Microlensing variability in the gravitationally lensed quasar Q2237+0305 = the Einstein Cross, I. Spectrophotometric monitoring with the VLT

1.2 MB·English

by  A. Eigenbrod

Astronomy&Astrophysicsmanuscriptno.8703 (cid:13)c ESO2008
February1,2008
Microlensing variability in the gravitationally lensed quasar
+ ≡ ⋆
QSO 2237 0305 the Einstein Cross
8
0
0 I. Spectrophotometric monitoring with the VLT
2

n
a A.Eigenbrod1,F.Courbin1,D.Sluse1,G.Meylan1,andE.Agol2
J

2
2 1 Laboratoired’Astrophysique,EcolePolytechniqueFe´de´raledeLausanne(EPFL),ObservatoiredeSauverny,1290Versoix,Switzerland
2 AstronomyDepartment,UniversityofWashington,Box351580,Seattle,WA98195,USA

]
h
Received...;accepted...
p
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o ABSTRACT
r
t
s Wepresenttheresultsofthefirstlong-term(2.2years)spectroscopicmonitoringofagravitationallylensedquasar,namelytheEinsteinCross
a QSO2237+0305. Thegoalofthispaperistopresenttheobservational factstobecomparedinfollow-uppaperswiththeoreticalmodelsto
[
constraintheinnerstructureofthesourcequasar.

3 Wespatiallydeconvolve deepVLT/FORS1spectratoaccuratelyseparatethespectrumof thelensinggalaxy fromthespectraofthequasar
v images.Accuratecross-calibrationofthe58observationsat31-epochfromOctober2004toDecember2006iscarriedoutwithnon-variable
8 foregroundstarsobservedsimultaneouslywiththequasar.Thequasarspectraarefurtherdecomposedintoacontinuumcomponentandseveral
2 broademissionlinestoinferthevariationsofthesespectralcomponents.
8
Wefindprominent microlensing eventsinthequasar imagesA andB,whileimagesCand Darealmost quiescent onatimescaleofafew
2
months. Thestrongest variationsareobserved inthecontinuum of imageA.Their amplitudeislargerintheblue(0.7mag) thaninthered
.
9 (0.5mag),consistentwithmicrolensingofanaccretiondisk.Variationsintheintensityandprofileofthebroademissionlinesarealsoreported,
0 most prominently in the wings of the CIII] and center of the CIV emission lines. During a strong microlensing episode observed in June
7 2006inquasar imageA,thebroadcomponent oftheCIII]ismorehighlymagnifiedthanthenarrow component. Inaddition, theemission
0
lineswithhigherionizationpotentialsaremoremagnifiedthanthelineswithlowerionizationpotentials,consistentwiththeresultsobtained
:
v withreverberation mapping. Finally, wefind that the V-band differential extinction by the lens, between the quasar images, is inthe range
i 0.1−0.3mag.
X
r Keywords.Gravitationallensing:quasar,microlensing—Quasars:general.Quasars:individualQSO2237+0305,EinsteinCross
a
1. Introduction laysbetweenthe fourquasarimagesare ofthe orderof a day
(Rixetal.1992,Wambsganss&Paczyn´ski1994),meaningthat
The gravitational lens QSO 2237+0305, also known as
intrinsic variability of the quasar can easily be distinguished
“Huchra’s lens” or the “Einstein Cross”, was discovered by
from microlensing events. In addition, the particularly small
Huchra et al. (1985) during the Center for Astrophysics
redshift of the lensing galaxy implies large tangential veloci-
Redshift Survey. It consists of a z = 1.695 quasar gravita-
s ties for the microlenses. Furthermorethe quasar images form
tionallylensedintofourimagesarrangedinacrosslikepattern
right in the bulge of the lens where the stellar density is the
aroundthenucleusofaz =0.0394barredSabgalaxy.Theav-
l highest.Thecombinationofthesepropertiesmakesmicrolens-
erageprojecteddistance of the imagesfromthe lens centeris
ingeventsverylikelyintheEinsteinCrossandveryrapid,with
0.9′′.
timescalesofafewweekstoafewmonths.Indeed,Irwinetal.
A few years after this discovery, Schneider et al. (1988)
(1989)reportedsignificantbrightnessvariationsofthebright-
andKent&Falco(1988)computedthefirstsimplemodelsof
estquasarimageA,whichtheyinterpretedasthefirstdetection
thesystem,leadingtotheconclusionthatthissystemwasvery
everofmicrolensingintheimagesofamultiply-imagedquasar.
promisingtostudymicrolensing.Indeed,thepredictedtimede-
Sincethen,microlensingeventshavebeenobservedinsev-
⋆ Based on observations made withthe ESO-VLTUnit Telescope eral other gravitationally lensed quasars, and are expected to
# 2 Kueyen (Cerro Paranal, Chile; Proposals 073.B-0243(A&B), occur in virtually any quadruply lensed quasar (Witt et al.
074.B-0270(A),075.B-0350(A),076.B-0197(A),177.B-0615(A&B), 1995). Probably the most compelling examplesof microlens-
PI:F.Courbin). inglightcurvesaregivenbytheOpticalGravitationalLensing
2 A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross
Experiment (OGLE) (Woz´niak et al. 2000a, Udalski et al. coupled with quasar models and will be the subject of future
2006). Started in 1997, this project monitors regularly the papers.
four quasar images of QSO 2237+0305, showing continuous
microlensing-inducedvariationsinthelightcurves.
Mostofthequasarmicrolensingstudiessofararebasedex-
clusivelyonbroad-bandphotometricmonitoring(e.g.Woz´niak
et al. 2000b; Schechter et al. 2003; Colley & Schild 2003).
These observations, even though dominated by variations of
the continuum,make itverydifficultto disentanglevariations
in the continuum from variations in the broad emission lines
(BELs). Both types of regions are affected by microlensing,
butindifferentwaysdependingontheirsize.
Microlensingofanextendedsourcecanoccurwhenitssize
is smaller than or comparableto the Einstein radius of a star,
i.e.oftheorderof1017cmor10−1pcinthecaseoftheEinstein
Cross(Nemiroff1988;Schneider&Wambsganss1990).From
reverberationmapping,the broadline region(BLR) was long
estimated to be larger than this, of the order of 1018 cm or
1pc,henceleavinglittleroomforBELmicrolensing.However,
more recent reverberation mapping studies revise this down-
wards, to 1016 cm (Wandel et al. 1999, Kaspi et al. 2000),
which is also consistent with the disk-wind model of Murray
et al. (1995). Inspired by these numbers, Abajas et al. (2002)
and Lewis & Ibata (2004) investigated BEL microlensing in
furtherdetailandcomputedpossiblelineprofilevariationsfor
variousBLRmodels. Fig.1. VLT/FORS1 field of view showing the lensed quasar
Observations of significant continuum and BEL mi- QSO 2237+0305, along with the four PSF stars used to spa-
crolensing have been reported in a number of systems tiallydeconvolvethespectra.Thesestarsarealsousedtocross-
(QSO 2237+0305, Filippenko 1989, Lewis et al. 1998, calibratetheobservationsinfluxfromoneepochtoanotherand
Wayth et al. 2005; HE 2149−2745, Burud et al. 2002a; tominimizetheeffectofskytransparency.
HE 0435−1223, Wisotzki et al. 2003; H 1413+117, Chartas
et al. 2004; SDSS J1004+4112, Richards et al. 2004;
HE 1104−1805, Go´mez-A´lvarez 2004; HE 0047−1756,
Wisotzki et al. 2004; SDSS J0924+0219, Eigenbrod et al.
2. Observations
2006a, Keeton et al. 2006 ; and RXJ 1131−1231, Sluse et
al.2007).Thesefirstobservationalindicationsofmicrolensing WeacquiredourobservationswiththeFOcalReducerandlow
can be turned into a powerfultool to probe the inner parts of dispersion Spectrograph (FORS1), mounted on Kueyen, the
quasars, providedregular spectroscopic data can be obtained. Unit Telescope # 2 of the ESO Very Large Telescope (VLT)
Several theoretical studies show how multiwavelength light located at Cerro Paranal (Chile). We performed our observa-
curves can constrain the energy profile of the quasar accre- tionsinthemulti-objectspectroscopy(MOS)mode.Thisstrat-
tion disk and also the absolute sizes of the line-emitting re- egy allowed us to get simultaneous observations of the main
gions(e.g.,Agol&Krolik1999,Mineshige&Yonehara1999, target and of four stars used as reference point-spread func-
Abajasetal.2002,Kochanek2004). tions(PSFs).Thesestarswereusedtospatiallydeconvolvethe
In this paper we present the results of the first long-term spectra, as well as to perform accurate flux calibration of the
spectrophotometricmonitoringoftheEinsteinCross.Thespec- targetspectrafromoneepochtoanother.Wechosethesestars
tral variations of the four quasar images are followed under to be located as close as possible to QSO 2237+0305 and to
sub-arcsecondseeingconditionswiththeVeryLargeTelescope have similar apparent magnitudes as the quasar images. The
(VLT) of the European Southern Observatory for more than PSF stars # 1, 2, 3, and 4 have R-band magnitudes of 17.5,
twoyears,fromOctober2004toDecember2006,withamean 17.0,15.5,and17.5mag,respectively.Fig.1showsthefieldof
temporalsamplingofaboutonepointeverysecondweek.This viewofourobservations.
firstpaperdescribestheobservations,themethodusedtosepa- We used the high-resolution collimator of FORS1 to
ratethequasarspectrafromthatofthelensinggalaxy,andthe achievethebestpossiblespatialsamplingofthedata,i.e.0.1′′
mainobservationalresults.Simpleconsiderationsoftheprop- per pixel. With this resolution, we observed a maximum of 8
ertiesofmicrolensingcausticsandofthegeometryofthecen- objectssimultaneouslyoverafieldofviewof3.4′×3.4′.One
tralpartsofthequasaralreadyallowustoinferinterestingcon- slit was alignedalongtwo ofthe quasarimagesandfourslits
straintsonthequasarenergyprofileintheEinsteinCross. werecenteredonforegroundPSFstars.Weplacedtheremain-
The full analysis of our monitoring data, still being ac- ingslits onemptyskyregionsandusedthemto carryoutsky
quired at the VLT, requires detailed microlensing simulations subtractionofthequasardata.
A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross 3
1" Table1.Journaloftheobservationstakenon31epochs.
B
ID CivilDate HJD Mask Seeing[′′] Airmass
C
1 13−10−2004 3292 1 0.86 1.204
1 14−10−2004 3293 2 0.87 1.221
2 14−11−2004 3324 1 0.75 1.184
2 14−11−2004 3324 2 0.68 1.305
mask 2
3 01−12−2004 3341 1 0.88 1.355
D 3 01−12−2004 3341 2 0.94 1.609
4 15−12−2004 3355 1 0.99 1.712
N 4 16−12−2004 3356 2 0.90 1.817
A 5 11−05−2005 3502 1 0.87 1.568
mask 1 5 12−05−2005 3503 2 0.51 1.389
6 01−06−2005 3523 1 0.63 1.342
E 6 01−06−2005 3523 2 0.64 1.224
7 01−07−2005 3553 1 0.57 1.153
8 14−07−2005 3566 1 0.89 1.620
Fig.2. FORS1 R-band acquisition image of QSO 2237+0305
9 06−08−2005 3589 1 0.51 1.135
takenonepoch# 12(12−09−2005).Theslits usedinthe two
9 06−08−2005 3589 2 0.61 1.173
masksareshown.Theirwidthis0.7′′.ThePositionAngle(PA) 10 15−08−2005 3598 1 0.86 1.140
ofmask1isPA=+56.5◦andthatofmask2isPA=+68.5◦. 11 25−08−2005 3608 1 0.49 1.261
11 25−08−2005 3608 2 0.54 1.461
12 12−09−2005 3626 1 0.70 1.535
12 12−09−2005 3626 2 0.69 1.341
13 27−09−2005 3641 1 0.92 1.480
13 27−09−2005 3641 2 0.73 1.281
Two masks were designed to observe the two pairs of
14 01−10−2005 3645 1 0.78 1.281
quasar images. The PSF stars in both masks were the same.
14 01−10−2005 3645 2 0.87 1.156
Fig.2showstheslitpositioningwithrespecttoourtarget.The
15 11−10−2005 3655 1 0.57 1.140
first mask was aligned on quasar images A and D, while the
15 11−10−2005 3655 2 0.66 1.134
second was aligned on images B and C. The masks were ro- 16 21−10−2005 3665 1 0.70 1.215
tated to position angles that avoid clipping of any quasar im- 16 21−10−2005 3665 2 0.74 1.156
age.Thisismandatorytocarryoutspatialdeconvolutionofthe 17 11−11−2005 3686 1 0.90 1.137
spectra. 17 11−11−2005 3686 2 0.90 1.185
18 24−11−2005 3699 1 0.78 1.265
Our observing sequences consisted of a short acquisition
18 24−11−2005 3699 2 0.90 1.443
image, an “image-through-slit” check, followed by a consec-
19 06−12−2005 3711 1 1.10 1.720
utive deep spectroscopic exposure. All individual exposures
19 06−12−2005 3711 2 1.09 1.445
were 1620 s long. We list the journal of our observations in
20 24−05−2006 3880 1 0.87 1.709
Table 1. The mean seeing during the three observing seasons 20 24−05−2006 3880 2 0.90 1.443
was0.8′′.Wechoseaslitwidthof0.7′′,approximatelymatch- 21 16−06−2006 3903 1 0.66 1.213
ing the seeing and much smaller than the mean separation of 21 16−06−2006 3903 2 0.51 1.155
1.4′′between the quasar images. This is mandatory to avoid 22 20−06−2006 3907 1 0.64 1.286
contaminationofanimagebytheothers. 22 20−06−2006 3907 2 0.58 1.189
23 27−06−2006 3914 1 0.41 1.145
WeusedtheG300VgrismincombinationwiththeGG375
23 27−06−2006 3914 2 0.50 1.133
order sorting filter. For our slit width, the spectral resolution
24 27−07−2006 3944 1 0.74 1.316
was ∆λ = 15 Å, as measured from the FWHM of night-sky
24 27−07−2006 3944 2 0.76 1.204
emissionlines,andtheresolvingpowerwasR = λ/∆λ ≃ 400 25 03−08−2006 3951 1 0.73 1.246
atthecentralwavelengthλ = 5900Å.Theusefulwavelength 25 03−08−2006 3951 2 0.65 1.169
rangewas3900 <λ< 8200Åwithascaleof2.69Åperpixel 26 13−10−2006 4022 1 0.59 1.176
inthespectraldirection.Thisconfigurationfavorsspectralcov- 26 13−10−2006 4022 2 0.52 1.300
erageratherthanspectralresolution,allowingustofollowthe 27 28−10−2006 4037 1 0.57 1.148
continuumover a broad spectral range, starting with the very 27 28−10−2006 4037 2 0.53 1.138
blue portion of the optical spectrum. Even so and in spite of 28 10−11−2006 4050 1 0.89 1.515
28 10−11−2006 4050 2 0.88 1.323
R=400,adetailedprofileoftheBELisstillaccessible.
29 27−11−2006 4067 1 0.87 1.255
We also observed spectrophotometric standard stars 29 27−11−2006 4067 2 0.92 1.391
(GD 108, HD 49798, LTT 377, LTT 1020, LTT 1788, and 30 19−12−2006 4089 2 1.04 2.125
LTT7987)toremovetheresponseofthetelescope,CCD,and 31 22−12−2006 4092 1 0.80 2.018
grism.Wedidtherelativecalibrationbetweentheepochsusing 31 23−12−2006 4093 2 0.76 2.248
thePSFstars(seeformoredetailsEigenbrodetal.2006a).
4 A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross
Fig.3.SpectraofthefourPSFstars.Thespectraineachpanel Fig.4.Fluxcorrectionfordifferentepochswithrespecttothe
correspond to different observing epochs, chosen to span the reference epoch # 2 (14−11−2004). Each panel corresponds
fulllengthofthemonitoring.TheIDsoftheobservingepochs, to one of the 4 PSF stars visible in Fig. 3. In each panel, the
as given in Table 1, are indicated. The differences in flux are dotted line shows the ratio of the spectrum of one PSF star
mainlydueto thepresenceofthinclouds.Thepurposeofus- takenatagivenepochandthespectrumofthesamestartaken
ingthesestarsasfluxcross-calibratorsispreciselytoeliminate atthe referenceepoch# 2.The curvesare polynomialsfitting
thesedifferences,bothinintensityandshape. thedata.Importantly,thecorrectionderivedatagivenepochis
aboutthesameforthefourstars.Themeanofthesefourcurves
isusedtocorrectthespectraoftheEinsteinCrossimages.The
small parts of the spectra with strong atmospheric absorption
Finally,itisworthemphasizingthatallourVLTdataused are masked. The different spectral ranges are due to different
in the present paper were obtained in service mode, without
clippingsofthespectrabytheedgesoftheCCD.
whichthisprojectwouldhavebeenimpossible.
3. Dataanalysis
3.1.Reduction We removedthe sky backgroundin a differentway in the
spectra ofthe PSF stars andin those ofthe gravitationallens.
The data reduction followed the same proceduredescribed in ForthePSFstars,whicharesmallcomparedwiththeslitlength
detailinEigenbrodetal.(2006b).Wecarriedoutthestandard (19′′), we used the IRAF task background. This task fits a
bias subtraction and flat field correction of the spectra using secondorderChebyshevpolynomialinthespatialdirectionto
IRAF1.Weobtainedthewavelengthcalibrationfromthespec- the areas of the spectrum that are not illuminated by the ob-
trumofhelium-argonlamps.Allspectra,fortheobjectandfor ject, and subtracts it from the data. As the lensing galaxy in
thePSFstarswerecalibratedintwodimensions. QSO2237+0305islargerthantheslitlength,thisprocedureis
Only one single exposure was taken per mask and per notapplicable.Instead,we used the slits positionedonempty
epoch.For thisreason,the usualcosmic-rayrejectionscheme skyregionsoftheFORS1fieldofview,andlocatednexttothe
applied to multiple images could not be applied. Instead, we gravitationallens.Theskywasfittedtotheseslitsandremoved
used the L. A. Cosmic algorithm (van Dokkum 2001), that fromtheslitcontainingtheimagesofQSO2237+0305.
can handle single images. We visually inspected the cosmic-
ray corrected images to check that no data pixel was affected
bytheprocess,especiallyintheemissionlinesandinthedata 3.2.Fluxcross-calibration
withthebestseeing.
Once the cosmic raysand sky backgroundwere removed,we
1 IRAF is distributed by the National Optical Astronomy applied a flux cross-calibrationof the spectra as described by
Observatories,whichareoperatedbytheAssociationofUniversities Eigenbrodetal.(2006a),usingthefourPSFstars.Thespectra
for Research in Astronomy, Inc., under cooperative agreement with of these stars are shown in Fig. 3 for five different observing
theNationalScienceFoundation. epochs.Ourobservationsshowthatthesestarsarenonvariable.
A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross 5
Fig.7. Deconvolved and extracted 1D-spectra of the lensing Fig.8. Example of a spectral decomposition. The top panel
galaxy. The two panels correspond to the two MOS masks. shows the two extracted spectra for the images A and D for
The shaded areas are the envelopescontaining all the spectra theobservationstakenonepoch#25(03−08−2006)withmask
of the lens obtained with the corresponding mask. The thick 1.Theextractedspectrumofthelensinggalaxy,inthebottom
black lines are the means. Note the small scatter between the panel, shows no trace of contamination by the quasar BELs.
twospectra. Forclarity,wehavemultipliedthefluxofimageDbyafactor
oftwo.
Wecreatedaratiospectrumforeachstar,i.e.wedividedthe
spectrumofthestarbythespectrumofthesamestarforacho- 3.3.Deconvolution
senreferenceexposure.Wechoseepoch#2(14−11−2004)as
our reference exposure because of the excellent weather con- The lensing galaxy in QSO 2237+0305 is bright. Its
ditions at this particular epoch for both seeing and sky trans- central parts have a surface brightness of approximately
parency.Thecomputationofthesefluxratioswasdoneforall 18 mag/arcsec2 in the R band, which is comparable to the
four stars in each exposureand we checked the compatibility quasarimages. Hencestudyingmicrolensingvariationsofthe
oftheresponsecurvesderivedwiththefourdifferentstarsare quasarimagesrequiresveryaccuratedeblending.
compatible(seeFig.4).Ifnot,werejectedoneoramaximum Inordertocarryoutthischallengingtask,weusedthespec-
of two ofthe PSF stars. This canhappenin some exceptional tralversionoftheMCSdeconvolutionalgorithm(Magainetal.
cases, e.g.whenthealignmentbetweenthestar andtheslitis 1998,Courbinetal.2000),whichusesthespatialinformation
not optimaland generatesa color gradientin the spectrum of containedinthespectraofthePSFstars.Thealgorithmsharp-
themisalignedobject.Asidefromthisinstrumentaleffect,the ens the spectra in the spatial direction, and also decomposes
observations show no trace of intrinsic variability of the PSF themintoa“point-sourcechannel”containingthespectraofthe
stars. two quasarimages,andan “extendedchannel”containingthe
Aftercheckingthatthecorrectionspectraobtainedforthe spectrumofeverythingintheimagethatisnotapointsource,
four stars were very similar, we computed their mean, which inthiscase,thespectrumofthelensinggalaxy.InFig.5,weil-
wetookasthecorrectiontobeappliedtothegravitationallens. lustratetheprocessandthedifferentoutputs.InFig.7,weshow
The high stability of the corrections across the field demon- howsimilarthespectraofthelensinggalaxyare,extractedei-
strates that all residual chromatic slit losses due to the atmo- ther from two different masks or from data taken at different
sphericrefractionarefully corrected.Thiscorrectionis eased epochs, henceillustrating the robustnessof the deconvolution
bythefactthat:(1)thepositionangleofthemasksisthesame technique.InFig.8, we givean exampleofdecompositionof
forthequasarimagesandforthePSF stars(i.e.thePSFclip- thedataintothequasarandlensspectraafterintegratingalong
ping is the same for the target and the reference stars); (2) the spatial direction. The lensing galaxy spectrum shows no
weavoidobservationsatlargeairmasses(i.e.neverlargerthan traceoftheresidualquasarBELs.Evenwhenthecontrastbe-
2.5);and(3)theatmosphericrefractioncorrectoronFORS1is tween the quasar and the galaxy is particularly large, the de-
veryefficient. compositionisaccurate.Forexample,theCaIIH+Kdoubletin
6 A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross
Fig.5. Left: portion of the VLT 2D-spectrum of quasar images D and A, taken on epoch # 25 (03−08−2006),on which are
indicatedthemainspectralfeaturesofeitherthequasarsorthelens.Centerleft:spatiallydeconvolvedspectrum.Thetwoquasar
images are very well separated. Center right: spectrum of the lensing galaxy alone. Right: residual map of the deconvolution
aftersubtractionofthequasarandlensspectra.Notethattheresidualsare displayedwithmuchnarrowercutsthanthoseused
in the other panels. The darkest and brightest pixels correspond to −3σ and +3σ respectively. No significant residuals of the
spectralfeaturesarevisible.
Fig.6. DeconvolvedandextractedspectraofquasarimageAforfiveobservingepochs.Chromaticvariationsinthespectraare
conspicuouswiththebluepartofthespectrabeingmoremagnifiedthantheredpart.
thelensspectrumiswellvisible,inspiteofthepresenceofthe 3.4.Cross-checkwiththeOGLE-IIIlightcurves
strongquasarCIVemissioninthesamewavelengthrange.
After reduction and spatial deconvolution, we obtained the
extracted spectra of quasar images A and D on 30 different
A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross 7
ofimageD.However,asidefromthisshift,theagreementbe-
tweentheOGLEphotometryandourintegratedVLTspectrais
alsoverygoodforimageD.
4. Multi-componentdecomposition
Different emission features are known to be produced in re-
gionsofdifferentcharacteristicsizes.Asmicrolensingmagni-
ficationvariesonshortspatialscales,sourcesofdifferentsizes
are magnified by differing amounts (e.g. Wambsganss et al.
1990).Emissionfeaturesfromsmallerregionsofthesourceare
morehighlyvariableduetomicrolensingthanfeaturesemitted
in more extended regions. In order to study the variation of
eachspectralfeatureindependently,weneedtodecomposethe
spectraintotheirindividualcomponents.
4.1.Method
Inouranalysisofthe1-Dspectraofthefourquasarimages,we
follow the multi-component decomposition (MCD) approach
(Wills et al. 1985, Dietrich et al. 2003) implementedin Sluse
etal.(2007).Thismethodisappliedtotherest-framespectra,
Fig.9. OGLE-IIIlightcurves(Udalskiet al. 2006) of allfour
assuming they are the superposition of (1) a power law con-
quasar images from April 2004 to December 2006 (dots),
tinuum, (2) a pseudo-continuum due to the merging of FeII
compared with the photometry derived by integrating our
and FeIIIemission blends, and(3) an emission spectrumdue
VLT spectra through the OGLE V-band (dark triangles). The
totheotherindividualBELs.Weconsiderthefollowingemis-
1−sigma error bars correspond to the photon noise in the
sionlines:CIVλ1549,HeIIλ1640,OIII]λ1664,AlIIλ1671,
spectrum. We shift the OGLE-III light curve of image D by
AlIIIλ1857,SiIII]λ1892,CIII]λ1909,andMgIIλ2798.All
−0.5 mag with respect to the published values. The bottom
thesefeaturesarefittedsimultaneouslytothedatausingastan-
paneldisplaystheseeingvaluesforeachobservations.
dard least-square minimization with a Levenberg-Marquardt
based algorithm adapted from the Numerical Recipes (Press
etal.1986).
In the first step, we identify the underlying nonstellar
epochs, and of B and C on 28 different epochs. Several ex- power-law continuum from spectral windows that are free
tracted spectra of image A are shown in Fig.6. As a sanity (or almost free) of contributions from the other components,
check,wecomparedourresultswiththeOGLE-IIIphotomet- namelythe ironpseudo-continuumandthe BELs. We use the
ric monitoring of QSO 2237+0305(Udalski et al. 2006). We windows 1680 ≤ λ ≤ 1710 Å and 3020 ≤ λ ≤ 3080 Å.
integrated our quasar spectra in the corresponding V-band to AftervisualinspectionoftheirontemplatesbyVestergaardet
estimate, from the spectra, the photometric light curves as if al.(2001),wedonotexpectsignificantironemissioninthese
they were obtained from imaging. In Fig. 9, we compare our windows.
magnitudeestimateswiththeactualOGLE-IIImeasurements. We characterize the spectral continuum (measured in the
The overall agreement is very good for images A, B, and C. restframe)withapowerlaw fν ∝ναν,whichtranslatesinwave-
For image D, we have to shift the OGLE-III light curve by lengthto fλ ∝λαλ withtherelationαν =−(2+αλ),i.e.
−0.5 mag with respect to the published values. Interestingly,
thisshiftisnotneededwhenwe compareourresultswiththe λ αλ λ −(2+αν)
f = f = f
previousOGLEdatafromtheprovisionalcalibrationpresented λ 0 λ ! 0 λ !
0 0
intheyears2004−2006.ThepreviousOGLEdataalsoagreed
with the photometryof Koptelovaet al. (2005). Thischanged whereλ =2000Åandwhereα isthecommonlyusedcanon-
0 ν
whenUdalskietal.(2006)reviewedtheircalibrationandgave icalpowerindex.
image D a larger magnitude of approximately0.5 mag. They Next,wefittheBELswithGaussianprofiles.Weconsider
stated that the steep rise of brightness of image D at the end asumofthreeprofilestofittheabsorptionfeatureintheCIV
of the 2000 OGLE-II season leaded to an overestimate of the emissionline.TwoprofilesareusedfortheCIII]lineandone
extrapolatedmagnitudeforthe beginningof the 2001OGLE- single profile is used to fit simultaneouslythe OIII] and AlII
III season. But this is now discrepant with the photometry of lines. All other BELs are fitted with one single profile. We
Koptelovaetal.(2005).Wethinkthatthenewextrapolationof then subtract the BELs and the continuum from the spectra.
thelightcurveofimageDfromtheendofseason2000tothe Weconsidertheresidualsascomingfromtheemissionblends
beginning of season 2001 might be uncertain, leading to the of FeIIandFeIII.Hencetheaveragedandnormalizedresidu-
observedshiftbetweenourdataandtheOGLE-IIIlightcurve alsoverallepochsdefineourfirstironpseudo-continuumtem-
8 A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross
Fig.10.Multi-componentdecompositionofthespectrumofthebrightestquasarimage,A,takenonepoch#2(14−11−2004).
The upper panelsshow the detailed spectral decompositionof the BELs, while the middle paneldisplays the entire spectrum.
The continuum is indicated as a dotted curve. The Gaussian lines and iron pseudo-continuumtemplates are shown below the
spectrum.Thebottompanelistheresidualforeachpixelnormalizedbythephotonnoiseperpixel(i.e.they-axisistheresidual
fluxinunitsofσ).
Fig.11.Left:ExamplesoflightcurvesforthequasarimageA.Theintegratedfluxforthecontinuum,theHeII,andCIII]BELs
aregivenfromtoptobottom.Thecontinuumisintegratedovertheentireavailablewavelengthrange.Ineachpanel,wefitascaled
version(solidline)oftheOGLE-IIIlightcurve(Udalskietal.2006).ThisnicelyillustratesthattheBELsvarysimultaneously
andproportionallytothe continuum.Right:variabilityofthebest-fitparametersα and f ofthecontinuum(see Section4.1).
A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross 9
imagesAandB,indicatingthatsignificantmicrolensingevents
occuredinthesetwoimages.
Inaccuratealignmentofthequasarimagesintheslitofthe
spectrograph is a possible instrumental effect that can mimic
microlensing changes in the spectral slope of the quasar im-
ages.Indeed,smallclippingofoneofthequasarimageswould
lead to a stronger flux loss at the bluer wavelengths, hence
producing a color gradient in the spectrum and a decrease in
themeasuredvalueα .Wehavecheckedallthe“through-slit”
ν
imagestakenbeforeeachspectrum.Notonlydotheseimages
showthatthealignmentiscorrect,butitisalsoveryeasilyre-
produciblefromoneepochto another,evenwhenthe FORS1
hasbeendismountedfromandremountedonthetelescope.
Wehavealsocheckedthatourfittingproceduredoesnotin-
troduceanyspuriouscorrelationbetweenα and f .Wecheck
ν 0
this by using simulated spectra. In order to do that we take a
referencespectrumforeachquasarimageandsubtractitscon-
tinuum. We then take random pairs of (α , f ) parameters so
ν 0
that the α vs. f plane is well sampled. We chose 400 such
ν 0
pairs and create the corresponding continuum to be added to
the reference spectrum. The decomposition procedure is then
run on the 400 spectra. We find no correlation at all between
Fig.12. Correlation between the intensity f0 and slope αν of the measured αν and f0. In addition, the parameters used to
the continuum spectra for all four quasar images. The points
build the simulated spectra are almost perfectly recovered by
are connected chronologically. The first observation epoch is
thedecompositionprocedure.
marked by a star and the last one by a square. The correla-
Weconcludethatgenuinechromaticvariationsarepresent
tion is obviousin images A and B spanning a broad range of inthecontinuumofallimagesofQSO2237+0305.Theeffect
spectral slopes. In these two images, an increase in intensity
ismostpronouncedin imageA duringthelastobservingsea-
isaccompaniedbyanincreaseinsteepness,i.e.whenaquasar
son, and in image B at the beginning of our monitoring. We
imagegetsbrighter,italsogetsbluer. showinthefollowingthattheseobservedvariationsare,inad-
dition,wellcompatiblewiththeOGLE-IIIsingle-bandphoto-
metricobservations.
plate.Wecanthenproceediterativelybyincludingthispseudo- 5. MicrolensingvariabilityintheOGLE-III
continuumiron template in the fitting procedureand rerun it. photometry
Thisgivesa better fitting ofthe emissionlines anddefinesan
The photometric variations in most gravitationally-lensed
improvedironpseudo-continuumtemplate.Afterfiveofthese
quasarsaredominatedbytheintrinsicvariationsofthequasar,
iterations, typically the fitting does not change significantly
typically of the order of 0.5 − 1.5 mag, hence making them
anymore. Fig. 10 shows an example of the fitting decompo-
usefultomeasurethetimedelaysbetweenthe quasarimages.
sitiondescribedabove.
Microlensingvariationsareusuallysmaller,intherange0.05−
0.1 mag (e.g. the lensed quasarsB 1600+434by Burud et al.
4.2.Results 2000; RX J0911+0551by Hjorth et al. 2002; SBS 1520+530
by Burud et al. 2002b; FBQ 0951+2635 by Jakobsson et al.
The lightcurvesfor the continuumand for the emission lines 2005).
can be constructed from the above multi-component decom- The Einstein Cross is differentfrom this generalbehavior
position. We show in Fig. 11 an example of variation in the in two ways:(1)the time delaysbetweeneachpairof images
brightestquasarimage,A,forthecontinuumandfortwoBELs. areexpectedtobeoftheorderofoneday,hardlymeasurable,
Theerrorbarsgivethephotonnoise,integratedoverthecorre- and(2) themicrolensingvariationsdominatethe lightcurves.
sponding wavelength range. In the right panel of Fig. 11, we Forthesetworeasons,microlensingcanbefairlywellisolated
show the variability of the continuum in intensity, f , and in in each quasar image, because it acts differently on the four
0
slope,α ,forthe4quasarimages.Itisimmediatelyclearthat sightlines.
ν
the continuum variations with the largest amplitude are ob- Toseparatetheintrinsicfluxvariationsofthequasarfrom
served in image A, betweenHJD = 3600and 3900 days, and the microlensing ones, we perform a polynomial fit to the
inimageBbetweenHJD=3300and3500days.Thesevaria- OGLE-III light curves (Udalski et al. 2006) of Fig. 9. This
tionsareaccompaniedbyanincreaseinsteepness,i.e.whena simple and fully analytical method has been developed by
quasarimagegetsbrighter,italsogetsbluer.Thisisparticularly Kochaneketal.(2006),andisalsodescribedbyVuissozetal.
obviousinFig.12,where f andα arestronglycorrelatedfor (2007).Inthepresentapplication,thevariationsofeachquasar
0 ν
10 A.Eigenbrodetal.:MicrolensingvariabilityintheEinsteinCross
cover the simulated intrinsic light curve of the quasar with a
typicalerroroflessthan0.1mag.Thevariationsofmorethan
0.4 mag, shown in Fig. 13, both for microlensing and quasar
variations, are well above the error estimated from the simu-
latedlightcurves.Inoursimulations,weadoptthesamepho-
tometricerrorbarsas inthe lightcurvesofallquasarimages,
i.e. there-scalingofthe errorbarsdescribedaboveinthereal
data is taken into account. If, on the contrary,we adopt error
barsthatfollowthephotonnoise,thefittingprocedureconsid-
ersthehighestsignal-to-noiselightcurveastheintrinsicquasar
lightcurve.
The light curve most affected by microlensing is that of
imageB,withapeak-to-peakamplitudeofmorethan0.7mag
over 3 years. The other quasar images show microlensing-
inducedvariationsofupto0.4mag,withquasarimageAhav-
ingasharpeventduringthelastobservingseason.Theintrinsic
quasarlightcurvedisplaysavariationofabout0.4mag.
Thepolynomialdecompositionofthelightcurvesarecom-
patiblewiththespectroscopicresults.QuasarimagesAandB,
whichhavethelargestmicrolensingcontributioninFig.13,re-
spectivelyatHJD∼3500daysandHJD∼3900days,alsohave
asharpriseinα atthesameepochs.
ν
Fig.13. Decomposition of the OGLE-III photometric light
curves(Udalskiet al. 2006) of the quasar images, into intrin-
6. Microlensingvariabilityinthespectra
sicquasarvariationsandmicrolensing-inducedvariations(see
Section5).Theintrinsicvariationsareshownatthebottomof Chromatic variationsof the continuumof images A and B of
the figure as a continuous line, while the pure microlensing QSO2237+0305areclearlyseeninourdata.Inaddition,dif-
variations are the data points. The curves are shifted arbitrar- ferential magnification of the continuum with respect to the
ily alongthe y-axisforclarity.Thetickmarksat the topshow BELsisalsoseeninallfourquasarimages.Sucheffectshave
theepochsofourobservations. alreadybeenobservedbyLewisetal.(1998)andWaythetal.
(2005),butonlyfordataovertwoepochs.OurVLTspectraal-
lowustofollowthevariationsovertwofullyears,providedthe
intrinsicvariationsofthequasarareremoved.
imagearemodeledasasumoftwoLegendrepolynomials:one
polynomialiscommontoallfourquasarimagesandrepresents
6.1.ContinuumandBELsrelativemagnifications
the intrinsic variations of the source while a second polyno-
mial,differentforeachquasarimage,representstheadditional SincethetimedelaysinQSO2237+0305arenegligible,taking
microlensingvariations.Indoingso,werescaletheOGLE-III theratiobetweentheabovequantitiesinpairsofquasarimages
errorbarsofeachimagebyafactorequaltothefluxratiobe- cancelstheintrinsicvariations.LetF(t)betheintrinsicsource
tweeneachimageandimageC. Thisrescalingsuppressesthe flux,andM,µ bethemacroandmicrolensing-magnifications
i i
potentialproblemexistingifthefittingprocedureconsidersthe ofquasarimagei,respectively.Theobservedfluxratiobetween
variation of image A (with the highest signal-to-noise) as the imagesiand jattimetisthen:
intrinsicvariationofthequasar.Thechosenorderofthepoly-
µ(t) M F(t) µ(t)M
nomialis7fortheintrinsicvariation,and10forthemicrolens- Rij(t)= µi(t) Mi F(t) e−(τi−τj) = µi(t)Mi e−(τi−τj) . (1)
ingvariation.Higherorderpolynomialsdonotsignificantlyim- j j j j
provethefit.TheresultsaredisplayedinFig.13,wherethein- The extinction e−τi remains constant in time and is rela-
trinsicvariationofthesourcerecoveredbythesimultaneousfit tivelysimilarinallfourquasarimagesasweshowinSec.6.3.
isshowntogetherwiththepuremicrolensingvariations. Hence,it is notexpectedto stronglyaffectour resultsandwe
We check theefficiencyofour methodbygeneratingarti- will neglect it in the following. The macromagnifications Mi
ficial light curves and then using the above polynomial fit to arebestestimatedinthemid-IRandradiodomain(Falcoetal.
recovertheintrinsicandmicrolensinglightcurves.Thesearti- 1996,Agoletal.2000).Atthesewavelengths,thesourcesize
ficial lightcurvesare generatedin the same way as described is much largerthan the typicalspatialscale in the microcaus-
in Eigenbrod et al. (2005), and are composed of an intrinsic ticsnetwork,henceleavingitfairlyunaffectedbymicrolensing
light curve to which we add microlensing fluctuations. Both (i.e. µi = 1). By multiplyingRij by Mj/Mi, using the mid-IR
arecreatedinarandomwalkmanner(i.e.notfrompolynomi- observations,we find the pure-microlensingmagnificationra-
als). They are constructed to match the variability properties tios:
oftheactuallightcurves,i.e.theirtimescaleandamplitudeof µ(t)
r (t)= i . (2)
variation(forfurtherdetailsseeEigenbrodetal.2005).Were- ij µ (t)
j