Color-Shift Measurement in Microlensing-Induced Stellar Variation from Future Space-Based Surveys

0.15 MB·English

by  Byeong-Gon Park

SUBMITTEDTOTHEASTROPHYSICALJOURNAL
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
COLOR-SHIFTMEASUREMENTINMICROLENSING-INDUCEDSTELLARVARIATIONFROMFUTURE
SPACE-BASEDSURVEYS
BYEONG-GONPARK
KoreaAstronomyandSpaceScienceInstitute,838Daedeok-Rho,Yuseong-Gu,Daejeon305-348,Korea;
[email protected]
AND
CHEONGHOHAN∗
ProgramofBrainKorea21,AstrophysicalResearchCenterfortheStructureandEvolutionoftheCosmos,SRC,
DepartmentofPhysics,ChungbukNationalUniversity,Chongju361-763,Korea;
8 [email protected]
0 SubmittedtoTheAstrophysicalJournal
0
2 ABSTRACT

n Ifamicrolensingeventiscausedbyastar,theeventcanexhibitchangeincolorduetothelightfromthelens.
a Inthepreviousandcurrentlensingsurveys,thecolorshiftcouldnotbeusedtoconstrainthelenspopulation
J becausetheblendedlightresponsibleforthecolorshiftismostlyattributedtonearbybackgroundstarsrather

1 thanthelens. However,eventstobeobservedinfuturespace-basedsurveysdonotsufferfromblendingand
3 thus the color information can be used to constrain lenses. In this paper, we demonstrate the usefulness of
future surveys in measuring color shifts. By conducting simulation of galactic lensing events based on the

] specificationofaproposedspace-basedlensingsurvey,weestimatethattheshiftinthecolorofR- H willbe
h
measuredat5σ levelfor∼12%ofeventsthatoccuron sourcestars with apparentmagnitudesbrighterthan
p
J=22.5.Color-shiftedeventstendtohavehighmagnificationsandthelenseswillhavebrightnessesequivalent
-
o tothoseofsourcestars. Thetimescalesofthecolor-shiftedeventstendtobelongerthanthosewithoutcolor
r shifts. Fromthemassdistributionoflenses,wefindthatmostofthecolor-shiftedeventswillbeproducedby
t
s stellarlenseswithspectraltypesdowntomidM-typemainsequencestars.
a
Subjectheadings:gravitationallensing
[

1
v 1. INTRODUCTION color-shiftedeventswould be higherin the space-basedsur-
5 Oneimportantcharacteristicofamicrolensingeventisthat veybecauseitwillmonitormuchfainterstarsthancurrentsur-
2 the colorof the lensed star doesnot changeduringthe lens- veys. Asthemonitoredstarbecomesfainter,therelativeflux
8 of the lens to the source star increases and thus the event is
ing magnification. However, eventsobserved in actual lens-
4 morelikelytoproducelargecolorshift.Third,withhighpho-
ing surveys can exhibit color shift. This color shift occurs
. tometricprecision,the surveycandetectmuchsmallercolor
1 whenthefluxfromthelensedsourcestarisblendedwiththe
shiftthanground-basedsurveys. Withtheincreasedfraction
0 flux from other stars located in the seeing disk of the star.
8 Thelensedandblendedstarsgenerallyhavedifferentcolors. of large color-shifted events and higher sensitivity to small
0 Then, color shift occurs as the source/blend relative bright- color shift combined with nearly an order higher event rate,
: thefuturespace-basedlensingsurveywouldbeabletodetect
v nesschangesduringlensingmagnification.
colorshiftsforalargenumberofevents.
i Kamionkowski(1995) and Buchalteretal. (1996) pointed
X In this paper, we demonstrate the usefulness of future
outthatiftheobjectresponsiblefora lensingeventisastar,
space-basedlensingsurveysinmeasuringcolorshiftsoflens-
r it is possible to obtain information about the lens from the
a ing events. For this, we estimate the fraction of eventswith
measuredcolorshift. However,thisideacouldnotbeimple-
measurablecolorshiftsamongtheeventstobedetectedfrom
mented for the actual analysis of lens population. The most
theproposedMPFsurvey. Wealsoinvestigatetheproperties
importantreasonforthisisthatunderthepreviousandcurrent
ofthecolor-shiftedeventsbyconductingdetailedsimulation
lensingsurveysconductedbyusingground-basedtelescopes,
ofgalacticlensingeventsunderrealisticobservationalcondi-
the blended flux is mostly attributed to nearby background
tions. Thefractionofcolor-shiftedeventswaspreviouslyes-
starsratherthanthelens.
timatedbyBuchalteretal. (1996). However,their workwas
However, the situation will be different in future space-
intended as a template for general comparison with various
basedlensingsurveys,suchastheMicrolensingPlanetFinder
observationalassumptions and thus is not focused on a spe-
(MPF). The MPF is a proposed space mission to NASA’s
cific survey. In addition, they did not provide information
DiscoveryProgramexclusiveformicrolensinganditwillbe
aboutthepropertiesofcolor-shiftedevents.
equipped with a 1.1 m aperture telescope (Bennett&Rhie
Thepaperisorganizedasfollows.In§2,weintroducefor-
2002;Bennettetal.2004).Suchasurveyisidealforthemea-
malism used for the description of the color shift in general
surementofthecolorshiftinlensingeventsduetothefollow-
cases and under various limiting cases. In § 3, we describe
ingreasons.First,thankstothehighresolutionprovidedfrom
the simulation conducted to estimate the fraction of color-
space observation, the survey does not suffer from blending
shifteventsandtheirproperties.In§4,wepresenttheresult-
caused by background stars. Then, one can safely attribute
ingdistributionofcolorshift. Weprobethepropertiesofthe
the observed color shift to the lens. Second, the fraction of
color-shiftedeventsby investigatingthe distributionsof var-
∗correspondingauthor iousquantitiesrelatedtotheeventsincludingthe sourceand
2 MICROLENINGCOLORSHIFT
lensbrightness,lenslightfraction,magnification,lensmass, 3. SIMULATION
andeventtimescale. In§5,wesummarizeandconclude.
We estimate the color-shift distribution of events ex-
2. FORMALISM pectedfromfuturespace-basedlensingsurveysbyconduction
Bayesiansimulationofgalacticmicrolensingeventsunderthe
Thedifferencebetweenthe colorsof a lensingeventmea-
observationalconditionsoftheMPFsurvey. Forthissimula-
suredduringandbeforelensingmagnificationisexpressedas
tion,itisrequiredtomodelofthephysicalparametersinclud-
F /F
∆(R- H)=- 2.5log R H , (1) ingthemassdensityandvelocitydistributionsofmatteralong
(cid:18)FR,0/FH,0(cid:19) thelineofsighttowardthefield, lensmassfunction,andlu-
where F represents the observed flux, the subscript ‘0’ de- minosityfunctionofsourcestarsandlenses. Weconductthe
notes the measured quantity without lensing magnification, simulationaccordingtothefollowingprocedure.
andtheothersubscriptsk=RandHdenotetheobservedpass- Thesurveyisassumedtobeconductedtowardthegalactic
bands.1 The ratio between the observed fluxes measured in bulgefieldandthelocationsofthesourceandlensalongthe
theindividualpassbandsare line of sight are allocated based on the spatial mass density
F AF +F F F +F distribution. Followingthe specification of the MPF survey,
FR = AFR,S+FR,L, FR,0 = FR,S+FR,L, (2) wesetthecenterofthesurveyfieldat(l,b)=(1◦.2,- 2◦.4).The
H H,S H,L H,0 H,S H,L spatialmassdensitydistributionismodeledbyadoptingthat
where F and F representthe fluxesfrom the source star
k,S k,L ofHan&Gould(2003). Inthemodel,thedensitydistribution
and lens, respectively. With some algebra, the color shift is
ofbulgematterisbasedonthedeprojectedinfraredlightden-
representedas
sityprofileofDweketal.(1995),specificallymodelG2with
∆(R- H)=- 2.5log (A+ηR)/(A+ηH) , (3) Rmax=5kpcfromtheirTable2. Thediskdensitydistribution
(1+η )/(1+η ) ismodeledbyadouble-exponentialdisk,i.e.
(cid:20) R H (cid:21)
where ηk denotes the ratio between the fluxes from the lens R- R |z|
andsource,i.e. ρ(R,z)=ρ exp - 0+ , (9)
0
h h
η = FR,L, η = FH,L. (4) (cid:20) (cid:18) R z(cid:19)(cid:21)
R H
FR,S FH,S where (R,z) are the galactocentric cylindrical coordinates,
The sign of the color shift is such that it becomes negative R0 =8 kpc is the distance of the Sun from the galactic cen-
when the apparentsource star becomesbluer duringlensing ter,ρ0=0.06M⊙ pc- 3 isthelocalmassdensity,andhR=3.5
magnificationandviceversa. kpcandhz=325pcare theradialandverticalscale heights,
Inthelimitingcaseofaverylowmagnification(A→1.0), respectively.
theamountofthecolorshiftisapproximatedas Once the locations of the lens and source star are set, we
η - η thenassigntheirvelocitiesbasedonthevelocitydistribution
∆(R- H)∼- 2.5log 1- ǫ R H , (5) model. Themodelvelocitydistributionhasa gaussianform.
(1+η )(1+η )
(cid:20) R H (cid:21) The mean and dispersion of the bulge velocity distribution
where ǫ = A- 1.0. As A → 1.0, ǫ → 0, and thus ∆(R- are deduced from the tensor virial theorem. The disk ve-
H)→0, implying that the color shift expected from a low- locitydistributionisassumedtohaveaflatrotationspeedof
magnificationeventissmall. v =220kms- 1 andvelocitydispersionsalongandnormalto
c
In the opposite limiting case of a very high-magnification thediskplaneofσ =30kms- 1 andσ =20kms- 1,respec-
k ⊥
event (A ≫ 1.0), the numerator on the right side of equa- tively.Theresultingdistributionofthelens-sourcetransverse
tion(3) become(A+ηR)/(A+ηH)→1, andthe colorshiftis velocity from the combinationsof the bulge and disk veloc-
approximatedas ities is listed in Table 1 of Han&Gould (1995), specifically
1+η thenon-rotatingbarredbulgemodel.
∆(R- H)∼2.5log R . (6)
1+η Weassignthesourcestarbrightnessbyusingtheluminosity
(cid:18) H(cid:19) functionofHoltzmanetal.(1998). TheHoltzmanluminosity
Ifthelensisveryfaint(i.e.,η ≪1.0),equation(6)isfurther
k function is expressed in terms ofV band. Once theV-band
simplifiedas
absolutemagnitudeofeachstaris chosenfromthe luminos-
∆(R- H)∼2.5log[1+(η - η )]. (7)
R H ity function, we determine the R and H band magnitude by
Consideringthatthelens/sourcefluxratioissmall,ηR- ηH ≪ usingthecolorinformationlistedinCox(1999). Theappar-
1.0 and thus the expectedcolor shift is also small. This im- entmagnitudesarethendeterminedconsideringthedistance
plies that high magnification is not a sufficient condition to tothesourcestarandextinction.Theextinctionisdetermined
produce noticeable color shift. To produce noticeable color suchthatthesourcestarfluxdecreasesexponentiallywiththe
shift,itisadditionallyrequiredthatthelensshouldbebright. increaseofthedustcolumndensity.Thedustcolumndensity
Inthelimitingcasewherethelensdominatesoverthesource is computed on the basis of an exponentialdust distribution
starinbrightness(i.e.,ηk≫1.0),thecolorshiftisrepresented modelwith a scale heightof hz=100pc, i.e. ∝exp(- |z|/hz)
as (Drimmel&Spergel2001). We set the normalizationof the
∆(R- H)∼2.5log ηR ≡(R- H) - (R- H) , (8) extinctionintheindividualpassbandssuchthatAR=1.8and
where (R- H) and (R- H(cid:18))ηHr(cid:19)epresenttheScolorsofLthe lens AtaHrg=et0fi.8elfdo.rastarlocatedatadistanceDS=8kpctowardthe
L S Themassofthelensisassignedbasedonthemassfunction
andsource,respectively.Thisimpliesthatthecolorshiftcor-
ofGould(2000).Themodelmassfunctioniscomposedofnot
respondstothedifferencebetweenthecolorsofthelensand
onlystars but also browndwarfs(BDs) and stellar remnants
source.Underthiscondition,thecolorshiftismaximized.
ofwhitedwarfs(WDs),neutronstars(NSs),andblackholes
1WechooseRandHpassbandsbecausetheMPFsurveyplanstoobserve (BHs). The model is constructed under the assumption that
inthesebands.Seedetailsin§4. bulgestarsformedinitiallyaccordingtoa doublepower-law
PARK&HAN 3
distributionoftheform widepassbandspanningthefull600–1700nmrangeandthe
dN M γ othertwonarrowbandsateachendoftherange(Bennettetal.
=k , (10) 2004).Theverywidefilterhasnoequivalenceinstandardfil-
dM 0.7M
(cid:18) ⊙(cid:19) ter,butweassumeitcorrespondstoJ filterbecausethecen-
whereγ=- 2.0forM≥0.7M andγ=- 1.3forM<0.7M . tral wavelengthmatchesthat of the J filter. The two narrow
⊙ ⊙
TheseslopesareconsistentwithZoccallietal.(2000)except filters are approximatedby the R and H filters. The observ-
thattheprofileisextendedbelowtheirlowerlimitof0.15M ing strategy for MPF is to do most of the observationswith
⊙
down to a BD cutoff of M=0.03 M . Based on this initial theverywidefilterandasmallnumberofobservationsinthe
⊙
mass function, remnants are modeled by assuming that the RandH filters. We choosecolorismeasuredonthe images
stars with initial masses 1 M <M <8 M , 8 M <M < takeninRandH filtersbecauselargercolorshiftisexpected
⊙ ⊙ ⊙
40M ,andM>40M haveevolvedintoWDs(withamean asthewavelengthgapbetweenthefiltersbecomeswider. We
mass⊙hMi∼0.6M ),⊙NSs(withhMi∼1.35M ), andBHs assume that MPF can detect 14.3 and 5.0 photons s- 1 for a
⊙ ⊙
(with hMi∼5 M ), respectively. Then, the resulting mass 22magnitudestarintheRandH bands,respectively(Bessel
⊙
fractions of the individual lens populations are stars: BD : 1979;Campinsetal.1985).
WD:NS:BH=62:7:22:6:3. Oncethemassofthelensis Fortheindividualevents,wecalculatethemaximumcolor
set,itsbrightnessesinRandHbandsaredeterminedbyusing shift by using equation (3). The MPF plans to take images
the mass-M relation and the colorinformationpresentedin with 100 sec exposure at a 2 min interval and combine the
V
Cox(1999).WenotethatBDandremnantlensesaredarkand imagestomakea10minexposureimage,resultinginadata
thuseventscausedbythemdonotproducecolorshift. acquisitionrateof∼3–5imageshr- 1or∼100imagesday- 1.
With all the assigned physical parameters of the lens and If20%oftheobservationsaredoneinthenarrowfilters,each
source, we then produce lensing events. We do this under of the R and H-band image is obtained every 2.4 hrs. This
theassumptionthattheimpactparametersofthelens-source rateisfrequentenoughtocoverthepeakofnearlyalllensing
encounterare randomlydistributed. Sincethe lensfluxdoes eventsduringwhichthecolorshiftismaximized.Weassume
notparticipateinlensingmagnification,itlowerstheapparent thatcolorshiftisdetectableonlyifthecolorshiftmeasuredat
magnificationoftheevent,i.e. thepeakoftheeventisfivetimesgreaterthantheuncertainty
AF +F u +2 inthecolor-shiftmeasurement,i.e.5σdetection.
A = S L; A= 0 , (11) We determine the uncertainty of the color shift measure-
app F +F u (u +4)1/2
S L 0 0 ment as follows. Let us define R as the ratio between the
F
whereu istheimpactparameterofthelens-sourceencounter fluxratiosofaneventmeasuredintwopassbandsduringand
0
normalizedbytheEinsteinradiusofthelens. We definede- beforelensing,i.e.,
tectable events as those with apparentmagnificationshigher
F /F
thanathresholdvalueofAth=3/51/2,thatcorrespondstothe RF = R H . (14)
F /F
magnification when the source star just enters the Einstein R,0 H,0
ring of the lens, i.e. u =1.0. The apparent magnification
0 Accordingtothestandarderroranalysis,thefractionaluncer-
varies dependingon the observedpassband. We use the ap-
taintyinthemeasurementofRisestimatedas
parentmagnificationmeasured in J band as the criterion for
eovbesnertvdaettieocnta(bseileitybebleocwa)u.seWietiasstshuemmeatihnaptatshsebraenidsonfothbeleMndPeFd σRF ≃ σFR/FH 2+ σFR,0/FH,0 2 1/2, (15)
flux other than the flux from the lens. We restrict that the RF "(cid:18)FR/FH(cid:19) (cid:18)FR,0/FH,0(cid:19) #
surveymonitorsstarswithapparentmagnitudesbrighterthan
J =22.5, which correspondsto early M-type main-sequence wheretheindividualtermsontherightsideare
stars.
σ 2 σ 2 σ 2
Onceeventsareproduced,therateoftheindividualevents FR/FH ≃ FR + FH , (16)
areweightedbythefactor F /F F F
(cid:18) R H(cid:19) (cid:18) R (cid:19) (cid:18) H (cid:19)
Γ∝ρ(D )D2ρ(D )r v, (12) and
S S L E
σ 2 σ 2 σ 2
whereρ(D)isthematterdensity,DL andDSarethedistances FR,0/FH,0 ≃ FR,0 + FH,0 . (17)
tothelensandsource,respectively,thefactorD2S isincluded (cid:18)FR,0/FH,0(cid:19) (cid:18)FR,0(cid:19) (cid:18)FH,0(cid:19)
toaccountfortheincreaseofthenumberofsourcestarswith
Under the assumption that the photometry is photon domi-
theincreaseofdistance,r istheEinsteinradiuswhichcorre-
E nated, i.e. σ =F1/2, equations (16) and (17) are approxi-
spondstothecross-sectionofthelens-sourceencounter,and F
matedas
v is the lens-source transverse speed. The Einstein radius is
relatedtothephysicalparametersofthelensandsourceby σ 2 1 1 F +F
FR/FH ∼ + = R H, (18)
r = 4GMDL(DS- DL) 1/2. (13) (cid:18)FR/FH(cid:19) FR FH FRFh
E (cid:20) c2 DS (cid:21) and
From the simulation, we find that 66% and 34%of the total σFR,0/Fh,0 2∼ 1 + 1 = FR,0+FH,0. (19)
eventsarecausedbythelenseslocatedinthebulgeanddisk, F /F F F F F
respectively. Wealsofindthateventscausedbystellarlenses (cid:18) R,0 H,0(cid:19) R,0 H,0 R,0 H,0
comprise48%andothersare producedbydarklenscompo- Then,fromequation(15),(18),and(19),onefinds
nents.
TheMPFsurveyplanstoobserveinthewavelengthrange σRF ≃ FR+FH +FR,0+FH,0 1/2. (20)
∼600–1700nminthreepassbands. Theseconsistofavery R F F F F
F (cid:18) R H R,0 H,0 (cid:19)
4 MICROLENINGCOLORSHIFT
FIG.1.—Colorshiftdistributionofeventsexpectedtobedetectedfromthe
futureMPFlensingsurvey. Darkershaderegionrepresentsthedistribution
foreventswherethecolorshiftcanbedetectedat5σlevel.
The uncertainty in units of magnitude is related to the frac-
tionaluncertaintyσ /R by
RF F
σ σ
σ∆(R- H)=2.5loge RF ∼1.1 RF . (21)
R R
(cid:18) F (cid:19) (cid:18) F (cid:19)
Then,thecolor-shiftuncertaintyisexpressedas
F +F F +F 1/2
σ∆(R- H)∼1.1 R H + R,0 H,0 . (22)
F F F F
(cid:18) R H R,0 H,0 (cid:19)
4. RESULT
InFigure1,wepresentthecolorshiftdistributionofevents
expectedtobedetectedfromtheMPFsurvey.Fromthedistri- FIG.2.—Toppanelshowsthedistributionoftheapparentbrightnessofthe
combinedimageofthesourcestarandlens. Secondandthirdpanelsarethe
bution,wefindthatcolorshiftcanbemeasuredfor∼12%of
brightnessdistributionsoftheseparatesourcestarsandlenses,respectively.
the total events. Consideringthateventsproducedby stellar BottompanelshowsthedistributionoftheH-bandlenslightfraction. The
lensescomprise∼48%ofthetotalevent,thiscorrespondsto lenslightfractionis1.0whentheobservedfluxispurelyfromthelens.Dark
∼23%ofalleventsproducedbystellarlenses. We findthat shaderegionsrepresentthedistributions foreventswherethecolorshiftis
detectableat5σlevel.
thefractionsofcolor-shiftedeventsamongthediskandbulge
eventsare∼18%and9%, respectively. Thefractionforthe havehighmagnifications.Weestimatethatthefractionofthe
disk-lenseventsishigherbecausethelensesarelocatedcloser color-shiftedeventswithimpactparameterslessthanu =0.1
0
totheobserverandthustheyarebrighter. (orA&10)is∼31%. Ontheotherhand,thefractionofthe
We investigate the properties of the color-shifted events. color-shiftedeventsamongthose with u >0.5 (or A<2.4)
0
First,weexaminethebrightnessofthesourcestarsandlenses. ismerely∼10%. Theseresultsimplythatcolorshiftswillbe
In Figure 2, we present the H-band brightness distributions detectedmainlyfromhigh-magnificationevents.
ofthesource+lenscombinedimages(toppanel),andseparate Third,weinvestigatetheeventtimescales. Theeventtime
sourcestarsandlenses(secondandthirdpanels,respectively). scaleisdefinedasthetimerequiredforthesourcestartocross
From the distributions, we find that the color-shifted events theEinsteinradiusofthelens,i.e.t =r /v.Themiddlepanel
E E
haveapparentbrightnessdistributedintherangeof17.H. ofFigure3showsthedistributionofthetimescale. Bycom-
21.Wealsofindthatthesourceandlensstarsofcolor-shifted paringthedistributionwiththatofallevents,wefindthatthe
eventshave similar brightnessrangesof 18.H .22. This timescalesofthecolor-shiftedeventstendtobelongerthan
implies that color shift occurs when the lens brightness is the events without color shifts. The most frequent value of
equivalent to that of the source star. This can also be seen the time scale for the color-shifted events is ∼18 days. On
inthebottompanelofFigure2, wherewepresentthedistri- theotherhand,themodevalueofalleventsis∼6days. We
butionoftheH-bandlenslightfraction. Wefindthat∼45% find this tendency is because the lenses of the color-shifted
ofthecolor-shiftedeventswillbeproducedbylensesbrighter eventstendtobebrighterandthusheavierthanthelensesof
thansourcestarsintheH bandand∼11%ofthemwillhave eventswithoutcolorshifts.Wefindthatthelensesresponsible
lenslightfractionsgreaterthanF /(F +F )=0.9. forthecolor-shiftedeventshavemasses locatedin therange
H,L H,S H,L
Second, we investigate the magnifications of the color- of 0.2 M .M .1.0 M . These correspond to stars with
⊙ ⊙
shifted events. For this, we construct the distribution of the spectral types from G down to mid M-type main-sequence
impactparametersofthelens-sourceencounter.Thedistribu- stars. Color shift measurement for events produced by late
tionispresentedinthetoppanelofFigure3. Fromthedistri- spectral-type lens stars is possible because the MPF survey
bution,wefind,asexpected,thatcolor-shiftedeventstendto will observe in near infrared through which the lens/source
PARK&HAN 5
Therefore,itwouldbepossible tocharacterizethehoststars
of planets from color-shift measurements for an important
fractionof planetaryevents. For some cases, the sourceand
lens stars may have similar colors resulting in small color
shifts. Inthiscase, the lensstarscan still bedetectablewith
space-based follow-up observations conducted several years
aftertheevent(BennettAnderson&Gaudi).
5. CONCLUSION
We investigatedthe usefulnessof futurespace-basedlens-
ing surveys in measuring color shifts of microlening events
caused by the flux from the lens. By conductingsimulation
ofgalactic microlensingeventsbased onthe specification of
the proposedMPF survey, we estimated that the shift in the
color of R- H would be measured at 5σ level for ∼12% of
events that would occur on source stars with apparent mag-
nitudes brighter than J =22.5. Color-shifted events tend to
have high magnifications and the lenses would have bright-
nessesequivalenttothoseofsourcestars. We estimatedthat
∼31%ofthecolor-shiftedeventswouldhavemagnifications
A>10 and the lenses of ∼45% of the color-shifted events
would be brighter than source stars. The time scales of the
color-shiftedeventswouldbelongerthanthosewithoutcolor
shiftsbecausetheseeventstendtobebrighterandthusheav-
ierthanthosewithoutcolorshifts. Weestimatedthatthemost
FIG. 3.—Distributionsofthenormalizedimpactparametersofthelens- frequenttimescaleofthecolor-shiftedeventswouldbe∼18
sourceencounter(top),eventtime-scale(middle),andlensmasses(bottom) days,whilethemodevalueofalleventswouldbe∼6days.
ofeventstobedetectedbythefutureMPFlensingsurvey.Darkshaderegion Thespectraltypeofthelensstarsofthecolor-shiftedevents
representsthedistributionforeventswherethecolorshiftisdetectableat5σ
would extenddown to mid M type because the MPF survey
level.
will observe in near infrared through which the lens/source
fluxratioisnotnegligible.
fluxratioisnotnegligible. Beingabletoextractinformation
Theselectioneffectofcolor-shiftmeasurementsthatfavors
about the lens from the measured color shift, future space-
eventswithhighermagnificationsandlongertimescalesim-
based lensing surveys would be able to better constrain the
plies that the fraction of planetary microlensing events with
lenspopulationofgalacticmicrolensingevents.
color-shiftmeasurementswould be substantially higherthan
theaveragevalueofallevents. Thisisbecauseplanetdetec-
tion has a similar selection effect of preferring events with This work was supported by the Basic Research Fund of
higher magnifications and longer time scales (Han 2007). ChungbukNationalUniversity.
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