How-Lumpy-is-the-Milky-Ways-Dark-Matter-Halo

arXiv:astro-ph/0111196v19Nov2001HowLumpyistheMilkyWay’sDarkMatterHalo?KathrynV.Johnston1,DavidN.Spergel2andChristianHaydn1ABSTRACTCDMsimulationspredictthattherearehundredsoflumpsofwithmassesgreaterthan107M⊙intheMilkyWayhalo.However,weknowofonlyadozendwarfsatellitesclosetothismass.Aretheselumpssimplylackinginstarsoristhereafundamentalflawinourmostpopularcosmology?Bystudyingthetidaldebrisofknownsatelliteswecanpotentiallyaddressthisquestion.Inthispaper,wequantifythetheeffectsofthedarkmatterlumpsontidaltails.Thelumpsscatterstarsinthetidaltailsfromtheiroriginalorbitsproducingadistinctivesignature.Wesimulatedebrisevolutioninsmoothandlumpyhalospotentialsanduseoursimulationstomotivateandtestastatisticalmeasureofthedegreeofscatteringapparentintheangularpositionandradialvelocitymeasurementofdebrisstars—the“scatteringindex”.WefindthatthescatteringindexcaningeneraldistinguishbetweenthelevelsofsubstructurepredictedbyCDMcosmologiesandsmoothMilkyWaymodels,butthatthesensitivityofthedebrisdependsontheorientationoftheparentsatellite’sorbitrelativetothelargestlumpsorbits.WeapplyourresultstothecarbonstarstreamassociatedwiththeSagittariusdwarfgalaxy(Sgr)andfindthatthesestarsappeartobemorescatteredthanweexpectfordebrisorbitinginasmoothhalo.However,thedegreeofscatteringisentirelyconsistentwiththatexpectedduetotheinfluenceoftheLargeMagellanicCloud,whichisonanorbitthatintersectsSgr’sown.WeconcludethatthecurrentdataisunabletoconstrainCDMmodels.Nevertheless,ourstudysuggeststhatfuturedatasetsofdebrisstarsassoci-atedwithotherMilkyWaysatellitescouldprovidestrongconstraintsonCDMmodels.Subjectheadings:Galaxy:halo—Galaxy:kinematicsanddynamics—Galaxy:structure—cosmology:darkmatter1VanVleckObservatory,WesleyanUniversity,Middletown,CT06459—[e-mail],[e-mail]2PrincetonUniversityObservatory,PrincetonUniversity,Princeton,NJ08544—[e-mail]–2–1.IntroductionCDMmodelspredicttwoordersofmagnitudemoredarkmatterhalosthansatellitesobservedaroundtheMilkyWay(Mooreetal.1999;Klypinetal.1999).Solutionstothisproblemincludeself-interactingdarkmatter(Spergel&Steinhardt2000),truncatedpowerspectra(Kamionkowski&Liddle2000)andtherestrictionofgasaccretiontothelowestmassdarkmatterhalostobebeforetheepochofreionization(Bullock,Kravtsov&Weinberg2001).Thefirsttwosolutionswouldgetridofthesmallestdarkmatterhalosentirely,whilethelatterwouldpredictthatonlyonepercentofthesatellitehalosactuallycontainstars.Inthispaper,ratherthanattemptingtosolvetheproblem,wediscusshowwemighttellobservationallywhetheritisaprobleminthefirstplace.ThesatellitedarkmatterhalosintheCDMmodelscompriseabout10%ofthetotalmassoftheparentgalaxyonroughlyisotropicorbitsdistributedthroughoutthegalaxy(Font&Navarro2001).Oneideaistolookforsignaturesoftheselumpsaroundexternalgalaxiesingravitationallylensedimagesofbackgroundquasars(Chiba2001;Metcalf2001).Weconcentrateourstudyratherclosertohome.IfsuchlumpstrulyexistaroundtheMilkyWaythenwewouldexpectthemtohavesomedynamicalinfluenceontherestvisibleGalaxy.Forexample,accordingtoLacey&Ostriker(1985)ifthehaloisentirelymadeof106M⊙blackholestheywouldsignificantlyheatourGalacticdisk.Font&Navarro(2001)usednumericalsimulationstoaskwhetherthecoldnessofourdiskcouldbeusedinasimilarfashiontolimitthedistributionofdarkmatterlumpsseenincosmologicalsimulationsthatcouldbeorbitingtheGalaxy.UsingonerealizationoflumpmassesandorbitstakenfromaΛCDMmodelofaGalaxy-sizedhalo,theyfoundthattheheatingcausedbythelumpswaslessthantheheatingobservedinthestellarpopulationsinthediskandconcludedthatthediskisnotanefficientprobeofthismodel.StreamsofdebrisfromthedestructionofGalacticsatellitesareanotherexampleofcoldstructureswithintheMilkyWaythatcouldbescatteredbysubstructureinthepoten-tial.Thesestreamstendtoalignalongasingleorbit(Johnston,Hernquist&Bolte1996;Johnston1998;Helmi&White1999)andhencewouldindividuallyhavelowercrosssectiontointeractionsthantheGalacticdisk.Neverthelesswechosetoexaminetheresponseofthesetoperturbationsratherthanthediskforseveralreasons:theywillexploretheouterregionsoftheGalacticpotentialthatthediskdoesnotexperience;weexpectothersourcesofheatinginthisregion(structuressuchasthebar,spiralarmsandgiantmolecularcloudsinthedisk)tobenegligible;ifstreamsfromseveralsatellitescouldbestudied,wehavethepotentialofprobingalargerportionoftheGalaxy;finally,thesestreamsareoftenevencolderthanthediskitselfandhenceshouldbemoresensitivetoscattering.Weapproachthisproblemofscatteringnumericallyratherthananalyticallybothbe-–3–causeofthenatureofthepredictedCDMmassdistributionoflumpsandthelowcrosssectionsofthestreams.Scatteringbythefewmostmassivelumpsinthedistributionisexpectedtobemostimportant,andtheexactdegreeofscatteringwilldependontherel-ativeorientationofthelumpanddebrisorbits.Hencetheprocessisdominatedbyafewstrongencountersratherthanonethatcanbemodeled(say)byintegratingovermanyweakencountersintheimpulsiveregime.Norwouldasimpleanalyticrepresentationincludehowthewakeinthehalo,excitedbythemostmassivelumps,wouldaffectthestreamorbits.Weinberg’sstudies(Weinberg1998a,1995)oftheaffectof