Implication of Dark Matter in Dwarf Spheroidal Gal

arXiv:astro-ph/9905135v112May1999PASJ:Publ.Astron.Soc.Japan51,–12(2008)ImplicationofDarkMatterinDwarfSpheroidalGalaxiesHiroyukiHirashita,1∗HideyukiKamaya,2∗andTsutomuT.Takeuchi1∗1DepartmentofAstronomy,FacultyofScience,KyotoUniversity,Sakyo-ku,Kyoto606-8502E-mail(HH):[e-mail]2DepartmentofPhysics,FacultyofScience,KyotoUniversity,Sakyo-ku,Kyoto606-8502(Received1999February12;accepted1999April9)AbstractWeexaminethecorrelationbetweenphysicalquantitiestoexploretheexistenceofdarkmatter(DM)intheLocalGroupdwarfspheroidalgalaxies(dSphs).InordertoclarifywhetherDMexistsinthedSphswecomparetwoextrememodelsoftheirinternalkinematics:[1]atidalmodel(themassofadSphisestimatedwiththeluminousmass,sincetheobservedlargevelocitydispersionsofthedSphsareattributedtothetidalforcebytheGalaxy),and[2]aDMmodel(themassofadSphisestimatedwiththevirialmass,sincethevelocitydispersionisconsideredtoreflecttheDMpotential).Inbothmodels,wefindthattherelationbetweenthesurfacebrightnessofthedSphsandthetidalforcebytheGalaxyisconsistentlyinterpreted.ThismakesacriticalremarkaboutthepreviousstudiesthatconcludedthatthetidalforceiseffectiveforthedSphsbasedonlyonmodel[1].WealsocheckthecorrelationbetweentheGalactocentricdistanceandthetidalforce.Consequently,bothmodelsarealsosupportedinthistest.Thus,weareunabletojudgewhichofthetwoismorepromisingforthedSphsincorrelationinvestigations.Thephysicalprocessoftidaldisruptionisalsoconsidered.SincethetimescaleforthetidallyperturbedstarstoescapeismuchshorterthantheorbitalperiodsofthedSphs,itisdifficultforthetidallyperturbeddSphstoexistasanassembly.Thus,wesuggestthatthegravitationalfieldofDMisnecessarytobindthedSphswithalargevelocitydispersion.Keywords:Darkmatter—Galaxies:elliptical—Galaxies:evolution2H.Hirashita,H.Kamaya,andT.T.Takeuchi[Vol.51,1.IntroductionRecentobservationshavebeenrevealingthepropertiesoftheLocalGroupdwarfspheroidalgalaxies(dSphs).ThedSphshaveluminositiesoforder105–107L•⊙,andarecharacterizedbytheirlowsurfacebrightnesses(Gallagher,Wyse1994forreview).Theobservationsofsuchfaintobjectsareimportantforseveralreasons.Forexample,inagalaxy-formationtheorybasedonthecolddark-matter(CDM)model,low-massgalaxiesareconsideredtobethefirstboundluminousobjects(e.g.,Blumenthaletal.1984).Thus,thedSphsareexpectedtohavealargeamountoftheCDM(seealsoFlin1999foranobservationalapproach).Todate,thestellarvelocitydispersionsofdSphshavebeenextensivelymeasured(e.g.,Mateoetal.1993andreferencestherein),which,ingeneral,indicateatoolargemasstobeaccountedforbythevisiblestarsinthedSphs.Inotherwords,dSphsgenerallyhavehighmass-to-lightratios(Mvir/LV,whereMviristhevirialmasscalculatedfromobservedsizeandstellarvelocitydispersionandLVisthetotalluminosityattheVband;the6thcolumnintable1).Thisfactcanimplythepresenceofdarkmatter(DM)inthesesystems(e.g.,Mateoetal.1993).TheexistenceofDMisalsosupportedbythelargespatialdistributionofstarsintheirouterregions(Faber,Lin1983;Irwin,Hatzidimitriou1995).However,theaboveargumentsmaybechallengedifwetakeintoaccountthetidalforceexertedbytheGalaxy.IfadwarfgalaxyorbitingtheGalaxyissignificantlyperturbedbytheGalactictidalforce,theobservedvelocitydispersionofthedwarfgalaxycanbelargerthanthegravitationalequilibriumdispersion(Kuhn,Miller1989;Kroupa1997).Moreover,theresultsinKuhn(1993)implythatthelifetimesofinternallyunboundsatellitesmightbelongerthanoneorbitalperiod(butseeJohnston1998).Thetimescaleforsuchanunboundobjecttosurviveisestimatedlaterinthispaper(subsubsection3.2.1).ThistidalpictureofthedSphsalsosuggeststhatthelargevelocitydispersionsdonotnecessarilyshowtheexistenceofDM(butseePiatek,Pryor1995;Ohetal.1995).Wewillconsiderwhethertheobservedlargemass-to-lightratiosofdSphsarereallyduetothetidaleffect.Theplanofthispaperisasfollows.Firstofall,inthenextsection,wepresentcorrelationsamongtheobservedquantities.Wesummarizeourresultsinsection3.Inthesamesection,somediscussionsarealsomade,andwecommentabouttheenvironmentaleffectsonthedSphs.∗ResearchFellowoftheJapanSocietyforthePromotionofScience.No.3]ImplicationofDMinDwarfSpheroidals32.CorrelationamongObservedQuantities2.1.SurfaceBrightnessandGalactocentricDistanceInthissection,weconsiderwhatdeterminesthephysicalconditionofthedSphs.Were-examinethecorrelationwhichBellazzinietal.(1996;hereafterB96)havepresented.First,adimensionlessformoftheGalactictidalforceisdefined.TheGalacticpotentialismodeledbyasphericaldarkhalowithaflatrotationcurveofamplitudeVrot(Honma,Sofue1997forthelatestresults).WeassumethatthedarkhaloextendsuptoRGC=100kpc.Withtheaboveflat-rotationmodeloftheGalacticpotential,themassoftheGalaxywithintheGalactocentricdistanceRGCisexpressedasMG(RGC)=V2rotRGCG=1.1×1012M•⊙RGC100kpcforRGC≤100kpc,1.1×1012M•⊙forRGC≥100kpc,(1)whereweassumedVrot=220kms−1(e.g.,Burkert1997).WeconsiderasphericalsatellitegalaxyorbitingtheGalaxy.Thetidalforcewhichastar(whosemassism∗)atthecoreradius(rc;theradiuswherethesurfacebrightnessfallstohalfitscentralvalue;Binney,Tremaine1987,p.25)ofthesatellitegalaxyexperiencesisapproximatelyFT≡Gm∗MGrcR3GC.(2)Thestaralsoexperiencesagravitat