COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses V. The time delay in SDSS J1650+4251

0.27 MB·English

by  C. Vuissoz

Astronomy&Astrophysicsmanuscriptno.5823 (cid:13)c ESO2008
February5,2008
COSMOGRAIL: the COSmological MOnitoring of
GRAvItational Lenses
7
0 V. The time delay in SDSS J1650+4251
0
2
C.Vuissoz1,F.Courbin1,D.Sluse1,G.Meylan1,M.Ibrahimov2,I.Asfandiyarov2,E.Stoops1,3,A.Eigenbrod1,L.
n
a LeGuillou4,H.vanWinckel4,andP.Magain3
J

8
1 Laboratoired’Astrophysique,EcolePolytechniqueFe´de´raledeLausanne(EPFL),Observatoire,CH-1290Sauverny,Switzerland

2 UlughBegAstronomicalInstitute,AcademyofSciences,Tashkent,Uzbekistan
2
3 Institutd’AstrophysiqueetdeGe´ophysique,Universite´deLie`ge,Alle´edu6aouˆt17,Sart-Tilman,BatB5C,B-4000Lie`ge,Belgium
v
7 4 InstituutvoorSterrenkunde,KatholiekeUniversiteitLeuven,Celestijnenlaan200B,B-3001Heverlee,Belgium
1
3 Received...;accepted...
6
0
ABSTRACT
6
0
Aims.Ouraimistomeasurethetimedelaybetweenthetwogravitationallylensedimagesofthez =1.547quasarSDSSJ1650+4251, in
/ qso
h ordertoestimatetheHubbleconstantH .
0
p Methods.OurmeasurementisbasedonR-bandlightcurveswith57epochsobtainedatMaidanakObservatory,inUzbekistan,fromMay2004
- toSeptember2005.Thephotometryisperformedusingsimultaneousdeconvolutionofthedata,whichprovidestheindividuallightcurvesof
o
theotherwiseblendedquasarimages.Thetimedelayisdeterminedfromthelightcurvesusingtwoverydifferentnumericaltechniques,i.e.,
r
t polynomialfittinganddirectcross-correlation.ThetimedelayisconvertedintoH followinganalyticalmodelingofthepotentialwell.
s 0
a Results.Ourbestestimateofthetimedelayis∆t=49.5±1.9days,i.e.,wereacha3.8%accuracy.TheR-bandfluxratiobetweenthequasar
: images,correctedforthetimedelayandforslowmicrolensing,isF /F =6.2±5%.
v A B
Conclusions.The accuracy reached on the time delay allows us to discriminate well between families of lens models. As for most other
i
X multiplyimagedquasars,onlymodelsofthelensinggalaxythathaveadeVaucouleursmassprofileplusexternalsheargiveaHubbleconstant
r compatiblewiththecurrentmostpopularvalue(H0=72±8kms−1Mpc−1).Amorerealisticsingularisothermalspheremodelplusexternal
a sheargivesH =51.7+4.0kms−1Mpc−1.
0 −3.0
Keywords.Gravitationallensing:quasar,microlensing,timedelay–Cosmology:cosmologicalparameters,Hubbleconstant,darkmatter.
1. Introduction in front of the latter. While this is very hard for lenses with
shorttimedelays(Kochaneketal. 2006,Morganetal.2006),
longer time delays can be measured accurately (Eigenbrodet
The so-called time-delay method in gravitationally lensed
al.2005).
quasars (Refsdal 1964) is one of the rare techniques that can
yield a measurement of the Hubble constant H at truly cos- Inthispaper,we presentthefirstresultfromourmonitor-
0
mologicaldistances, independentlyofanylocalcalibrationor ing program: the time delay measurement in the gravitation-
standard candle. Until now, however, no concerted and long- allylensedquasarSDSSJ1650+4251(16h50m43s.5,+42◦ 51′
termprojecthassucceededinapplyingitinasystematicway, 45′.′0; J2000.0),discoveredby Morganet al. (2003) as a dou-
at a level really competitive with other techniques, such as blyimagedz = 1.547quasar,with anangularseparationof
qso
Cepheids, supernovae or the fluctuations of the cosmic mi- 1.2′′. At the time of the discovery,the B-bandmagnitudes of
crowave background radiation. The COSMOGRAIL project components A and B were 17.8 and 20.0 respectively. The
aimsatmeasuringtimedelaysformostknowngravitationally lensing galaxy is detected by Morgan et al. (2003) in the I
lensed quasars, as well as improving their lens models, us- band.Absorptionlinesseen inthespectrumofthequasarim-
ing deep high resolution imaging and spectroscopy. The con- ages suggest a lens redshift of z = 0.577. In a cosmology
lens
tribution of the error on the time delay measurement to the withH =75kms−1 Mpc−1,Morganetal.(2003)predictthat
0
total error budget on H is about 50%, the other half being the time delay between the quasar images is of the order of
0
due to degeneracies in the lens models. The immediate goal a month,assuminga SingularIsothermalSphere(SIS) poten-
of COSMOGRAIL is to make the former close to negligible tial for the lensing galaxy, plus an external shear. Following
2 C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251
Fig.1.A R-bandimageof SDSSJ1650+4251obtainedatMaidanakObservatory.Thisimageis a combinationof376frames,
totalising 31 hoursof exposure.The mean seeing is 1.0′′, and the field of view is 3.5′×8.9′. The two stars labeled PSF1 and
PSF2areusedtomodelthePointSpreadFunctionrequiredfortheMCSdeconvolutionmethod.The4referencestarsusedfor
thephotometriccalibrationarestar#3,#4,PSF1andPSF2.Star#5isusedasacross-checkofthedeconvolutionphotometry.
thenon-parametricmodelsofSahaetal. (2006) andthesame The resulting non-visibilitywindow is thereforeof about150
cosmology, the expected time delay between the two quasar days. Additional, but smaller, gaps are due to bad seeing or
imagesis∆t∼30−60days. weather conditions. The photometric points presented here
The first two seasons of the photometric monitoring of span a total of 333 days between May 2004 and September
SDSS J1650+4251were carried outwith the 1.5-m telescope 2005,afterremovalofthenon-visibilityperiod.Themeantem-
at Maidanak Observatory,in Uzbekistan.Given the high dec- poralsamplinginthevisibilitywindowisonepointevery5th
lination of SDSS J1650+4251 and the pointing limits of the day.
telescope, SDSS J1650+4251 can be followed for about 8 The CCD camera used at Maidanak Observatory is a
months per year under good airmass and seeing conditions. 800×2000 array with a pixel size of 0.266′′ on the plane of
This combination of time delay and visibility window makes thesky.Theusefulfieldofviewis3.5′×8.9′.Alldataaretaken
SDSSJ1650+4251anexcellenttargetforanaccuratetimede- through the Cousins R filter. The seeing varies between 0.7′′
lay measurement. From numericalsimulations using artificial and2.0′′ overthetwoobservingseasons,1.1′′ beingthemost
lightcurves,Eigenbrodetal. (2005) predictthat the accuracy frequentvalue. For each observingepoch, unless technical or
onthetimedelaycanbeasgoodas1%,assumingthatthepeak meteorological problem occurs, 6 dithered images are taken.
topeakamplitudeofthequasarlightvariationis0.2magover The exposure time for each of the 6 frames is 300 s, and the
thetwoyearsofobservationandusingatemporalsamplingof sizeoftheditheringboxis15′′.
atleastoneobservingpointperweek.Althoughmorethantwo
observingseasonswillbenecessarytoachievethisfinalgoal,it
3. Reductionsanddeconvolution
isalreadypossibletomeasurethetimedelaywith3.8%accu-
racy,whichissufficienttoshowthatlensmodelswithconstant The field of view of the camera is shown in Fig. 1, where
mass-to-lightratioandmodelswithdarkmatterprofilesthatdo SDSSJ1650+4251hasbeenslightlyoff-centeredinordertoin-
nottracelightgivediscrepantvaluesofH . cludemorestarsusefulfortheconstructionofthePointSpread
0
The photometric monitoring, the data reduction and the Function(PSF).Anautomatedpipelineisusedtocarryoutthe
light curves are presented in Sects. 2 and 3 respectively. The pre-reductionof all the individualCCD frames. This pipeline
determinationofthetimedelaybetweenthetwolensedimages first subtracts a master-bias from each image, then for each
is described in Sect. 4. In Sect. 5, we discuss the mass mod- night,correctsfortheflatfieldusingtwilightflats,andremoves
elsfor thelensinggalaxyandthe implicationsfor theHubble a sky-image. The accurate positions of 15 reference stars are
constant.Finally,Sect.6summarisesthemainresults. then measured on all images with the Sextractor package
(Bertin&Arnouts1996)andusedinIRAF1tocomputethege-
ometricaltransformationbetweentheimages.Rebinningofthe
2. Observations
1 IRAF is distributed by the National Optical Astronomy
Theobservationspresentedinthisarticleconsistoftwofullob- Observatories,whichareoperatedbytheAssociationofUniversities
servingseasons.SDSSJ1650+4251isvisiblefromtheendof for Research in Astronomy, Inc., under cooperative agreement with
FebruarytothebeginningofOctoberatMaidanakObservatory. theNationalScienceFoundation.
C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251 3
Fig.2.R-bandlightcurvesforthetwoquasarimagesinSDSSJ1650+4251,aswellasforareferencestarinthefieldofview.
Themagnitudesaregiveninrelativeunits.Inordertoavoidthepointsoverlaps,thecomponentBandthestarcurveshavebeen
shiftedinmagnitude.The5epochsmarkedbytrianglesdeviateveryfarawayfromtheotherwisesmoothvariationsofthelight
curveofcomponentB.Theyhavebeenremovedfromthecurveswhendeterminingthetimedelay(seeSection4).
data using polynomial interpolations is necessary, since rota- use fournon-variablestars, labeledPSF 1,PSF 2,star #3and
tionandscalingareincludedinthetransformation,inaddition #4inFig.1.
totheimageshift.Wedonotperformanycosmicrayremoval,
sincenocosmicrayispresentinthetinyfieldofviewconsid- Thecalibratedframesaresimultaneouslydeconvolvedus-
ered around SDSS J1650+4251and around the PSF stars, as ing the MCS algorithm (Magain et al. 1998), which provides
indicatedbytheresidualimagesofthedeconvolution. thephotometryofthetwo blendedquasarimages,freeofany
mutual light contamination. This procedure has already been
Since the airmass and the transparencyof the sky change successfully applied to the monitoring data of several lensed
with time, cross-calibration of the photometric zero point be- quasars (Burud et al. 2000, 2002a, 2002b, Hjorth et al. 2002,
tweenalltheimagesisnecessarypriortoanymagnitudemea- Jakobssonet al. 2005). Itsmain advantageis its ability to de-
surement. We find that the best way to carry out this task on convolveall the framesfromdifferentepochssimultaneously,
images taken at Maidanak, is to use reference stars as close constrainingwellthe positionsofthetwo quasarimageseven
as possible to the target. This choice leaves us with few cal- whenpartofthedataisobtainedinpoorseeingconditions.In
ibration stars but the determinationof the photometricoffsets addition, no prior knowledge is used on the shape and posi-
achieved in this way remains better than the one using many tionofthelensinggalaxyandonthelensedhostgalaxyofthe
morereferencestarslocatedfurtherawayfromthequasar.We quasar. All extended objects are treated as a fully numerical
4 C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251
array of pixels. The flux of the quasar images, treated analyt-
ically, are allowed to vary from one frame to another, hence
leadingto the lightcurves.The resolutionin the deconvolved
image is a parameter given to the algorithm: the deconvolu-
tionmethodsplits eachpixelof the initialimagein 4 partsof
thesamesize,andthefinalresolutioncorrespondstothesizeof
twoofthesesmallpixels,accordinglytothesamplingtheorem.
Thereforeit is givenby the detectorpixelsize, i.e. 0.27′′. We
usetwostarstoconstructthePSFrequiredfortheMCSdecon-
volution to work. They are labeled PSF1 and PSF2 in Fig. 1.
Theyarealsousedasfluxcalibrators.
Althoughthe two quasarimagesare well separatedin our
deconvolved image with a final resolution of 0.27′′, both the
lensinggalaxyandthelensedhostgalaxyofthequasararetoo
fainttobedetected.
The R-bandlightcurvesobtainedusingthe deconvolution
photometryarepresentedinFig.2andinTable1.Theyconsist
of 62 data points. Each point correspondsto one given night,
and is the mean of 6 independentconsecutive measurements.
The error bar for each epoch is the 1σ standard error on this
meanvalue.Thisempiricalwayofdeterminingtheerrorfrom
six independentmeasurements obtained using deconvolution, Fig.3.a) The dispersionfunctionobtainedwhenthe normali-
ensuresthatPSFerrorsarepropagatedinthefinalphotometry sationofthelightcurvesisdetermineddirectlyfromthedata.
inarealisticway. Severallocalminimaappear.Apolynomialfittothedispersion
WealsoshowinFig.2thephotometryobtainedviathede- function (solid line) allows the determination of a time delay
convolutionoftheisolatedstar#5.Itslightcurveisflatandthe of∆t ∼ 34.4days.b)ThecorrespondingresultoftheMonte-
standarddeviationbetweenalltheepochs(σ = 0.006mag) Carlo simulation for 100’000 slightly modified light curves:
tot
iscompatiblewiththemeanoftheerrorbaroneachindividual ∆t ∼ 34.4 ± 1.4 days. c) The dispersion function obtained
epoch(σ =0.007mag). for the light curves optimally shifted in magnitude (see text
mean
andFig.4).Thefunctionisnowmuchsmootherandhasonly
one clear minimum at ∆t ∼ 52.6 days. d) The corresponding
4. Measurementofthetimedelay
Monte-Carlo simulation result and the final time delay esti-
A roughguess of the light curvesshift indicates a time delay mate:∆t∼52.3±1.6days.
ofabout50days,i.e.,20dayslongerthanpredictedinthedis-
coveryarticle(Morganetal.2003).Thebrightestquasarimage
is the leading image, consistent with the arrivaltime surfaces
presentedinSahaetal.(2006).Derivingaprecisevalueforthe
time delay requiresnumericalmethods. We use two very dif- delays to be tested in an arbitrarily long interval around the
ferenttechniques:theminimumdispersionmethod(Peltetal. guessvalue.Pairsof pointsareformedwith eachpointofthe
1996),andapolynomialfittothedata,e.g.,asimplementedin referencecurveanditsnearestcorrespondingneighbourinthe
Kochaneketal.(2006). shiftedversionofthesecondlightcurve,andameandistance,
Ourfulldatasetconsistsof62observingepochs.However, in magnitude, is computed between the two curves. The best
the photometric points for 5 of the epochs, marked by trian- valueofthetimedelayistheonethatminimisesthedispersion
glesin Fig.2, deviateveryfarawayfromthegeneraltrendin function constructed in that way. The method has to be used
the light curve of the quasar image B. These deviating points withcaution,inparticularwhendealingwiththefluxnormali-
donotseemtobe artifactsduetobadPSForproblemsinthe sationofthelightcurves.
fluxcalibration.However,theyintroduceinstablebehaviourof Themeanmagnitudeofthedatapointsofbothlightcurves
the dispersion function and they do not reflect the otherwise must be set to zero prior to their cross-correlation. However,
smoothvariationofthequasar.Wechoosetoremovethemfrom the required normalisation factors are often determined from
thedata,priortothetimedelaymeasurement. thelightcurvesthemselves,whichcanleadtoawrongnormal-
isation as soon as the time delay becomes significantly long
comparedwiththetotallengthoftheobservations.Ideally,the
4.1.Theminimumdispersionmethod
normalisation must be done on the exact same portion of the
The minimum dispersion method has been already applied intrinsic light curve of the quasar. In lensed quasars, we see
manytimestosparselysampledlightcurvesoflensedquasars severalversionsofthisintrinsiclightcurve,whichareshifted
(e.g.,Peltetal.1998).Inthismethod,aguessedvalueischo- in magnitude and time, and clipped by the visibility window.
sen for the time delay. The light curve of one quasar image Determining the factors directly from the data will therefore
is taken as a referenceand the other is shifted by all the time leadtoawrongnormalisation.
C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251 5
ror on this mean value. The result of the Monte-Carloruns is
shownintherightpanelsinFig.3.Ourfinalvalueofthetime
delayusing57epochsandtheminimumdispersionmethodis
∆t=52.3±1.6days.
Finally,notethatthesevaluesdonottakemicrolensinginto
account.Theminimumdispersionmethodis,however,notvery
sensitivetolowamplitudemicrolensingvariations,asshownin
Eigenbrodetal.(2005).Addingmicrolensingdoesnotchange
the time delay obtained above, but only slightly enlarges the
distribution.
4.2.Polynomialfittothelightcurves
A completelydifferentapproachto measure the time delay is
to fit fully analytical functions to the light curves. An imple-
mentationofthistypeofmethodhasbeenusedinKochaneket
al. (2006) and in Morganetal. (2006), where Legendrepoly-
nomialswere simultaneouslyfittedto the lightcurvesofeach
quasar image. The time delay between each pair of images is
oneoftheparametersofthefit,aswellasthefluxratioofthe
images,correctedbythetimedelay.Ourownimplementation
Fig.4.ValueoftheminimumD of thedispersionfunction, ofthemethoddoesnotuseanystabilisationorsmoothingterm,
min
as a function of the magnitude shift between the two light whichisnotmandatoryaslongasthepolynomialorderischo-
curves. A fit (solid line) to the measurements yields the op- sen in adequation with the number of data points in the light
timal magnitude shift ∆m = −0.056. In the figure, a shift of curves. In addition, a slow photometric variation is added to
0 correspondsto the normalisationcarried out directly on the eachlightcurve,inordertotakemicrolensingintoaccount.
data.Thedottedlineandtheverticalaxisontherightgivethe Thismethodisappliedto thedataintwoways,whichare
correspondingvalueofthetimedelay∆t ≃ 52.6days(forone fully equivalentfora doublequasar with little contributionof
singlerealisationoftheMonte-Carlosimulation). microlensing. First, we assume that the intrinsic photometric
variationofthequasariswellrepresentedbythelightcurveof
thebrightestquasarimageA.Theresultingmicrolensingcon-
tribution to the total variation in the light curve of the quasar
IfwenormalisethedataofSDSSJ1650+4251withouttak- imageBthenonlyreflectsdifferentialmicrolensingrelativeto
ingintoaccounttheclippingofthelightcurves,thedispersion the componentA. A secondway to implementthemethod,is
function,asshownintheupperleftpanelofFig.3,reachesits to use one single light curve to represent the intrinsic varia-
minimum for a ∆t = 34.4 days, with a secondary minimum tionsofthequasarandtofititsimultaneouslytothetwoquasar
around55days. images.Twoindependentmicrolensingcurvesarefittedtothe
In order to estimate the correct normalisation factors, we twolightcurves,allowingustorecoverabsolutemicrolensing
follow an iterative procedure. We first estimate a rough nor- curves.Thefittothedataisperformedinaniterativewayand
malisationfactorfromthedataandwemeasuretheminimum thealgorithmisrun100’000timesonmodifiedversionsofthe
D of the dispersion function as well as the position ∆t of lightcurvesfollowingthestatistical1σerrorsonthephotom-
min
thisminimum.Wethenslightlychangethemagnitudeshift∆m etry.As for the minimumdispersionmethod,the mean ofthe
betweenthetwolightcurvesandwerepeatthe(D ,∆t)mea- timedelaydistributionobtainedinthatwayistakenasthetime
min
surement, so that we can explore the ∆m vs. D plane. The delaymeasurement,anditsstandarddeviationasthe1σerror
min
resultis shown in Fig. 4. We considerthat the correctmagni- (Fig.5).
tude shift between the light curves, and hence, the best time Acriticalstepintheuseofthisfittingmethodisthechoice
delay, is the one that minimises Dmin. We obtain in that way of an optimal order for the Legendre polynomials. The data
∆t = 52.6days. Note that the magnitudeshift that minimises consistintwoobservingseasons,forwhichpeak-to-peakvari-
Dminalsogivesamuchcleaner,single-peakeddispersionfunc- ations and lengths are different. We therefore fit polynomials
tion,asshowninthelowerleftpanelofFig.3. with different orders for the two seasons. We progressively
The accuracy on the time delay value is estimated using increase the degree of the polynomial until the χ2 to the fit
a statistical Monte-Carlo method: the data points in the light does not significantly improve. Microlensing is estimated in
curvesareslightlymodifiedfollowingarandomGaussiandis- thesame way,butweassume thatthemicrolensingvariations
tributionthatmimicsthemeasuredphotometricerrors,andthe areslowcomparedtotheintrinsicvariationsofthequasar.We
algorithmisrunonthesenewmodifieddata.Theoperationis therefore fit a single polynomial for both seasons. Fast mi-
repeated100’000times.Thefinaltimedelayisthemeanofthe crolensing,actingontime-scalesofaweek,isseenasanaddi-
100’000measurementsandthe1σerroronthisvalueistheer- tionalsourceofnoise,andnotasasystematiceffect.Although
6 C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251
rectedforthetimedelayandtheslowmicrolensingisF /F =
A B
6.2.Notethatthisfluxratioisconstantinthetimedelayrange.
5. Parametricmodeling
Theobservationalconstraintsavailablesofartomodelthepo-
tentialwellinSDSSJ1650+4251consistoftherelativeastrom-
etry of the lensed imagesA and B with respectto the lensing
galaxyG (Morganetal. 2003), andthe imageflux ratio mea-
sured in Section 4. Lacking a direct spectrum of the lensing
galaxy,weassumealensredshiftz =0.58,asdeducedfrom
lens
the MgII and FeII absorption lines observed in the spectra of
the lensedquasar(Morganetal. 2003).Thisvalueofthelens
redshift drives all the following estimates of the Hubble con-
stant,whichscalesas(1+z ).
lens
Usingthe lensmodelpackage(v1.08;Keeton2001), we
fitthelenssystemwith(i)aSingularIsothermalSpheremodel
plusexternalshear(SIS)and(ii)adeVaucouleursmodel(DV).
Due to the misalignmentbetween componentsA, B and G of
the lens system, we break the circular symmetry of the lens
potential by adding external shear to the models. While it is
Fig.5.a) Best polynomialfit to the lightcurves.The orderof likely that the gravitational potential of the lensing galaxy is
the Legendre polynomial is 5 for the first season and 4 for notcircular,thepresentobservationaldataavailableforSDSS
the second season. b) Result of the Monte-carlo simulation J1650+4251 do not offer enough constraints to allow the si-
for100’000modifiedlightcurves,leadingtoameantimede- multaneous fit of an elliptical potential plus external shear γ.
lay of ∆t = 46.7 ± 2.2 days. c) Light curves shifted by the However,the time delay of doublyimagedquasarswhere the
time delay and corrected for slow microlensing variations. d) lenslies almoston the line joiningthe two quasarimagesde-
Microlensing variations of quasar image B relative to quasar pendslittle on thestructureof the quadrupoleterm ofthe po-
imageA,takenasaslowlineartrendoverthewholeperiodof tential(Kochanek2002).
observation. The constraints on our models are the relative astrometry
of the lensed images with respect to the lensing galaxy (us-
ing a 1σerror barof 0.002′′ onthe positionsof A and B and
0.03′′forG)andthefluxratiobetweenAandBasfoundafter
weincreasethedegreesoftheintrinsicandmicrolensingvaria- correctionfromtimedelayandobservedrelativemicrolensing
tions separately when trying different fits, both contributions (i.e. F /F =6.2;Sect.4).We considera5%uncertaintyon
A B
are simultaneously fitted to the data, once the orders of the thefluxratioinordertoincludedifferentialdustextinctiondue
polynomial are chosen. The optimal combination of polyno- to the lensing galaxy, as suggested by the multi-color data of
mialordersisN=5forthefirstseasonofobservationandN=4 Morganetal.(2003).Themodificationofthefluxratiodueto
forthesecondseason.Themicrolensingvariationsaremodeled the time delay uncertainty or microlensing is negligible over
usingasimplelinearslope.Thedifferencebetweenthefitand theperiodofobservation,aspointedoutinSection4.Inaddi-
thedataisshowninthelowerrightpanelofFig.5,wherethe tion,ourfluxratiodoesnotdiffermuchfromthatofMorganet
dispersionbetweenthepointsiswellcompatiblewiththeerror al.(2003),obtained13monthsbeforethestartofourobserva-
barontheindividualpoints. tions,butuncorrectedforthetimedelay.
Thetwowaysofapplyingthefittingmethodtothedataare The SIS+γ model has just enough parameters to be ex-
fullyequivalentintheparticularcaseofSDSSJ1650+4251,as actly constrained by the data (i.e. zero degree of freedom),
weonlyuseafirstorderpolynomialtomodelthemicrolensing but the DV model has one more parameter, the effective ra-
and as thereare onlytwo light curvesavailable.The time de- dius R of the lensing galaxy,that is unknownwith the exist-
e
laysobtainedinthetwowaysareindeedinagreementandyield ingimagingdataof SDSSJ1650+4251.We thereforerunour
∆t=46.7±2.2days.Wefindthatslowmicrolensingisalmost modelswithafixedeffectiveradius.Weconsiderawiderange
negligibleinSDSSJ1650+4251,withaglobalvariationof0.02 of plausible effective radii, 0.2 kpc < R < 20 kpc, and take
e
magnitudeover500days(seeFig.5).Takingthemeanofthe the two boundariesfor our calculations.These valuesenclose
twovaluesobtainedusingtheminimumdispersionmethodand the range of measured effective radii in the Sloan-Lens ACS
usingtheanalyticalfittinggives∆t=49.5±1.9days,whichwe Survey(SLACS)sampleof15early-typelensgalaxies(Treuet
takeasourfinalestimateofthetimedelay.Thistranslatesinto al. 2006).Theycorrespondtoangularscalesofθ ∼0.3′′ and
e
a relative error of 3.8%, which is also in agreement with the 3.0′′ atthelensredshift,adoptingH =70kms−1 Mpc−1,Ω
0 m
predictederrorbarfromEigenbrodetal.(2005)forlightcurves =0.3,Ω =0.7.
Λ
withthesamecharacteristicsastheonesofSDSSJ1650+4251. Using the time delay measuredin Section 4, ∆t = 49.5±
Finally,the R-bandfluxratiobetweenthe quasarimages,cor- 1.9days,wefindH =51.7+4.0kms−1 Mpc−1 withtheSIS+γ
0 −3.0
C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251 7
images, corrected for microlensing and for the time delay, is
F /F =6.2±5%.
A B
The amplitude of the external shear in the circular lens
modelsislargerthanγ =0.15,andsuggeststhatbothexternal
shear and ellipticity in the main lensing galaxy are necessary
to model the total potentialwell. However,the presentobser-
vational constraints available for SDSS J1650+4251 prevent
usfromintroducingalensellipticityandpositionangleinthe
models. Deep, high resolution images of SDSS J1650+4251
willbenecessarytoestimatethelattertwoparameters.
Withthepresent3.8%accuracyonthetimedelay,wecan
efficiently discriminate between families of lens models or,
conversely, estimate H assuming a lens model. Our results
0
suggest that SIS models are not acceptable in order to match
thecurrentfavoredvalueoftheHubbleconstant(H =72±8
0
kms−1 Mpc−1)andthatonlymodelsofthelensinggalaxythat
Fig.6.AzoomontheR-bandimageofSDSSJ1650+4251ob-
haveadeVaucouleursmassprofilecanreproduceit.
tainedatMaidanakObservatory(seeFig. 1).Thepositionsof
Slowmicrolensingisnegligibleinthe firsttwoseasonsof
thequasarimagesaremarkedbywhitecircles.Thedirectionof
monitoring,withaglobalvariationoflessthan0.02magover
theshearforourSIS+γandfortheDVmodelisindicatedby
500days.
two lines. Itdoesnotpointtowardsanyspecific galaxyin the
Finally,notethattheredshiftofthelensinggalaxyisbased
fieldofview.Itslargeamplitudemakesitmandatorytomodel
onMgIIandFeIIabsorptionlinesinthespectrumofthequasar
theoveralllensingpotential.
images.Althoughtheimpactparameternecessarytoformthese
lines is small, we cannot exclude that the true lens redshift
doesnotcorrespondtotheabsorptionlines,asinothersystems
model.TheDV+γmodel,withthelowerboundvalueofθe = (HE 1104-1805;Lidman et al. 2000). A genuine spectrum of
0.3′′, yields H0 = 80.8 +−73..00 km s−1 Mpc−1. Using the upper thelensinggalaxymustbeobtainedtoconfirmitsredshift.
value θ = 3.0′′, the DV model gives H = 55.1+5.1 km s−1
e 0 −3.8
Mpc−1. Clearly only large valuesof the effective radiusθ (ie Acknowledgements. COSMOGRAILis financially supported by the
e
θ > 3′′)reconcilethevalueofH givenbytheSIS+γandby Swiss National Science Foundation (SNSF). Pierre Magain is fi-
e 0
thedeVaucouleursmodels.Ontheotherhand,H =72kms−1 nancially supported by the Belgian Science Policy (BELSPO) in
0
Mpc−1isfoundforθ =0.8′′. the framework of the PRODEX Experiment Arrangement C-90195.
e
M. Ibrahimov is partially supported by the Swiss National Science
As previously argued, the unkown lens ellipticity is not a
Foundation(SNSF)andEPFLinthecontextofCOSMOGRAIL.
major source of uncertainty on the predicted value of H . In
0
orderto probeits effect, we fitted on the observedastrometry
andfluxratio,16200ellipticallensmodelswithfixedellipticity References
e,lensmajoraxispositionangleφandshearpositionangleθ ,
γ Bertin,E.,Arnouts,S.1996,A&AS117,393
uniformly distributed in the ranges [0:0.4] (e) and [-90◦:90◦]
Burud,I.,Hjorth,J.,Jaunsen,A.etal.2000,ApJ544,117
(φandθ ).Followingthisprocedure,wefindthatincludingthe
γ Burud,I.,Courbin,F.,Magain,P.etal.2002,A&A383,71
ellipticityinthelensmodeldoesnotenlargethedistributionof Burud,I.,Hjorth,J.,Courbin,F.etal.2002,A&A391,481
predictedvaluesofH0. Eigenbrod,A.,Courbin,F.,Vuissoz,C.,etal.2005,A&A436,25
Allthe1σuncertaintiesquotedabovearededucedbyeval- Hjorth,J.,Burud,I.,Jaunsen,A.etal.2002,A&A572,L11
uatingH from1σ∆χ2 contoursintheplaneγ-θ (i.e.∆χ2 = Jakobsson,P.,Hjorth,J.,Burud,I.,etal.2005,A&A431,103
0 γ
2.3fortwo degreesof freedom).The externalshear predicted Keeton,C.R.2001,astro-ph/0102340
byboththeSIS+γandDVmodelsislarge:γ = 0.15±0.04 Kochanek,C.S.2002,ApJ578,25
SIS
(θ = −42◦ ±10) and γ = 0.23±0.07 (θ = −49◦ ±13), Kochanek,C.S.,Morgan,N.D.,Falco,E.E.etal.2006,ApJ640,47
γ DV γ
forθ =0.3′′.Thedirectionofthesheardoesnotpointtowards Lidman,C.,Courbin,F.,Kneib,J.-P.etal.2000,A&A364,L62
e Magain,P.,Courbin,F.,Sohy,S.,1998,ApJ494,452
obvious specific external perturber in Fig. 6. Its large ampli-
Morgan,N.,Snyder,J.A.,Reens,L.H.,2003,AJ126,2145
tudesuggests,however,thatothermassclumpsalongtheline
Morgan,N.D.,Kochanek,C.S.,Falco,E.E.,Dai,K.,submittedtoApJ
ofsightdomodifytheoverallpotentialwell.
(astro-ph/0605321)
Pelt,J.,Kayser,R.,Refsdal,S.,&Schramm,T.,1996,A&A305,97
Pelt,J.,Schild,R.,Refsdal,S.,Stabell,R.1998,A&A336,829
6. Conclusions
Refsdal,S.,1964,MNRAS,128,307
Themainresultofthepresentworkisthefirsttimedelaymea- Saha,P.,Courbin,F.,Sluse,D.,Dye,S.,Meylan,G.,2006,A&A450,
surement of the COSMOGRAIL project, for the doubly im- 461
Treu,T.,Koopmans,L.V.,Bolton,A.S.,Burles,S.,Moustakas,L.A.
agedquasarSDSSJ1650+4251.Ourbestestimateofthetime
2006,ApJ,640,662
delayis∆t = 49.5±1.9days(1σ).Thiscorrespondstoarela-
tiveaccuracyof3.8%.TheR-bandfluxratioofthetwoquasar
8 C.Vuissozetal.:COSMOGRAILV:timedelaymeasurementinSDSSJ1650+4251
Table1.PhotometryofSDSSJ1650+4251andofreferencestar#5,asinFig.2.TheJuliandatecorrespondstoHJD-2450000
days.Thefivepointsmarkedbyanasteriskarenotusedinthedeterminationofthetimedelay.
HJD seeing[”] magA σ magB σ magstar#5 σ
A B star#5
3133.412 1.5 0.273 0.006 2.244 0.016 -0.175 0.013
3134.362 1.1 0.291 0.002 2.241 0.011 -0.166 0.004
3135.385 0.9 0.282 0.004 2.268 0.012 -0.177 0.008
3142.386 1.3 0.287 0.002 2.273 0.007 -0.167 0.003
3146.415 1.2 0.276 0.001 2.264 0.006 -0.178 0.002
3150.406 0.9 0.264 0.001 2.300 0.006 -0.176 0.001
3152.367 1.0 0.279 0.004 2.231 0.011 -0.172 0.008
3154.407 0.9 0.267 0.002 2.252 0.007 -0.175 0.003
3159.364 1.1 0.253 0.003 2.254 0.018 -0.174 0.005
3163.315 1.7 0.249 0.002 2.301 0.010 -0.173 0.003
3166.425 1.0 0.248 0.002 2.244 0.008 -0.177 0.003
3169.393 1.1 0.222 0.003 2.317 0.011 -0.189 0.006
3171.430 1.5 0.234 0.002 2.284 0.008 -0.172 0.004
3173.298 1.1 0.233 0.001 2.275 0.006 -0.168 0.002
3175.300 1.1 0.230 0.001 2.279 0.006 -0.178 0.001
3189.265 1.1 0.208 0.007 2.236 0.023 -0.172 0.012
3191.360 1.1 0.215 0.003 2.255 0.018 -0.167 0.004
3193.304 1.3 0.194 0.006 2.246 0.018 -0.166 0.012
3195.252 1.0 0.217 0.002 2.239 0.007 -0.170 0.004
3203.314* 1.4 0.186 0.001 2.345 0.007 -0.173 0.002
3209.256 1.0 0.189 0.003 2.198 0.010 -0.167 0.007
3213.256 1.0 0.166 0.003 2.190 0.010 -0.183 0.007
3216.310 1.7 0.149 0.006 2.189 0.018 -0.163 0.011
3219.281 1.6 0.151 0.004 2.198 0.018 -0.155 0.008
3221.234 1.0 0.178 0.002 2.241 0.009 -0.179 0.003
3224.209 1.2 0.140 0.005 2.228 0.015 -0.166 0.010
3232.187 1.1 0.215 0.003 2.198 0.009 -0.168 0.005
3246.163 1.3 0.133 0.013 2.148 0.035 -0.142 0.026
3248.138* 1.5 0.172 0.004 2.054 0.013 -0.114 0.007
3254.125 0.9 0.156 0.004 2.139 0.013 -0.160 0.007
3256.135 1.0 0.188 0.001 2.181 0.005 -0.173 0.003
3261.115 1.5 0.203 0.011 2.153 0.029 -0.178 0.017
3271.109 1.3 0.191 0.005 2.167 0.014 -0.183 0.009
3273.103 1.2 0.163 0.007 2.117 0.020 -0.176 0.013
3277.104 1.0 0.190 0.004 2.179 0.014 -0.191 0.007
3281.106 1.4 0.146 0.006 2.151 0.016 -0.167 0.011
3283.100 1.2 0.146 0.004 2.129 0.012 -0.164 0.008
3430.540 0.9 0.167 0.002 2.078 0.009 -0.135 0.003
3434.546 0.8 0.175 0.007 2.088 0.019 -0.143 0.009
3461.499 0.9 0.166 0.003 2.138 0.009 -0.150 0.005
3475.491 0.9 0.175 0.004 2.120 0.012 -0.179 0.008
3482.443 1.1 0.177 0.002 2.124 0.011 -0.149 0.004
3500.415 1.3 0.206 0.004 2.147 0.011 -0.168 0.008
3507.348 1.0 0.177 0.005 2.106 0.012 -0.153 0.009
3508.403* 0.9 0.199 0.003 2.222 0.009 -0.171 0.006
3511.303 1.0 0.172 0.007 2.153 0.018 -0.151 0.012
3517.383 0.8 0.163 0.004 2.146 0.012 -0.168 0.007
3524.391 0.9 0.194 0.002 2.118 0.006 -0.183 0.003
3533.412* 1.6 0.193 0.002 2.002 0.007 -0.171 0.004
3540.345 1.0 0.194 0.003 2.124 0.011 -0.168 0.006
3542.323 1.1 0.172 0.007 2.132 0.020 -0.194 0.014
3552.291 0.9 0.201 0.001 2.149 0.005 -0.179 0.001
3556.295 0.9 0.204 0.003 2.185 0.008 -0.176 0.005
3559.280 1.0 0.181 0.002 2.134 0.007 -0.160 0.004
3564.295* 1.3 0.228 0.001 2.300 0.007 -0.167 0.003
3570.247 1.0 0.192 0.005 2.094 0.015 -0.165 0.010
3575.323 1.3 0.198 0.010 2.084 0.026 -0.172 0.019
3576.264 1.0 0.211 0.001 2.195 0.008 -0.181 0.002
3578.275 1.2 0.189 0.002 2.133 0.007 -0.177 0.003