DRAFTVERSIONFEBRUARY1,2008 PreprinttypesetusingLATEXstyleemulateapjv.16/07/00 THEMACHOPROJECTHUBBLESPACETELESCOPEFOLLOW-UP:PRELIMINARYRESULTSONTHE LOCATIONOFTHELARGEMAGELLANICCLOUDMICROLENSINGSOURCESTARS C.ALCOCK1,2,R.A.ALLSMAN3,D.R.ALVES1,4,T.S.AXELROD5,A.C.BECKER6,D.P.BENNETT2,7, K.H.COOK1,2,N.DALAL2,8,A.J.DRAKE1,5,K.C.FREEMAN5,M.GEHA1,9,K.GRIEST2,8, M.J.LEHNER10,S.L.MARSHALL1,D.MINNITI1,11,C.A.NELSON1,12,B.A.PETERSON6,P.POPOWSKI1, M.R.PRATT6,P.J.QUINN13,C.W.STUBBS2,14,W.SUTHERLAND15,A.B.TOMANEY14,T.VANDEHEI8 (TheMACHOCollaboration) DraftversionFebruary1,2008 ABSTRACT 1 WeattempttodeterminewhethertheMACHOmicrolensingsourcestarsaredrawnfromtheaveragepopulation 0 of the LMC or from a populationbehindthe LMC by examiningthe HST color-magnitudediagram (CMD) of 0 microlensingsourcestars. WepresentWFPC2HSTphotometryofeightMACHOmicrolensingsourcestarsand 2 the surroundingfields in the LMC. The microlensing source stars are identified by deriving accurate centroids n intheground-basedMACHOimagesusingdifferenceimageanalysis(DIA)andthentransformingtheDIAco- a ordinatestotheHST frame. We considerindetailamodelforthebackgroundpopulationofsourcestarsbased J on that presentedbyZhao, Graff& Guhathakurta. In this model, the sourcestars have an additionalreddening 3 =0.13magandaslightlylargerdistancemodulus<∆µ>∼0.3magthantheaverageLMCpopu- lation. Wealsoinvestigateaseriesofsourcestarmodels,varyingtherelativefractionofsourcestarsdrawnfrom 2 theaverageandbackgroundpopulationsandthedisplacementofthebackgroundpopulationfromtheLMC.Due v tothesmallnumberofanalyzedeventsthedistributionofprobabilitiesofdifferentmodelsisratherflat. Ashallow 2 maximumoccursatafractions ∼0.8ofthesourcestarsintheLMC.Thisisconsistentwiththeinterpretation 8 LMC 2 thatasignificantfractionofobservedmicrolensingeventsareduetolensesintheMilkyWayhalo,butdoesnot 8 definitivelyexcludeothermodels. 0 1 0 LawrenceLivermoreNationalLaboratory,Livermore,CA94550 Email:alcock, kcook, adrake, cnelson, popowski, stuart@igpp.ucllnl.org 0 2 / h CenterforParticleAstrophysics,UniversityofCalifornia,Berkeley,CA94720 3 p SupercomputingFacility,AustralianNationalUniversity,Canberra,ACT0200,Australia - o Email:Robyn.Allsman@anu.edu.au r 4 t SpaceTelescopeScienceInstitute,3700SanMartinDr.,Baltimore,MD21218 s Email:alves@stsci.edu a 5 : v ResearchSchoolofAstronomyandAstrophysics,Canberra,WestonCreek,ACT2611,Australia i Email:tsa, kcf, peterson@mso.anu.edu.au X 6 BellLaboratories,LucentTechnologies,600MountainAvenue,MurrayHill,NJ07974 r a Email:acbecker@physics.bell-labs.com 7 DepartmentofPhysics,UniversityofNotreDame,IN46556 Email:bennett@bustard.phys.nd.edu 8 DepartmentofPhysics,UniversityofCalifornia,SanDiego,CA92039 Email:endall@physics.ucsd.edu, kgriest@ucsd.edu, vandehei@astrophys.ucsd.edu 9 DepartmentofAstronomyandAstrophysics,UniversityofCalifornia,SantaCruz95064 Email:mgeha@ucolick.org 10 DepartmentofPhysics,UniversityofSheffield,SheffieldS37RH,UK Email:m.lehner@sheffield.ac.uk 11 Depto.deAstronomia,P.UniversidadCatolica,Casilla104,Santiago22,Chile Email:dante@astro.puc.cl 12 DepartmentofPhysics,UniversityofCalifornia,Berkeley,CA94720 13 EuropeanSouthernObservatory,KarlSchwarzchildStr.2,D-85748GärchingbelMünchen,Germany Email:pjq@eso.org 14 DepartmentsofAstronomyandPhysics,UniversityofWashington,Seattle,WA98195 Email:stubbs@astro.washington.edu 15 DepartmentofPhysics,UniversityofOxford,OxfordOX13RH,U.K. Email:w.sutherland@physics.ox.ac.uk 1 2 Subjectheadings:darkmatter—Galaxy:halo—Galaxy:structure—gravitationallensing—Magellanic Clouds 1. INTRODUCTION However, observational work on RR Lyrae by Kinman et al. (1991), which does not rely on the specific kinematics of The crucial observable in microlensing, the event duration, the spheroidi,limits the totalmassof anytype ofhalo (virial- admits degeneracy in the three fundamental microlensing pa- izedornon-virialized)toperhaps5%ofthemassoftheLMC, rameters: the mass, distance and velocity of the lens. This too small to contribute more than ∼5% of the observed opti- makes it difficult to distinguish between the two principalge- caldepth. A morerecentrevisitingof thisargumentbyAlves ometric arrangements which may explain Large Magellanic (2000)findsroomtoincreasethisopticaldepthcontributionto Cloud (LMC) microlensing: a) MW-lensing, in which the atmost20%,stillonlyasmallfractionofthetotal. lensed object is part of the Milky Way (MW) and b) self- In order for an LMC shroud to account for the total opti- lensing,inwhichthelensedobjectispartoftheLMC.Inself- cal depth it must have a mass comparableto that of the LMC lensing,thelensmaybelongtothedisk+bar,haloor“shroud” disk+bar(Gyuk,Dalal,&Griest2000). Evenifweacceptthe of the LMC, while the source star may come from any of existenceofsucha massiveshroud,the microlensingimplica- thesecomponentsorsomesortofbackgroundpopulationtothe tionsaresomewhatindispute. Weinberg(2000)findsanLMC LMC. self-lensing optical depth comparable to the observed optical Most efforts to distinguish between MW-lensing and self- depth.However,thisestimateisreducedbyafactorofthreeby lensing event distributions focus on modeling the LMC self- Gyuk,Dalal,&Griest(2000)whorepeattheWeinberg(2000) lensingcontributiontotheopticaldepthandcomparingthisto microlensinganalysisusinglowervaluesforthedisktotalmass theobservedopticaldepth.EarlyworksbySahu(1994)andWu andinclinationangleandaproperweightingoverallobserved (1994)consideredthetraditionalLMCself-lensinggeometryin MACHOfields. whichboththesourceandlensareinthedisk+baroftheLMC. Yet another self-lensing geometry was introduced by Zhao Bothworkssuggestedthatdisk+barself-lensingcouldaccount (1999)whosuggeststhattheobservedeventsaredueto“back- for a substantial fraction of the observed optical depth. This ground” self-lensing in which the source stars are located in claim has since been disputed by several other groups(Gould some background population, displaced at some distance be- 1995;Alcocketal.1997,2000a)whoshowthatwhenconsid- hind the LMC. A veritable plethora of lenses for this popula- eringonlydiskstarstherateofLMCself-lensingisfartoolow tionisthensuppliedbythedisk+baroftheLMC.Abackground toaccountfortheobservedrate. Gyuk,Dalal,&Griest(2000) populationhastheadvantageofbeingnearlyimpossibletocon- showthatallowingforcontributionstothelensandsourcepop- firmorrejectobservationally,astherearenearlynolimitsonits ulationsfromthe LMCbardoesnotsubstantiallyincrease the sizeorcontent(providedofcourse,itissmallenoughto“hide” LMC self-lensing optical depth. Alves & Nelson (2000) find behindtheLMC). a low LMC self-lensing optical depth for a flared LMC disk. A final possibility is “foreground”self-lensing. This is not Gyuk, Dalal, & Griest (2000)also show thatmuchof the dis- self-lensinginthe classicalsense asinthiscase thelensesare agreementinmodelsofthedisk+barself-lensingopticaldepth notdrawnfromtheLMCitself,butratherfromsomekinemat- resultsfromdisagreementaboutthefundamentalparametersof ically distinct foreground population, such as an intervening the LMC, such as the total disk mass and inclination angle. dwarfgalaxy.Zaritsky&Lin(1997)claimadetectionofapop- WithintheirregionofallowedparametersGyuk,Dalal,&Gri- ulationofstarsfromsuchanentity.However,Beaulieu&Sack- est (2000) also make a strong case that disk+bar self-lensing ett(1998)claimthatthis“population”isamorphologicalfea- makes a small contribution to the observed optical depth, at tureoftheLMCredclump,whileothersshowthatsuchapopu- most∼20%. lationconsistentwithotherobservationalconstraintscouldnot However, self-lensing becomes a much more plausible hy- produceasubstantialmicrolensingsignal(Gould1998;Bennett pothesis if one allows for lenses in an LMC stellar halo pop- 1998). ulation. The principal problem surrounding an LMC stellar In this work we attemptto determinewhetherthe MACHO halo contribution is that no tracers of old populations in the source stars belong to the average population of the LMC or LMC have ever revealed a population with high enough ve- toabackgroundpopulationdisplacedatsomedistancebehind locitydispersionstosuggestavirializedspheroidalcomponent the LMC disk. The determination of source star location is (Olszewski,Suntzeff&Mateo1996). based on the suggestion of Zhao (1999), Zhao (2000), and Recently however,a new possibility hasarisen fromthe re- Zhao,Graff&Guhathakurta(2000)whopointoutthatsource sults of Weinberg (2000) who claims that LMC microlensing stars from a background population should be preferentially maybecausedbyanon-virializedstellarhaloor“shroud”.This fainter and redder than the average population of the LMC termwasintroducedbyEvans&Kerins(2000)andismeantto due to the extinction of the LMC disk and their displacement implyanLMCpopulationwhichislikeahalointhatitisspa- along the line of sight. Zhao, Graff & Guhathakurta (2000) cially not part of the LMC disk, but unlike a halo in that it is present a model for this backgroundpopulationwith an addi- non-virializedandthusmayhavearelativelylowvelocitydis- tionalmeanreddeningrelativetotheaveragepopulationofthe persion. Such a populationis suggestedby the simulationsof LMC =0.13 mag and a displacement from the Weinberg(2000)whofindsthattheLMC’sdynamicalinterac- LMCof∼7.5kpcresultinginanincreaseofdistancemodulus tionwiththeMWmaytorquetheLMCdiskinsuchawaythat of<∆µ>∼0.3mag. theLMCdiskisthickenedandaspheroidcomponentispopu- Thelocationofthesourcestarshasimplicationsfortheloca- latedwithoutisotropizingthestellarorbitsandtherebyleaving tionofthelensesandthusforthenatureofLMCmicrolensing. disklike kinematics intact. Statistically marginal evidence for Ifallthesourcestarsareinthebackgroundpopulation,thenthe such a kinematically distinct populationis found observation- greatmajorityofthelensesarefoundintheLMCdisk+barand allyinastudyofcarbonstarvelocitiesbyGraffetal.(2000). LMC microlensing is dominated by background self-lensing. TheLocationoftheSourceStars 3 Conversely, if all the source stars are in the LMC, then mi- WecreateacompositeLMCCMDbycombiningthePCand crolensingmaybeduetoMW-lensing,disk+barself-lensingor WFphotometryforallofourfieldsexceptthefieldofLMC-1. foregroundself-lensing. However,sincethecontributionfrom In the case of LMC-1 theV and I observationswere taken at disk+bar self-lensinghasbeen shownto be small and the evi- differentrollanglesandthereislittleareaofoverlapexceptin denceforaforegroundinterveningpopulationisunconvincing, thePCframe. We thereforeincludethePCfieldfromLMC-1 a result which places all source stars in the LMC would sug- butnotthe WF fields. The compositeHST CMD is shown in gest thatLMCmicrolensingis dominatedby MW-lensing. If, Figure1. however,wefindamoreequaldivisionofsourcestarsbetween the LMC and the backgroundpopulationthen this implies ei- 3. SOURCE STARIDENTIFICATIONTHROUGH DIFFERENCE ther some mixture of MW-lensing and disk+bar self-lensing, IMAGE ANALYSIS or a more symmetric self-lensing geometry such as the LMC shrouddiscussedabove. Aground-basedMACHOimagehasapixelsizeof0.6′′and We first investigate two models: the first putting all source a seeing of at least 1.5′′. Thus, in a typically crowded re- starsintheLMC(Model1),andthesecondputtingallsource gion of the outer LMC bar, a MACHO seeing disk will con- stars in a background population (Model 2). We compare a tain ∼11 stars of V . 24. This means that faint “stars” in Hubble Space Telescope (HST) CMD of MACHO microlens- ground-basedMACHOphotometryareusuallynotsinglestars ing source stars to efficiency weighted CMDs of the average at all, but rather blended composite objects made up of sev- population of the LMC and the Zhao, Graff & Guhathakurta eral fainter stars. Henceforth, we distinguish between these (2000)backgroundpopulation. In §2 we constructa CMD of twowordscarefully,usingobjecttodenoteacollectionofstars theaverageLMCpopulationbycombiningtheCMDsofeight blended into one seeing disk, and star to denote a single star, HSTWideFieldPlanetaryCamera2(WFPC2)fieldscentered resolved in an HST image or through DIA. The characteris- on past MACHO microlensing events in the outer LMC bar. tics of the MACHO object that was lensed tell us little about In§3wedescribetheidentificationofthemicrolensingsource the actual lensed star. However, with the microlensing object stars in these fields by differenceimage analysis(DIA). In §4 centroidfromtheMACHOimageswecanhopetoidentifythe we constructthe backgroundpopulationCMD by shifting the microlensingsourcestarinthecorrespondingHSTframe. HST CMD by the appropriate amount of extinction and dis- AdirectcoordinatetransformationfromtheMACHOframe tance modulus. We then describe the convolutionof the aver- totheHSTframeoftenplacesthebaselineMACHOobjectcen- age and backgroundHST CMDs with the MACHO efficiency troidinthemiddleofaclusteroffaintHSTstarswithnosingle fordetectingamicrolensingeventinasourcestarofgivenmag- starclearlyidentified. Toresolvethisambiguitywehaveused nitude. In§5wedeterminethelikelihoodsthatthemicrolens- DIA.ThistechniqueisdescribedindetailinTomaney&Crotts ingsourcestarsweredrawnfromtheaveragepopulationofthe (1996), butwe review the main pointshere. DIA is an image LMC (Model1) and from a population of backgroundsource subtractiontechniquedesignedtoprovideaccuratephotometry stars (Model 2) by using Kolmogorov-Smirnov (KS) tests to andcentroidsofvariablestarsincrowdedfields. Thebasicidea compare our observed and model distributions. Finally, in §6 is to subtractfromeach programimage a high signal-to-noise we generalize our analysis and consider intermediate models reference image, leaving a differenced image containing only with varying distance moduli and fractions of source stars in thevariablecomponents. Appliedtomicrolensing,wesubtract thebackgroundandLMC.Weconcludeanddiscusstheimpli- baselineimagesfromimagestakenatthepeakofthemicrolens- cationsforthelocationofthelensesin§7. inglightcurve,leavingadifferencedimagecontainingonlythe fluxfromthemicrolensingsourcestarandnottherestoftheob- ject. We also find a centroidshiftbetweenthe baselineimage 2. HSTOBSERVATIONS andthedifferencedimagetowardsthesinglestar thatwasmi- Observationsweremadewith theWFPC2 onHSTbetween crolensed. Ifthecentroidfromthe differencedimageistrans- May 1997 and October 1999 through the F555W (V) and formedtotheHSTframewefindthatitusuallyclearlyidenti- F814W (I) filters. The Planetary Camera (PC) was centered fiestheHSTmicrolensedsourcestar. Thisprocessisillustrated onthelocationofpastMACHOmicrolensingevents. Themi- inFigures2and3. crolensing events, positions, and exposure times are listed in This technique allows us to unambiguously identify 7 of 8 Table1. microlensedsource stars. In the case ofLMC-9 the DIA cen- Multipleexposuresofafieldwerecombinedusingasigma- troid lands perfectly between two stars; fortunately these two clipping algorithm to remove deviant pixels, usually cosmic stars are virtually identicalsub-giantsand the choice between rays. ThePC hasa pixelsize of0.046′′ whicheasily resolves thetwohasnoeffectonourresults.InTable2wepresenttheV the great majority of stars in our frames. Most stars are also magnitudesand(V- I)colorsofoursourcestarsfromtheHST resolvedintheWideField(WF)fieldswhichhaveapixelsize data. Theerrorspresentedherearetheformalphotoncounting of 0.1′′. Instrumental magnitudes were calculated from aper- errorsreturnedbyDAOPHOTII.We estimatethatallWFPC2 turephotometryusingDAOPHOTII(Stetson1987,1991)with magnitudeshaveanadditional0.02- 0.03maguncertaintydue aradiusof0.25′′andcentroidsderivedfrompoint-spreadfunc- toaperturecorrections. InthecaseofLMC-9wetabulateboth tion (PSF) fitting photometry. Aperture corrections to 0.5′′ possibilitiesanduseLMC-9aintheremainderofthiswork. wereperformedindividuallyforeachframe.Wecorrectforthe OuridentificationofLMC-5revealedittobetheratherrare WFPC2chargetransfereffectusingtheequationsfromInstru- caseofasomewhatblendedHSTstar. Althoughtherearetwo ment Science ReportWFPC2 97-08. We also make the mini- stars evident, at an aperture of 0.25′′ the flux of one star was malcorrectionsforcontaminantswhichadheretothecoldCCD contaminated by that of its neighbor. Therefore, in this case, window according to the WFPC2 Instrument Handbook. We weperformPSFfittingphotometryusingPSFskindlyprovided transformourinstrumentalmagnitudesto LandoltV andI us- by Peter Stetson. The errors presented in Table 2 for LMC-5 ingthecalibrationsfromHoltzmanetal.(1995). arethosereturnedbytheprofilefittingroutineALLSTAR.The 4 DIAcentroidfalls2pixelsclosertothecentroidofstaronethan we mustconvolvethe HST CMD with the MACHO detection startwo,clearlypreferringstaroneasthesourcestar. Further- efficiency. TheMACHO efficiencypipelineis extensivelyde- more,aspredictedbyAlcocketal.(1997)andGould,Bahcall, scribedinAlcocketal.(2000a)andAlcocketal.(2000b)and & Flynn (1997), star two is a rather red object which is very thedetectionefficiencyasafunctionofstellarmagnitude,V , star faint in the V band. Fits to the MACHO lightcurvepresented and Einstein ring crossing time has been calculated. We av- in Alcock etal. (2000a)suggestlensedflux fractionsin the V erage this function over the event durations of the candidate andRbandsof1.00and0.46respectively,confirmingtheDIA microlensing events derived using detection criterion A from choiceofthemuchbluerstarasthelensedsourcestar. Alcock et al. (2000a) and present the MACHO detection ef- Since this work specifically addressesthe backgroundlens- ficiency as a function of V in Figure 4. We convolve this star inggeometry,wealsodiscussherethe(remote)possibilitythat functionwithourHSTCMDstoproducethefinalModel1and our HST images of the source stars are actually completely 2distributionsofsourcestars. InFigure5,weshowourmodel blended objects consisting of a faint background source star sourcestarpopulationswiththeobservedmicrolensingsource andabrighterLMClens. Suchaconfigurationwouldseriously starsofTable2overplottedaslargeredstars. skewourCMDdistributionofsourcestarsaswewouldinstead Thisprocedureadmitsseveralassumptions.First,weassume bepresentingphotometryofthelenses.Webeginbynotingthat thatoureightHSTfieldscollectivelywellrepresentthestellar theMACHOefficiencyfordetectionofamicrolensingeventin population of the LMC disk. This assumption has two parts, a star has fallen to zero atV ∼22.5 (see Figure 4 and expla- the first being that an observationat a randomline of sight in nation below). This means that a “faint” background source the LMC bar is dominated by stars in the LMC disk and the starmusthaveV <22.5inordertoproduceadetectableevent. secondthatthestellarpopulationacrosstheLMCisfairlycon- S The the lens in this scenario is assumed to haveV =0.13 and ∆µ=0.3. Since, Holtzman good substitute in two dimensions is the integrated probability in each of fourright-angledquadrantssurroundinga given et al. (1995)calibrate instrumentalWFPC2 magnitudesto the point (Fasano & Franceschini 1987; Peacock 1983). Leaving Landoltsystem,weusetheappropriateLandoltsystemextinc- asidetheexactalgolrithmicdefinition(Pressetal.1992)atwo- tion coefficients of Table 6 in Schlegel, Finkbeiner & Davis dimensional KS test yields a distance statistic D and a corre- (1998)totranslatetheseestimatestoourfilters. Thetotalshifts, sponding P(D) with the same interpretation as in the one di- takingintoaccountbothreddeninganddistancemodulus,are mensionalcase. ∆V =AV+∆µ=0.73, ∆(V- I)=E(V- I)=0.18 (Model2) We use the two-dimensionalKS test to test hypothesis that Thus far we have constructed two CMDs representing the the CMD of observed MACHO microlensing events is drawn distributionofallpossiblesourcestarsdowntoV ∼24. How- fromthesamepopulationaseachofthemodelsourcestardis- ever, not all possible microlensing events are detected in the tributions. We find distance statistics D =0.394±0.005 and 1 MACHO images. To createa CMD representinga population D =0.473±0.009,forModels1 and 2 respectively. Eachof 2 of source stars which produce detectable microlensing events thesedistancestatisticshasa correspondingprobability,P(D), TheLocationoftheSourceStars 5 that if we draw an 8 star samples from the model population withs =1.0containonlysourcestarsdrawnfromtheLMC LMC a larger value than D will result. As explained above, this is disk, all curvesfordifferent∆µ must convergeat s =1.0. LMC equivalenttoexcludingthismodelpopulationastheactualpar- Furthermore, we learn from Figure 6 that the value of ∆µ ent of our observed microlensing source stars at a confidence makeslittledifferenceevenats =0.0. Solongastheback- LMC levelof1.0- P(D). TheseprobabilitiesareP =0.319±0.027 groundpopulationis behindthe LMC and thereforereddened 1 and P = 0.103±0.023. The error quoted for each of these by=0.13itsexactdisplacementisoflittleimport. 2 quantitiesisthescatteraboutthemeanvaluein50simulations Inallcasesasmallervalueof∆µflattensthecurvessomewhat. for each model. Because the creation of the efficiency con- Thisis expectedas a smaller valueof ∆µimpliesoverallless volvedCMDisaweightedrandomdrawfromtheHSTCMD, differencebetween the two extreme modelsat s =0.0 and LMC themodelpopulationcreatedineachsimulationdiffersslightly. s =1.0. ThetwodimensionalKStestoftheCMDdisplays LMC ThisinturnleadstosmalldifferencesintheKSstatistics. ashallowmaximumats ∼0.8. LMC Theseresultstellusthatthese8MACHOeventsareinsuffi- cienttoreliablydistinguishtheMWandselflensinghypothe- 7. DISCUSSION sis. ThebestwecandoistoexcludeModel2atthestatistically marginal90%confidencelevel. We have compared two models for LMC microlensing: source stars drawn from the average population of the LMC andsourcestarsdrawnfromapopulationbehindtheLMC.By 6. INTERMEDIATEMODELS comparingtheCMDofobservedmicrolensingsourcestarstoa Thus far we have considered the possibilities that the ob- CMD representingalldetectable microlensingeventsforeach served MACHO source stars are either all LMC stars or all of these modelswe find by two-dimensionalKS tests that the background stars at a mean distance of ∼7.5 kpc behind the datasuggestthatitismorelikelythatallthesourcestarsarein LMC.However,asdiscussedinZhao(1999),Zhao(2000)and the LMC than that all the source stars are in the background. Zhao,Graff&Guhathakurta(2000)thereissubstantialmiddle However,wecanonlyexludethepossibilitythatallthesource ground. In a complete analysis, we may treat both the frac- starsareinthebackgroundatastatisticallymarginal90%con- tionofsourcestarsdrawnfromthebackgroundpopulationand fidencelevel. thedistancetothebackgroundpopulationasadjustableparam- Wealsoconsideranumberofintermediatemodelsinwhich eters. Whilethesize,locationandcontentoftheLMChasbeen we vary the distance modulus of the background population well constrained by observations, the existence, size and lo- as well as the fraction of stars drawn from average and back- cation of a background population is constrained only by the ground populations. In these models we find that for all dis- fact that it must be small enoughto have evaded directdetec- placements the most highest probability occurs for a fraction tion. The distance to the background population from Zhao, s ∼0.8LMCsourcestarsands =1.0- s =0.2back- LMC BKG LMC Graff&Guhathakurta(2000)isverylooselyderivedbythere- groundsourcestars. Wealsofindthatthevalueofthedistance quirementthatthebackgroundpopulationbeatleasttransiently modulushasverylittleeffectonourresultsatallvaluesofs . LMC gravitationallyboundtotheLMC.However,thereddeningofa Our results are completely consistent with the interpreta- backgroundpopulationisamuchmorephysicallyconstrained tionthatMACHOmicrolensingeventsaredominatedbyMW- number since a population behind the LMC should certainly lensing. In the MW-lensing geometry, the source stars re- sufferfromthemeaninternalextinctionoftheLMC,anumber side in the LMC and the lenses are in the halo or disk of the whichhasbeenwelldeterminedinanumberofstudiesinclud- MW.TheMW-lensinginterpretationformicrolensingrequires ingOestricher&Schmidt-Kaler(1996)andHarris,Zaritsky& thats ∼1.0, consistentwith ourresult. We note that both LMC Thompson (1997). Therefore, all our background population disk+barself-lensingandforegroundself-lensingalsoplaceall models have the same reddening =0.13, as in- theirsourcestarsintheLMC.However,thesecontributionsto ferredfromthemeanextinctionoftheLMCfromHarris,Zarit- thenumberofeventshavebeenshowntobesmallandwene- sky&Thompson(1997)correctedforGalacticforegroundex- glecttheircontributionhere. Wealsonotethatthecontribution tinction. from the known stellar populationsof the MW is expected to We define s to be the fractionof the source stars drawn besmall(∼1eventsofthe13-eventcutAsampleofAlcocket LMC from the LMC disk+bar population, leaving a fraction 1.0- al.(2000a)butnotentirelynegligible. Alenspopulationinthe s sourcestarsdrawnfromthe backgroundpopulation,and MW is likely to be dominated by MACHOs in the MW halo LMC ∆µtobetheexcessdistancemodulusofthebackgroundpopu- andnotfaintstarsintheMWdiskorspheroid. lation. We consider values ∆µ=0.0,0.30,0.45 and for each Zhao(1999),Zhao(2000)andZhao,Graff&Guhathakurta value of the distance modulus we consider the full range of (2000)proposeamodelforLMCmicrolensinginwhichallthe s from0.0to1.0.Forexample,amodelwith∆µ=0.45and sourcestarsaredrawnfromsomebackgroundpopulationtothe LMC s =0.5containsamixtureofsourcestarsinwhichhalfthe LMC.SuchamodelsuggeststhatLMCmicrolensingisdomi- LMC source stars are drawn from the population of the LMC disk, natedbybackgroundself-lensingandthats ∼0.0. Wefind LMC and half the source stars are drawn from a backgroundpopu- thisarrangementtobethemodelexcludedatthehighestconfi- lation displaced from the LMC by ∼11kpc and reddened by dence;however,wecannotruleitoutwithanygreatstatistical =0.13. Allmodelswiths =0.0containonly weight. LMC sourcestarsdrawnfromaspecifiedbackgroundpopulation,and Recently,Weinberg(2000)andEvans&Kerins(2000)have all modelswith s =1.0 are identical, containingonlystars suggested a model of LMC microlensing in which all mi- LMC drawnfromtheLMCdisk. crolensing events are due to a non-virialized shroud of stars WepresenttheresultsinFigure6,showingtheKStestprob- which surrounds the LMC. In shroud self-lensing there are abilities as a function of s for each of our values of ∆µ. four event geometries: a) backgroundshroud source and disk LMC Again,theerrorbarsreflectthescatteraboutthemeanforfifty lens,b)disksourceandforegroundshroudlens,c)disksource simultations of each model. We note that since all models anddisklensandd)backgroundshroudsourceandforeground 6 shroud lens. We might naively expect the former two types At present, the strength of this analysis is severely limited dominate the numberof expectedeventsand so if we were to by the numberof microlensingeventsfor which we havecor- ignorethecontributionfromthelattertwotypeswewouldcon- respondingHSTdata. AfortuitousdistributionintheCMDof cludethatshroudlensingwouldimplys ∼0.5.However,in all13criterionAeventspresentedinAlcocketal.(2000a)may LMC order to producethe entire observedopticaldepth, the shroud allowustodefinitivelyexcludeamodelinwhichallthesource mustbesomassivethatitisnolongerself-consistenttoignore starsaredrawnfromthebackgroundpopulation. Itisdifficult the latter terms. Calculations performed in the formalism of toestimatehowmanyeventsareneededtodefinitelydetermine Gyuk, Dalal, & Griest (2000)suggestinsteadthateventswith s asthenumberdependsonthetruevalueofs aswell LMC LMC a backgroundshroudsourceanda foregroundshroudlensbe- thedegreeofaccuracyonewishestoachieve. However,when comeanimportantcontributorandreducetheexpectedfraction we perform Monte Carlo simulations where we draw a sam- ofsourcestarsintheLMCtos ∼0.3- 0.4. Ourresultsare pleofNeventsfromthedistributionwiths =0.0andcom- LMC LMC notinconsistentwithsuchamodel,howeverwenotethatthere pareitwiththe2-DKStesttothedistributionwiths =1.0 LMC is a profoundlack of observationalevidencefor such a stellar wefindthatforN ∼20- 25,P<0.01foratleast99%ofour shroud. simulations. Thisimpliesthatifthetruevalueofs isnear LMC Furthermore, if we assume that a substantial LMC stellar either extreme (s ∼0 or s ∼1) then a CMD of 20-25 LMC LMC halo or shroud is not a realistic possibility, then we may di- events virtually guarantees that we will be able to exclude a rectly relate the fraction of source stars in the LMC, s , to modelatthe otherextremeatthe 99%confidencelevel. Even LMC thefractionofmicrolensingeventswhichareMW-lensing, f moreeventsarenecessarytoexcludeintermediatemodelswith MW in the followingway. All eventsin whichthe source stars are variousfractionsof LMCand backgroundstars. Ongoingmi- locatedinthebackgroundare,bydefinition,backgroundlens- crolensingsearchprojects(EROS,OGLEII)maysupplyasuf- ing events. Therefore, s = f , where f indicates the ficient sample of events in the next few years. The technique BKG BKG BKG fractionofobservedeventswhicharebackgroundlensing.The outlined in this paper should provea powerfulmethod for lo- totalfractionoflensingeventsduetohalo-lensing f , LMC catingthelenseswiththesefuturedatasets. MW self-lensing, f ,andbackgroundself-lensing, f ,mustbe LMC BKG equaltounity. f +f +f =1.0 (1) SupportforthispublicationwasprovidedbyNASAthrough MW LMC BKG proposalnumbersGO-5901andGO-7306andfromtheSpace Thismayberearrangedtoread Telescope Science Institute, which is operated by the Associ- f =1.0- f - f =s - f (2) MW BKG LMC LMC LMC ationofUniversitiesforResearchinAstronomy,underNASA Equation (2) is strictly true even if we allow for LMC shroud contractNAS5-26555. WorkperformedatLLNLissupported lensing. However, if we ignore the possibility of LMC self- bytheDOEundercontractW7405-ENG-48. Workperformed lensing by a non-virialized stellar shroud, then all models bytheCenterforParticleAstrophysicspersonnelissupported withreasonableparametersfortheLMCfindthat f .0.2. LMC inpartbytheOfficeofScienceandTechnologyCentersofNSF Therefore,ifs ∼1,wemaymaketheapproximation LMC under cooperative agreement AST-8809616. DM is also sup- fMW∼sLMC (3) portedbyFondecyt1990440. CWS thanksthe PackardFoun- Thereforewe estimate, with low statistical significancedueto dationforthegeneroussupport.WJSissupportedbyaPPARC thesmallsamplesizeofoursample,thatafraction f ∼0.8 Advanced Fellowship. CAN is supported in part by a NPSC MW of observedmicrolensingeventsare halo-lensing. We empha- Graduate Fellowship. TV and KG were supported in part by sizeonceagainthatthisconclusionignoresthepossibilityofa theDOEundergrandDEF0390-ER40546. TVwassupported non-virializedLMCshroud. inpartbyanIGPPgrant. APPENDIX REFERENCES Alcock,C.,etal.1997,ApJ,486,697 Oestricher,M.O.,&Schmidt-Kaler,T.1996,A&AS,117,303 Alcock,C.,etal.2000a,ApJ,542,281 Kinman,T.D.,etal.1991,PASP,103,1279 Alcock,C.,etal.2000b,ApJ,inpress,astro-ph/0003236 Olsen,K.A.G.,1999,AJ,117,2244 Alves,D.R.2000,in“GalaxyDisksandDiskGalaxies,”eds.S.Funes&E. 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Bennett,D.P.1998,ApJ,493,L79 Press) Evans,N.W.&Kerins,E.2000,ApJ,529,917 Sahu,K.S.1994,Nature,370,275 Fasano,G.,&Franceschini,A.1987,MNRAS,225,155 Schlegel,D.J.,Finkbeiner,D.P.,&Davis,M.1998,ApJ,500,525 Geha,M.,etal.1998,AJ,115,1045 Stetson,P.B.1987,PASP,99,191 Gould,A.1995,ApJ,441,77 Stetson,P.B.1991,DataAnalysisWorkshopIII(Garching:ESO),187 Gould,A.1998,ApJ,499,728 Tomaney,A.B.,&Crotts,A.P.S.1996,AJ,112,2872 Gould,A.,Bahcall,J.N.,&Flynn,C.1997,ApJ,482,913 Weinberg,M.2000,ApJ,532,922 Graff,D.S.,Gould,A.P.,Suntzeff,N.B.,Schommer,R.A.,&Hardy,E.2000, Wu,X.1994,ApJ,435,66 ApJ,540,211 Zaritsky,D.,&Lin,D.N.C.1997,AJ,114,2546 Gyuk,G.,Dalal,N.,&Griest,K.2000,ApJ,535,90 Zhao,H.1999,ApJ,527,167 Harris,J.,Zaritsky,D.,&Thompson,I.1997,AJ,114,1933 Zhao,H.2000,ApJ,530,299 Holtzman,J.A.,Burrows,C.J.,Casertano,S.,Hester,J.J.,Trauger,J.T., Zhao,H.,Graff,D.S.,&Guhathakurta,P.2000,ApJ,532,L37 Watson,A.M.,&Worthey,G.1995,PASP,107,1065 TheLocationoftheSourceStars 7 FIG.1.—ThecompositeHSTCMDcreatedbycombiningthephotometryfrom8WFPC2fieldscenteredonobservedMACHOmicrolensingevents. [f1.ps] FIG.2.—Theleftpanelshowsa0.6’X0.6’sectionofthebaselineimageofMACHOeventLMC-4.Themiddlepanelshowsthesameregiontakenatthepeak ofthemicrolensingevent.Therightpanelshowsthedifferencedimage.Thefluxatthelefthandsideofthedifferencedimageisduetoanasymptoticgiantbranch variablestaratthatlocation. [f2.ps] 8 HST Centroid MACHO Centroid DIA Centroid FIG.3.—A3”X3”HSTimageofLMC-4.ThecirclecontainstheseveralHSTstarswhichareallcontainedwithintheMACHOseeingdiskofthelensedobject. ThearrowsindicatetheMACHObaselinecentroid,theDIAcentroidandtheHSTcentroid. [f3.ps] 0.5 0.4 0.3 0.2 0.1 0 16 18 20 22 24 FIG.4.—TheMACHOdetectionefficiencyasafunctionofstellarV-magnitude.Thatis,ifamicrolensingeventoccursinastarofgivenmagnitudeVstar,thisis thegivenefficiencyfordetectingthatevent. [f4.ps] TheLocationoftheSourceStars 9 16 Model 1 Model 2 18 20 22 24 26 0 0.5 1 1.5 0 0.5 1 1.5 V-I FIG. 5.—Themodelsourcestarpopulations. Model1representsasourcestarpopulationinthediskoftheLMC,Model2representsasourcestarpopulation behindtheLMC.TheMACHOmicrolensingeventsofTable2areoverplottedinred. Weperform2-DKSteststodeterminetheprobabilitythatthemicrolensing events aredrawnfromeach modelsourcestarpopulations. Wefindprobabilities P1=0.319±0.027andP2=0.103±0.023that themicrolensing events are consistentwiththesourcestarpopulationsofModels1and2,respectively. [f5.ps] 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 FIG. 6.—TheKStestprobabilities,P,forvariousvaluesofthefractionofsourcestarsintheLMC,sLMC,andthedisplacementofthebackgroundpopulation, ∆µ. Weshowtheresultsfor∆µ=0.45,0.30,0.0inbluecircles,redtrianglesandgreensquares,respectively. Theerrorbarsindicatethescatteraroundthemean valueof50simulationsdoneforeachmodel. [f6.ps] 10 TABLE1 SUMMARYOFOBSERVATIONS Event RA DEC VExposureTimes IExposureTimes ObsDate LMC-1 05:14:44.50 -68:48:00.00 4X400s 40X500s 1997-12-16 LMC-4 05:17:14.60 -70:46:59.00 4X400s 2X500s 1998-08-19 LMC-5 05:16:41.10 -70:29:18.00 4X400s 2X500s 1999-05-13 LMC-6 05:26:14.00 -70:21:15.00 4X400s 2X500s 1999-08-26 LMC-7 05:04:03.40 -69:33:19.00 4X400s 2X500s 1999-04-12 LMC-8 05:25:09.40 -69:47:54.00 4X400s 2X500s 1999-03-12 LMC-9 05:20:20.30 -69:15:12.00 4X400s 2X500s 1999-04-13 LMC-14 05:34:44.40 -70:25:07.00 4X500s 4X500s 1997-05-13 TABLE2 PHOTOMETRYOFMICROLENSINGSOURCESTARS Event V V- I LMC-1 19.782±0.003 1.167±0.004 LMC-4 21.331±0.008 0.502±0.009 LMC-5 21.016±0.096 0.677±0.122 LMC-6 20.041±0.004 0.471±0.007 LMC-7 21.993±0.013 0.672±0.022 LMC-8 20.195±0.004 0.203±0.009 LMC-9a 21.137±0.007 0.991±0.011 LMC-9b 21.250±0.008 1.002±0.012 LMC-14 19.467±0.002 0.106±0.004

The MACHO Project Hubble Space Telescope Follow-Up: Preliminary Results on the Location of the Large Magellanic Cloud Microlensing Source Stars

Similar The MACHO Project Hubble Space Telescope Follow-Up: Preliminary Results on the Location of the Large Magellanic Cloud Microlensing Source Stars