The Cluster Distribution as a Test of Dark Matter

arXiv:astro-ph/9511066v115Nov1995Mon.Not.R.Astron.Soc.000,000–000(0000)Printed5February2008(MNLATEXstylefilev1.4)TheClusterDistributionasaTestofDarkMatterModels.III:TheClusterVelocityFieldL.Moscardini1,E.Branchini2,3,P.TiniBrunozzi4,5,S.Borgani2,5,M.Plionis2,6&P.Coles71DipartimentodiAstronomia,Universit`adiPadova,vicolodell’Osservatorio5,I–35122Padova,Italy2SISSA–InternationalSchoolforAdvancedStudies,viaBeirut2–4,I–34013Trieste,Italy3DepartmentofPhysics,UniversityofDurham,SouthRoad,DurhamDH13LE,UK4DipartimentodiFisica,Universit`adiPerugia,viaA.Pascoli,I–06100Perugia,Italy5INFNSezionediPerugia,c/oDipartimentodiFisicadell’Universit`a,viaA.Pascoli,I–06100Perugia,Italy6NationalObservatoryofAthens,LofosNimfon,Thesio,18110Athens,Greece7AstronomyUnit,SchoolofMathematicalSciences,QueenMary&WestfieldCollege,MileEndRoad,LondonE14NS,UK5February2008ABSTRACTWestudythelarge–scalevelocityfieldstracedbygalaxyclustersinnumericalsimulationsofaboxofside960h−1Mpc,andcomparethemwithavailabledataonrealclusters.Inordertotestthereliabilityofthesimulations,whicharebasedonanoptimizedversionoftheZel’dovichapproximation,wecom-paretheirclustervelocitieswiththoseof“exact”N–bodysimulations,andfindaremarkableagreementbetweenthetwoaccordingtoavarietyofstatisticaltests.WeanalyseColdDarkMatter(CDM)modelswithdensityparameterintherange0.2≤Ω0≤1,bothwithandwithoutthecosmologicalconstanttermtoprovideaflatgeometry.WealsosimulateaCold+HotDarkMatter(CHDM)model,with30%providedbythehotcomponent.Comparisonwithrealdataisperformedbyapplyingtestsbasedonthecumulativevelocityfre-quencydistribution(CVFD)andbulkflowstatistics.FortheCVFD,weuseobservationalvelocitydatafromdifferentauthors.Bymergingallavailabledatainacombinedsample,theCVFDtestisabletoexcludeonlyopenmod-elswithΩ0≤0.4andflatmodelswithΩ0=0.2.However,theanalysisofindividualobservationalsamplesgivescontradictoryresults;inparticulartherecentGiovanelli(1995)data,whichimplymuchlowervelocities(withsignifi-cantlysmalleruncertainties)thantheotherdata,areactuallyonlyconsistentwiththeopenΩ0=0.4andtheflatΩ0=0.2models,i.e.themodelswhichareexcludedbytheotherdata.Furthermore,CVFDandbulkflowanalysesoftheBranchinietal.(1995)reconstructedvelocitydatadisfavourpreciselythosemodelsacceptedonthegroundsofGiovanelli’ssample.Finally,weconfirmthattheLauer&Postman(1994)bulkflowdeterminationisanextremelyrareeventinthecosmologicalmodelswehaveanalysed.Keywords:Cosmology:theory–darkmatter–galaxies:clustering,forma-tion–large–scalestructureofUniversec0000RAS2L.Moscardinietal.1INTRODUCTIONThequalityandquantityofgalaxypeculiarvelocitydataderivedfromtheInfra–RedTully–Fisher(IRTF)andDn–σscalingrelationsisprogressivelyincreasing,providinganevermoreprecisedescriptionoflarge–scalecosmicflows.Moreover,anindependenttechniquetoes-timatethedistanceofhighredshiftgalaxieswithverysmallerrors,basedontheshapesoftypeIasupernovalightcurves,recentlydevelopedbyRiess,Press&Kir-shner(1995),couldallowadescriptionofmotionsonevenlargerscales.Consequentlythestudyoflarge–scaleflowsispotentiallyoneofthemostpowerfultoolswithwhichtounderstandthestructureoftheuniverseonlarge(∼50h−1Mpc)scales(seereviewsbyDekel1994;Strauss&Willick1995andreferencestherein).Further-more,thehypothesisofgravitationalinstabilityallowsonetorelatethepeculiarvelocityfielddirectlytotheentiremassdistribution,undertheplausibleassump-tionthatatsuchlargescalesgalaxiessharethesamedynamicsasthedarkmatterdistribution.Clustersofgalaxiesprovideaparticularlyefficientandprecisewaytoestimatepeculiarmotions,sincethedeterminationofmanyredshift–independentdis-tancesofclustermembersleadstoasubstantialreduc-tioninthestatisticalerrorscomparedtostudiesofiso-latedgalaxies.Moreover,newtechniquesbasedontheSunyaev–Zel’dovich(1980)effect(Haenhelt&Tegmark1995)andonthebrightestclustergalaxydistancein-dicatormethod(Lauer&Postman1994)arebeginningtoprovideindependentestimatesofclusterpeculiarve-locitieswhosereliabilityisexpectedtoincreaseconsid-erablyinthenextfewyears.Afurtherimportantmotivationforconsideringclustersisthattheycansamplethecosmicvelocityfielduptodistanceslargerthanthosepresentlyaccessiblebygalaxies.Ontheselargerscales,fluctuationsarelargelyinthelinearregimeandare,therefore,morecloselyre-latedtothe“initialconditions”fromwhichlarge–scalestructuredeveloped.Inaddition,sincelarge–scaleve-locitiesaremostlysensitivetolong–wavelengthdensityfluctuations,oneexpectsthat,forafixedchoiceofthefundamentalcosmologicalparameters(HubbleconstantH0,densityparameterΩ0andcosmologicalconstanttermΩΛ),theamplitudeoflarge–scalemotionsisal-mostindependentofthecompositionofthedarkmat-ter(DM)component(i.e.,coldvs.hotDM).Forthesereasons,severalauthors(e.g.,Bahcall,Cen&Gramann1994;Croft&Efstathiou1994;Bahcall,Gramann&Cen1994;Cen,Bahcall&Gramann1994;Straussetc0000RAS,MNRAS000,000–000TheClusterVelocityField3al.1995;Gramannetal.1995)haverecentlyaddressedtheissueofwhetherclustermotionscanbeusedtoconstraincosmologicalmodels.Variousstatisticaltestshavebeenusedforthispurpose,amongwhichtheve-locityfrequencydistribution,bulkflows,velocitydis-persions,pairwisevel