Dark Energy and Dark Matter Halos

arXiv:astro-ph/0402210v223Nov2004Mon.Not.R.Astron.Soc.000,1–16(2004)Printed2February2008(MNLATEXstylefilev2.2)DarkEnergyandDarkMatterHaloesMichaelKuhlen1,LouisE.Strigari2,AndrewR.Zentner3,4,JamesS.Bullock5⋆andJoelR.Primack61DepartmentofAstronomyandAstrophysics,UniversityofCaliforniaatSantaCruz,1156HighStreet,SantaCruz,CA950642DepartmentofPhysics,TheOhioStateUniversity,174W.18thAvenue,Columbus,OH432103CenterforCosmologicalPhysics,TheUniversityofChicago,5640S.EllisAvenue,Chicago,IL606374DepartmentofAstronomyandAstrophysics,TheUniversityofChicago,5640S.EllisAvenue,Chicago,IL606375Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA021386PhysicsDepartment,UniversityofCaliforniaatSantaCruz,1156HighStreet,CA95064Submitted2004April05ABSTRACTWeinvestigatetheeffectofdarkenergyonthedensityprofilesofdarkmatterhaloeswithasuiteofcosmologicalN-bodysimulationsanduseourresultstotestanalyticmodels.Weconsiderconstantequationofstatemodels,andallowbothw≥−1andw−1.Usingfivesimulationswithwrangingfrom−1.5to−0.5,andwithmorethan∼1600well-resolvedhaloeseach,weshowthatthehaloconcentrationmodelofBullocketal.(2001)accuratelypredictsthemedianconcentrationsofhaloesovertherangeofw,halomasses,andredshiftsthatwearecapableofprobing.WefindthattheBullocketal.(2001)modelworksbestwhenhalomassesandconcentrationsaredefinedrelativetoanouterradiussetbyacosmology-dependentvirialoverdensity.Forafixedpowerspectrumnormalizationandfixed-masshaloes,largervaluesofwleadtohigherconcentrationsandhigherhalocentraldensities,bothbecausecollapseoccursearlierandbecausehaloeshavehighervirialdensities.Whileprecisepredictionsofhalodensitiesarequitesensitivetovariousuncertainties,wemakebroadcomparisonstogalaxyrotationcurvedata.Atfixedpowerspectrumnormalization(fixedσ8),w−1quintessencemodelsseemtoexacerbatethecentraldensityproblemrelativetothestandardw=−1model.Forexample,modelswithw≃−0.5seemdisfavoredbythedata,whichcanbematchedonlybyallowingextremelylownormalizations,σ8∼0.6.Meanwhilew−1modelshelptoreducetheapparentdiscrepancy.WeconfirmthattheJenkinsetal.(2001)halomassfunctionprovidesanexcellentapproximationtotheabundanceofhaloesinoursimulationsandextenditsregionofvaliditytoincludemodelswithw−1.Keywords:cosmology:theory–darkmatter–large-scalestructureofuniverse–methods:N-bodysimulations1INTRODUCTIONIntheprevailingmodelofgalaxyformation,galaxiesassem-bleandevolveinthepotentialwellsestablishedbygravita-tionallyboundhaloesofcoldandcollisionlessdarkmatter(CDM).Exceptforsomepossibledifficultiesonsmallscales,theCDMmodelisremarkablysuccessfulinexplainingalargenumberofobservations.However,thissuccessrequiresanadditional“darkenergy”component,thatdrivesanac-celeratedcosmicexpansion,tobeaddedtotheuniversalenergybudget.Whilethepresenceofdarkenergyisfirmlyestablishedobservationally,measuringitsequationofstate⋆HubbleFellowaswellasdevelopingatheoreticalunderstandingofthena-tureofthedarkenergyaretwoofthebiggestoutstandingproblemsincosmologytoday.Darkenergynotonlyaffectsthelarge-scaleevolutionoftheUniverse,butalsothecol-lapsehistoriesanddensitystructuresofdarkmatterhaloes.Understandingtheprecisenatureoftheseeffectsisimpor-tantforstudiesthataimtoquantifythenatureofdarken-ergyusingstrong(e.g.,Sarbu,Rusin,&Ma2001;Huterer&Ma2004;Kuhlen,Keeton,&Madau2004)andweak(e.g.Hu&Jain2003;Bartelmannetal.2002)gravitationallensing.Changingthedarkenergymodelshouldsimilarlychangeexpectationsforgalaxyrotationcurves,andcouldaffectoneofthemainsmall-scaleproblemsfacingCDM–thecentraldensityproblem(e.g.,Zentner&Bullock2002;McGaugh,Barker,&deBlok2003,andreferencestherein).2Kuhlenetal.Inthepresentpaper,weuseasuiteofN-bodysimulationstostudyhowhalodensityprofileschangeasafunctionofdarkenergyequationofstate,discussourresultsinthecontextofanalyticmodels,anddiscusstheobservationalimplicationsofdarkenergyongalaxyscales.Theexistenceofsomeformofdarkenergyissupportedbyapreponderanceofdata.Takentogether,observationsofthemagnitude-redshiftrelationoftypeIasupernovae(SNIa;Perlmutteretal.1999;Riessetal.2001;Knopetal.2003;Barrisetal.2003),thepowerspectrumofcosmicmicrowavebackground(CMB)anisotropy(Spergeletal.2003;Tegmarketal.2003a),thepowerspectrumofgalaxyclustering(Do-delsonetal.2003;Tegmarketal.2003b),andtheluminosityfunctionandbaryonfractionofclusters(Allenetal.2003)providenearlyunimpeachableevidencefortheexistenceofdarkenergy.Themostcommonsuppositionisthatthedarkenergytakestheformofacosmologicalconstantorvac-uumenergy.Inthiscase,theenergydensityρ,andpressurep,arerelatedthroughp=−ρ.Anattractivealternativecandidateforthedarkenergyisthepotentialenergyofaslowly-varyingscalarfieldφ,or“quintessence”(e.g.,Ratra&Peebles1988;Caldwell,Dav´e,&Steinhardt1998).Aconvenientparametrizationofthedarkenergyisthroughanequationofstatew≡pφ/ρφrelatingitsen-ergydensityandpressure.Ingeneral,theequationofstateparameterwistime-varying,butitisusefultomodelquintessencewithaconstantequationofstateparame-terbecausecurrentobservationaldatasetshavelimitedpowertodistinguishbetweenatime-varyingandconstantequationofstate(e.g.,Kujatetal.2002).Usefullimitsonth