Detection of (dark) matter concentrations via weak

arXiv:astro-ph/9601039v216Jan1996Detectionof(dark)matterconcentrationsviaweakgravitationallensingPeterSchneiderMax-Planck-Institutf¨urAstrophysikPostfach1523D-85740Garching,GermanyAbstractThedistortionofimagesoffaintbackgroundgalaxiesby(weak)gravitationallensingcanbeusedtomeasurethemassdistributionofthedeflector.Reconstructionmethodsforthemassprofileoflensingclustershavebeendevelopedandsuccessfullytested.Alternatively,theimagedistortionscanbeusedtodefineaweightedmeanofthemassinsideacircularaperture,aswasfirstsuggestedbyKaiser.This“aperturemass”hastheadvantagethatstricterrorbarscanbeobtainedfromthedataitself,andthatastrictlowerlimitofthelensmassinsideacirclecanbeobtained.Theaperturemasscanthusbeusedtodetectdarkmatterconcentrations.Keepinginmindthatwide-fieldcameraswillbecomeincreasinglyavailable,thismethodcanbeusedtosearchformassconcentrationsonwide-fieldimages.Todothis,theaperturemassmeasureisgeneralizedtoaccountfordifferentweightingfunctions.Foreachsuchweightingfunction,asignal-to-noiseratiocanbecalculated.Foranassumedmassprofileofthedensityconcentrations,theweightingfunctioncanbechosensuchastomaximizetheresultingsignal-to-noiseratio.Assumingthatdarkmatterhaloscanbeapproximatedbyanisothermalprofileoveralargerangeofradius,aweightingfunctionisconstructedwhichisadaptedtothisdensityprofileandwhichyieldsasmoothsignal-to-noisemap.Numericalsimulationswhichadoptparameterscharacteristicof4-mclasstelescopesarethenusedtoshowthatdarkhaloswithavelocitydispersioninexcessof∼600km/scanbereliablydetectedassignificantpeaksinthesignal-to-noisemap.TheeffectsofseeingandananisotropicPSFaretheninvestigatedandshowntobelessimportantthanmightbefeared.Itisthussuggestedthatthemethodofaperturemassmeasuresdevelopedherecanbeusedtoobtainamass-selectedsampleofdarkhalos,incontrasttoflux-selectedsamples.Shearfieldsaroundhigh-redshiftbrightQSOsasdetectedbyFortetal.provideafirstsuccessfulapplicationofthisstrategy.Thesimplicityofthemethodallowsitsroutineapplicationtowide-fieldimagesofsufficientdepthandimagequality.11IntroductionObjectsintheuniverseareusuallydiscoveredbymeansoftheiremittedradiation–thebrightertheobjectsare,theeasiertheyaredetected.Therefore,allsamplesofobjectsarefluxlimited.Theinclusionofobjectsthusdepends,amongotherthings,onthewavelengthofobservation.Asanexample,clustersofgalaxiescanbeselectedeitherbyX-raysurveysorfromopticalimages.Thereisnoreasontoexpectthattheclustersselectedbythesetwomethodswillsharemostoftheirproperties;intheformercase,clusterswithadenseintraclustermediumwillbepreferentiallyincludedinthesamples,whereasopticalsurveyaresensitivetoclusterswhichcontainmanybrightgalaxies.Giventhattheintraclustergasandthegalaxiesconstituteonlyasmallfractionoftheclustermass,whichisthequantitycosmologistsaremostinterestedin,itisbynomeansclearthatflux-limitedsamplesrevealafairrepresentationof(dark)matterconcentrationsintheuniverse.Gravitationallensingoffersthepossibilitytodetect‘unseen’matterconcentrationsjustfromtheirgravitationaleffectonlightrays.Forexample,thequantitativeanalysisofthecurrentlyexistingsurveysforgravitationally-lensedQSOscanruleoutasignificantdensityofcompactlensesintheuniversewithmass∼1011M⊙(e.g.,Kochanek1993,1995;Maoz&Rix1993).ConstraintsfromQSOvariabilityandspectralcharacteristicshaveyieldedstrictupperlimitsonthecosmologicaldensityofcompactobjectswith10−3M⊙∼M∼102M⊙(e.g.,Schneider1993;Dalcantonetal.1994).Sincemostgroupsandclustersofgalaxiesareexpectednottobesufficientlycompacttoyieldmultiply-imagedQSOimages,thesesurveysdonotyieldsignificantconstraintsontheircosmicnumberdensity.Ontheotherhand,themassdistributioninclusterscanbeinvestigatedwithgrav-itationallensing,eitherfromstudyingarcsandarclets(seetherecentreviewbyFort&Mellier1994),orfromthe‘weak’distortionofnumerousfaintbackgroundgalaxiesbythetidalgravitationalfieldofthecluster(Tyson,Valdes&Wenk1990;Kaiser&Squires1993).Thesetechniqueshavealreadyyieldedmostinterestingresults;e.g.,thecoreradiusofthedarkmatterinclusterswasfoundtobeconsiderablysmallerthanthatnormallyconcludedfromX-raystudies(e.g.,Miralda-Escud´e&Babul1995andreferencestherein),andthemass-to-lightratiointheclusterMS1224wasfoundtobeconsiderablylargerthan‘typical’estimatesinotherclusters(Fahlmanetal.1994).Thisobjectsupportsthepossibilitythatclustersofratherdifferentmass-to-lightratiosexist,andthatopticalsurveyare(strongly)biasedtowardsthedetectionofonlythebrightestsubsetoftheseclusters.TheselensingstudiesofclustershavebeenperformedexclusivelyonclusterswhichwereknownbeforefromopticalorX-raysurveys.However,Fortetal.(1996)havere-centlystartedtodevelopastrategyforthedetectionofmassconcentrationswhicharenotincludedinexistingsamples.Supportedbythefindingsthatthereisastatisti-callysignificantoverdensityof(foreground)galaxiesandclustersaroundhigh-redshiftbrightQSOs(Fugmann1990;Bartelmann&Schneider1993,1994;Rodrigues-Williams&Hogan1994;Benitez&Martinez-Gonzalez1995;Hutchings1995;Seitz&Schneider1995b),onscalesinexcessofseveralarcminutes,theyassumedthattheseapparentlymostluminousQSOsareaffectedbythemagnificationbias.Thismagnificationcannotbed