The Structure and Dynamical Evolution of Dark Matt

arXiv:astro-ph/9603132v217Jun1997Mon.Not.R.Astron.Soc.000,000–000(1997)Printed1February2008(MNLATEXstylefilev1.3)TheStructureandDynamicalEvolutionofDarkMatterHalosGiuseppeTormen1,2,3,Fran¸coisR.Bouchet1andSimonD.M.White31InstitutD’AstrophysiquedeParis,98bisBoulevardArago,75014Paris-FRANCE2InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA-UK3MaxPlanckInstitutef¨urAstrophysik,Karl-Schwarzschild-Strasse1,85740GarchingbeiM¨unchen-GERMANYEmail:[e-mail],[e-mail],[e-mail]1February2008ABSTRACTWeuseN-bodysimulationstoinvestigatethestructureanddynamicalevolutionofdarkmatterhalosinclustersofgalaxies.OursampleconsistsofninemassivehalosfromanEinstein-DeSitteruniversewithscalefreepowerspectrumandspectralindexn=−1.Halosareresolvedby20000particleseach,onaverage,andhaveadynamicalresolutionof20-25kpc,asshownbyextensivetests.LargescaletidalfieldsareincludeduptoascaleL=150Mpcusingbackgroundparticles.Wefindthatthehaloformationprocesscanbecharacterizedbythealternationoftwodynamicalconfigurations:amergingphaseandarelaxationphase,definedbytheirsignatureontheevolutionofthetotalmassandrootmeansquare(rms)velocity.Halosspendonaverageonethirdoftheirevolutioninthemergingphaseandtwothirdsintherelaxationphase.Usingthisdefinition,westudythedensityprofilesandshowhowtheychangeduringthehalodynamicalhistory.Inparticular,wefindthattheaveragedensityprofilesofourhalosarefittedbytheNavarro,Frenk&White(1995)analyticalmodelwithanrmsresidualof17%betweenthevirialradiusRvand0.01Rv.TheHernquist(1990)analyticaldensityprofilesfitsthesamehaloswithanrmsresidualof26%.ThetrendwithmassofthescaleradiusofthesefitsismarginallyconsistentwiththatfoundbyCole&Lacey(1996):comparedtotheirresultsourhalosaremorecentrallyconcentrated,andtherelationbetweenscaleradiusandhalomassisslightlysteeper.Wefindamoderatelylargescatterinthisrelation,duebothtodynamicalevolutionwithinhalosandtofluctuationsinthehalopopulation.WeanalyzethedynamicalequilibriumofourhalosusingtheJeans’equation,andfindthatonaveragetheyareapproximatelyinequilibriumwithintheirvirialradius.Finally,wefindthattheprojectedmassprofilesofoursimulatedhalosareinverygoodagreementwiththeprofilesofthreerichgalaxyclustersderivedfromstrongandweakgravitationallensingobservations.Keywords:cosmology:theory–darkmatter1INTRODUCTIONObservationalstudiesofgalaxyclustersareprovidingevermoredatathatneedtheoreticalinterpretationinordertounderstandclusterformationandevolution.Incurrentcos-mologicalmodelsthemassanddynamicsofgalaxyclustersaredominatedbysomekindofnon-baryonic,darkmatter,whichinteractswithordinarybaryonicmatteronlythroughgravity.Instudiesfocussingonthedynamicsofgalaxyclus-ters,theycanthusberegardedashalosmadeofcollision-lessdarkmatter.Fromthetheoreticalpointofviewonecanstudythestructureofdarkmatterhalosbothanalyt-icallyandnumerically.Muchoftheanalyticalworkdonesofarisbasedonthesecondaryinfallparadigm,(Gunn&Gott1972).Thesimplestversionofthispictureconsidersaninitialpointmass,whichactsasanonlinearseed,sur-roundedbyanhomogeneousuniformlyexpandinguniverse.Matteraroundtheseedslowsdownduetoitsgravitationalattraction,andeventuallyfallsbackinconcentricspheri-calshellswithpurelyradialmotions.Calculationsbasedonthismodelpredictthatthedensityprofileofthevirializedhaloshouldscaleasρ(r)∝r−9/4.SelfsimilarsolutionswerefoundbyFillmore&Goldreich(1984)andbyBertschinger(1985).Hoffman&Shaham(1985)appliedanextensionof2G.Tormenetal.thisideatothegravitationalinstabilitytheoryofhierarchi-calclustering.IntheircalculationstheyassumedaGaussianrandomfieldofinitialdensityperturbationwithscale-freepowerspectra:P(k)∝kn.Theyfoundthatthevirializedstructuresoriginatingfromdensitypeaksshouldhaveden-sityprofileswhoseshapedependsonspectralindexnasρ(r)∝r−(9+3n)/(4+n).Inrealitythecollapseofaninitialoverdensityisnotsosimple.Inparticular,motionsarenotpurelyradial,andaccretiondoesnothappeninsphericalshells(asassumedinthesecondaryinfallmodel),butbyaggregationofsub-clumpsofmatterwhichhavealreadycollapsed;alargefrac-tionofobservedgalaxyclustersexhibitsignificantsubstruc-ture(Kriessleretal.1995).Itisthereforeveryimportanttocomplementandcomparetheseanalyticalstudieswithnumericalsimulations.Thesearenotboundbysuchrestric-tionsandsocantellifthegravitationalcollapseofacol-lisionlesssystemeliminatesallmemoryofthecosmologicalparameterswhichdetermineditsinitialconditions.Theycanalsoshowwhetherscale-freeuniverses,whichhavenochar-acteristicscale,giverisetoscale-freepower-lawdensitypro-files.WorkinthisdirectionincludesQuinn,Salmon&Zurek(1986),Efstathiouetal.(1988)andWest,Dekel&Oemler(1987),butthesomewhatconflictingresultsofthesestud-iesshowthatbetternumericalresolutionisneededtosettletheissue.Recentresultsfromhigherresolutionsimulations(Navarroetal.1995(hereafterNFW),Lemson1995,Cole&Lacey1996(hereafterCL),Xu1996),producedbydifferentN-bodycodeswithdifferentsetupsfortheinitialconditions,seemfinallytoagreeonthefollowingresults:(i)halodensityprofilesarecurved,andarewellapprox-imatedbyafittingformulagovernedbyasinglescalera-diusrsandbelongingtothefamil