Structure of Dark Matter Halos From Hierarchical C

arXiv:astro-ph/0306203v110Jun2003StructureofDarkMatterHalosFromHierarchicalClustering.III.ShallowingofTheInnerCuspToshiyukiFukushigeDepartmentofGeneralSystemsStudies,CollegeofArtsandSciences,UniversityofTokyo,3-8-1Komaba,Meguro-ku,Tokyo153,JapanAtsushiKawaiFacultyofHumanandSocialStudies,SaitamaInstitueofTechnology,1690Fusaiji,Okabe,Ohsato,Saitama369-0293,JapanJunichiroMakinoDepartmentofAstronomy,SchoolofSciences,UniversityofTokyo,7-3-1Hongo,Bunkyo-ku,Tokyo117,JapanABSTRACTWeinvestigatethestructureofthedarkmatterhaloformedinthecolddarkmatterscenariosbyN-bodysimulationswithparalleltreecodeonGRAPEclustersystems.Wesimulated8haloswiththemassof4.4×1014M⊙to1.6×1015M⊙intheSCDMandLCDMmodelusingupto30millionparticles.Withtheresolutionofoursimulations,thedensityprofileisreliabledownto0.2percentofthevirialradius.Ourresultsshowthattheslopeofinnercuspwithin1percentvirialradiusisshallowerthan−1.5,andtheradiuswheretheshallowingstartsexhibitsrun-to-runvariation,whichmeanstheinnermostprofileisnotuniversal.Subjectheadings:cosmology:theory—darkmatter—galaxies:clusters:general—methods:N-bodysimulations1.IntroductionSincethe”finding”oftheuniversalprofilebyNavarro,Frenk,andWhite(1996,1997,hereafterNFW),thestructureofdarkmatterhalosformedthroughdissipationless–2–hierarchicalclusteringfromcosmologicalinitialsettinghasbeenexploredbymanyresearchers.NFWperformedanumberofN-bodysimulationsofthehaloformationusing10-20kparticlesandfoundthattheprofileofdarkmatterhalocouldbefittedtoasimpleformula(hereafter,NFWprofile)ρ=ρ0(r/r0)(1+r/r0)2(1)whereρ0isacharacteristicdensityandr0isascaleradius.Theyalsoarguedthattheprofilehasthesameshape,independentofthehalomass,thepowerspectrumoftheinitialdensityfluctuationorothercosmologicalparameters.Severalgroupsreportedtheresultsofsimilarsimulationswithmuchhigherresolutions.However,disagreementconcerningtheinnerstructurestillremains.SomeresearchersclaimedthattheslopeoftheinnercuspissteeperthanthatintheNFW’sresults.FukushigeandMakino(1997)performedasimilarsimulationwith768kparticlesandfoundthatthegalaxy-sizedhalohasacuspsteeperthanρ∝r−1.Mooreetal.(1998,1999hereafterM99)andGhignaetal.(2000)performedsimulationswithupto4Mparticlesandobtainedtheresultsthattheprofilehasacuspproportionaltor−1.5bothingalaxy-sizedandcluster-sizedhalos.M99proposedthemodifieduniversalprofile(hereafter,M99profile),ρ=ρ0(r/r0)1.5[1+(r/r0)1.5].(2)FukushigeandMakino(2001,PaperI;2003,PaperII)performedtwoseriesofN-bodysimulations,andfoundthatthehaloshavedensitycuspsproportionaltor−1.5,independentofthehalomassandcosmologicalmodels.Ontheotherhands,otherresearchersobtainedtheslopeofinnercuspshallowerthan−1.5andclosetothatintheNFWprofile.JingandSuto(2000,2002)performedaseriesofN-bodysimulationsandconcludedthatthepowerofthecuspdependsonmass.Itvariesfrom−1.5forgalaxymasshaloto−1.1forclustermasshalo.Klypinetal.(2001)obtainedtheslopeatthecenterthatcouldbeapproximatedbyr−1.5.They,however,arguedthattheNFWfitisstillgooduptotheirresolutionlimit.Poweretal.(2003)simulatedanLCDMgalaxy-sizedhalowith3MparticlesandclaimedthattheircircularvelocityprofileobtainedisinbetteragreementwiththeNFWprofilethanwiththeM99profile.ThepurposeofthispaperistoexploretheinnerstructureofthedarkmatterhalobymeansofN-bodysimulationswithabout10timeshighermassresolutionthanthatofprevioussimulations.Wesimulatedtheformationof8cluster-sizedhalosintheSCDMandLCDMmodelsusingparallelBarnes-HuttreecodeonparallelGRAPEcluster.Thestructureofthispaperisasfollows.Insection2,wedescribethemodelofour–3–N-bodysimulation.Insection3,wepresenttheresultsofsimulation.Section4isforconclusionanddiscussion.2.SimulationMethodWeconsidertwocosmologicalmodels,SCDMmodel(Ω0=1.0,h=0.5,σ8=0.6)andLCDMmodel(Ω0=0.3,λ0=0.7,h=0.7,σ8=1.0).Here,Ω0isthedensityparameter,λ0isthedimensionlesscosmologicalconstant,andH0=100hkm/s·Mpc−1atthepresentepoch.TheamplitudesofthepowerspectruminCDMmodelsarenormalizedusingthetop-hatfilteredmassvarianceat8h−1Mpcaccordingtotheclusterabundance(Kitayama&Suto1997).Wesimulatetheformationofthedarkmatterhalosusingthe”re-simulation”method,whichhasbeenastandardmethodforthesimulationofhaloformationsinceNFW(1996).TheprocedureforsettingtheinitialconditionofhalosarethesameasthatusedinPaperII.Wefirstperformedlargescalecosmologicalsimulationswith3.7×106particlesinasphereof300hMpccomovingradius.Weregardsphericaloverdensityregionsaroundlocalpotentialminimawithinrvascandidatehalos.Wedefinetheradiusrvsuchthatthesphericaloverdensityinsideis178Ω0.30timesthecriticaldensityforSCDMand178Ω0.40timesforLCDMmodel(Eke,Cole,Frenk1998).Weselected8halosfromthecatalogofcandidatehalos.TheselectedhalosaresummarizedinTable1.Weselectedthethreemostmassivehalosandonehalorandomlyfromhalocandidateslyingwithin200hMpcfromthecenterinbothmodels(sothattheexternaltidalfieldcanbeincluded).Weexpressaregionwithin5rvfromthecenterofthehaloatz=0inthecosmologicalsimulationwithlargernumberofparticles.Weplaceparticleswhosemassisassameasthatinthecosmologicalsimulationinasphereof∼100hMpccomovingradiussurroundingthehighresolutionregion,inordertoexpresstheexternaltidalfield