Table Of ContentDRAFTVERSIONFEBRUARY1,2008
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 <E(B- V)>=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, [email protected]
0
2
/
h CenterforParticleAstrophysics,UniversityofCalifornia,Berkeley,CA94720
3
p
SupercomputingFacility,AustralianNationalUniversity,Canberra,ACT0200,Australia
-
o Email:[email protected]
r 4
t SpaceTelescopeScienceInstitute,3700SanMartinDr.,Baltimore,MD21218
s
Email:[email protected]
a
5
:
v ResearchSchoolofAstronomyandAstrophysics,Canberra,WestonCreek,ACT2611,Australia
i Email:tsa, kcf, [email protected]
X 6
BellLaboratories,LucentTechnologies,600MountainAvenue,MurrayHill,NJ07974
r
a Email:[email protected]
7
DepartmentofPhysics,UniversityofNotreDame,IN46556
Email:[email protected]
8
DepartmentofPhysics,UniversityofCalifornia,SanDiego,CA92039
Email:[email protected], [email protected], [email protected]
9
DepartmentofAstronomyandAstrophysics,UniversityofCalifornia,SantaCruz95064
Email:[email protected]
10
DepartmentofPhysics,UniversityofSheffield,SheffieldS37RH,UK
Email:[email protected]
11
Depto.deAstronomia,P.UniversidadCatolica,Casilla104,Santiago22,Chile
Email:[email protected]
12
DepartmentofPhysics,UniversityofCalifornia,Berkeley,CA94720
13
EuropeanSouthernObservatory,KarlSchwarzchildStr.2,D-85748GärchingbelMünchen,Germany
Email:[email protected]
14
DepartmentsofAstronomyandPhysics,UniversityofWashington,Seattle,WA98195
Email:[email protected]
15
DepartmentofPhysics,UniversityofOxford,OxfordOX13RH,U.K.
Email:[email protected]
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 <E(B- V)>=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 <V . We stant. Thefirstpartholdssolongasthesurfacedensityofthe
L S
estimate that we would notrecognizea blendedobjectof two backgroundpopulationis much smaller than that of the LMC
starswithV <22.5assuchifthecentroidscoincidedtowithin itself.Ifthiswerenotthecase,thispopulationwouldhavebeen
1.5pixels. InourmostcrowdedPCfield wefind∼1000stars directlydetected.Thesecondparthasbeenconfirmedbymany
with V <22.5 spread over an area of 720 X 720 pixels. In LMCpopulationstudiesincludingAlcocketal.(2000b),Olsen
simulations, we draw 1000 stars with V <22.5 weighted ac- (1999), and Geha et al. (1998), as well as our own compari-
cording to our luminosity function and spread randomly over sonofindividualCMDsandluminosityfunctions. Second,we
720X720 pixels. For each star we then check to see if it is assume that the underlying stellar content of the background
foundwithin1.5pixelofabrighterstar. Wefindthatonaver- populationisidenticaltothatoftheLMC.
age,therewillbe5starsofV <22.5whichareblendedwitha
brighterstar. Therefore,forourmostcrowdedfield,thechance
5. THELOCATIONOF THESOURCE STARS
thatoursourcestar isan unrecognizedblendofa faintsource
star and a brighter lens is about 5 in a thousand. In a more We now attempt to determine whether the CMD of mi-
typically crowdedfield, this falls to around1 chance in 1000. crolensed source stars is consistent with the average popula-
Therefore,itisextremelyunlikelythatanyofour8HSTsource tion of the LMC (Model 1) or whether it is more consistent
starsareblendedobjectscomposedofafaintsourcestaranda withabackgroundpopulation(Model2)byperformingatwo-
brightlens. dimensionalKolmogorov-Smirnov(KS)test.
Inthe familiaronedimensionalcase, a KStest oftwo sam-
4. CREATION OF THEMODELSOURCE STARPOPULATIONS pleswithnumberofpointsN1andN2returnsadistancestatistic
D,definedtobethemaximumdistancebetweenthecumulative
If the microlensing events are due to MW lenses, then one
probability functions at any ordinate. Associated with D is a
wouldexpectthedistributionofobservedmicrolensingsource
correspondingprobabilityP(D)thatif tworandomsamplesof
starstoberandomlydrawnfromtheaveragepopulationofthe
size N and N are drawn from the same distribution a worse
LMC corrected only for the MACHO detection efficiency for 1 2
valueofDwillresult. Thisisequivalenttosayingthatwecan
starsofagivenmagnitude(Model1). Weassumethatthepop-
excludethehypothesisthatthetwosamplesaredrawnfromthe
ulationoftheLMCiswellrepresentedbyourcompositeHST
samedistributionataconfidencelevelof1.0- P(D).IfN ≫N
CMD to V .24. If the microlensing events are background 2 1
then this is also equivalentto excludingat a 1.0- P(D) confi-
self-lensingeventsweexpectthesourcestarstobedrawnfrom
dencelevelthehypothesisthatsample1isdrawnfromsample
a background population which suffers from the internal ex-
2.
tinction of the LMC (Model 2). To represent such a back-
The concept of a cumulative distribution is not defined in
ground populationwe shift the composite HST CMD accord-
more than one dimension. However, it has been shown that a
ing to the amountssuggested by Zhao, Graff & Guhathakurta
(2000), <E(B- V)>=0.13 and ∆µ=0.3. Since, Holtzman good substitute in two dimensions is the integrated probabil-
ity 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<E(B- V)>=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 <E(B- V)>=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
<E(B- V)>=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
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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
