The rotation curves of dwarf galaxies a problem fo

arXiv:astro-ph/0311020v327Sep2004Therotationcurvesofdwarfgalaxies:aproblemforColdDarkMatter?GeorgeRheePhysicsDepartment,UniversityofNevada,Box454002,LasVegas,NV89154andOctavioValenzuelaAstronomyDepartment,UniversityofWashingtonBox351580,Seattle,WA98195AnatolyKlypin,JonHoltzmanandBhaskerMoorthyAstronomyDepartment,NewMexicoStateUniversity,POBox30001,LasCrucesNM88003ABSTRACTWeaddresstheissueofaccuracyinrecoveringdensityprofilesfromobservationsofrotationcurvesofgalaxies.We“observe”andanalyzeourmodelsinmuchthesamewayasobserversdotherealgalaxies.Ourmodelsincludestellardisks,diskswithbars,andsmallbulges.Wefindthatthetiltedringmodelanalysisproducesanunderestimateofthecentralrotationalvelocity.Insomecasesthegalaxyhalodensityprofileseemstohaveaflatcore,whileinrealityitdoesnot.Weidentifythreeeffects,whichexplainthesystematicbiases:(1)inclination(2),smallbulge,and(3)bar.Inclinationeffectsareduetofinitethicknessofdisk,bar,orbulge.Admixtureofanon-rotatingbulgecomponentreducestherotationvelocity.Asmall(200-500pc)bulgemaybeoverlookedleadingtosystematicbiasevenonrelativelylarge∼1kpcdistances.Inthecaseofadiskwithabar,theunderestimateofthecircularvelocityislargerduetoacombinationofnon-circularmotionsandrandomvelocities.Theeffectofthebardependsontheanglethatthebarmakeswiththelineofsight.Signaturesofbarscanbedifficulttodetectinthesurfacebrightnessprofilesofthemodelgalaxies.Thevariationofinclinationangleandisophotepositionanglewithradiusaremorereliableindicatorsofbarpresencethanthesurfacebrightnessprofiles.Thesystematicbiasesinthecentral∼1kpcofgalaxiesarenotlarge.Eacheffectseparatelygivestypicallyafewkm/serror,buttheeffectsaddup.Insomecasestheerrorincircularvelocitywasafactoroftwo,buttypicallywegetabout20percenteffect.Theresultisthefalseinferencethatthedensityprofileofthehaloflattensinthecentralparts.Ourobservationsofrealgalaxiesshowthatforalargefractionofgalaxiesthevelocityofgasrotation(asmeasuredbyemissionlines)isveryclosetotherotationofstellarcomponent(asmeasuredbyabsorptionlines).Thisimpliesthatthesystematiceffectsdiscussedinthispaperarealsoapplicablebothforthestarsandemission-linegas.Subjectheadings:galaxies:halos—galaxies:localgroup—galaxies:dwarf—galaxies:kinematicsanddynamics—cosmology:darkmatter—11.IntroductionThecosmologicalcolddarkmatter(CDM)modelanditspresentvariantwithcosmologi-calconstant(ΛCDM)havebeenverysuccessfulinaccountingforthepropertiesofgalaxiesandtheirdistributioninspace.AcurrentproblemforCDMliesinobservationsofdwarfandlowsur-facebrightnessgalaxies.TherotationcurvesandderiveddensityprofilesofthesegalaxiesappeartobeinconflictwiththeCDMmodel(Moore1994;Flores&Primack1994;Burkert1995;Hern´andez&Gilmore1998).TheproblemarisesbecausenumericalsimulationsoftheformationofhalosintheCDMmodelrevealsteeplycuspeddensityprofileswhileobservationsfavorshallow(core)profiles.Thetheorypredictsthatthemassdensityintheinnerpartsofthedarkmatterha-losisbestdescribedasanr−α,α=1powerlaw(Navarro,Frenk,&White1997;Poweretal.2003;Colin,Klypin,Valenzuela,Gottloeber2004)orpossiblybyapower-lawwithaslightlysteeperα=1.2−1.5slope(Mooreetal.1999;Ghignaetal.2000;Klypin,Kravtsov,Bullock,&Primack2001;Reedetal.1999;Tasitsiomi,Kravtsov,Got-tloeber,&Klypin2004).Theobservedrotationcurvesofasignificantfractionofdwarfgalaxies,however,suggestthattheircoresdonothavesteepdensitycusps(deBlok&McGaugh1997;Blais-Ouellette,Amram&Carignan2001;deBlok,McGaugh,Bosma,&Rubin2001;McGaugh,Ru-bin,&deBlok2001;Bolatto,Simon,Leroy,&Blitz2002;Weldrake,deBlok&Walter2002;Simon,Bolatto,Leroy,&Blitz2002).Notethatthisisnottrueforsomegalaxiesandthatsomeobservationalresultsarestillconsistentwithcos-mologicalpredictions(vandenBoschetal.1999;Swaters,Madore,&Trewhella2000;vandenBosch&Swaters2001).McGaugh,Rubin,&deBlok(2001)haveanalyzedHαobservationsof50lowsurfacebrightnessgalaxiesofwhich36areofsufficientqualitythatrotationcurvescanbederived.Thespatialresolutionisimprovedbyanorderofmagnitudeoverold21cmdata.InacompanionpaperdeBlok,McGaugh,Bosma,&Rubin(2001)concludethatatsmall(0.5-1kpc)radii,themassdensitydistributionisdominatedbyanearlyconstantdensitycore.Thedistri-butionofinnerslopesisstronglypeakedaroundα=−0.2withclearcontradictionwiththeCDMpredictions.Thus,thereappearsacontroversyconcerningthedensitydistributionofmatterintheinnerpartsofdwarfgalaxies.Weproposeasomewhatdifferentapproachtothisproblemwhichwebelievecanhelptoclarifythesedebates.Weconstructrealisticmodelsofgalaxiesand“observe”themasrealgalaxiesusingthesametechniquesoralgorithmsthatobserversapplytorealdata.Westudythedetailsoftheanalysisofobservationsandwefinddiscrepanciesbetweenrecoveredandtruepropertiesofthesim-ulatedgalaxies.Weinvestigateprojectioneffectsandtheeffectsofbarsandbulgesontheobservedrotationcurves.Weshowthattheseeffectsareoftenfarfromnegligible.Someoftheeffectswhichwestudy,haveal-readybeendiscussed.Athanassoula(1984)dis-cussedthebiasesintheobservedrotationcurvesofhighsurfacebrightnessgalaxiescreatedbystrongbars.Morerecently,Koda&Wada(2002)haveinvestigatedtheeffectsofaweakbaronmassde-terminationinthecentralpartsofspiralgalaxies.Theyexaminerot