Halo Cores and Phase Space Densities Observational

arXiv:astro-ph/0004381v127Apr2000HaloCoresandPhaseSpaceDensities:ObservationalConstraintsonDarkMatterPhysicsandStructureFormationJulianneJ.Dalcanton1&CraigJ.Hogan2DepartmentofAstronomy,UniversityofWashington,Box351580,SeattleWA,98195ABSTRACTWeexploreobserveddynamicaltrendsinawiderangeofdark-matter-dominatedsystems(aboutsevenordersofmagnitudeinmass)toconstrainhypotheticaldarkmattercandidatesandscenariosofstructureformation.First,wearguethatneithergenericwarmdarkmatter(collisionlessorcollisional)norself-interactingdarkmattercanberesponsiblefortheobservedcoresonallscales.Bothscenariospredictsmallercoresforhighermasssystems,inconflictwithobservations;somecoresmustinsteadhaveadynamicalorigin.Second,weshowthatthecorephasespacedensitiesofdwarfspheroidals,rotatingdwarfandlowsurfacebrightnessgalaxies,andclustersofgalaxiesdecreasewithincreasingvelocitydispersionlikeQ∝σ−3∝M−1,aspredictedbyasimplescalingargumentbasedonmergingequilibriumsystems,overarangeofabouteightordersofmagnitudeinQ.Wediscusstheprocesseswhichsettheoverallnormalizationoftheobservedphasedensityhierarchy.Asanaside,wenotethattheobservedphase-spacescalingbehavioranddensityprofilesofdarkmatterhalosbothresemblestellarcomponentsinellipticalgalaxies,likelyreflectingasimilarcollisionless,hierarchicalorigin.Thus,darkmatterhalosmaysufferfromthesamesystematicdeparturesfromhomologyasseeninellipticals,possiblyexplainingtheshallowerdensityprofilesobservedinlowmasshalos.Finally,weusethemaximumobservedphasespacedensityindwarfspheroidalgalaxiestofixaminimummassforrelativistically-decoupledwarmdarkmattercandidatesofroughly700eVforthermalfermions,and300eVfordegeneratefermions.Subjectheadings:cosmology:darkmatter,cosmology:observations,galaxies:kinematicsanddynamics,galaxies:structure,galaxies:formation,cosmology:theory1.IntroductionRecentworkhasdrawnattentiontotheapparentconflictbetweenpredictionsofcollisionlessColdDarkMatter(CDM)onsmallscalesandobservationsofrotationcurvesofdarkmatter1e-mailaddress:[e-mail]2e-mailaddress:[e-mail]–2–dominatedgalaxies.NumericalsimulationssuggestthatinaCDMcosmology,darkmatterhalosshouldhavesteeplyrisingcentralcusps(ρ∝r−1.5)andhighdensities.Whiletheobservationalconclusionsaresomewhatambiguousontheinnermostprofileshapes(e.g.Swatersetal.2000,vandenBoschetal.2000,vandenBosch&Swaters2000,Borriello&Salucci2000,Dalcanton&Bernstein2000,Burkert1997),rotationcurvesconsistentlyimplylowcharacteristichalodensitiesinthecentralregions.Becauseρ(r)∝(V(r)/r)2,thecharacteristicslopeoftherotationcurveisproportionaltothesquarerootofthemeanencloseddensity.ObservationsofdarkmatterdominatedgalaxiesconsistentlyfindrotationcurveswhichrisewithV/R∼10−20km/s,suggestingmuchlowercharacteristicdensitiesthanimpliedbysimulationsofhalosinviableCDMcosmologies,whereV/R∼30−50km/s(Mooreetal.1998,1999,Navarroetal.1996,1997).Thegrowingbeliefthattheretrulyisaconflictbetweentheoryandobservationshasledtoarenaissanceinexploringalternativemodelsfordarkmatter.Byviolatingeitherthe“collisionless”or“cold”propertiesoftraditionalCDM,orbyconsideringadditionalexoticproperties,manyauthorshavesoughttopreservethesuccessesofCDMonlargescales,whilemodifyingthemanifestationsofdarkmatteronsmallscales(Spergel&Steinhart1999,Hogan&Dalcanton2000,Sommer-Larson&Dolgov1999,Mohapatra&Teplitz2000,Peebles2000,Goodman2000,Riotto&Tkachev2000,Huetal.2000,Shi&Fuller1999,Colinetal.2000.)Inthispaper,weplacebroadconstraintsuponthesealternativestoCDM,byrevisitingobservationsofthestructureandphasespacedensityofhalosoverawiderangeofscales.Manyoftheabovealternativedarkmatterscenariosmakespecificpredictionsforthesizesofdarkmattercoresasafunctionofmassscale(seeSpergel&Steinhart1999,Hogan&Dalcanton2000,Hannestad1999,Burkert2000,Kochanek&White2000,Yoshidaetal.2000,Mooreetal.2000,althoughsomeoftheseareinconflictwitheachother,particularlyregardingthelongtermstabilityofself-interactingcores).Weconfrontthesepredictionswithexistinglimitsonthescaleofinnerhalocoresin§2,andarguethatneitherpackingofphasespacenorhighlycollisionaldarkmattercanbeprimarilyresponsiblefortheobservedbehaviorofdarkmattercoresatallscales.Inadditiontodiscussingthescalingbehaviorofdarkmattercores,wefocusupontrendsofphasespacedensityQasaprobeofstructureformationhistory.In§3.1wesummarizethestatisticalanddynamicalbehaviorofQinhierarchicalclustering,includingasimpleargumentpredictingthedecreaseofQwithmassandvelocitydispersion.Currentobservationallimitsonthevariationofphasespacedensitywithmassarereviewedandsummarizedin§3.2.Weshowin§4thatthephasespacedensityofthedarkmatterhalosisaverystronglydecliningfunctionofmass(consistentwiththenearlyconstantdensityseenacrossasimilarmassscaleinFirmanietal.2000).Thisbehaviorisexactlyaspredictedbymodelswherehalosformedhierarchically,withsuccessivemergersleadingtophasemixinganddilutionofthecoarse-graineddistributionfunction.Wealsonotethattheobserveddeclineinphasespacedensityfordarkmatterhalosandtheirpredicteddensityprofilesresemblesthatobservedinthebaryon-dominatedcentralregionsofgiantellipticalgalaxies,andthat