 7.
(Brown et al. 2003; Kitchingetal. 2007) and theCOSMOS §
field(Masseyetal.2007;Schrabbacketal.2010).Tousefully
derive cosmological parameters from general cosmic shear
work,deepall-skysurveyshavebeenproposed(e.g.,LSST1, 2 SUBARU DATA REDUCTION
DES2, JDEM3, EUCLID4).
Weanalyzedeepimages ofthreeintermediate-redshiftclus-
Here we make use of detailed colour-colour (CC) in-
ters, A370 ZwCl0024+17 and RXJ1347-11, observed with
formation for three intermediate redshift lensing clusters,
the wide-field camera Suprime-Cam (Miyazaki et al. 2002)
A370 (z = 0.375), ZwCl0024+17 (z = 0.395), RXJ1347-11
in several optical bands, at the prime focus of the 8.3m
(z=0.451)anddefineseveralsamplesofgalaxiesofdiffering
Subaru telescope. The clusters are publicly available from
the Subaru archive, SMOKA5. Subaru reduction software
1 http://www.lsst.org/lsst (SDFRED) developed by Yagi et al. (2002) is used for flat-
2 https://www.darkenergysurvey.org/ fielding, instrumental distortion correction, differential re-
3 http://jdem.gsfc.nasa.gov
4 http://sci.esa.int/science-e/www/object/index.cfm?
fobjectid=42266 5 http://smoka.nao.ac.jp
(cid:13)c 0000RAS,MNRAS000,000–000
WL Detection of the Distance-Redshift Relation 3
fraction,skysubtractionandstacking.Photometriccatalogs spacewhicharedominatedbyclusterandforegroundgalax-
are created using SExtractor (Bertin & Arnouts 1996). ies to minimize contamination by these unlensed galaxies,
Sinceourworkreliesmuchonthecoloursofgalaxies,wepre- as described below.
ferusingisophotalmagnitudes.WeusetheColorpro(Coe To identify background populations in M10, we took
etal. 2006) program todetectin theRC-bandandmeasure into account both the WL signal and the density distribu-
colours through matched isophotes in the other two bands. tionofgalaxiesintheCCplane.InCCspacearelativelyred
AstrometriccorrectionisdonewithScamp(Bertin2006)us- populationcanberatherwelldefined,dominatedbyanobvi-
ing reference objects in the NOMAD catalogue (Zacharias ousoverdensity(aroundBJ RC 0.5andRC z′ 0.8),
− ∼ − ∼
et al. 2004) and the SDSS-DR6 (Adelman-McCarthy et al. and the bluest population is confined to a separate cloud
2008) where available. The observational details are listed (around BJ RC 0.3 and RC z′ 0.2) of faint galax-
− ∼ − ∼
in Table 1. ies with a clear lensing signal. Looking at the WL profiles
of the red and blue samples, we see very similar behaviour,
with a continuous rising signal toward the cluster center.
Both cases show good agreement with each other (M10).
3 SAMPLE SELECTION FROM THE
Combinedtogether,theyformourreference background
COLOUR-COLOUR DIAGRAM
sample, to which all theother samples we derivebelow will
For each cluster we use Subaru observations in three broad benormalized.
optical passbands and all observations are of good seeing, The validity of our selection was also demonstrated in
representingsomeofthehighestqualityimagingbySubaru M10 by comparison with the spectral evolution of galax-
in terms of depth, resolution, and colour coverage. We first ies calculated with the stellar synthesis code Galev6 (Ko-
describehowweseparatethebackgroundgalaxiesfromfore- tulla et al. 2009). Here we overlay the CC diagram with
ground and cluster galaxies, combining WL measurements colour-tracks of galaxy models: E-type (exponentially de-
and the distribution of objects in the CC plane and their clining SFR with Z⊙), S0 (gas-related SFR with Z⊙), Sa
clustering relative to the center of the cluster. We then ex- (gas-related SFR with 2.5Z⊙), and Sd (constant SFR with
amine the redshift distribution of objects selected to lie in 0.2Z⊙). These evolutionary tracks originate in the low-
the background using the CC plane with reference to the redshiftcloudweestablishedasforegroundinCCspaceand
COSMOS field where deep photometric redshifts areestab- evolvetohigherredshiftpassingthroughtheclusterredshift
lishedtofaint limitsusing30independentpassbandscover- and thento bluercolours as shown in Fig. 5 (right),and fi-
ing a very wide range of wavelength. nally end at the top-left corner of our CC space, dropping
Note that with only three bands, only a small fraction out of theBJ-band at a redshift of z 3.5
∼
of the objects have well defined photometric redshifts, in Inthispaperwe addadditional samples of background
thesenseofhavingasingle,narrowpeakintheirprobability galaxies.Twosampleswillconsistofgalaxiesatredshiftsnot
p(z),andthereforetheirusetoseparateamongdifferentred- farbeyondthatofthecluster,which weterm“orange” and
shift populations is very limited. Using the BRz′ CC space “green”. These are selected to lie on the upper-right of the
in this way with reference to the now well established red- CCspace,correspondingreasonablytocolour-tracksofE/S0
shift surveys is arguably more reliable in separating galaxy galaxieswhicharepredictedtoshowabendintheCCplane,
populations of differing depths, in agreement with the sim- becoming bluer (BJ RC 2 2.5 and RC z′ 1 1.5)
− ∼ − − ∼ −
ulations of Jain et al. (2007). towardhigherredshift,matchingwellourobserveddistribu-
Inourpreviousanalysisofthesedata,Medezinskietal. tion.Athirdgroupcomprisesthered-clouddescribedabove,
(2010, hereafter M10), we demonstrated how the cluster centered on BJ RC 0.5 and RC z′ 0.8, we call
− ∼ − ∼
and foreground galaxies can be reliably identified and sep- the“red” sample. This sample consists of an overdensityof
arated from background galaxies in the CC diagram, using background galaxies from the known “red” branch of the
BJ,RC,z′ bands(Fig.1).Wefoundinthefield ofA370the bimodality of field galaxies colours (Capak et al. 2007). A
prominent overdensity of galaxies centered on BJ RC 2 Forthsample consists of theprominentbluepeak identified
andRC z′ 0.8denotesthered-sequenceofclus−tergal∼ax- as background galaxies, lying at redshifts beyond the red
ies (see−Fig.∼1, left-hand panel, where this overdensity is galaxies, corresponding to the “blue” branch of the colour
enclosed bydashed whiteline). This was also shown by the bimodality,wherethecolour-tracksturnredderat BJ RC
−
relatively small mean distance from cluster center of galax- as the UV-fluxstarts to drop out of the blueBJ band with
ies in that region in CC space (Fig. 1 in M10). The WL increasingredshift,abovearedshiftofapproximately,z 2.
∼
measurementsfor thispopulation of objects isveryclose to Finally,weselectgalaxiesfromthetop-leftcorneroftheCC
zero, with a measured tangential distortion profile, gT(r), plane,correspondingtothepredictedlocationofBJ-dropout
consistent with zero all the way out to the virial radius, as galaxies at an average redshift of z 3.5.
∼
expected for cluster galaxies which are unlensed. The main Foreachsampleselectedweexaminethecolourbound-
central overdensity around BJ RC 1 and RC z′ 0.3 ariesofeachsampleasafunctionoftheWLsignal,toensure
consists of many foreground ga−laxies∼(see Fig. 1,−left-∼hand we keep well clear of foreground or cluster members which
panel, with an overdensity enclosed by solid white line). otherwisedilutetheWLsignalofbackgroundgalaxies.This
ThesegalaxiesshowaverylowlevelgT comparedtotheref- approach has been investigated in our earlier work, where
erence background, marked in gray on Fig. 1 (right panel), thisproblemwasfirstidentifiedasamajorproblemforWL
and their surface density profile shows only modest central workandrectifiedusingappropriateCC-selection(Medezin-
clustering (see M10) indicating that most of these objects
lie in the foreground of the cluster. When selecting back-
groundgalaxieswestaywellawayfrom theseregionsofCC 6 http://www.galev.org/
(cid:13)c 0000RAS,MNRAS000,000–000
4 Medezinski et al. 2010
skietal.2007;Umetsu&Broadhurst2008;Medezinskietal. where α2 is the softening constant variance. We choose
2010; Umetsu et al. 2010). α=0.4, which is a typical value of the mean RMS σ¯g over
We apply this selection scheme for two more clusters, thebackgroundsample.Weaccuratelycombinethephotom-
ZwCl0024+17andRXJ1347-11,thoughherethedataisnot etrywithweak-lensingmeasurementsofasmanygalaxiesas
asdeep.Furthermore,thecolourcoverageislesswideinthe possible, discarding objects below theseeing limit (given in
caseofRXJ1347-11(onlyVRz′)allowingtheselectionofthe table 1) plus two standard deviation of that value in the
correspondingorange,green,redandbluebackgroundsam- detection band, to remove stars and avoid unreliable shape
ples, as above, but not sufficient for separation of dropout measurements.
galaxies for a significant WL detection.
ThegreaterdepthoftheA370imagingallowsustofur-
therdividethegreen,redandbluebackgroundsamplesinto 4.1 Formalism: Relative Distortion Strength
independent bright and faint subsamples for our WL mea-
surements.Foreachofthesesamples,wenowestimatetheir For a given source redshift zs and a fixed lens redshift zl,
average WL signal, by comparing the tangential distortion the observable (complex) reduced gravitational shear g(zs)
in the subcritical regime is expressed in terms of the gravi-
measurements to that of the reference background sample,
tationalshearγ andthelensconvergenceκas(e.g.,Seitz&
and derive what we call mean “gT amplitude” (see § 5.1). Schneider1997; Medezinski et al. 2007)
Subsequently,wealsoestimatethemedianredshiftfromthe
CO5.S2)M.OWSespuhmotmo-azrizceattahloegpureopaenrdtieitssoefqtuhievaselelenctteddls/sadms p(sleees g(zs)=γ(zs)(1−κ[zs])−1 =γ∞ ∞ βk+1(zs)κk∞ (5)
§in Table 2. Xk=0
whereκ∞ andγ∞ arethelensingconvergenceandthegrav-
itational shear, respectively, calculated for a hypothetical
4 WEAK LENSING MEASUREMENTS source at zs , and β(zs) is the lensing strength of
→ ∞
a source at zs relative to a source at zs , β(zs)
→ ∞ ≡
TomaketheWLcatalogs,weusetheIMCATpackagedevel- D(zs)/D(zs ); D(zs) dls/ds. Hence, the reduced
oped by N. Kaiser7 to perform object detection and shape shear average→d o∞ver the sour≡ce redshift distribution is ex-
measurements, following the formalism outlined in Kaiser, pressed as
Squires & Broadhurst (1995, hereafter KSB). Our analysis
∞
pipelineisdescribedinUmetsuetal.(2010).Wehavetested g =γ∞ βk+1 κk∞, (6)
our shape measurement and object selection pipeline using h i Xk=0h i
STEP (Heymans et al. 2006) data of mock ground-based
observations (see Umetsu et al. 2010, 3.2). Full details of where βk is definedsuch that
§ h i
tUhmeemtseutheotdasl.ar(e20p0r9e)seanntdedUinmeUtmsuetestua&l. (B2r0o1a0d)h.urst(2008), βk dzsN(zs)βk(zs) (7)
The shape distortion of an object is described by the h i≡ R dzN(zs)
R
complex reduced-shear, g = g1 +ig2, where the reduced- withtheredshiftdistributionN(zs).IntheWLlimit where
shear is defined as: κ∞ , γ ∞ 1, then
| | | | ≪
gα≡γα/(1−κ). (1) hgi≈hβiγ∞ =hγi. (8)
The tangential component gT is used to obtain the az- Thus,themeanreducedshearissimply proportionaltothe
imuthallyaverageddistortionduetolensing,andcomputed mean lensing strength, β D . The next order approxi-
h i∝h i
from the distortion coefficients g1,g2: mation is
gT =−(g1cos2θ+g2sin2θ), (2) g γ (1+fβ κ ) hγi , (9)
h i≈h i h i ≈ 1 fβ κ
where θ is the position angle of an object with respect to − h i
the cluster centre, and the uncertainty in the gT measure- wherefβ ≡hβ2i/hβi2isaredshift-momentratiooftheorder
ment is σT =σg/√2 σ in terms of the RMS error σg for of unity (Seitz& Schneider1997).
≡
the complex shear measurement. To improve the statistical Sincethetangentialdistortionsignal,gT,isafunctionof
significanceofthedistortion measurement,wecalculatethe cluster radius, we first decompose the tangential distortion
weighted average of gT and its weighted error, as profile of our background sample (B), defined above as our
reference (see 3), into thefollowing form:
hgT(θn)i = Piuigu,igg,iT,i, (3) gT,B(θ)=aBθ−§bB, (10)
P
σT(θn) = vuuPiiuu2gg,i,iσi22, (4) dpwiohswteorerert-iltoahnwearwmaidtpihaliltausdhpeaopwoeferooufinrgdTree(xfθe)rbeBins,caeasnsbudamcakeBgdrortueopnrbdee.seIanntsspinrtaghclee-
t
(cid:0)P (cid:1)
wheretheindexirunsoveralloftheobjectslocatedwithin tice,wefittheouterprofileofgT(θ),excludingthenonlinear
then-thannuluswithamedianradiusofθn,andug,i isthe regime (θ.1),to thepower-law model, constraining simul-
inversevarianceweight for i-thobject, ug,i =1/(σg2,i+α2), taneously the distortion amplitude aB and the outer slope,
bB. Next, for each of our other defined samples, we fit a
power law with thesame slope bB, butallow theamplitude
7 http://www.ifa.hawaii.edu/~kaiser/imcat ai to vary:
(cid:13)c 0000RAS,MNRAS000,000–000
WL Detection of the Distance-Redshift Relation 5
Table 2.CC-selectedSampleProperties
Cluster Sample magnitudelimits N n¯ Γ χ2/dof <zs>
arcmin−2 (gT-amplituderatio) (PL)
A370 foreground 18<z′<22 1235 1.3 -0.04 13/6 0.33
orange 19<z′<23 450 0.5 0.41 1/6 0.73
green-bright 20<z′<22.5 839 0.9 0.85 11/6 0.9
green-faint 22.5<z′<25 1240 1.3 0.88 6/7 0.99
red-bright 22<z′<24 5454 5.6 0.87 17/8 1.11
red-faint 24<z′<26 6986 7.1 1.1 27/8 1.14
blue-bright 23<z′<24.6 1679 1.7 0.95 6/8 1.79
blue-faint 24.6<z′<25.5 2857 2.9 1.15 23/8 1.78
drops 24<z′<26.5 1529 1.6 1.3 13/8 3.86
background 22<z′<26 19362 19.8 1 19/8 1.31
ZwCl0024+17 foreground 18<z′<22 734 0.9 0.08 5/9 0.29
orange 18<z′<23 687 0.9 0.55 11/9 0.73
green 21<z′<25 1582 2 0.83 23/9 0.98
red 21<z′<25.5 7716 9.7 0.97 8/9 1.11
blue 23<z′<25 2420 3 0.99 13/9 1.62
drops 25<z′<27 625 0.6 0.93 23/9 3.71
background 21<z′<25.5 10488 13.1 1 7/8 1.24
RXJ1347-11 foreground 19<z′<24 2452 3.4 -0.04 14/8 0.43
orange 19<z′<26 473 0.5 0.76 5/8 0.76
green 21<z′<25 1296 1.1 1.1 5/8 0.94
red 21<z′<26 4880 3.9 0.92 9/8 1.11
blue 23.5<z′<26 1509 2.1 1.18 35/8 1.95
background 21<z′<26 7139 6.3 1 4/6 1.24
x 10−6
7
3 6
2.5 5
B − R1.25 342Number/pix
1 2
0.5 1
0 0
0 0.5 1 1.5
R − Z
Figure 1.Left:NumberdensityinBJ−RC vs.RC−z′ CCspace forA370.Thefourdistinctdensity peaks areshowntobedifferent
galaxypopulations-thereddestpeakintheupperrightcorneroftheplots(dashedwhiteline)depictstheoverdensityofclustergalaxies,
whosecolourslayontheredsequence; themiddlepeaklyingbluewardoftheclustercomprisesmainlyforegroundgalaxies(solidwhite
line); the two peaks in the bottom part (bluest in BJ−RC) can be demonstrated to comprise of blue and red background galaxies.
Together, the red+blue galaxies will serve as our “reference” background sample for WL purposes. Right: BJ−RC vs. RC−z′ CC
diagram, showing the distribution of galaxies in A370. Marked are the selected foreground sample (gray) and background samples:
orange(orange),green(green),red(red),blue(blue)anddropout(magenta)backgroundgalaxies,selectedtoincludegalaxieslyingaway
fromtheclusterandforegroundregions.Overlaidaresyntheticcolourtracks includingevolution,calculatedwiththeGalevcodeforan
elliptical,S0,SaandSdtypemodels.
gT,i(θ)=aiθ−bB. (11) Fromequation(8),weobtainthefollowingexpressioninthe
WL approximation ( κ , γ 1):
Therefore, if we calculate the lensing signal of i-th sample |h i| |h i|≪
relative to thereference background (B),
Γi gT,i(θ)/gT,B(θ)=ai/aB. (12) Γi=ai/aB β i/ β B = D i/ D B, (13)
≡ ≈h i h i h i h i
(cid:13)c 0000RAS,MNRAS000,000–000
6 Medezinski et al. 2010
wherehii (i=1,2,...,B)representsaveragingoverthered- 1 A370
shift distribution Ni(zs) of i-thgalaxy sample. Therelative 0.9
distortion strength Γi can be regarded as a function of the
0.8
discrete background sample i with the redshift distribution
0.7 χ2/dof = 19/8
Ni(zs),which is observationally available and calibrated by
0.6
deep, multi-band blank surveys such as the COSMOS sur-
vey. For a given cosmological model, one can readily con- gT0.5
struct its theoretical prediction Γi (i = 1,2,...,B) using a 0.4
set of redshift distribution functions Ni(zs). The function 0.3
Γi can beformally labeled byits mean redshift 0.2
0.1
hzsii≡Z dzsNi(zs)zs/Z dzsNi(zs) (14) 0 1 2 θ [arcmin]5 10
which is independentof thecosmological model. ZwCl0024
1
Tothenextorderofapproximation, thedistortion am-
0.9
plituderatio iswritten as (AppendixBofMedezinski etal.
0.8
2007)
0.7 χ2/dof = 7/8
Γi = hhDDiiBi (cid:8)1+(fβ,ihβii−fβ,BhβiB)κ∞(θ)+O(κ2∞)(cid:9)(15) gT00..56
with fβ,i ≡ hβ2ii/hβi2i and fβ,B ≡ hβ2iB/hβi2B. The 00..34
next order correction term is proportional to (fβ,i β i
h i − 0.2
fβ,B β B)κ∞(θ), which is much smaller than unity for the
h i 0.1
galaxysamplesofourinterestinthemildlynonlinearregime
(θ & 1). We thus simply adopt equation (13) obtained in 0 1 2 5 10
θ [arcmin]
theWLapproximation. Thiscanbefurtherjustifiedbythe
RXJ1347
fact that the slope parameter bB is constrained by a least 1
χ2 fit to the outer distortion profile. The mean weighted 0.9
cluster radius hθi ≡ iug,iθi/ iug,i used for a fit is 0.8
hθi∼10−11arcminforPourclusterPs,wheretheweaklensing 0.7 χ2/dof = 4/6
approximation is valid.
0.6
gT0.5
0.4
0.3
5 RESULTS
0.2
5.1 Weak lensing profiles 0.1
0
For each cluster, a reference background sample has been 1 2 5 10
θ [arcmin]
defined(explainedabovein 3).TheWLtangentialdistor-
§
tion,gT,vs.distancefromclustercenter,θ,ofeachreference Figure2.TangentialdistortiongT vs.distancefromclustercen-
background is plotted in Fig. 2 (black crosses). Each refer- terforA370(top),ZwCl0024+17(middle)andRXJ1347-11(bot-
ence background sample is fitted by a power-law according tom)referencebackgroundsamples.Overlaidisthepower-lawfit
to Eq. 10, but only in the WL regime, i.e., outside θ & 1′. (dashed black line) with 1−σ confidence levels (shaded region)
Thefit is estimated using twoways –we fit theentiresam- andthePL-fitχ2 isindicated.
ple dataset, weighting each galaxy gT,i by ug,i (see 4),
§
andwealsofitthebinnedgT profile, gT(θn) ,weightingby
thebinerror,1/σT2(θn).Wefindgoohdconsisitencybetween the foreground samples, the gT(θ) profile agrees with zero
thetwofittingschemes.Thegoodness-of-fitχ2 valuesofthe throughout,and gives a relative WL amplitudeof zero.
binnedfitaredisplayednexttoeachpower-lawfit,andalso As another consistency check, we plot the galaxy sur-
in Table 2. As can be seen, a simple power-law serves as a facenumberdensityvs.radiusforA370samplesinFigure 3.
reasonable fit in all cases. As can be seen, no clustering is observed toward thecenter
For each of our defined samples (foreground, orange, for any of the samples, which demonstrate that there is no
green, red, blue and dropouts) we again plot gT vs. radius contamination by cluster members in the samples compris-
in Figure 4 (gray, orange, green, red, blue and dropouts, ingonlybackgroundmembers.Theforegroundsample(gray
respectively, top to bottom panels of each cluster). We fit triangles)showsamodestincreaseinnumberdensity(factor
each sample with the same power-law index, bB, given by of2increasefrom θ=20toθ=2)comparedtothecluster,
its relevant reference background (the sample fit is shown despite the exclusion of the cluster early-type galaxies by
as dashed black line with 1 σ confidence bounds,and the colour.Bluerlater-typeclustermembersaretobeexpected
−
referencebackgroundfitisalsoshownasadottedline).The heregiventheredshiftwindowsampledbyreferencetoFig-
WLamplitudeofeachsamplerelativetothereferenceback- ure 6, which shows that the tail of the distribution reaches
ground is given in each panel as Γi ai/aB (as defined by just beyondthe redshift of A370 5.2).
≡ §
Eq. 12) and detailed in Table 2. We see that indeed, for The data for A370 represents the best available data,
(cid:13)c 0000RAS,MNRAS000,000–000
WL Detection of the Distance-Redshift Relation 7
0.4
foreground
orange
101 0.35 green−b
green−f
red−b
0.3 red−f
blue−b
−2n] 0.25 bdlruoep−sf
arcmi N(z) 0.2
n [100 0.15
0.1
0.05
0
0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
θ [arcmin] z
Figure 3. Galaxy surface number density vs. radius for A370 Figure 6.RedshiftdistributionofallA370samples:foreground
foreground sample (gray triangles), orange (orange diamonds), (dashed gray), orange (dotted-dashed orange), green (green)
green (green pentagrams), red (red squares), blue (blue circles) bright (solid) and faint (dashed), red (red) bright (solid) and
anddropout(magentahexagrams)background samples. faint(dashed), blue(blue)bright(solid)andfaint(dashed), and
dropout(dotted-dashed magenta) usingCOSMOSphoto-z’s.
both in terms of thefilter coverage – B,R,z′, and in terms
of total exposure times in each band. For RXJ1347-11 we
only have V,R,z′ coverage, making it somewhat harder to
set apart the different populations, and also dropping out
betweenV andRisnotasclearsincethetwofiltersareless
wellseparatedinwavelength,preventingusfromselectinga
dropoutsample.ForZwCl0024+17 wedohaveB,R,z′,but
thez′ band is much shallower.
5.2 COSMOS photometric redshifts
To estimate the respective depths of the different samples
definedabovefrom ourSubaruphotometry,wemakeuseof
theaccuratephotometricredshiftsderivedforthewellstud-
ied multi-band field survey, COSMOS (Capak et al. 2007).
For COSMOS, photometric redshifts have been derived by
Ilbert et al. (2009) using 30 bands in the UV to mid-IR.
Figure 7. Redshift distribution of the dropout-selected sample
Since the COSMOS photometry does not cover the Subaru
usingCOSMOSphoto-z’s (lightred)andusingGOODS-MUSIC
RC band, we estimate RC-band magnitudes for it. For this photo-z’s (dark blue). The low-z peak seen more notably from
weusetheHyperZ(Bolzonella, Miralles &Pello´2000) tem-
theCOSMOSphoto-z’sismostlikelyduetomisclassifiedgalaxy
platefittingcodetoobtainthebest-fittingspectraltemplate
redshifts, supported by the smaller numbers found when using
for each galaxy, from which the RC magnitude is derived theGOODS-MUSICphoto-zcatalogue.
with the transmission curve of the Subaru RC-band filter
(see Umetsu et al. 2010).
We then select samples by applying the same tleWLsignalimplyingtheseobjectliepredominantlyinthe
CC/magnitude limits as we did above for each of our clus- foreground of the cluster. We also see from this figure that
ters - A370, ZwCl0024+17 and RXJ1347-11. This is shown the region where we picked “red” galaxies corresponds to
in Fig. 5 (left) for the COSMOS catalogue and plotted in z 1 1.5,andthe“blue”galaxiesoccupyaregionofmean
∼ −
terms of the same CC plane as A370. The colour distribu- redshift around z 2. Most notably, the top left corner of
tionofCOSMOSfieldgalaxiesseeninthisB,R,z′CC-space “dropout” galaxies∼corresponds to high-z with z &3.5. We
is very similar to that of A370, displaying the same mor- further plot the redshift distribution of all the samples in
phology, including red, blue and dropout populations, but Fig.6.Wecalculatethemedianredshiftofeachsampleand
without the density peak associated with the massive clus- summarized in Table 2.
terA370.WealsoshowhowredshiftvariesinthisCC-plane However, if we look at the distribution of COSMOS
bycalculating themean photo-z redshift from COSMOSin redshifts of the dropout sample (Fig. 7, red), we find it is
fine bins over the CC plane (Fig. 5, right), with the sam- somewhat double-peaked, with most galaxies lying around
ples boundaries displayed as well. This demonstrates that z 3.5, but a significant fraction identified as having
∼
themainoverdensityintheCCplanenearBJ RC 1and z 0.4. Since we are certain most of the galaxies in this
RC z′ 0.3 hasa mean redshift of around z−.0.5∼, which reg∼ion are in fact high redshift dropout galaxies, justified
− ∼
agreeswithourestimationforA370wherewefoundverylit- by the apparent high WL distortions measured for these
(cid:13)c 0000RAS,MNRAS000,000–000
8 Medezinski et al. 2010
A370 bright A370 faint
1 χ2/Γd=o−f 0=. 0143±/60.1 1 Γ=0.88±0.2
gT 0.5 gT 0.5 χ2/dof = 6/7
0
gT 0.15 θ [arcmin] χ2/Γd=o0f .=4 11±/60.2 01 θ [arcmin] Γ=1±0.1
gT 0.00115 θθ [[aarrccmmiinn]] χχ22/Γ/Γdd==oo00ff ..==88 5711±±1700//68..21 ggT T 00..0155 θ [arcmin] χχ22Γ//dd=oo1ff .==1 ±22073.//288
gT 0.5 0
gT 0.015 θ [arcmin] χ2/Γd=o0f .=9 56±/80.2 gT 0.15 θ [arcmin] χ2Γ/d=o1f .=3 ±103./28
0 0
1 2 5 10 1 2 5 10
θ [arcmin] θ [arcmin]
ZwCl0024 RXJ1347
1.5
gT 0.015 χ2Γ/d=o0f .=0 854/9±0.1 gT 0.15 χ2Γ/d=o−f 0=. 0144±/80.1
0
T 1 θ [arcmin] χ2Γ/d=o0f .=5 51±10/9.2 1.5 θ [arcmin]
g0.05 gT 0.15 χ2Γ/d=o0f .=7 65±/80.3
gT 0.15 θ [arcmin] χ2Γ/d=o0f .=8 32±30/9.2 1.05 θ [arcmin]
T 01 θ [arcmin] χ2Γ/d=o0f .=9 78±/90.1 gT 0.015 χ2Γ/d=o1f .=1 ±50/8.3
gT 0.015 θ [arcmin] χ2Γ/d=o0f .=9 91±30/9.2 gT 01..155 θ [arcmin] χ2Γ/d=o0f .=9 29±/80.2
g0.5 0
0 1.5 θ [arcmin]
gT 0.15 θ [arcmin] χ2Γ/d=o0f .=9 32±30/9.2 gT 0.15 χ2Γ/d=o1f .=2 ±305./38
0 0
1 2 5 10 1 2 5 10
θ [arcmin] θ [arcmin]
Figure 4. gT vs. cluster radius for A370 bright samples (top left: foreground, orange, green, red & blue) and faint (top right: green,
red, blue & dropouts), ZwCl0024+17 (bottom left: foreground, orange, green, red, blue & dropouts) and RXJ1347-11 (bottom right:
foreground,orange,green,red&blue),wherethefixedpower-lawfitisoverlaid(dashedblackline)with1−σconfidencelevels(shaded
region). Also plotted is the power-law fit of the equivalent “reference” background sample (dotted curve). In each case the resulting
normalizedgT amplituderatio,Γ,isdenoted nexttotheprofile.
galaxies (see Fig. 4) and by reference to deep spectroscopic distribution of the same dropout sample (Fig. 7, blue), but
workinthisrisingplumeof“dropout”galaxies(Steideletal. here practically no low-z peak is observed, and all galaxies
1999), we may conclude the low redshifts assigned to some in this region are estimated to have high redshifts, z &2.5.
of these galaxies may be misclassified as low redshift early This comparison between COSMOS and GOODS-MUSIC
type/dusty galaxies in the photo-z catalogue of the COS- redshiftsallowsustosecurelysetaconservativelowerB R
−
MOS field.This isnot surprising, since at faint magnitudes limit to avoid inclusion of real low-z objects. We can thus
theCOSMOSphoto-zhavearelativehighcatastrophicfail- safelyassumeallobjectsidentifiedaslow-z intheCOSMOS
urerate (Ilbert et al. 2009). cataloguearelargelymistakenlyclassified,apointalsomade
We further examine this issue using the somewhat in relation to this by Schrabback et al. (2010). Estimating
deeperGOODS-MUSICcatalogue(Grazianetal.2006;San- the median redshift of the dropout sample gives z 3.8,
≃
tini et al. 2009), which has 15 bands, including high qual- a value very close to the mean redshift of all galaxies ly-
ity ACS photometry (GOODS-S) and deep IRAC imaging ing above z > 1.5 galaxies. This further demonstrates the
which is very helpful in reducing the outlier rate a high-z. low-z peak is a low-significance contamination. A further
Usingthez′-bandselectedGOODS-MUSICphoto-z,wede- examinationofthephotometricredshiftestimation forsuch
rive a spectral classification for each galaxy using a library objects in the COSMOS field seems worthwhile in view of
of 200 PEGASE (Fioc & Rocca-Volmerange 1997) tem- theseresults.
∼
platesverysimilartothatdescribedinGrazianetal.(2006),
as included in the EAZY software (Brammer et al. 2009),
5.3 Lensing strength dependence on magnitude
and then calculate Subaru magnitudes for all the galaxies
using theBPZ (Ben´ıtez 2000) code. Asanothercheck,weplot Γ,thegT-amplituderatio, vs.z′-
By making thesame CC selection, we plot theredshift bandmagnitudeforA370selectedsamples,toseeifthereis
(cid:13)c 0000RAS,MNRAS000,000–000
WL Detection of the Distance-Redshift Relation 9
3.5
4
3
3.5
2.5
3
B − R1.25 22.5redshift z
1.5
1
1
0.5
0.5
0
−0.5 0 0.5 1 1.5 2
R − z
Figure5.Left:BJ−RC vs.RC−z′CCdiagram,showingthedistributionofgalaxiesinCOSMOSfield.ApplyingthesameCC-cutsas
ourselectionforA370,wedefinegalaxysamples:foreground(gray),orange(orange), green(green), red(red),blue(blue), anddropout
(magenta)galaxies,inordertoestimatethemeanredshiftsandmeandepthsofthesesamplesusingCOSMOSphoto-z’s.Right:Average
COSMOSredshiftinCCbins.Overlaidaretheboundariesoftheforeground(thindashedgrayline),orange(thickdotted-dashedorange
line), green (thin solid green line), red (thick dashed red line), blue (thin dotted-dashed blue line) and dropout (thick solid magenta
line)samplesselectedintheCOSMOSfieldaccordingtoA370CC-cuts.Evidently,differentregionsofCCspacecorrespondtodifferent
redshiftpopulationsofgalaxies.Mostnotably,Thetopleftcornerdenotesdropoutgalaxiesofz&3.5,correspondingwelltoourselection
ofhighlydistorteddropoutgalaxies.
piricalsimulationswithhigherspacebasedresolutioncanbe
2
1 madetoexaminethisbetter.Thedecliningtrendofthepre-
0 dicteddls/ds inthecaseofbluegalaxies,basedontheCOS-
−1
MOS photo-z estimation, shown in Fig. 8 (dashed curves),
2
o) 1 could possibly point to amiss-classification of bluegalaxies
ati 0 withphoto-zmethods,awellknownproblemforbluegalax-
de r ies, or even simply a limiting magnitude beyond which the
plitu 2 photo-zmethodfailsinthiscatalogue.Wesetourmagnitude
m
Γ (g aT 02 lwfiomirthitths1e9cog<nreseezrn′va<staimv2e3plylfeo,tro2t3hme<inoirmza′inz<geet2sha5emsfeoprlpeo,ths2se0ibbl<elupezr′os<abmle2pm4l.es5,,
03 22 < z′ < 26 for the red sample, and 24.5 < z′ < 26.5
2
for the dropout sample, in the case of A370. Similar exam-
1
ination and limits were also applied for ZwCl0024+17 and
0
20 21 22 23 24 25 26 RXJ1347-11, with results discussed below.
z’ [mag]
Figure8.Γ,thegT amplituderatio,vs.magnitude(z′band)for
A370orange,green,red,blueanddropoutgalaxysamples(topto 5.4 Lensing strength vs. redshift
bottom).Overlaidisthelensingdepth,dls/ds,vs.magnitudecal-
culatedfromCOSMOSphoto-z’sforeachofthesamples(dashed WemaynowfinallycombinetheWLdistortioninformation
blackline)with1−σ confidence levels(shadedregion). with the redshift information for all the samples of back-
groundgalaxiesdefinedabove.First,weplottheWLampli-
tude,a,as a function of redshift in Fig.9 for thethreeclus-
anytrendofthelensingamplitudewithmagnitude.Wealso ters– A370 (top),ZwCl0024+17 (middle) and RXJ1347-11
plot the mean dls/ds as a function of magnitude (all values (bottom).Aclear trendof increasingWL amplitudeisseen
normalized to the reference background values) calculated with redshift, especially in the case of A370. A null result
in independent magnitude bins for each sample using the is easily excluded with low significance – χ2/N = 91/8 for
COSMOS photo-z catalogue. This serves as a further con- A370,χ2/N =34/4forZwCl0024+17 andχ2/N =42/3for
sistency check. Interestingly, for the blue galaxies (and the RXJ1347-11, for a case of non-increasing horizontal line. In
dropout galaxies to some extent),themean signal seems to order to compare the resulting trend with the cosmological
drop slightly with fainter magnitudes. This trend is some- trend,weplotΓ,thegT-amplituderatio,againstmedianred-
whatcounter-intuitive,sinceweexpectthatfaintergalaxies shift, zs ,inFig.10foreachoftheclustersexamined–A370
h i
will be at higher redshifts, and therefore have on average a (top), ZwCl0024+17 (middle) and RXJ1347-11 (bottom).
higher signal. The horizontal bars show the width of the source redshift
ThediminishedWLsignalcouldpossiblyhintataprob- distribution, given as the 68% range of data about the me-
lemwithestimatingtheWLsignalfromfaintbluegalaxies, dian redshift. Each point in a figure represents an indepen-
whichareingeneralquiteirregularinmorphology,andem- dentsample,wherethefirstpointrepresentstheforeground
(cid:13)c 0000RAS,MNRAS000,000–000
10 Medezinski et al. 2010
A370 A370
0.8 1.6
0.7 1.4
0.6 1.2
0.5 o) 1
a (g amplitude)T 000...234 Γ (g amplitude ratiT 000...468
0.1 0.2 ΛCDM; χ2/N=3.4/8
EdS; χ2/N=3.3/8
0 0 ΩM=0,ΩΛ=0; χ2/N=3.5/8
−0.1 −0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
<z> <z>
ZwCl0024 ZwCl0024
0.7
0.6 1.2
0.5 1
o)
a (g amplitude)T 000...234 Γ (g amplitude ratiT000...468
0.1
0.2 ΛCDM; χ2/N=3.7/5
0 EdS; χ2/N=4.2/5
0 ΩM=0,ΩΛ=0; χ2/N=3.2/5
−0.1
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
<z> <z>
RXJ1347 RXJ1347
0.6 1.5
0.5
0.4
o) 1
a (g amplitude)T 00..23 Γ (g amplitude ratiT0.5
0.1
ΛCDM; χ2/N=0.95/4
0 EdS; χ2/N=1/4
0 ΩM=0,ΩΛ=0; χ2/N=0.88/4
−0.1
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
<z> <z>
Figure 9. gT amplitude, a, vs. redshift for A370 (top) bright Figure 10. gT amplitude ratio, Γ, vs. redshift for A370 (top)
(stars) and faint (circles) samples, ZwCl0024+17 (middle) and bright (stars) and faint (circles) samples, ZwCl0024+17 (mid-
RXJ1347-11(bottom).AtrendofhigherWLamplitudewithred- dle) and RXJ1347-11 (bottom). Also plotted is the lensing
shiftisseen. depth,dls/ds,vs.redshiftfordifferentcosmologies-ΛCDM(cir-
cles+solidline),Einstein-deSitter(crosses+dashedline),andan
emptyUniverse(squares+dashed-dottedline)estimatedusingthe
COSMOSphotometricredshiftcatalogue. Horizontalbarsrepre-
sample in front of each cluster, and the other points repre-
sent the width of the source redshift distribution, given as the
sent background galaxy samples. For each sample, we also
68%rangeofdataaboutthemedianredshift.
calculatethemedianlensingdistanceratio, dls/ds ,foreach
h i
cosmological model – ΛCDM (empty circles), Einstein-de
Sitter(crosses),andanemptyuniverse(emptysquares),us-
ing the COSMOS photo-z measurements of galaxies within
the same CC-magnitude boundaries defined for each back-
ground sample and thus obtain the predicted depth. We
interpolate between these discrete predicted values to pro-
(cid:13)c 0000RAS,MNRAS000,000–000
