The EROS2 search for microlensing events towards the spiral arms: the complete seven season results

8.5 MB·English

by  Y. R. Rahal

Astronomy&Astrophysicsmanuscriptno.eros-gsa (cid:13)c ESO2009
January25,2009
The EROS2 search for microlensing events towards the spiral
arms: the complete seven season results
Y.R.Rahal1⋆,C.Afonso2⋆⋆,J.-N.Albert1,J.Andersen3,R.Ansari1,E´.Aubourg2⋆⋆⋆,P.Bareyre2,J.-P.Beaulieu4,
X.Charlot2,F.Couchot1,C.Coutures2,4,F.Derue1†,R.Ferlet4,P.Fouque´7,8,J.-F.Glicenstein2,B.Goldman2‡,
9 A.Gould5,D.Graff5§,M.Gros2,J.Ha¨ıssinski1,C.Hamadache2¶,J.deKat2,E´.Lesquoy2,4,C.Loup4,L.LeGuillou2k,
0 C.Magneville2,B.Mansoux1,J.-B.Marquette4,E´.Maurice6,A.Maury8∗∗,A.Milsztajn2††,M.Moniez1,
0
2 N.Palanque-Delabrouille2,O.Perdereau1,S.Rahvar9,J.Rich2,M.Spiro2,P.Tisserand2‡‡,A.Vidal-Madjar4,
TheEROS-2collaboration
n
a
J
1 Laboratoiredel’Acce´le´rateurLine´aire,IN2P3-CNRS,Universite´deParis-Sud,B.P.34,91898OrsayCedex,France

9 2 CEA,DSM,DAPNIA,Centred’E´tudesdeSaclay,91191Gif-sur-YvetteCedex,France
3 TheNielsBohrInstitute,AstronomyGroup,JulianeMariesvej30,DK-2100Copenhagen,Denmark
] 4 Institutd’AstrophysiquedeParis,UMR7095CNRS,Universite´Pierre&MarieCurie,98bisBoulevardArago,75014Paris,France
A
5 DepartmentofAstronomy,OhioStateUniversity,Columbus,Ohio43210,U.S.A.
G 6 ObservatoiredeMarseille,INSU-CNRS,2placeLeVerrier,13248MarseilleCedex04,France
7 ObservatoireMidi-Pyre´ne´es,LATT,Universite´deToulouse,CNRS,14av.E.Belin,F-31400Toulouse,France
.
h 8 EuropeanSouthernObservatory(ESO),Casilla19001,Santiago19,Chile
p 9 Dept.ofPhysics,SharifUniversityofTechnology,Tehran,Iran
-
o Received??/??/2008,accepted
r
t
s ABSTRACT
a
[
Aims. TheEROS-2projecthasbeendesignedtosearchformicrolensingeventstowardsanydensestellarfield.Thedensestpartsof
1 theGalacticspiralarmshavebeenmonitoredtomaximizethemicrolensingsignalexpectedfromthestarsoftheGalacticdiskand
bulge.
v
5
2 Methods. 12.9 million stars have been monitored during 7 seasons towards 4 directions in the Galactic plane, away from
theGalacticcenter.
3
1
. Results. A total of 27 microlensing event candidates have been found. Estimates of the optical depths from the 22 best
1 eventsareprovided.AfirstorderinterpretationshowsthatsimpleGalacticmodelswithastandarddiskandanelongatedbulgeare
0 inagreementwithourobservations.WefindthattheaveragemicrolensingopticaldepthtowardsthecompleteEROS-catalogedstars
9 ofthespiralarmsisτ¯ = 0.51±.13×10−6,anumberthatisstablewhentheselectioncriteriaaremoderatelyvaried.AstheEROS
0 catalog is almost complete up to I = 18.5, the optical depth estimated for the sub-sample of bright target stars with I < 18.5
C C
: (τ¯ =0.39±.11×10−6)iseasiertointerpret.
v
i
X Conclusions. The set of microlensing events that we have observed is consistent with a simple Galactic model. A more pre-
ciseinterpretationwouldrequireeitherabetterknowledgeofthedistancedistributionofthetargetstars,orasimulationbasedona
r
a Galacticmodel.Forthispurpose,wedefineanddiscusstheconceptofopticaldepthforagivencatalogorforalimitingmagnitude.
Keywords.Cosmology:darkmatter-Galaxy:disk-Galaxy:bulge-Galaxy:structure-Galaxy:spiralarms-Galaxy:microlensing
1. Introduction
Send offprint requests to: M. Moniez, e-mail:
[email protected]
After the first reports of microlensing candidates
seealsoourWWWserveratURL:
(Aubourgetal.1993, Alcocketal.1993, Udalskietal.1993),
http://www.lal.in2p3.fr/recherche/eros
the EROS team has performed extensive microlensing surveys
⋆ NowatElectronicsArtsCanada,Vancouver,Canada
from 1996 to 2003, that monitored the Magellanic clouds and
⋆⋆ Now at Max-Planck-Institut fu¨r Astronomie, Koenigstuhl 17, D-
large regions in the Galactic plane. The EROS-2 search for
69117Heidelberg,Germany
lensing towards the Magellanic clouds (Tisserandetal.2007)
⋆⋆⋆ AlsoatAPC,10rueAliceDomonetLonieDuquet,F-75205Paris
Cedex13,France
† NowatLPNHE,4placeJussieu,F-75252ParisCedex5,France k NowatLPNHE,4placeJussieu,F-75252ParisCedex5,France
‡ Now at Max-Planck-Institut fu¨r Astronomie, Koenigstuhl 17, D- ∗∗ Now at San Pedro de Atacama Celestial Exploration, Casilla 21,
69117Heidelberg,Germany SanPedrodeAtacama,Chile
§ Now at Division of Medical Imaging Physics, Johns Hopkins †† Deceased
UniversityBaltimore,MD21287-0859,USA ‡‡ Now at Mount Stromlo Observatory, Weston P.O., ACT, 2611,
¶ Also at CSNSM, Universit Paris Sud 11, IN2P3-CNRS, 91405 Australia
OrsayCampus,France
2 EROScollaboration:Microlensingtowardsthespiralarms
yieldedsignificantupperlimitsonthefractionoftheMilkyWay where u(t) is the distance of the deflecting object to the unde-
halothatcanbecomprisedofdarkobjectswithmassesbetween flectedlineofsight,expressedinunitsofthe“EinsteinRadius”
10−7M and 10M . For objects of mass 0.4M the 95% CL R :
⊙ ⊙ ⊙ E
limit is 8%, in conflict with the suggestion by the MACHO
collaboration (Alcocketal.2000) that between 7% and 50% 4GM
R = Lx(1−x), (4)
ofthehaloismadeupofsuchobjects.TheEROS-2searchfor E r c2
(mHicarmoalednascihnegeotfaGl.a2la0c0t6ic)BguivlginegclaumGpaglaicatnicts-lyaiteitluddeed1d2e0peenvdeenntst ≃ 4.54A.U.× M 12 × L 21 × [x(1−x)]12.
opticaldepthof "M⊙# "10kpc# 0.5
τ/10−6 =(1.62 ±0.23)exp[−a(|b|−3◦)], (1) HereGistheNewtoniangravitationalconstant,Listhedistance
of the observer to the source and xL is its distance to the de-
with
flector of mass M. The motion of the deflector relative to the
a = (0.43 ±0.16) deg−1 . (2) lineofsightmakesthemagnificationvarywithtime.Assuming
a deflector moving at a constant relative transverse speed V ,
T
This optical depth agrees with Galactic models
reachingitsminimumdistanceu (impactparameter)totheun-
0
(Evans&Belokurov2002 ; Bissantzetal.1997) and with
deflectedlineofsightattimet ,u(t)isgivenby
0
the results of the MACHO (Popowskietal.2005) and Ogle-II
(Sumietal.2006) collaborations. The duration distribution of
u(t)= u2+((t−t )/t )2, (5)
the events discovered by the three collaborations have been 0 0 E
q
recently analyzed by CalchiNovatietal.2008 to constrain the
GalacticBulgeInitialMassFunction. wheretE = VRTE,the“lensingtimescale”,istheonlymeasurable
Ourteamhasdevotedabout15%oftheobservingtimedur- parameterbringingusefulinformationonthelensconfiguration
ing 7 seasons to the search for microlensing events towards intheapproximationofsimplemicrolensing:
the Galactic Spiral Arms (GSA), as far as 55 degrees in lon-
gitude away from the Galactic center. In our previouspublica- t (days)=79. VT −1 M 12 L 21 [x(1−x)]21 .(6)
tions(Derueetal.1999,Derueetal.2001,hereafterreferredas E "100km/s# "M⊙# "10kpc# 0.5
papersIandII)describingthedetectionofrespectively3and7
events,ourattentionwascalledonapossibleopticaldepthasym- This simple microlensing description can be broken in
metry,accompaniedbyanasymmetriceventdynamicswithre- many different ways : double lens (Mao&Stefano1995), ex-
spect to the Galactic center. This marginaleffect (a 9% proba- tended source, deviations from a uniform motion due ei-
bility to be accidental) could be interpreted as an indication of ther to the rotation of the Earth around the Sun (parallax
alongGalacticbarwithinthebulge.Itsinvestigationrequireda effect)(Gould1992,Hardy&Walker1995),ortotheorbitalmo-
significantincreaseinthenumberofevents. tion of the source aroundthe center-of-massof a multiple sys-
In addition to the observing time increase (by more than a tem, or to a similar motion of the deflector (see for example
factor2),weimprovedourcatalogofmonitoredstarsbyincreas- Mo¨llerach&Roulet2002).
ingthelimitingmagnitudeaswellasbyrecoveringsomefields Theopticaldepthτtowardsaparticularsetoftargetstarsis
andsub-fieldsthatwerenotanalyzedpreviously.Theseimprove- defined as the average probabilityfor the line of sight to inter-
ments allowed us to recover another factor ∼ 1.5 in sensitiv- cept the Einstein disk of a deflector (magnification A > 1.34).
ity. Moreover the discrimination power for microlensing event This probability is independentof the deflector mass function,
identificationhasbeensignificantlyimproved,partlybecausethe since the surface of the Einstein disk is proportionalto the de-
lightcurvesarelongerandthusprovideabetterrejectionofre- flector’smass.Whenthetargetconsistsofapopulationofstars,
currentvariableobjects. themeasuredopticaldepthisobtainedfrom
Aspecificdifficultyintheanalysisofthespiralarmssurvey
1 π t
comesfrom the poorknownledgeof the source distance distri- τ= E , (7)
N ∆T 2 ǫ(t )
bution;incontrastwiththeLMC,theSMCandtheGalacticcen- obs obs eXvents E
ter red giantclump, the monitoredsourcesin the Galactic disk
where N is the number of monitored stars; ∆T is the du-
spanawiderangeofdistances(±5kpcaccordingtopreliminary obs obs
rationoftheobservingperiod;ǫ(t )istheaveragedetectionef-
studies, see Sect. 6.4.2). Their mean distance is also uncertain E
ficiencyofmicrolensingeventswith a time scale t , definedas
andhasbeenestimatedtobe7±1kpc(Derue1999b).Wedefine E
theratioofdetectedeventstothenumberofeventswithu < 1
inthispaperthenotionof“catalogopticaldepth”(Sect.9)and 0
whosemagnificationreachesitsmaximumduringtheobserving
provideallthenecessarydatatotestGalacticmodels.
period.Similarly,theeventratecorrectedforthedetectioneffi-
ciencyis
2. Microlensingbasics
1 1
Gravitational microlensing (Paczyn´ski1986) occurs when a Γ= × . (8)
N ∆T ǫ(t )
massivecompactobjectpassescloseenoughtothelineofsight obs obs eXvents E
of a star, temporarily magnifying the received light. In the ap-
proximationofasinglepoint-likeobjectactingasadeflectoron 3. Experimentalsetupandobservations
a single point-likesource,the total magnificationof the source
luminosity at a given time t is the sum of the contributions of The telescope, the camera and the observations, as well as the
twoimages,givenby operationsand data reduction are described in paper I and ref-
erencestherein.Thestarpopulationlocationsandtheamountof
u(t)2+2 datacollectedtowardsthe29fieldsthathavebeenmonitoredin
A(t)= , (3)
u(t) u(t)2+4 fourdifferentregions(βSct,γSct,γNorandθMus)aregivenin
p
EROScollaboration:Microlensingtowardsthespiralarms 3
Fig.1andtable1.Takingintoaccountthedeadzones,thelower
efficiency sectors of our CCDs and the blind zones around the
brighteststars, weestimatethat75±4%ofthetotalCCD area k 16 k 16
(0.95deg2)waseffectivelysensitive.Thisnumberwasobtained wee 14 γ Sct. wee 14 β Sct.
by estimating the excess of 10 × 10 pixel domains (6′′ × 6′′) nts/ 12 nts/ 12
e e
containingzerostar,withrespecttothenumberofvoiddomains m m
e 10 e 10
expectedfromthePoissoniandistributionofthestellar number ur ur
as 8 as 8
dbeenrsoitfyd.eItteisctiendasgtraeresm(seunmtwmiethdtohveerraatilol fibeetlwdse)eanntdhethtoetanlunmubme-r d me 6 d me 6
e e
g 4 g 4
extrapolatedfrom the stellar density observedin the CCD best ra ra
zones.Wetookexposuresof120stowardsβSct,γSctandγNor ave 2 ave 2
and 180 s towards θ Mus. The observations span a period of 0 0 100 200 300 400 0 0 100 200 300 400
∆T =2325days,startingJuly1996andendingOctober2002; weeks since 1996 Jan 1. weeks since 1996 Jan 1.
obs
369 measurements per field were obtained on average in each k 16 k 16
of the REROS and BEROS bands. Our fields were calibrated us- wee 14 γ Nor. wee 14 θ Mus.
ingtheDENIScatalog(Epchteinetal.1999)andthecalibration nts/ 12 nts/ 12
was checked with the OGLE-II catalog (Udalskietal.2000b). me me
e 10 e 10
WefoundthatREROS andBEROS bandsarerelatedtotheCousins asur 8 asur 8
I andJohnsonV magnitudesthroughthefollowingcolorequa- e e
tions,toaprecisionof∼0.1mag: d m 6 d m 6
e e
g 4 g 4
a a
r r
R = I , B =V −0.4(V −I ). (9) ve 2 ve 2
EROS C EROS J J C a a
0 0
Figure2showstheobservationtimespanandtheaveragesam- 0 100 200 300 400 0 100 200 300 400
weeks since 1996 Jan 1. weeks since 1996 Jan 1.
plingforthefourdifferentdirections.
Fig.2. Time sampling for each monitored direction: weekly average
Table1.Characteristicsof the29 fieldswhichweremonitored inthe numberofmeasurementsperstarsinceJanuary1rst,1996.
EROSspiralarmprogram:Locationsofthefieldcenters,averagesam-
pling (number of photometric measurements per light curve and per
color)andnumberofstarsmonitoredforeachfield.Theobservingtime
was∆Tobs = 2325days.Thetotalnumbersofobserved starstowards 4. Thecatalogs
γ Nor and θ Mus are smaller than the sum of the numbers given for
eachfieldbecauseofsomeoverlapbetweencontiguousfields.Thetotal The catalogs of monitoredstars have been produced following
fieldsofview(f.o.v.)aretheareaseffectivelymonitored(0.71deg2per theproceduredescribedinpapersIandII,basedonthePEIDA
field,seetext),correctedfortheoverlapbetweenfields.
photometricsoftware(Ansari1996).Allobjectsarewellidenti-
fiedinbothcolorsandunambiguouslyassociatedbetweenthese
Field α◦(J2000) δ◦(J2000) b◦ l◦ Nmeas Nobs(106) two colors. We have removedobjects that suffer from a strong
βSctExposure=120s.f.o.v.=4.3deg2. 268 3.00
bs300 280.8417 -7.6814 -1.75 25.20 269 0.48 contamination by a nearby bright star; the contribution to the
bs301 280.8625 -6.2283 -1.11 26.51 266 0.47 backgroundflux from such a nearby star at the position of the
bs302 281.5667 -7.3792 -2.25 26.80 272 0.50
objectshouldnotexceed150%ofitspeakflux.
bs303 281.5833 -5.9264 -1.60 27.09 261 0.47
bs304 282.3375 -6.7642 -2.70 26.71 269 0.52 Thesevenseasondatasetcontains12.9millionobjectsmea-
bs305 283.1083 -6.5956 -3.26 27.19 271 0.54 sured in the two colors: 3.0 towards β Sct, 2.4 towards γ Sct,
γSctExposure=120s.f.o.v.=3.6deg2. 277 2.38
5.2towardsγNorand2.3towardsθMus.Thenumberofmoni-
gs200 277.0125 -14.8517 -1.64 17.72 282 0.47
gs201 277.8125 -14.2439 -2.12 18.00 266 0.49 toredstarswasincreasedby∼ 50%sincetheanalysisofpapers
gs202 277.8875 -12.8147 -1.52 19.30 291 0.49 I and II, by producing a richer catalog from a wider choice of
gs203 278.5917 -14.5275 -2.92 18.09 281 0.46
gs204 278.6167 -13.0753 -2.28 19.40 267 0.47 goodqualityimagesthanavailablebefore.Wewerealsoableto
γNorExposure=120s.f.o.v.=8.4deg2. 454 5.24 solvesometechnicalproblemsthatpreventedusfromproducing
gn400 242.4375 -53.1175 -1.17 330.49 496 0.42 the catalog for some fields (Tisserand2004, Rahal2003). The
gn401 244.5917 -51.7453 -0.99 332.04 475 0.41
gn402 243.7375 -53.0764 -1.59 330.74 463 0.45 recoveredstars are mainlyfaintstars with a comparativelylow
gn403 245.6167 -52.1056 -1.69 332.24 420 0.42 microlensingsensitivity.
gn404 244.7875 -53.4439 -2.29 330.94 435 0.43
gn405 246.7167 -52.3506 -2.35 332.54 445 0.44
gn406 245.9750 -53.7314 -2.99 331.23 443 0.46
gn407 247.8792 -52.4789 -2.95 332.93 443 0.47 4.1.Completeness,blending
gn408 247.1750 -53.8661 -3.60 331.63 453 0.47
gn409 243.9625 -54.8125 -2.86 329.82 482 0.47 We have compared a subset of the gs201 EROS field cata-
gn410 245.1250 -55.0717 -3.59 329.93 443 0.46 log (Fig. 3a) with the catalog extracted from the deeper HST-
gn411 242.4042 -55.1686 -2.54 328.78 449 0.48
θMusExposure=180s.f.o.v.=3.8deg2. 375 2.28 WFPC2 (Wide Field Planetary Camera 2) images (Fig. 3b)
tm500 201.7667 -63.0383 -0.47 306.98 391 0.44 named U6FQ1102B (exposure 210s with filter F606W) and
tm501 202.8250 -63.5781 -1.07 307.37 355 0.44 U6FQ1104B (exposure 126s with filter F814W), centered at
tm502 203.7167 -64.1750 -1.72 307.66 376 0.47
tm503 200.9917 -64.9978 -2.36 306.38 375 0.36 (α = 277.6281◦, δ = −14.4823◦) or (b = 17.689814◦,l =
tm504 198.0500 -64.1136 -1.35 305.22 392 0.43 −2.039549◦), obtained from the HST archive (HST2002). We
tm505 199.0625 -64.6806 -1.96 305.60 360 0.43
detected3518starsinbothcolorsintheHSTimagescorrespond-
Total 12.9
ingtotheEROSmonitoredfield;wesystematicallytriedto as-
sociate thesestarswith anEROSobjectwithin1 arcsec.Allof
the 869 EROS-objects properly identified as stars in the field
4 EROScollaboration:Microlensingtowardsthespiralarms
l
Fig.1.TheGalacticplanefields(Galacticcoordinates)monitoredbyEROSsuperimposedontheimageoftheMilky-way.Thelocationsofour
fieldstowardsthespiralarms,aswellasourGalacticbulgefields(notdiscussedinthispaper)areshown.ThelargebluedottowardsγSctindicates
thepositionoftheHSTfieldusedtoestimateourstardetectionefficiency(seetext).Northisup,Eastisleft.
lar populations. Since our studies of HST images have shown
that the spiral arm stars are less blended than the LMC stars,
and consideringthe similarity between the SMC and the LMC
populations,weconcludethatblendingshouldhavelessimpact
towardsthespiralarmsthantowardstheSMC.Therefore,tobe
conservative, we will use the estimates of (Afonsoetal.2003)
as upper limits on the optical depth systematic uncertaintiesin
Section7.2.
FromtheHST-EROSstarassociation,wehaveextractedour
detection efficiencies as a function of the B stellar magni-
EROS
tudes(seefigure4).AsF814WandF606WHST-WFPC2filters
Fig.3. (a) The R composite image (used to detect the cataloged
EROS are respectively very close to our R and B bands, we
stars) and (b) the U6FQ1104B-HST image of the same sub-field to- EROS EROS
could directly measure detection efficiencies for HST objects.
wardsgs201.
We foundthateveryHSTstar thatisdetectedintheEROSim-
ages (i.e. that is located within 1 arcsec of an EROS object) in
theB bandisautomaticallydetectedintheR band(the
EROS EROS
wereassociatedwithoneormoreHSTstar,allowingastudyof reverse is false). This is due to the different limit magnitudes
theblendingandofthedetectionefficiencyasafunctionofthe of the B and R templates. Therefore the efficiency to
EROS EROS
magnitude.We foundthat56%oftheEROSobjectsareblends detecta HST star in EROS is the probabilityforthatstar to be
with more than one HST-star within 1 arcsec distance. In this foundintheB band.Thecolor-magnitudediagramsofFig.
EROS
case the brightest HST-star accounts for an average of 72% of 5showthatthediagonaldelimitationsofthepopulationsinthe
the BEROS flux of the EROS object. These numbers vary with bottom right sector follow a BEROS = constant line, thus con-
theEROSobjectmagnitudeasfollows: firmingthatthedetectionthresholdissetbyB .Weestimate
EROS
the efficiencywithin the activeregionof the CCD-array,corre-
spondingto the effectivefield of 0.71deg2 for the fullmosaic.
B 15-17 17-19 19-21
EROS
WeprovideinFig.4theprobabilityforaHSTstartobethemain
fractionofblendedEROS-objects 70% 59% 54%
contributionofmainHSTstar 88% 77% 68% contributorofanEROSobject.Astarcanalsohaveaminorcon-
tributiontothefluxofanEROSobject,asaresultofblending;
we show also the probability for HST stars to contribute to an
EROSobject(evenifnotasthemaincontributor).
Thecomparisonofthesenumberswiththeonesfoundfrom
asimilarstudyofaLMCdensefield(Tisserandetal.2007)in-
dicates that EROS cataloged objects towards gs201 are on av- 4.2.Thecolor-magnitudediagram
erage less blended than the objects found towards dense re-
Figure 5 gives the color-magnitude diagrams n (I,V − I) of
gionsofLMC.Suchblendingcouldaffectthemicrolensingop- ourcatalogs1. Theglobalpatternofthese diagraermossfollowsthe
ticaldepthdetermination,as discussedin detailforSMCfields
expected magnitude versus color lines resulting from the light
in (Afonsoetal.2003), andthe distributionofthe lensing time
absorptionofadistance-distributedstellarpopulation.Twopar-
scale t (Rahvar2004;Bennett2005). The averagedensitiesof
E allelfeaturesarevisible,withverydifferentdensities.
the EROS catalogsare similar towardsthe SMC and the spiral
arms;thereforeoneshouldexpectdifferencesinblendingonlyif 1 2D-tables of these diagrams can be found on the Web-site:
thereisadifferencebetweenthespatialrepartitionsofthe2stel- http://users.lal.in2p3.fr/moniez/
EROScollaboration:Microlensingtowardsthespiralarms 5
x 10 2 x 10 2
13 2000 13 2000
C C
I β Sct. I γ Sct.
14 1800 14 1800
1600 1600
15 15
1400 1400
16 16
1200 1200
17 17
1000 1000
18 18
800 800
19 19
600 600
20 20
400 400
21 200 21 200
22 0 22 0
0 2 4 6 0 2 4 6
V -I V -I
J C x 10 2 J C x 10 2
13 2000 13 2000
C C
I γ Nor. I θ Mus.
14 1800 14 1800
1600 1600
15 15
1400 1400
16 16
1200 1200
17 17
1000 1000
18 18
800 800
19 19
600 600
20 20
400 400
21 200 21 200
22 0 22 0
0 2 4 6 0 2 4 6
V -I V -I
J C J C
Fig.5.Color-magnitudediagramsn (I,V −I)ofourcatalogstowardsthe4monitoreddirections.Thegreyscalegivesthenumberdensityof
eros
starspersquaredegree,perunitofmagnitudeandperunitofcolorindex.
We were ableto qualitativelyreproducethese featureswith 4.3.Photometricprecision
a(simple)simulatedcatalog(Fig.21).Thecolor-magnitudedia-
Tocompletethedescriptionofourobservations,Fig.6givesthe
gramofthissynthesizedcatalogshowstwoparallelfeaturesdue
average point-to-point photometric dispersion along the light-
to the main sequence and the red giant clump, that are similar
curvesasafunctionofthemagnitudeI .
to the onesobservedin the data.Withoutspectroscopicdataor C
a moredetailed simulation,it is notpossible to go furtherthan
thisqualitativecomparisonfortheinterpretationoftheobserved
color-magnitudediagrams. 5. Thesearchforlensedstars
Ourmicrolensingeventdetectionschemeisthesameastheone
described in papers I and II. In the following, we will outline
thefewspecificitiesthatarisebecauseofanalysisimprovements,
specificseasonalconditionsorparticularproblems,andbecause
6 EROScollaboration:Microlensingtowardsthespiralarms
5.1.Prefiltering
ag.106 WeusedthesamenonspecificprefilteringdescribedinpaperII,
m HST
2/ andpreselectedthemostvariablelightcurvessatisfyingatleast
eg. oneofthefollowingcriteria:
d
s/
ar105 EROS – The strongest fluctuation along the light curve (a series of
st consecutive flux measurements that lie below or above the
“base flux”, i.e. the average flux calculated in time regions
devoid of significant fluctuations) has a small probability
(typicallysmallerthan10−10)tohappenforastablestar,as-
104
B sumingGaussianerrors;
EROS
– The dispersion of the flux measurements is significantly
22 21 20 19 18 17 16 15
largerthanexpectedfromthephotometricprecision;
bility0.19 – Tfluhxeidsisintrciboumtipoantibolfetwheithdetvhieatdiiosntrsibwuittihonreesxppeeccttetodftrhoembathsee
a0.8
b measurementsofastablesourcewithGaussianerrors(using
o
pr0.7 theKolmogorov-Smirnovtest).
n 0.6
o
cti0.5 The thresholds of these three criteria have been tuned to se-
ete0.4 lecta totalof∼ 20%ofthelightcurves.Afterthisprefiltering,
d 2446843lightcurvesareenteringthemorediscriminatinganal-
0.3
ysisdescribedbelow.Wealsoincludedarandomlyselectedset
0.2
oflightcurves(∼2%)toproduceunbiasedcolor-magnitudedia-
0.1 B = I +0.6(V -I )
EROS C J C gramsandforourefficiencycalculation(Sect.7.1).Furthermore,
0
22 21 20 19 18 17 16 15 we have corrected the photometric measurements presenting a
Fig.4.-Toppanel:TheEROS(thickline)andHST(thinline)B = significantcorrelationbetweenthefluxandtheseeinginaway
EROS
I +0.6(V −I )magnitudedistributionsoftheidentifiedobjectsina thatisdescribedin(Tisserand2004).
C J C
sub-fieldofgs201.ObjectsbrighterthanB =16areallidentifiedin
EROS
bothimages,buttheirmagnitudesaresystematicallyoverestimatedby
our photometry intheHSTimage, explainingtheapparent deficiency 5.2.Filtering
ofbrightHSTobjects.
– As in paper II, we first searched for bumps in each light
-Lowerpanel:ThethinlineshowstheprobabilityforanHSTstarto
curve.Abumpisdefinedasaseriesofconsecutivefluxmea-
contributetoanEROSobject,i.e.tobecloserthan1arcsecfromsuch
anobjectversusB =I +0.6(V −I ). surementsthatstartswithapositivefluctuationofmorethan
EROS C J C
ThethicklinegivestheprobabilityforanHSTstartobethemaincon- onestandarddeviation(+1σ)fromthebaseflux,endswhen
tributortothefluxofanEROSobjectfoundwithin1arcsec. 3consecutivemeasurementsliebelow1σfromthebaseflux
and contains at least four measurementsdeviating by more
than +1σ. We characterize such a bump by the parameter
Q = −log (P)where P istheprobabilitythatthe bumpbe
10
due to an accidentaloccurrencein a stable star lightcurve,
of the fact that the time baseline is twice to three times longer assumingGaussianerrors.Weselectthelightcurveswhose
thaninourpreviouspublications. mostsignificantfluctuation(bump1)ispositiveinbothcol-
ors.
– Thenwerequirethetimeoverlapbetweenthemainbumpsin
eachcolortobeatleast10%ofthecombinedtimeintervals
ofthetwobumps.
– Torejectmostoftheperiodicorirregularvariablestars,we
φbase0.19 rpeomsiotivveetohrosneegliagthivtec)uwrviethstQh2at>haQv1e/a2siencoonnedcboulmorp. (bump2,
σ/φ 0.8
0.7 After this filtering, the 1097 remaining light curves can
0.6 be fitted assuming the simplest microlensing hypothesis, i.e. a
0.5 point-likesourceandapoint-likedeflectorwithaconstantspeed.
0.4
0.3
5.3.Candidateselection
0.2
0.1 TheobservedfluxversustimedataΦ (t)isfittedwiththeex-
obs i
022 21 20 19 18 17 16 15 pression Φ(t) = Φbase × A(t), where Φbase is the unmagnified
I fluxandA(t)isgivenbyexpression(3).Thecandidateselection
C
is based on the fit quality (χ2) and on variables obtained from
Fig.6. Average photometric point-to-point precision along the light- the Φbase, t0, tE and u0 fitted parameters. We apply the follow-
curvesversusI .Theverticalbarsshowthedispersionofthisprecision ing criteria, tuned to select not only the “simple” microlensing
C
inoursourcesample.Thehistogramshowsthemagnitudedistribution events,butalsoeventsthatareaffectedbysmalldeviationsdue
ofthefullcatalog(averageover4directions). toparallax,sourceextension,binarylenseffects...mentionedin
Sect.2.Theefficiencytodetectcausticsshouldbeverylimited
EROScollaboration:Microlensingtowardsthespiralarms 7
withthissetofcuts,butnonewasfoundfromasystematicvisual Fig.7togetherwithasampleofpointsrepresentingthepopula-
inspectionofthe1097lightcurves. tionobtainedafterselectionofsimulatedeventsasexplainedin
Sect. 7.1.One clearly sees how the maximalsource magnitude
– C1. Minimum observation of the unmagnified epoch : requiredfordetectiondecreaseswhentheimpactparameterin-
We first reduce the background due to instrumental effects creases. AnnexA showsthe light-curvesandthe findingcharts
andtofieldcrowdingproblemsbyselectinglightcurvesthat ofthe27candidates,andtable2givestheircharacteristics.The
aresufficientlysampledbothduringtheunmagnifiedandthe finding charts are obtained from the reference images used for
magnifiedstages.Forthispurposewedefinethe“high”mag- theproductionofthecatalogs.
nificationepoch(called peak,labeled“u<2”)astheperiod
oftimeduringwhichthefittedmagnificationAisabove1.06,
5.4.Nonstandardmicrolensingevents
associated to an impact parameter u < 2. The complemen-
tary“low”magnificationepochs,duringwhichA<1.06,are
Some of our candidates are significantly better fitted with mi-
labeled′′base′′.Werequirethat
crolensing curves resulting from complex configurations than
with the basic point-like source, point-like deflector with a
∆T −∆T >600days, (10)
obs u<2 constant-speed microlensing curve. The refinements that have
where ∆T = 2325.days is the observationduration,and beenintroducedinthesecasesare:
obs
∆T isthedurationofthe“high”magnificationepoch.
u<2
– Theblendingofthelensedsourcewithanearby,unresolved
object.Inthatcase,thelight-curveΦ (t)hastobefittedby
– C2. Sampling during the magnified epoch : We also re- obs i
thefollowingexpression
quire that the intervalbetween the peak magnificationtime
t andthenearestmeasurementissmallerthan0.4×∆T .
0 u<2 Φ(t)=C×Φ ×A(t)+(1−C)×Φ , (14)
– C3.Goodnessofasimplemicrolensingfit:Toensurethe base base
fit quality, we require χ2 /N < 1.8 separately for both
ml dof where C depends on the color. In supplement to the stan-
colors,whereχ2mlandthenumberofdegreesoffreedomNdof dard fit, this fit provides the CR and CB parameters, where
areobtainedfromthefulllight-curve. C=(base flux of magnified component)/(totalbase flux). In
– C4.Impactparameter:Wealsorequirethatthefittedim- the notes of table 2, we give the magnitudes and colors of
pactparameteru0belessthan1forbothcolors. themicrolensedcomponentsthattakeintoaccountthecolor
– C5. Stability of the unmagnified object : One important equations(9).
featureofamicrolensinglightcurveisitsstabilityduringthe – Parallax. Due to the rotation of the Earth around the Sun,
lowmagnificationepochs,exceptfortherareconfigurations the apparent trajectory of the deflector with respect to the
ofmicrolensedvariablestars.Werejectlightcurveswith line of sight is a cycloid instead of a straight line. For
some configurations (a nearby deflector and an event that
χ2 (R)+χ2 (B)
base base >8, (11) lastsafewmonths),theresultingmagnificationversustime
Ndof(R)+Ndof(B) curve may be affected by this parallax effect (Gould1992,
Hardy&Walker1995).Thespecificparametersthatcanbe
wheretheχ2base andNdof valuescorrespondtothemeasure- fitted in this case are the Einstein radius r˜E and an orienta-
mentsobtainedduringthelowmagnificationepochs. tion angle, both projected on the observer’s plane which is
– C6. Improvement brought by the microlensing fit com- orthogonaltothelineofsight.
pared to a constant fit : We use the same ∆χ2 variables – “Xallarap”. This effect is due to the rotation of the source
as in paper II to select light curves for which a simple mi- around the center-of-mass of a multiple system. In this
crolensingfitissignificantlybetterthanaconstantvaluefit: case, the light-curve exhibits modulations with a charac-
teristic time given by the period of the source rotation
χ2 −χ2 1
∆χ2 = cst ml . (12) (Derueetal.1999, Mo¨llerach&Roulet2002). Assuming a
B,R χ2ml/Ndof 2Ndof(cid:12)(cid:12)B,R circularorbit, the extra-parametersto be fitted or estimated
(cid:12) aretheorbitalperiodP,theluminosityratioofthelensedob-
p (cid:12)
Weselectlightcurveswith∆χ2 +∆χ2 >60. jecttothemultiplesystem,andtheprojectedorbitradiusin
B R
– C7.Overlapinthetwocolors:Defining∆T asthetime thedeflector’splaneρ = ax/R , whereaistheorbitradius
u<1 E
intervalduringwhich the fitted magnificationis largerthan andx= D /D .
lens source
1.34 (u < 1), we require a minimum overlap between the
timeintervalsfoundinthetwocolors: Insomecases,thevaluesobtainedfort withthebasicfitandthe
E
refined one may differ considerably. For time duration studies
∆T (R)∩∆T (B)
u<1 u<1 >0.4. (13) and for optical depth calculations, we use the tE values given
∆Tu<1(R)∪∆Tu<1(B) bythebestfit.Butasfarasefficiencyvaluesareconcerned,we
mustuse thoseobtainedwith the standardfitsince theyarethe
Thislooserequirementonthesimultaneityofthemagnifica-
onesthatentertheselectionprocedure.
tionsinthetwocolorsallowsonetokeepagoodsensitivity
to“complex”microlensingevents;forexample,thiscuttol-
eratessomedifferencebetweenthefittedimpactparameters
6. Themicrolensingcandidates
obtainedin the two colors(which mayoccur in the case of
strongblending).
6.1.Generalfeatures
Thenumberofmicrolensingcandidatessofaris27includingan Inordertoquantifytherelevanceoftheinterpretationofthe27
uncertainone,labeledGSA-u1(seebelow).The I magnitudes selectedobjectsasmicrolensingevents,wedefinetwovariables
C
and(V −I )colorsversusu ofthesecandidatesareshownin asfollows:
J C 0
8 EROScollaboration:Microlensingtowardsthespiralarms
Table2.Characteristicsofthe27microlensingcandidates.Forthoseeventsthathaveabetterfitthanthepoint-likepoint-sourceconstantspeed
microlensingfit(theso-calledstandardfit),wealsoprovidethestandardfitparameters.
-Namesinboldtypecorrespondtoeventsselectedfortheopticaldepthanddurationanalysis(withu <0.7).
0
-I (V −I )arethefittedunmagnifiedmagnitudesofthelensedobject(includingthecontributionofapossibleblend).
C J C
-t isthetimeofmaximummagnification,giveninHJD-2,450,000.
0
-t istheEinsteindiskcrossingtime,indays.
E
-u isthedimensionlessimpactparameter.
0
-χ2/dof correspondstothebestmicrolensingfit.
-τistheindividualcontributionofeacheventtotheopticaldepthtowardsthecorrespondingtarget.Inthecaseof“nonstandard”events,weuse
thet valueobtainedfromthebest(nonstandard)fitandtheefficiencyevaluatedatt ofthestandardfit(seetext)forthecalculationofτ.
E E
candidate field α◦ δ◦(J2000) I (V −I ) t (days) t (days) u χ2/d.o.f τ(10−6) note
C J C 0 E 0
γSct
GSA1 200 277.2888 -14.2528 18.3(3.1) 301.2±0.1 64.0±1.2 .043±.0010 299.7/435 0.146
GSA8 200 276.8042 -15.0311 16.6(3.7) 996.9±0.1 40.6±1.0 .145±.003 981./533 0.114 (1)
Standardfitparameters: 993.0±0.1 35.2±0.7 .155±.002 1400./535
GSA9 200 277.1750 -15.1644 18.8(2.8) 1760.3±1.7 57.9±3.6 .482±.0158 262.9/565 0.142
GSA10 200 277.2813 -14.8931 18.1(2.3) 1806.1±0.8 24.6±1.3 .574±.0179 237.9/596 0.081
GSA11 201 278.1650 -14.1094 18.8(2.5) 1725.3±0.4 44.3±1.4 .187±.0049 367.2/558 0.116
GSA12 203 278.5875 -13.9794 17.1(1.8) 1378.6±0.2 50.1±0.7 .225±.0030 89.3/359 0.123
GSA13 203 278.9404 -14.5803 17.2(1.9) 313.9±1.2 37.2±2.1 .898±.0153 244.9/617 -
GSA14 204 278.4388 -12.8678 16.7(2.2) 1637.7±3.4 68.4±3.7 .785±.0097 421.2/392 - (2)
βSct
GSA15 301 281.0654 -6.0339 18.3(3.5) 1399.8±1.4 72.2±2.8 .337±.0126 212.2/411 0.110 edge
GSA16 301 280.7646 -6.7583 16.4(3.1) 1997.0±3.2 60.6±4.0 .796±.0141 341.8/361 -
GSA17 302 281.3950 -7.8867 16.4(1.7) 1947.2±3.8 50.0±2.4 .532±.1079 156.9/400 0.096
GSA18 304 282.2879 -7.2500 16.1(2.1) 1718.7±0.1 55.0±2.0 .137±.0009 133./514 0.098 (3)
Standardfitparameters: 1718.4±0.1 58.0±0.3 .137±.0009 155.6/516
γNor
GSA2 400 242.9592 -52.9464 18.6(2.3) 534.4±0.2 98.3±0.9 .342±.002 973.4/934 0.059 (4)
Standardfitparameters: 533.6±0.5 137.8±2.6 .233±.0029 1196.5/937
GSA19 401 244.1379 -52.0272 15.5(5.1) 2367.7±1.3 90.4±3.0 .043±.025 893./880 0.063 (5)
Standardfitparameters: 2373.5±0.1 93.1±0.7 .022±.007 1388.5/888
GSA20 402 243.7758 -52.9700 16.4(1.3) 2465.5±1.0 40.±5.0 .72±.02 414./696 0.039 (6)
Standardfitparameters: 2487.1±0.3 46.3±0.7 .565±.0050 712.4/698
GSA21 404 244.3063 -53.1100 16.8(2.7) 1587.3±.03 74.±3.0 .0142±.0008 259./565 0.077 (7)
Standardfitparameters: 1587.2±.03 39.1±0.2 .037±.0007 1884.4/567
GSA22 404 244.4263 -54.0508 18.4(2.0) 2182.4±0.2 26.6±1.1 .048±.0180 429.5/742 0.031
GSA23 404 245.1208 -53.9825 18.3(1.7) 1573.8±3.8 78.5±5.7 .542±.0152 522.3/784 0.062 corner
GSA24 406 246.5442 -54.0394 18.0(1.9) 2002.5±1.4 55.5±2.6 .720±.0158 579.4/786 -
GSA25 408 247.6917 -53.9281 21.1(1.4) 850.9±.03 67.6±2.9 .003±.0001 876.2/771 0.057 (8)
GSA3 409 244.1129 -54.6303 17.7(1.4) 696.0±2.0 60.4±3.0 .615±.0102 606.7/1090 0.051
GSA26 411 241.8729 -55.3814 17.8(2.2) 1642.1±0.3 23.2±0.8 .504±.0138 441.5/759 0.030
GSA27 411 242.4846 -55.2292 18.3(1.7) 2193.8±0.1 6.8±0.4 .210±.0068 433.6/831 0.022
θMus
GSA28 501 202.2838 -64.2750 19.3(3.7) 1992.2±0.4 205.±20.0 .029±.004 717/499 0.431 (9)
Standardfitparameters: 1992.0±0.4 87.3±3.0 .094±.0046 868.5/500
GSA29 502 204.0683 -63.7117 19.3(2.5) 1229.7±0.3 74.2±2.7 .082±.0042 161.7/354 0.166
GSA30 505 199.2942 -64.2592 16.5(2.7) 2396.9±0.1 12.4±0.2 .062±.0023 792.0/856 0.073
Uncertain candidate
GSAu1 202 278.0371 -13.2851 18.1(2.9) 1695.8±6.9 409.3±20.9 .708±.0155 426.9/613
Notes:(1) GSA8:Blended;C = 1.00±0.03, C = 0.68±0.02; lensedstarhas I∗ (V∗−I∗) = 16.6(4.4).(2)GSA14:Light-curveexhibits
R B C J C
typicalfeaturesofabinarylenssystem.Giventhesmallnumberofmeasurementswithsignificantmagnification,noreliableanalysisoftheshape
canbeperformed.(3)GSA18:Parallax;projectedEinsteinradiusinthesolarplaner˜ =12.5±7.0AU.(4)GSA2:DescribedinpaperI.Foundat
E
thattimeasthefirstcandidateforabinarylensedsource(Xallarap).(5)GSA19:Xallarapandblend;thebestfitisperformedignoringthe3most
magnifiedmeasurements,thatareaffectedbythenon-linearityoftheCCD. C =1., C =0.160±0.013;lensedstarhasI∗ (V∗−I∗)=15.5(8.4).
R B C J C
The light-curve distortion could be due to the face-on circular orbiting of the source around the center-of-mass of a system including a non
luminousobject,withperiodP = 294.±47.days,andwithaprojectedorbitradiusofρ = ax/R = 0.081±0.023,whereaistheorbitradius
0 E
andx=D /D .Seealsotext.(6)GSA20:Parallax;r˜ =0.94±0.07AU.(7)GSA21:Blended;C =0.53±0.02, C =0.34±0.02;lensed
lens source E R B
starhasI∗ (V∗−I∗) = 17.5(3.5).(8)GSA25:Animprobableconfiguration,butagenuineone(verysmallu onaveryfaintstar).(9)GSA28:
C J C 0
Blended;C =0.30±0.03, C =1;lensedstarhasI∗ (V∗−I∗)=20.6(1.5).Theχ2/dof ofthefitisaffectedbyanunderestimateoftheerrors
R B C J C
duetobrightneighboringstars.
– Ideally, the goodnessof the microlensingfit should be uni- restrictedtothehighmagnificationepoch(u< 2, A >1.06,
form throughoutthe observationduration. Here we use fits seeSect.5.3).Letχ2 andn bethecomplementaryvari-
base base
madeseparatelyin thetwo colors.Letχ2 andn bethe
u<2 u<2
microlensing fit χ2 and the number of degrees of freedom,
EROScollaboration:Microlensingtowardsthespiralarms 9
Ic 15 δfit35 GSA-19 GSA-21
GSA-19 GSA-20
30
16 GSA-18
GSA-20 GSA-16
GSA-30
GSA-8 GSA-17 GSA-14 25
GSA-21
17 GSA-12 GSA-13 GSA-2
20
GSA-26GSA-3
18 GSA-27 GSA-10 GGSSAA-2-u41
GGSSAA--122 GSA-15GSA-23 15
GSA-2 GSA-8
GSA-11 GSA-9 GSA-14
19
10
GSA-29
GSA-28
20 5 GSA-28 GSA-G24SA-22
GSA-u1 GSA-23 GSA-30
GSA-13 GSA-18
0 GSA-1G1SA-25 GSA-27 GSA-12
21 GSA-25 GSA-9 GSA-26 GSA-1
GSA-16 GSA-29
-5 GSA-3 GSA-17GSA-10
GSA-15
22
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10-1 1 10 102
u ∆χ2/t
0 E
Fig.8.δ versus(∆χ2 +∆χ2)/t forthemicrolensingcandidates.Red
fit B R E
dotscorrespondtoeventswithfittedu <0.7.Thesmalldotsrepresent
0
I5.5 thesimulatedeventsthatsatisfythemicrolensingselection.
-
V
5
−1
1 1 2
4.5 × + (15)
"n (R)+n (B) n (R)+n (B)#
u<2 u<2 base base
4
quantifiesthedifferenceofthestandardfitqualityduringand
outsidethemicrolensingpeak,expressedinstandarddevia-
3.5
tions(thanksto the second factor). A negativevalue of δ
fit
(< −5) is an indication of a non constant base, and points
3
to a variable star instead of a microlensing event. For non-
standardmicrolensing(parallax,blending...)δ willbepos-
fit
2.5
itiveandmaybelarge(> 10),becausethefitisexpectedto
belessgoodinthepeakthaninthebase.
2
– ManyoftheEROSinstrumentaldefects—suchasbadpix-
elsordiffractionfeatures—havealonglifetime,andlastfor
1.5
entireobservingseasons.Thisproduceslongtimescalefalse
candidates.Asignaltonoiseindicatorisprovidedbythera-
1 tio(∆χ2 +∆χ2)/(t /1day)where∆χ2isdefinedabove(cri-
B R E
terionC6)andwheret characterizestheeventtimescale.
E
0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
u0 Figure 8 shows the distribution of δfit versus (∆χ2B +
∆χ2)/(t /1 day) forthe data satisfying the filtering conditions,
R E
forthe finalcandidatesandforthe simulatedsample (see Sect.
Fig.7.Toppanel:I versusfittedu forthe27microlensingcandidates.
Bottompanel:V −CI versusfitted0u .u isthefittedvalueassuminga 7.1).Withinourfinalsample,threesubgroupsareapparent:
J C 0 0
point-likesourceandapoint-likedeflectorwithaconstantspeed.The
– afew (6)selectedeventshavebotha largepositiveδ and
reddots (respectively black dots) correspond toevents withu < 0.7 fit
0 (∆χ2 +∆χ2)/t .Theseareeventsforwhichanon-standard
usedforopticaldepthstudies(resp.0.7<u0 <1.).Thesmalldotsare B R E
thesimulatedeventsthatsatisfythemicrolensingselectioncriteria. microlensing fit provides a better interpretation. Each of
themisdiscussedintheremarksoftable2.
– the bulk of our final sample (20) are events with a large
(∆χ2 +∆χ2)/t andδ compatiblewith 0,asexpectedfor
B R E fit
standardmicrolensingevents(andasisthecaseforoursim-
ablesoutsidethepeakperiod.Thevariable ulatedsample).
– EventGSA-u1hasasmall(∆χ2 +∆χ2)/t .Aftervisualin-
χ2 (R)+χ2 (B) χ2 (R)+χ2 (B) spection(seeAnnexA,lasteveBnt),weRcanEnotexcludeami-
δ = u<2 u<2 − base base
fit n (R)+n (B) n (R)+n (B) crolensinginterpretation,butthelongdurationandthelack
u<2 u<2 base base
 
10 EROScollaboration:Microlensingtowardsthespiralarms
ofareliablebasemakeitveryuncertain,consideringtherel-
ativelylowvalueof∆χ2 +∆χ2 (only73.).Thestatusofthis
B R
cloanngdeidrattiemreemraanignespceanndbinegmuandtiel.fOurntheesrhoobusledrvkaeteiopnisnomveirnda 000)2500 GSA-30 GSA-20
tthriabtuctioonnfitromtehdeeovpetnictsalodfetphtihs t(yGpSeAwuo1uwldoguilvdecaonmtraijbourtecofno-r 24502250 GGSSAA--1292 GSA-27
6W.2e.∼fiCr0sot.m5c×phea1cr0iks−eo6dnttowhweitahcrodthhseeθreEMnRcuOes)Sb.e3twyeeeanrtahneaplyressisen(ptarepseurltIsI)and t (HJD-012705000 GGSAS-A2-128 GSA-G18SA-11 GSGAS-GA9G-S2SA6AG--1S27A3-10 GGSSA-A-u21G4GSSAA--1146
twhiothseaomfpaaxpimeruImI.Tochcrueerraindgdidtiuorninaglctahnedfiirdsatttehsr(eGeSyAea8r,s1h3avaendbe2e5n) 1500 GSA-12 GSA-15
found.GSA13andGSA25belongtosubfieldsthatwerenotana- 1250 GSA-29
lyzedinpaperII.GSA8islocatedattheborderoftwosubfields,
caanldlyweaxspmloirsesethdeboyvoerulrapppreinvgioruesgaionnaslybseistwtheaetndsiudbnfioetldssy.stemati- 1000 GSA-25 GSA-8
Fourofthe7candidates,alltowardsγSct,foundinpaperII 750 GSA-3
arenowrejectedforthefollowingreasons:
GSA-2
– GSA4andGSA7bothshowedasecondfluctuationafterthe 500
firstthreeyears. GSA-1 GSA-13
– ForGSA5,theχ2improvementwhenreplacingaconstantfit 250
byamicrolensingfitisnolongersignificantenough,dueto 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
u
the low signal to noise ratio that prevailsfor its lightcurve 0
duringthe7yearsofdatataking.
– GSA6wasfoundtohaveanimpactparameterof0.98±0.04 Fig.9.t versusfittedu forthesimulatedeventssatisfyingtheanalysis
0 0
inpaperII.Takingintoaccountthefulllightcurve,thenew criteria(smalldots)andforthedetectedcandidates(bigdots).Reddots
fitted valueisu0 = 1.03±0.07,nowjustaboveourthresh- correspondtoeventswithfittedu0 <0.7(“standard”fit).Inthecaseof
old.Incidentally,∆χ2isalsomuchsmallerthanourthreshold complexevents,thebestfitu0valueisplotted.
(60),indicatingthatthepreviousselectionofthiseventcould
havebeenduetoafluctuation.
One notices that these rejected candidates were the low sig-
6.4.Statisticalpropertiesofthecandidateparameters
nal/noise ones towards γ Sct. Clearly, 7 years of observations
allowamuchbetternoisereductionthan3years. 6.4.1. Thelensconfigurations
Microlensingeventsoccurwithaflat-distributedimpactparam-
6.3.Overlapwithotherpublishedsurveys eter and minimumapproachtime. The sample of observedmi-
crolensing event (t , u ) configurations should be statistically
A very small region of γ Nor overlaps with the OGLE II mi- 0 0
representativeofsuchadistributionaftertakingintoaccountour
crolensingsurvey(OGLEwebpage).Noeventfromthisregion
detection efficiencies. This is illustrated in Fig. 9, where simu-
wasreportedinthelattersurvey(Udalskietal.2000a).
latedeventsaregeneratedasdescribedinSect.7.1.
A small region of our survey overlaps the MACHO fields
(Thomasetal.2005). Amongst the 9 MACHO candidates or
alertsfoundaroundγSct,3arelocatedwithinoneofourmon- 6.4.2. Themicrolensedstarpopulation
itored fields, but have not been selected in our analysis for the
followingreasons: The microlensed star population should also be representative
of the monitored population weighted by the microlensing de-
– MACHO alert number 302.44928.3523 is too faint to be tectionefficienciesandbytheopticaldepththatmayvaryfrom
measuredinBEROS andnomeasurementwasmadeinREROS sourcetosource.Asthesourcesarelikelytobedistributedalong
within40daysofthemagnificationmaximum.Nevertheless, the line of sight, a possible variation of the optical depth with
an object clearly appears in the BEROS images around the distancemustbeconsideredinthedataanalysis.Asthelightof
maximummagnificationdate. a remotesourceis expectedtobe morereddenedthanthelight
– MACHO alert number 301.45445.840 is too faint to be in of a close one, the optical depth τ should increase on average
the EROScatalog.Furthermore,EROSmissed the eventas with the color index. Figure 10 shows our color-magnitudedi-
itstimeofmaximummagnificationwas106daysbeforethe agram,weightedbythemicrolensingefficienciesandassuming
firstEROSobservationofthecorrespondingfield. thesameopticaldepthforallstars. Itisdirectlyobtainedfrom
– MACHO alert number 302.45258.1038 was very close to thesimulatedeventsthatsatisfytheanalysisrequirements.The
oneofthegapslocatedbetweenCCDs.Thusmanymeasure- distribution of the observed candidates is less peaked than the
ments are missing. Our standard procedure does not try to simulated one in the low color index region because the most
recover complete light-curves in such a case, and the stan- reddened stars are more likely to be lensed. We were able to
dard light-curve failed our selection process. Nevertheless, qualitatively confirm this color bias through the catalog pro-
weconfirmthepresenceofthebumpattherighttime,with ducedwithasimplesimulationtowardsγSctdescribedinSect.
the maximum magnification occurringduring the very first 9.2,thattakesintoaccountthesourcedistancedistribution(Fig.
daysoftheEROSdatataking. 11 left). Fig. 11(right) shows that the color distribution of the