The Structure of Dark Matter Haloes in Dwarf Galax

astro-ph/950404112Apr95TheStructureofDarkMatterHaloesinDwarfGalaxiesA.BurkertMax-Planck-InstitutfurAstronomieKonigstuhl17,D-69117Heidelberg,GermanyReceived;acceptedRevisedVersion,submittedtoAstrophysicalJournal,LetterstotheEditor{2{ABSTRACTRecentobservationsindicatethatdarkmatterhaloeshaveatcentraldensityproles.Cosmologicalsimulationswithnon-baryonicdarkmatterpredicthoweverself-similarhaloeswithcentraldensitycusps.Thiscontradictionhasleadtotheconclusionthatdarkmattermustbebaryonic.Hereitisshownthatthedarkmatterhaloesofdwarfspiralgalaxiesrepresentaone-parameterfamilywithself-similardensityproles.Theobservedglobalhaloparametersarecoupledwitheachotherthroughsimplescalingrelationswhichcanbeexplainedbythestandardcolddarkmattermodelifoneassumesthatallthehaloesformedfromdensityuctuationswiththesameprimordialamplitude.Wendthatthenitecentralhalodensitiescorrelatewiththeotherglobalparameters.Thisresultrulesoutscenarioswheretheathalocoresformedsubsequentlythroughviolentdynamicalprocessesinthebaryoniccomponent.Thesecoresinsteadprovideimportantinformationontheoriginandnatureofdarkmatterindwarfgalaxies.Subjectheadings:Darkmatter|galaxies:spiral|galaxies:structure{3{1.IntroductionThenatureofthedarkmatter(DM)isoneofthemostimportantandstillunsolvedproblemsinastronomy.Currentcosmologicalmodelsassumethatthereexistsanonbaryonic,colddarkmatter(CDM)componentwhichconsistsofnon-relativisticparticlesthatareassumedtobecollisionlessandtointeractwiththebaryonsonlythroughgravitationalforces.CDMsimulationsindeedreproducequitewelltheobservedclusteringongalacticscales(Davisetal.1985).Theyalsopredicttheexistenceofextendeddarkmatterhaloesaroundgalaxies(Frenketal.1985)withconstantouterrotationcurves,inagreementwiththeobservations(Casertano&vanGorkom1991).Inorderforthegalacticgasandstarstoachieveaconstantcircularvelocityintheouterregions,thedensityproleoftheDMhalomustfallapproximatelyproportionaltor2intherelevantradiusrange.Suchaproleresemblesthedensitystructureofanisothermal,self-gravitatingsystemofparticleswhichischaracterizedbyaconstantvelocitydispersion.DMhaloesarethereforeoftenapproximatedbyasocalledmodied,isothermaldensityprole(Begemanetal.1991)(r)=01+r2r2c(1)wherercisthecoreradiusand0isthecentraldarkmatterdensity.EarlycosmologicalN-bodycalculationsdidnothaveenoughresolutiontoresolvetheinnerstructureofDMhaloes.RecentCDM-simulationswithmuchhigherspatialresolution(Dubinski&Carlberg1991,Navarroetal.1995)howeverleadtoDMhaloeswithaninnerdensitydistributionthatisinconsistentwithequation1.Whereastheisothermaldensityprolebecomesalmostconstantatradiismallerthanrcandhasanitecentraldensity,thenumericalmodelsindicateadensitydistributionwhichdivergesasr1inthe{4{innerparts,leadingtoaninnitedensityinthecenter.Unfortunatelysuchcentraldensitycuspsarehardtoverifyinnormalspiralgalaxiesastheirinnerpartsaregravitationallydominatedbybaryons.TheinferredDMpropertiesthendependstronglyontheassumedmass-to-lightratiosofthegalacticdiskandofthespheroidalcentralstellarcomponent.Thesituationisdierentindwarfspiralsystemswhichrecentlyhavebeenobservedwithhighresolution.Ithasbeenshownthatsomeofthesesystemsarecompletelydominatedbydarkmatter(Carignan&Freeman1988).Theythereforerepresentidealcandidatesforaninvestigationoftheinnerstructureofdarkmatterhalos.Flores&Primack(1994)andMoore(1994)recentlyshowedthattheDDOgalaxieshaverotationcurveswhichruleoutsingularhaloproleswithinnitecentraldensitiesandareingoodagreementwiththemodiedisothermaldensitylaw(eq.1).TheoriginoftheseshallowDMcoresrepresentsaninterestingandchallengingcosmologicalpuzzlewhichisnotyetsolved.2.TheUniversalDensityProlesofDarkMatterHaloesScalefreecosmologicalscenarioswithnon-baryonic,dissipationlessDMpredictthatallDMhaloesshouldhavesimilarstructure(Navarroetal.1995).ThispredictionistestedinFigure1whichshowstheDMmassdistributionasderivedfromtheobservedneutralhydrogenrotationcurvesoffourwellstudieddwarfspiralgalaxies.ThesesystemsarecompletelyDMdominated,evenintheirinnermostregions.TheirrotationcurvesthereforetracedirectlytheDMmassdistributionandtheuncertaingravitationalcontributionofthebaryoniccomponentcanbeneglected.Allfourprolesindeedfollowthesameuniversalmassrelation,implyingauniversalhalostructure.Notethatthemodied,isothermalprole(dashedcurve)onlytstheinnerregions;itrisessomewhattoofastatlargeradii.Thedottedanddot-dashedcurvesshowthemassdistributionaspredictedfromcosmologicalCDMsimulationsonclusterscales(Navarroetal.1985).ThesecalculationspredictDM{5{proleswhicharegivenbythettingfunction(r)=300r3200r1(r+0:25r200)2whereisthemeandensityoftheuniverseattheepochwhentheDMhaloformed.r200denotestheradiusoftheDMsphereofmeanoverdensityof200.Theseprolespredicttoomuchmassatsmallradiiasaresultofthecentraldensitycusp(Flores&Primack1994,Moore1994).Theobserveduniversalmassprolescanbettednicelyoverthewholeobservedradiusrangebythefollowing,purelyphenomenologicaldensitydistribution:DM(r)=0r30(r+r0)(r2+r20):(2)whichisshowninFigure1bythesolidline.0andr0arefreeparameterswhichrepresentth