Probing MACHOs Toward the Galactic Bulge(7)

3.BackgroundfromSpheroid/BulgeStars

HalolensescouldproduceeventsanywherealongthelineofsightfromtheSuntothebulgeand,assuminganisothermalhalomodelwithcoreradiusa=5kpc,thedensity

ρhalo=2vc

dDl=ρhaloc2f(a/R0)2+(1 x)2.(5)

Here,rE=(4GMDlDs/c2Dos)1/2istheEinsteinradius,DlandDsarethesourceandlensdistances,Dls=Ds Dl,fisthefractionofthehalointheformofMACHOs,R0=8kpcistheSolarGalactocentricdistance,x≡Dl/R0,andM(whichcancelsout)isthemassofthelens.

However,intheinnerGalaxy,thesehalolensesarecompletelysubmergedintheback-groundofbulgelenses,andsincetheyhavesimilarkinematics,thereisnowaytoreliablydistinguishthem.ItisonlyoutclosertotheSun,wherethespheroidalpopulation(hereusuallycalled“spheroid”or“stellarhalo”),thinsoutthatonemayhopetoseparatethetwopopulations.Evenhere,thereissomepossibilityofcontamination.Thelocalspheroiddensityisonlyabout1%ofthedarkhalo,butiff～20%asAlcocketal.(2000)suggest,thenMACHOsareonly20timesmorecommonthanspheroidstarslocally.Moreover,asoneapproachestheGalacticcenter,thespheroiddensitygrowssubstantiallymorerapidlythandoesthedarkhalo.Tomakeaquantitativecomparison,Iadopt

ρspheroid=1×10 4M⊙

R0 3.2.(6)

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