Evolution of Characteristic Quantities for Dark Ma

arXiv:astro-ph/0610090v13Oct2006acceptedbytheAstrophysicalJournalPreprinttypesetusingLATEXstyleemulateapjv.6/22/04EVOLUTIONOFCHARACTERISTICQUANTITIESFORDARKMATTERHALODENSITYPROFILESEmilioRomano-D´ıaz1,2,YehudaHoffman1,ClaytonHeller3,AndreasFaltenbacher4,DanielJones2andIsaacShlosman2acceptedbytheAstrophysicalJournalABSTRACTWehaveinvestigatedtheeffectofanassemblyhistoryontheevolutionofgalacticdarkmatter(DM)halosof1012h−1M⊙usingConstrainedRealizationsofrandomGaussianfields.FivedifferentrealizationsofaDMhalowithdistinctmerginghistorieswereconstructedandhavebeenevolvedusingcollisionlesshigh-resolutionN-bodysimulations.Ourmainresultsare:Ahaloevolvesviaasequenceofquiescentphasesofaslowmassaccretionintermittedbyviolentepisodesofmajormergers.Inthequiescentphases,thedensityiswellfittedbyanNFWprofile,theinnerscaleradiusRsandthemassenclosedwithinitremainconstant,andthevirialradius(Rvir)growslinearlywiththeexpansionparametera.Withineachquiescentphasetheconcentrationparameter(c)scalesasa,andthemassaccretionhistory(Mvir)iswelldescribedbytheTasitsiomietal.fittingformula.IntheviolentphasesthehalosarenotinavirialdynamicalequilibriumandbothRsandRvirgrowdiscontinuously.TheviolentepisodesdrivethehalosfromoneNFWdynamicalequilibriumtoanother.Thefinalstructureofahalo,includingc,dependsonthedegreeofviolenceofthemajormergersandthenumberofviolentevents.Next,wefindadistinctdifferencebetweenthebehaviorofvariousNFWparameterstakenasaveragesoveranensembleofhalosandthoseofindividualhalos.Moreover,thesimplescalingrelationsc−Mvirdonotapplytotheentireevolutionofindividualhalos,andsoisthecommonnotionthatlateforminghalosarelessconcentratedthanearlyformingones.Theentireevolutionofthehalocannotbefittedbysingleanalyticalexpressions.Subjectheadings:cosmology:darkmatter—galaxies:evolution—galaxies:formation—galaxies:halos—galaxies:interactions—galaxies:kinematicsanddynamics1.INTRODUCTIONThehierarchicalbuildupofcolddarkmatter(CDM)halosisastronglynonlinearprocess.Itisassociatedwiththebuildupofauniquedensityprofile—oneofthemostfundamentalcharacteristicsoftheDMhalos.BasedonN-bodysimulations,Navarroetal.(1997,hereafterNFW)foundthattheCDMhaloscanbeuniversallyfit-tedbyatwo-parameterfunctionalform:ρ(r)=4ρs(r/Rs)(1+r/Rs)2,(1)whereRsisacharacteristic“inner”radiusatwhichthelogarithmicdensityslopeis−2andρsisthedensityatRs.ThecosmologicalevolutionoftheNFWparameters,therefore,isanissueofabroadinterestandisaddressedinthiswork.Ausefulalternativeparametertodescribetheshapeoftheprofileistheso-calledhaloconcentrationpa-rameterdefinedasc=Rvir/Rs,whereRviristhehalovirialradius.AlthoughsuchaprofilehasbeenconfirmedbynumerousN-bodysimulations,theex-actvalueoftheinnerslopeparameterisuncertain.Severalauthorshavefoundthathaloshavedensitycuspssteeper(e.g.,Fukushige&Makino1997,2003;Mooreetal.1999;Ghignaetal.2000)orshallower(e.g.,1RacahInstituteofPhysics,HebrewUniversity;Jerusalem91904,Israel2DepartmentofPhysicsandAstronomy,UniversityofKen-tucky,Lexington,KY40506-0055,USA3DepartmentofPhysics,GeorgiaSouthernUniversity,States-boro,GA30460,USA4PhysicsDepartment,UniversityofCalifornia,SantaCruzCA95064,USASubramanianetal.2000;Taylor&Navarro2001)than−1,theNFWvalue.TheNFWprofileanditsmodifica-tionsarespecificcasesofathree-parameterprofilefam-ilyproposedbyHernquist(1990),andfurtherdevelopedbyZhao(1996).Ontheotherhand,(Jing&Suto2000,2002),Klypinetal.(2001)andRicotti(2003)foundthattheCDMhalosdonotmaintaintheuniversaldensityprofiles,andtheinnerslopechangesfromgalaxy-sizeha-lostocluster-sizehalos(seealsoTasitsiomietal.2004).Thesenumericalresultsappearinconflictwiththeobservationalevidence—rotationcurvesoflowsur-facebrightnessgalaxiesyielddensityprofileswithnearlyconstantdensitycores(e.g.,Flores&Primack1994;Salucci&Burkert2000).Studiesofbrightergalax-iesimplysimilarproblems(Salucci&Burkert2000;deBlok&Bosma2002;Gentileetal.2004).WhilesomestudiesoftheweaklensingseemtosupporttheNFWdensityprofile(e.g.,Hoekstraetal.2004),inaspe-cificcaseoftheclusterA1689,therequiredconcentra-tionparameterisdramaticallylargerthanthetypicalvalueobtainedinthesimulationofacluster-sizeobject(Broadhurstetal.2005).Inprinciple,onecanlistthreedifferentoptionstoresolvetheabovedifficulties.First,theinnerfew-kpcrotationcurvesofdiskgalaxiescanbecontaminatedwiththe(unresolved)non-circularmotionstriggerede.g.,bystellarbars(e.g.,Blais-Ouelletteetal.2001;Bolattoetal.2002;Simonetal.2003;Weldrakeetal.2003;Simonetal.2005).Second,theNFWapproachistoneglectthetriaxialnatureofDMhalosby“spheri-calizing”whileanalyzingthem.Furthermore,theissueofthe“cusps”mightberelatedtotheeffectiveresolutioninN-bodysimulationsorothernumericaleffects(e.g.,2Romano-D´ıazetal.Mooreetal.1998).Finally,thedifferencebetweenthecollisionlesssimu-lationsandobservationscanunderscoreaphysicalef-fect,liketheabsenceofdissipationinthepureDMmod-elsandthepresenceofdissipativebaryonsintherealgalaxies.ThisapparentdiscrepancycanbereconciledwithinthecontextoftheCDMmodelbyconsideringtheeffectofclumpybaryonserasingthecuspsonrelevantspatialscales,fromgalactichalostoclustersofgalaxies(El-Zantetal.2001,2004).Alte