Probing the distribution of dark matter in the Abell 901/902 supercluster with weak lensing

23 Pages·2008·1.51 MB·English

ACCEPTEDFORPUBLICATIONINTHEASTROPHYSICALJOURNAL,NOVEMBER10,2001
PreprinttypesetusingLATEXstyleemulateapjv.14/09/00
PROBINGTHEDISTRIBUTIONOFDARKMATTERINTHE
ABELL901/902SUPERCLUSTERWITHWEAKLENSING
M.E.GRAY
InstituteofAstronomy,MadingleyRoad,CambridgeCB30HA,UnitedKingdom
[email protected]
A.N.TAYLOR
InstituteforAstronomy,BlackfordHill,EdinburghEH93HJ,UnitedKingdom
[email protected]
K.MEISENHEIMER
Max-Planck-Institutfu¨rAstronomie,Ko¨nigstuhl17,D-69117,Heidelberg,Germany
[email protected]
1
S.DYE
0
AstrophysicsGroup,BlackettLab,ImperialCollege,PrinceConsortRoad,LondonSW72BW,UnitedKingdom
0
[email protected]
2
C.WOLF,&E.THOMMES

v Max-Planck-Institutfu¨rAstronomie,Ko¨nigstuhl17,D-69117,Heidelberg,Germany
o [email protected]
N AcceptedforpublicationintheAstrophysicalJournal,November10,2001
4 ABSTRACT
1 WepresentaweakshearanalysisoftheAbell901/902supercluster,composedofthreerichclustersatz =0.16.
UsingadeepR-bandimagefromthe0.5◦×0.5◦MPG/ESOWideFieldImagertogetherwithsupplementaryB-
1
band observations, we build up a comprehensive picture of the light and mass distributions in this region. We
v
findthat,onaverage,thelightfromtheearly-typegalaxiestracesthedarkmatterfairlywell,althoughonecluster
8
isanotableexceptiontothisrule. Theclustersthemselvesexhibitarangeofmass-to-light(M/L)ratios,X-ray
8
properties,andgalaxypopulations. We attempttomodelthe relationbetweenthe totalmassandthelightfrom
2
1 the early-type galaxies with a simple scale-independentlinear biasing model. We find M/LB = 130h for the
1 earlytypegalaxieswithzerostochasticity,which,iftakenatfacevalue,wouldimplyΩm < 0.1. However,this
1 linearrelationbreaksdownonsmallscalesandonscalesequivalenttotheaverageclusterseparation(∼1Mpc),
0 demonstratingthatasingleM/Lratioisnotadequatetofullydescribethemass-lightrelationinthesupercluster.
/ Rather, thescatterinM/Lratiosobservedfortheclusterssupportsamodelincorporatingnon-linearbiasingor
h
stochasticprocesses.Finally,thereisacleardetectionoffilamentarystructureconnectingtwooftheclusters,seen
p
- inboththegalaxyanddarkmatterdistributions,andwediscusstheeffectsofcluster-clusterandcluster-filament
o interactionsasameanstoreconcilethedisparatedescriptionsofthesupercluster.
r
t Subjectheadings:gravitationallensing—cosmology:darkmatter—galaxies:clusters:general—galaxies:
s
a clusters:individual(Abell901a,Abell901b,Abell902)
:
v
i 1. INTRODUCTION cently,superclusterstudieshavebeenextendedtointermediate
X
redshiftswiththeweaklensingstudyofMS0302+16atz =0.4
Gravitationallensingisapowerfultoolthatallowsustodi-
r byKaiseretal.(1998),andpushedtoevenhigherredshiftswith
a rectlymapdarkmatteranddeterminetherelationbetweenthe
theopticaldetectionofaz ∼ 0.91superclusterbyLubinetal.
observeddistributionoflightandtheunderlyingmassdistribu-
(2000).
tion. In recent years, the development of sophisticated lens-
Superclusters are invaluable testing grounds for theories of
ing techniques coupled with a new generation of wide-field
cosmology,the growthofstructure, galaxyformation,andthe
imaging instruments has opened doors to lensing studies on
natureof darkmatter. Thepresenceorabsenceoffilamentary
unprecedentedly large scales. Weak lensing is now a well-
structure can be used to probe theories of structure formation
establishedmethodfordeterminingthemassdistributionofrich
(e.g.Cen etal. 1995). Thedegreeof substructureis reflective
clusters of galaxies (Bartelmann & Schneider 2001; Mellier
oftheuniversalmatterdensityparameter,Ω ,(Richstoneetal.
1999). With the increased confidence in lensing techniques, m
1992),andsimulationsfindthatthemassfractionin filaments
recent studies have turned from clusters to blank fields (Ba-
isexpectedtobeslightlylargerinalow-densityuniverse(Col-
con etal. 2000;Kaiser et al. 2000;Van Waerbekeet al. 2000;
berg et al. 1999). Furthermore, supercluster mass-to-light ra-
Wittmanetal.2000;Maolietal.2001)tomeasurethestatistical
tios(M/L)canbealsobeusedtodetermineΩ (Kaiseretal.
‘cosmicshear’duetolensingbylarge-scalestructures. m
1998). Thislatter calculation rests on the assumption that the
Superclusters,comprising∼2-10clustersofgalaxies,arethe
supercluster M/L ratio is representative of the Universe as a
largest known systems of galaxies in the Universe (Vogeley
whole, i.e. thatthe M/L ratioflattens to a constantonsuper-
et al. 1994) and representa stepping-stone between rich clus-
clusterscales(Bahcalletal.2000).
ters and large-scale structure. Clusters of clusters and associ-
InthispaperwepresentaweaklensinganalysisoftheAbell
atedfilamentarystructuresinthegalaxydistributionhavebeen
901(a,b)/Abell902supercluster(referredtohereafterasA901/902)
observedatlowredshiftthroughredshiftsurveysoftheCorona
using the 0.5◦ × 0.5◦ Wide-Field Imager (WFI; Baade et al.
Borealis,Shapley,andPerseus-Piscessuperclusters(e.g.Small
1998, 1999) on the MPG/ESO 2.2m telescope. Our aim is
et al. 1997; Quintana et al. 1995; Postman et al. 1988). Re-
to trace the dark matter distribution in the supercluster field
1
2 Grayetal.
and to investigate whether it is concentrated in cluster cores fordsus the opportunityto test this hypothesison another su-
or distributed through filamentary structures. In the ‘Cosmic perclustersystematlowerredshift,andtodetermineifasingle,
Web’ theory of structure formation (Bond et al. 1996), fila- scale-independentM/Lratiocandescribetherelationbetween
mentsemergefromtheprimordialdensityfieldafterclusterfor- massandlightintheentiresystem. Wewilldiscusstheresult-
mation. Thesefilamentsarethoughtto harbora largefraction ing implications of such a conclusion for values of Ω , and
m
ofpresentdaybaryonsintheformofhotgas,promptingcalls exploreotherpossiblebiasingrelations.
for X-ray searches (Pierre et al. 2000). However, attempts to
1.1. TheA901/902supercluster
detect filamentary X-ray gas have to date been unsuccessful,
yielding only upper limits (e.g. Briel & Henry 1995). As X- TheA901/902superclusteriscomposedofthreeclustersof
rayemissivityscalesasthesquareofthedensitywhilegravita- galaxies,allatz = 0.16andlyingwithin30′×30′onthesky.
tionalshearscaleslinearly,aweaklensing-basedapproachmay Abell901islistedasadoublecluster(A901aandA901b)with
prove more successful in uncovering such structures. Kaiser irregularmorphologyintheX-rayBrightestAbell-typeCluster
etal.(1998)reporttantalisingbuttentativeevidenceforalens- Sample (XBACS; Ebeling et al. 1996)of the ROSAT All-Sky
ing detection of a mass bridge within MS0302+16. Here we Survey, having L (0.1-2.4 keV)= 6.01 and 3.49× 1044 erg
X
will use weak shear reconstruction algorithms to create two- s−1.
dimensionalmapsofthemassdistributionandsearchforsimi- Pointed ROSAT HRI observations by Schindler (2000) re-
larfilamentarystructureswithintheA901/902superclusterre- veal that the emission from the ‘brighter subcluster’ of Abell
gion. 901 (labelled Abell 901a in the Ebeling et al. nomenclature
In addition, we also wish to determine how well the opti- used in this paper) suffers from confusion with several X-ray
cal light traces the underlying dark matter, and how the clus- pointsourcesinthevicinity.SheconcludesthattheX-rayemis-
ter masses determinedby weak lensing compareto those pre- sion from Abell 901a is in fact point-like and suggests emis-
dictedfromtheresultsofapreviousX-raystudyoftheregion sionfromanactivenucleusasalikelycandidateforthesource.
(Schindler 2000). Finally, we wish to examine the ratio of Abell 901b, on the other hand, is shown to exhibit very reg-
the total mass of the system to the B-band light of the early- ular and compactcluster emission, with a revised L (0.1-2.4
X
type supercluster galaxies, and to discuss the resulting impli- keV)=3.6±0.1×1044ergs−1,possiblycontainingacooling
cations for Ωm. Measurementsof the mass-to-(total)-lightra- flow.NoX-rayfluxisdetectedattheopticalcenterofAbell902
tio of clusters of galaxies typically yield values in the range (as determined by Abell, Corwin, & Olowin 1989), although
M/L ∼ 200 − 300h (Carlberg et al. 1996; Mellier 1999), there is point-like emission 2 arcmin to the west of this posi-
which,iftakenastheuniversalM/L,implyΩm = 0.2. How- tion.
ever, if the M/L ratio continues to increase with scale to the Boththeclusteringofnumbercounts(Abelletal.1989)and
regime of superclusters or beyond, Ωm could be considerably theX-rayemission(Ebelingetal.1996;Schindler2000)inthis
larger. This would require the galaxies to be significantly bi- fieldindicatethatthisisanoverdenseregion.Howexactlymass
ased with respectto the mass, so that the efficiencyof galaxy is distributed through the field and which of the objects dis-
formationisgreatlyenhancedinthedensestregions. cussed here deserves to be labelled a ‘cluster’ is not so clear,
Bahcall, Lubin, & Dorman (1995) explore this hypothesis, however. Wethereforeturntogravitationallensingtotracethe
and compile results from the literature to trace an increasing underlyingmassdistributionofthissystem.
M/L ratio as they proceed in scale from galaxies to groups The structure of the paper is as follows: in §2 we outline
and then to clusters. Their best-fit values for the M/L of in- the observations of the supercluster field and discuss the data
dividual galaxies result in a M/L ratio for ellipticals that is reductionandastrometricissues. In§3weperformthecorrec-
∼4timesthatforspirals,suggestingthatonaverage,ellipticals tionsforthepoint-spreadfunctionnecessarytoaccuratelymea-
containmoremassthanspiralsforthesameluminosityandra- suretheshapesofthebackgroundgalaxies.In§4wediscussthe
dius. Theyconcludethatthetotalmassofgroups,clustersand photometricpropertiesoftheclusters,andin§5wepresentthe
superclusterscanbeaccountedforbythemassofthedarkha- results of the weak lensing analysis. §6 contains a statistical
losoftheirmembergalaxies(whichmayhavebeenstrippedoff cross-correlationofthelightandmassdistributions. Finally,in
inadenseenvironmentbutstillremainwithinthesystem)plus §7wesummarizetheresultsandpresentourconclusions.
the massofthe hotinter-clustergas, andthatthereisnogreat
repositoryofdarkmatterhiddenonlargerscales. 2. OBSERVATIONS AND DATAREDUCTION
Indeed,onthescaleofsuperclusters,measurementsofgalaxy
2.1. Observingstrategy
velocity dispersions indicate that the universal M/L function
appears to flatten to ∼ 300h (assuming that the systems are Theobservationspresentedinthispaperwereundertakenas
bound but not necessarily in an equilibrium state). Bahcall partoftheCOMBO-17survey(Wolfetal. 2001). Thesurvey
et al. (1995) find little evidence that the M/L ratio continues has imagedone square degreeof sky split overfour fields us-
to increase with scale, implyingΩ ∼ 0.2. The issue of a low ingthe Wide-FieldImager(WFI) atthe MPG/ESO 2.2mtele-
supercluster M/L ratio was revisited by Kaiser et al. (1998) scopeonLaSilla, Chile. Forlensingstudies, oneofthefields
in a weak-shear study of a supercluster of three X-ray lumi- wascenteredontheA901/A902supercluster.Thefiltersetwas
nous clusters at z = 0.4. This was the first direct mapping chosensuchastoprovidereliableclassificationandphotomet-
ofdarkmatteronthesescales,independentofbiasingassump- ric redshift estimators, and consists of five broad-band filters
tions. Kaiser etal. presenttheremarkableresultthatthe light (UBVRI)and12narrow-bandfiltersrangingfrom420to914
from the color-selected early-type galaxies alone is sufficient nm. A deepR-bandimagetakenunderthebestseeingcondi-
totracethemassasrevealedbyweaklensing,withthemassno tions duringeach run providesexcellentdata for gravitational
more extendedthan the early-typegalaxiesand with late-type lensingstudies.
galaxieshavingnegligibleM/L . Ourweaklensingstudyaf- In §2.2, we outline the initial processing applied to images
B
under the standard WFI pipeline reduction developed at the
AweaklensinganalysisoftheAbell901/902supercluster 3
MPIAHeidelberg. Althoughtheresultingimagesareadequate Tothisend,flat-fieldcorrectedmosaicimagesarealignedwith
foralmostallastrophysicalapplications,weneedfurtherhigher- respect to moderatelybrightstars in the field (to integerpixel
order corrections for the detection of unbiased lensing shear. accuracy). The cosmic ray detection algorithm employs a σ-
Thisisdescribedin§2.3. clippingwithrespecttothemedianpixelvaluederivedfromat
The data used in this paper are the deep R-band and sup- leastfiveexposureswithcomparableseeing.Discrepantvalues
plementaryB-bandimagesfromtheCOMBO-17observations arereplacedbythemedianvalue.
of the superclusterfield. We will use the R-band image for a
weak shear analysis of the supercluster, in combination with 2.3. Astrometry
color information from the bluer band to separate foreground
2.3.1. Linearastrometricfitting
and backgroundgalaxypopulations. The details of the obser-
vations are presented in Table 2.1. The discussion of the full While the creation of mosaiced images by the standard re-
17filterdatasetfortheA901/902fieldandthephotometricred- ductionpipelinedescribedaboveissufficientformostpurposes,
shiftsderivedfromitisreservedforafurtherpaper. werequireamorerigorouscharacterizationofthegeometryof
the camera for our weak shear study. For example, intrinsic
2.2. InitialprocessingbystandardWFIpipeline rotationof the FOV of the WFI is knownto be caused byim-
perfectalignmentofthe2.2mtelescopeaxisofrotationwiththe
Imagingby the Wide Field Imager(WFI) onthe 2.2mtele-
celestialpoleaswellastelescopeflexureintrackingacrossthe
scope at La Silla, Chile is carried out with a 4 × 2 array of
sky.Othercausesareatmosphericinorigin,duetothedifferen-
2048× 4096 pixel CCDs. For clarity and ease of reference,
tial refractionof objectimagesby the Earth’satmosphereand
chipsarelabelledbytheletters‘a’,startingatthetopleftofthe
thefactthatanoffsetinrightascensionproducesarotationdue
mosaic,throughaclockwisedirectiontochip‘h’locatedatthe
to the non-perpendicularityof lines of declination away from
bottomleftofthemosaic. Withaverticalchip-to-chipsepara-
thecelestialequator.
tion of 59 pixelsanda correspondinghorizontalseparationof
Tothisend,wechosetotreateachCCDimageasanindivid-
98pixels,thescaleof1pix≡0.238′′givesatotalfieldofview
ualcontributiontothefinalcoaddedimage,andtocomputean
(FOV)fortheWFIof0.56◦×0.55◦.
astrometric solution separately for each chip image. For each
De-biasingisconductedbyindividuallysubtractingthe(ver-
debiased, normalized, flattened and cosmic-ray cleaned mo-
ticallysmoothed)levelmeasuredintheoverscanregionofeach
saic the approximaterotations described above were removed
chipimage. Non-linearity(i.e. departurefromtheproportion-
to restore the original detector coordinate system. Next, the
ality between the number of incidentphotons and the electric
eight component chip images were extracted from each mo-
chargereadoutattheendofanexposure,whichworsenswith
saic. Henceforth the term ‘image’ shall refer to an individual
increasing intensity), is corrected by scaling each de-biassed
2K×4Kchipimage.
chip image accordingto an ESO laboratory-determinedfactor
UsingSExtractor2.1(Bertin&Arnouts1996)aninitialcat-
(Baade1999)2. Onlychipsb,c,f&gneedbecorrectedinthis
alogueof brightobjectswas createdfor each image. A rough
way,theworstnon-linearitybeingexhibitedbychipfwhichat
transformationwasperformedtoconvertthepixelcoordinates
saturation(65000counts)deviatesby1.4%fromlinearity.
(x,y)tocelestialcoordinates(α,δ)usingthepointinginforma-
Production of mosaiced images must be handled with care
tionencodedintheimageheader. Theobjectsinthecatalogue
duetothephysicalcomplicationofchip-to-chipmisalignments
werethenmatchedtotheSuperCOSMOSSouthernSkySurvey
in the CCD array. Translational misalignments are easily ac- 3withinatoleranceof5′′. Thesereferenceobjectswereusedto
commodated, however intrinsic chip rotations with respect to
iterativelycalculatealinearastrometricsolutionfortheimage,
the array are not. A slight chip rotation produces the added
withthetangentpointforprojectionbeingtheopticalaxis. The
complexityofhavingtorotatethechipimagebeforeinsertion
rmsresidualsoftheobjectsusedinthefinalsolution(typically
intothemosaic.
numbering∼400perimage)differedfromthe medianby less
Ratherthanrebinimages,rotationsareapproximatedbydi-
than3σ.
viding up the misaligned chip images into horizontal strips.
Thelinearfitusedtakestheform:
Each strip istheninserted intoa temporarychipimagewith a
x = a +a ξ+a η
horizontaloffsetdeterminedbytherequiredrotation.Thistem- 0 1 2 (1)
y = a +a ξ+a η,
porarychip image is then dividedinto verticalstrips and then 3 4 5
finally insertedinto the mosaic with verticaloffsets according wherethe ‘expected’coordinates(standardcoordinateson the
totherotation.Adoptingthisshearingmethodconsiderablyre- tangentplane,projectedabouttheopticalaxis)arerelatedtothe
duces data reduction time, is optimal for cosmic ray removal ‘measured’coordinates(x-ycoordinatesonthedetectorplane)
(seebelow),andhasbeenshowntohavenoeffectonphotom- by a 6 coefficient linear fit. Note that field-to-field variations
etry. Table 2 lists chip rotations determined independentlyin were found to be significant, so the external calibration was
this workaspartofthe astrometricfitting describedin §2.3.1, calculatedforeachimageindividually.
althoughtheyareinagreementwiththerotationsincorporated The linear fit can be decomposed into terms such as pixel
intheWFIpipeline. scale,rotation,andnon-perpendicularityofthecoordinateaxes
Afterproducingmosaicimagesinthisfashion,scienceframes for each image. The average rotation angles requiredto align
were flattened with normalized mosaic flat-field frames pro- the x-y axes to a N-E orientation and the angle of deviation
duced in exactly the same way. Since each physical pixel is fromtheperpendicularforthex-yaxesarelistedinTable2.3.1
maintainedintactthroughoutthereductionprocess,cosmicray foreachchip.Theresultingfitsproducedmedianrmsresiduals
hits andcosmeticchipdefectscan bedetectedveryefficiently of 0.2 arcsec, i.e. less than 1 pixel and close to the limiting
by comparing dithered images taken through the same filter. accuracyofthephotographicdata.
2 The WFI user manual is available via the ESO homepage at 3http://www-wfau.roe.ac.uk/sss
http://www.eso.org.
4 Grayetal.
TABLE1
SUMMARYOFOBSERVATIONSUSEDFORTHEPRESENTSTUDY
Date Filter Exposures Date Filter Exposures
1999Feb18 B 10×500s 2000Jan31 R 8×600s
1999Feb19 B 12×500s 2000Feb06 R 27×500s
2000Feb12 R 9×500s
total: 3.05h total: 6.33h
TABLE2
DECOMPOSITIONOFTHEASTROMETRICFITS
LinearFit RadialFit
Chip Rotation ± Skew ± C
a -288.3 53.5 -104.5 21.4 6.4
b 276.0 54.0 -117.0 17.2 -38.7
c 126.0 53.2 120.1 20.2 -29.4
d 130.7 54.5 161.9 19.8 0.7
e 144.9 53.9 -157.3 11.6 1.6
f 123.8 53.0 -115.2 16.3 -39.8
g 120.9 53.5 104.8 24.4 -50.6
h -98.3 49.9 74.7 27.2 13.0
Note.—Columns2-5listtheanglesofrotationandnon-perpendicularity(inarcseconds)fortheeightchipsaccordingtothelinearastrometricfit.Thefinalcolumn
liststheradialdistortioncoefficient(radians−2)foundwhenaradialdistortionterm(asineq.[2])wasaddedtothefit.
2.3.2. Quantifyingshearinducedbyradialdistortions Itisquiteclearthatdespitethewidefieldofviewofthecam-
era, the instrumental distortion in the WFI is extremely small
Whilethelinearfitsproducedsatisfactoryresults,itisnever-
and will not significantly affect our shear measurements. We
thelessimportanttoconsiderhigher-orderorradialdistortions.
shallcontinuewiththeanalysisusingthesimplelinearfitwith
Asatesttosearchforpincushionorbarreldistortions,aradial
nocorrectionforthenegligibleradialdistortion. Notethatcor-
distortiontermwasaddedtothelinearfit,oftheform:
rections involving higher-order polynomials could be used to
r′ =r(1+Cr2), (2) remove any non-linear, non-radial distortions present, but we
where r is the radial distance from the tangent point (optical seelittleevidenceofthesefromtheresidualsfollowingthelin-
axis),cisthedistortioncoefficient,andr′ istheradialdistance earfit.
fromthetangentpointinthepresenceofthedistortion.
The fit for some chips (particularlythe y-componentof the 2.3.3. Registrationandcoaddition
fitfortheinnerfourchips)improvedsomewhatwhentheradial
term was added, but there was no significant improvementin
theresultingrmsresidualsfortheinstrumentasawhole.How-
ever,theresultsoftheradialfittingdoallowustoconstrainthe
amount of linear distortion found in each chip. The resulting
valuesofC (listedinthefinalcolumnTable2.3.1)weresmall,
andhadasmalldispersionforeachchipfromimagetoimage.
The contrast between the values for the inner and outer four
chips indicates that the mosaic as a whole does not display a
typicalradialdistortionpattern.
Knowingthedistanceoftheedgeofeachchipfromthetan-
gent point, this yields distortions of δr/r ∼ 0.025% at the
furthest corners of the camera, or slightly higher for the in-
nerchips. ThistallieswellwiththefiguresquotedintheWFI
manual,whichclaimsgeometricdistortions≤0.08%acrossthe
entirecamera.
Wecanfurtherquantifyanyartificialshearinducedbysucha
radialdistortionusingtherelationsofBaconetal.(2000).Ifthe
displacementδr=Cr3 andˆristheunitradialvector,thenthe
inducedinstrumentalshearisγ = Cr2eˆ,whereeˆ istheunit
i i i
radialellipticityvector. Usingtheradialdistortioncoefficients FIG. 2.—Candidategiantarc. Thepotentialdeflectinggalaxyisabarred
derivedfromour astrometricfits, we find a shear patternwith spiralwithR=18andislocated∼2.5arcminfromthecenterofAbell902.
amplitudeγ <0.0001throughout.
AweaklensinganalysisoftheAbell901/902supercluster 5
FIG. 1.—TheR-bandviewofthecentral20×20arcminofthesuperclusterfield(seenatreducedresolution). Thetwolargetrianglesmarkthepositionsof
Abell901andAbell902intheoriginalcatalogueofgalaxyclusters(Abelletal.1989),whilethethreelargecirclesindicatetheopticalcentersoftheclustersthat
wehaveadoptedinthispaper. ThesmallercirclesindicatethelocationsoftheROSAT/HRIX-raysourcesfromSchindler(2000). Theremainingobjectsmarked
bydiamondsaretwogalaxieswithknownredshift(alsofromSchindler2000),radiodetectionsfromtheNRAO/VLAAllSkySurvey(Condonetal.1998, labelled
‘VLA’)andtheIRASFaintSourceCatalogue(Moshir1990,labelled‘IRAS’).Northisup,eastistotheleft.
6 Grayetal.
The linear astrometric fits for each individual chip image usedtocalculatetheweightedquadrupolemoments,definedas
wereusedtoregistertheimagestothesamecoordinatesystem.
Theimageswerethusalignedandcombinedwith3σ clipping Iij ≡ d2xw(x)xixjI(x), (3)
Z
rejectionofbadpixels,scalingbythemedianandweightingby
exposure time. Due to the large number of images contribut- whereI(x)isthesurfacebrightnessoftheobjectatangularpo-
ingto eachpixelin thefinalimage(44fortheR-band,22for sitionxfromtheobjectcenter,andw(x)isaGaussianweight
the B-band), most bad columns and pixels were removed by function. Thescalelength,rg,oftheweightfunctionisprevi-
theσ-clippingalgorithm.Thecombinedmosaicedimageswere ouslydeterminedbyhfindpeaksastheradiusoftheMexi-
trimmedofthe noisyoutlyingregionswherethe overlapfrom canhatfilterfunctionthatmaximizesthesignal-to-noiseofthe
theditheringpatternwasnotcomplete. Theresultingfinalim- objectdetection.Finally,theweightedquadrupolemomentsare
ages used for the weak shear analysis measured8192×8192 usedtocalculatetheellipticitycomponents
pixels (32.5′ ×32.5′), and the measured seeing was 0.7′′ (R- I −I 2I
band)and1.1′′(B-band). e1 = 11 22, e2 = 21 . (4)
I +I I +I
Fig. 1 shows the inner regions of the R-band image, along 11 22 11 22
Photometric catalogues were also constructed for each im-
with the published positions of the clusters from Abell et al.
age, usingSExtractor2.1. Thedetectioncriteria were defined
(1989)and the X-raysourcesfromSchindler(2000). Inaddi-
such that an object was required to be 1.5σ above the back-
tion,Fig.2showsacandidatestronglylensedsource. Thearc-
groundandcomprisingatleast7connectedpixels. Thephoto-
like structure is located 13 arcsec from a bright barred spiral
metric information (from SExtractor) and the shape estimates
galaxy,whichisinturnlocated∼2.5arcminfromtheadopted
(fromimcat)werethenmergedtoprovidethefinalcatalogue
center of Abell 902. The deflecting galaxy has R = 18 and
forlensinganalysis, conservativelyrequiringthatanobjectbe
B−Rcolorsimilartotheclustergalaxies.
detectedbybothsoftwarepackages.Duetothesuperiorseeing
and longer exposure time, the shape parameters derived from
2.4. Photometriccalibration
theR-bandimagewill beused fortheweak shearreconstruc-
Photometriccalibrationwasprovidedfromtwospectropho- tions, although as we describe in §5.1, the B −R colors will
tometric COMBO-17 standards (Wolf et al. 2001, see) in the beusedto discriminatebetweentheforeground(includingthe
A901/902fieldselectedfromthespectraldatabaseoftheHam- clustergalaxies)andthebackgroundpopulations.
burg/ESO (HE) Survey (Wisotzki et al. 2000). Spectra were Finally, a mask was created directly from the image to re-
obtainedusing a wide (5′′) slit on the ESO/Danish 1.54mand moveobjectsfromthecataloguethatlayinareascontaminated
the ESO 1.52mtelescopeatLaSilla in November2000. Cor- bybrightstars,ghostimages,anddiffractionspikes.Thismasked
rectingtheobservedA901/902standardspectratoremovethe regiontotalledonly3.4%ofthetotalareaoftheimage,andcan
instrument,opticsandatmospheresignature,photometricscal- beseeninFig.6.
ingsweredeterminedfromtheHEsurveystandards. Usingthe
B- and R-band WFI filter responses, zero points were calcu- 3.2. AnisotropicPSFcorrection
latedandmagnitudestransformedtotheVegasystem.Apparent
Fig.3showsthesize-magnitudediagramforthefullsample
magnitudeswere correctedforextinctionusingtheIRAS dust
ofobjects. Thestarsareclearlyvisibleasacolumnofobjects
maps of Schlegel et al. (1998). For an average E(B −V) =
withhalf-lightradiiof1.8pixels,andcanbedistinguishedfrom
0.058andassuminganR = 3.1extinctioncurve,we derive
V
galaxiesdowntoR∼23.Toexaminethebehaviorofthepoint-
corrections∆m = 0.25and∆m = 0.16. Weestimatethat
B R
spread function(PSF) across the image we select a sample of
theS/N =3limitingmagnitudeinthetwobandsisR=25.7
non-saturated(R>16)stars.
andB =25.5.
ThestellarellipticitypatternacrossthefinalsummedR-band
imageisshowninFig.4,andthedistributionofellipticitiesin
3. POINT SPREAD FUNCTION CORRECTIONS
Fig.5. Whilethereisoverlapbetweenthechipregionsdueto
In this section we outline the correction for such effects as theditheringpattern,wedividethemosaicedimageinto8ap-
variableseeingconditionsfromexposuretoexposure,telescope proximatechipregionsforthepurposesofthePSFcorrection.
trackingerrors,aswellassmearingofobjectsduetoimperfect Within these regions, outlined in Fig. 4, the PSF is smoothly
alignment of images before coaddition and the circularization varyingandevenwithintheoverlapregionstherearenosharp
ofsmallobjectsbytheseeing.Thesecorrectionshavebeendis- discontinuitiesinthebehaviorofthePSF.
cussedin detailinseveralpreviouspapers(Kaiser, Squires,& We apply preliminary cuts to our catalogue to exclude ob-
Broadhurst1995,hereafterKSB, withrefinementsin Luppino jects unsuitable for shear analysis. We remove those objects
&Kaiser1997andHoekstraetal.1998). withahalf-lightradiussmallerthanthestellarhalf-lightradius,
aswellasobjectswithanimcatsignificanceν < 5andwith
3.1. Objectcatalogues ellipticity e > 0.5. Next, within each chip region we fitted a
The imcat software described in Kaiser et al. (1999) was two-dimensionalcubictothemeasuredstellarellipticities,iter-
used to determine the shape parameters for the faint galaxy atingtwicetoremoveoutlierswithlargeresiduals.
sampleusedintheweaklensinganalysis. Foreaseofcomput- Themodelledstellarellipticitieswereusedtocorrecttheel-
ing,thehfindpeaksobjectdetectionroutinewasperformed lipticitiesofthegalaxiesby
on2K×2Kimagesections,andtheresultingcataloguesshifted
P
bytheappropriateamountandconcatenatedtogether.Thelocal e =e− sme∗, (5)
skybackgroundwasestimatedusinggetskyandandaperture corr Ps∗m
magnitudes and half-light radii, rh, for each object were cal- wherestarredquantitiesreferredto stellarproperties,andPsm
culatedusingtheapphotroutine. Finally, getshapeswas istheimcat‘smearpolarizability’matrixofhighermoments
AweaklensinganalysisoftheAbell901/902supercluster 7
FIG. 4.—EllipticitypatternofstarsontheR-bandcoaddedimage,before(left)andafter(right)correctionfortheanisotropicPSF.Thehorizontalandvertical
linesshowtheapproximatechipdivisionsusedforthepolynomialfitting.
FIG.3.—Magnitudevs.half-lightradiusofallobjectsintheinitialR-band
catalogue. Stars formaclear vertical locus andcanbeeasily differentiated
FIG. 5.—Ellipticitiesdistributionofstars,before(crosses)andafter(dots)
from galaxies down toR ∼ 23. Saturated stars deviate from this column
correctionforPSFanisotropies.
towardslargerhalf-lightradiiatbrightmagnitudes.
8 Grayetal.
of surface brightness described in KSB. As the non-diagonal to the obvious brightest cluster galaxy of (close to the X-ray
elements are small (< 2 × 10−4) and the diagonal elements positionsofSchindler2000),andinAbell902themorenorth-
nearlyequal,wechoosetotreatthisasascalarequaltohalfthe ern of the two bright galaxies in the center of overdensity of
trace. The mean stellar ellipticity before correction and after numbers in that region. Note that these three positions differ
correctionwasthen slightlyfromthe(two)positionsgiveninAbelletal.(1989)for
e =0.014±0.011 e =−0.047±0.014 (before) Abell901andAbell902(seeFig1).
1 2
e =0.00013±0.006 e =0.00003±0.006 (after). Anattempttoquantifytherichnessofeachofthethreeclus-
1 2
ters is hampered by their close proximity. The original Abell
Fig.4andFig.5showtheresultingpatternanddistributionof
richnessclass (Abell1958)is determinedfromthe numberof
correctedstellarellipticities.
galaxies in the magnitude range m to m +2 (where m is
3 3 3
the magnitude of the third brightest cluster galaxy) contained
3.3. IsotropicPSFcorrection
within a 1.5h−1 Mpc radius. In the case of the A901/902su-
The isotropic correction recovers the lensing shear prior to percluster, the maximum separation between Abell 901a and
circularizationbythePSF.FollowingLuppino&Kaiser(1997) Abell902isonly7.8arcmin,or∼850h−1kpcatz =0.16.We
andHoekstraetal.(1998)weusethecorrectedgalaxyelliptic- can thereforeat best place a lower limit onthe Abellrichness
itiesinconjunctionwiththe‘shearpolarizability’tensorP to classbyconsideringthecountswithina3.9arcminradius.This
sh
calculatetheshearestimate yields N = 34,27, and 20 galaxies for A901a, A901b,
Abell
γ =P−1e , (6) andA902,respectively,whichcorrespondstoanAbellrichness
γ corr class0ineachcase. Moreinformative,however,istoconsider
where the superclusteras a single system. In this case we can probe
P∗
Pγ =Psh− Pss∗mhPsm. (7) tohfetheentcilruesRteArbpeollsi=tio1n.s5)ha−nd1 MfinpdcN(mAebaelslu=ri9n2g,fcroomrretshpeoncednintrgotiod
Again,thestarredquantitiesrefertostellarproperties,andP∗ anAbellrichnessclassII.
sh
andP∗ aretreatedasscalarsequaltohalfthetraceofthere-
spectivsmematrices. TocalculateP forthegalaxies,wefitP11 4.1. Colorselectionofearlytypegalaxies
γ γ
andP22asafunctionofsmoothingradiusr ,andinsertthefit- Dividingthecataloguespatiallyinto‘cluster’and‘field’re-
γ g
tedvalueintoequation(6)tocalculatetheshearmeasurement gions according to boundaries shown in Fig. 6, we plot the
for each galaxy. Finally, we remove from the catalogue any R-band number counts in Fig. 7. A clear excess xof bright
galaxies with a resulting |γ| > 2 due to noise. Note that this galaxies in the cluster region is visible. The B − R vs. R
procedureactuallyyieldsthereducedshear,γ/(1−κ),butin color-magnitude diagrams for the two regions (Fig. 8) reveal
thewide-field,weaklensinglimit(κ≪1,γ ≪1)inwhichwe a prominentsequenceof redgalaxieswithsmallscatter in the
areworkingthisreducestotheshear,γ. regionoftheclusters. Wefitthisrelationaccordingto
|B−R−(−0.0385R+2.21)|<0.1 (13)
4. CLUSTERPROPERTIES
andwillusethiscolor-cuttoseparatethesuperclustermembers
To identify the likely members of the supercluster, we first fromtheforegroundandbackgroundpopulationthroughoutthe
spatially separate the catalogue of galaxies. We then use the wholefieldofview,usingtheentirecatalogueofgalaxies.
resultingsamplestoisolatethetightsequenceofearly-typesu- Fig.9showstheresultofthiscolorcutwhenitisappliedto
percluster galaxieson the B −R vs. R color-magnitudedia- the entire catalogue. The left panel shows the distribution of
gram. all the bright (R < 20) galaxies in the field, and the promi-
Fig.6showsthelocationsofalltheobjectsinthecatalogue nent clustering present is clearly visible. When the color-cut
withinthe32.5′×32.5′ fieldofview. Thelargecirclesrepre- ofequation(13)isapplied,thestructureofthesuperclusteras
sentanapertureofradius4.6arcminaroundeachcluster. The
angularsizescalesas
R(θ)=0.87D (z )(θ/1′)h−1Mpc (8)
A L
wherethedimensionlessangulardistance
1 z dz
D (z)= , (9)
A (1+z)Z [Ω (1+z)3+Ω ]1/2
m Λ
z
≃ (10)
(1+z)(1+3/4Ω z)
m
andthesecondlineisagoodapproximationtothelow-redshift
angular distance in a spatially flat model with cosmological
constant. For our supercluster at z = 0.16 this is relatively
insensitivetocosmology,andyields
R(θ)=0.11(θ/1′)h−1Mpc (11)
=0.002(θ/1′′)h−1Mpc. (12)
Thusthe radiiof the aperturesin Fig. 6 correspondto 0.5h−1
Mpcattheredshiftofthesupercluster.
FIG. 7.—Number-magnitude relation for‘cluster’ and ‘field’ regions as
Table5.2.1liststhecoordinateschosenasthecenterofeach definedinFig.6. Aclearexcessofbrightgalaxiesintheclusteraperturesis
ofthethreeclusters:inAbell901aand901bthiscorresponded visibleuptoR∼22.
AweaklensinganalysisoftheAbell901/902supercluster 9
FIG.6.—Divisionofcatalogueinto‘cluster’and‘field’regions.Eachdotrepresentsonegalaxyinthecatalogue,withtheareamaskedoutduetocontamination
bybrightstarsanddiffractionspikesindicatedbytheblankrectangularregions. Thecirclesareaperturesofradius4.6arcmin(500h−1kpc)aroundtheoptical
centerofeachclusteranddefinethe‘cluster’regionsusedtoisolatethecolor-magnitudesequenceofsuperclustergalaxies(cf.Fig.7andFig.8).
10 Grayetal.
FIG. 8.—TheB−Rvs. Rcolor-magnitudediagramsforthe‘field’region(left)andthe‘cluster’region(right)asdefinedbytheboundariesinFig.6. The
early-typeclustergalaxiesareclearlyvisibleasatightredsequenceintheright-handplot. Thecolorselectioncriteria(eq.[13])usedtoisolatethesupercluster
galaxiesisshownbytheparallellines.DuetotherelativeshallownessoftheB-bandimagewithrespecttothedeepR-bandimage,approximatelyhalfthegalaxies
ineachsamplearedetectedintheR-bandalone.ThelowerlimitontheresultingB−Rcolorforthesegalaxiesisindicatedbythethicklineandarrow.Thedashed
lineatR=22servestofurthersubdividethepopulationsinto‘bright’and‘faint’samples.
traced by the early-typegalaxies is revealed. The distribution theclusters:
of these color-selected galaxies is shown in the right panel of N −N
f = blue,cluster blue,background . (14)
Fig.9.Thethreeclusters,sharingthesamecolor-magnitudere- b
N −N
total,cluster total,background
lationfortheirearly-typegalaxies,areclearlypresent.Further-
TheresultstabulatedinTable4.2confirmthatA902hasamuch
more,thelargersuperclusterstructurebecomesclear(including
higherf thantheothertwoclustersforavarietyofmagnitude
galaxies stretching between the clusters, and an obvious sub- b
limits, rangingashighasf = 0.58forR < 19. Weshallre-
clump of supercluster galaxies approximately12 arcmin west b
turntotheissueofvaryingclusterluminositieswhendiscussing
ofAbell902). Thisexcessofsuperclustergalaxiesoutsidethe
clusterM/Lratiosin§6.
clusterboundariesdefinedbytheaperturesaboveaccountsfor
asimilar(butmuchweaker)color-sequencealsovisibleinthe
5. WEAKSHEARANALYSIS
color-magnitudediagramforthe‘field’sample(left-handside
ofFig.8). 5.1. Selectionofbackgroundpopulation
Theobservedtangentialdistortionofthebackgroundgalax-
4.2. Fractionofblueclustermembers
ies allows us to reconstruct the dimensionless surface density
AnexaminationoftheR-bandimage(Fig.1)revealsthatthe oftheinterveningmatter,κ=Σ/Σcrit,where
three clusters are very different in morphologicalappearance. c2 D
A901amostresemblesthetraditionalpictureofarelaxedclus- Σcrit = s (15)
4πGD D
terdominatedbyacentralbrightellipticalgalaxy. A901balso d ds
isthecriticalsurfacemassdensity. Toturntheobservedκinto
containsa giantelliptical butthe nearbycluster galaxiestrace
physicalquantitiesrequiresknowledgeoftheangulardiameter
a more amorphous shape that appears to bleed into the mid-
distancestothesourceandlens(D ,D ),andtherelativedis-
dle of the supercluster (Fig. 9, left). This is at odds with the d s
tancebetweenthetwo(D ). Inthecaseofweaklensingbya
regular,compactX-rayemissiondetectedbySchindler(2000). ds
clusterofgalaxies,thestrengthofthelensingsignalisgoverned
Finally, A902 is the most irregularof the three, with no well-
bytheredshiftdistributionofthebackgroundsources. Thisin-
defined center. It is interesting, however, that Fig. 1 clearly
formationcanbeexpressedbytheparameterβ,suchthat
showsaprominentexcessofbright,diskygalaxiessurrounding
thiscluster(absentfromthevicinitiesoftheothertwo). D
β = ds , D ≥0. (16)
To better understand the galaxy populations that make up (cid:28) D (cid:29) ds
thesegalaxyclusters,wecalculatethefractionofbrightgalax- s zs
The galaxies we will use for our mass reconstructions will
ies too blue to survive the color selection but which may still
be composed for the most part of faint (R > 22) galaxies or
beclustermembers(presumablylate-types).Takinga4arcmin
subsetsthereof.Itisofgreatimportance,therefore,thatweare
radiusaperture,wecountthosegalaxieswithB−Rbluerthan
able to determine the appropriate value of β to use. Fig. 10a
theclustersequenceofequation(13)andcomparewiththeto-
showsthedependenceoftheβ parameterontheredshiftofthe
talnumberofgalaxieswithintheapertureforagivenmagnitude
backgroundsources, for a lens at z = 0.16. Unlike lenses at
limit. Wecorrectthesenumbersforbackgroundcontamination
higherredshift(seeHoekstraetal.2000;Cloweetal.2000),the
using the number density of similarly selected galaxies in the
complementary‘field’region,takingintoaccounttheareaob- relativelylowredshiftofoursuperclustermeansthatforzs>∼1,
β is relatively insensitive to the source redshift, regardless of
scuredbythemask.
thecosmologicalmodelused.
Wethencalculatethefractionofbrightbluegalaxieswithin
The CalTech Faint Galaxy Redshift Survey (CTFGRS; Co-
henetal.2000)isasurveyinthedirectionoftheHubbleDeep