COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses VII. Time delays and the Hubble constant from WFI J2033-4723

Abstract

Gravitationally lensed quasars can be used to map the mass distribution in lensing galaxies and to estimate the Hubble constant H0 by measuring the time delays between the quasar images. Here we report the measurement of two independent time delays in the quadruply imaged quasar WFI J2033-4723 (z = 1.66). Our data consist of R-band images obtained with the Swiss 1.2 m EULER telescope located at La Silla and with the 1.3 m SMARTS telescope located at Cerro Tololo. The light curves have 218 independent epochs spanning 3 full years of monitoring between March 2004 and May 2007, with a mean temporal sampling of one observation every 4th day. We measure the time delays using three different techniques, and we obtain Dt(B-A) = 35.5 +- 1.4 days (3.8%) and Dt(B-C) = 62.6 +4.1/-2.3 days (+6.5%/-3.7%), where A is a composite of the close, merging image pair. After correcting for the time delays, we find R-band flux ratios of F_A/F_B = 2.88 +- 0.04, F_A/F_C = 3.38 +- 0.06, and F_A1/F_A2 = 1.37 +- 0.05 with no evidence for microlensing variability over a time scale of three years. However, these flux ratios do not agree with those measured in the quasar emission lines, suggesting that longer term microlensing is present. Our estimate of H0 agrees with the concordance value: non-parametric modeling of the lensing galaxy predicts H0 = 67 +13/-10 km s-1 Mpc-1, while the Single Isothermal Sphere model yields H0 = 63 +7/-3 km s-1 Mpc-1 (68% confidence level). More complex lens models using a composite de Vaucouleurs plus NFW galaxy mass profile show twisting of the mass isocontours in the lensing galaxy, as do the non-parametric models. As all models also require a significant external shear, this suggests that the lens is a member of the group of galaxies seen in field of view of WFI J2033-4723. Comment: 14 pages, 12 figures, published in A&A

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arXiv:0803.4015v2 [astro-ph] 16 Sep 2008
Astronomy & Astrophysics manuscript no. 9866
September 16, 2008
c ? ESO 2008
COSMOGRAIL: the COSmological MOnitoring of
GRAvItational Lenses⋆
VII. Time delays and the Hubble constant from WFI J2033–4723
C. Vuissoz1, F. Courbin1, D. Sluse1, G. Meylan1, V. Chantry2⋆⋆, E. Eulaers2, C. Morgan3,4, M.E. Eyler4,
C.S. Kochanek3, J. Coles5, P. Saha5, P. Magain2, and E.E. Falco6
1Laboratoire d’Astrophysique, Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix,
Switzerland
2Institut d’Astrophysique et de G´ eophysique, Universit´ e de Li` ege, All´ ee du 6 aoˆ ut 17, Sart-Tilman, Bˆ at. B5C, 4000 Li` ege, Belgium
3Department of Astronomy and the Center for Cosmology and Astroparticle Physics, The Ohio State University, Columbus, OH
43210, USA
4Department of Physics, United States Naval Academy, 572C Holloway Road, Annapolis MD 21402, USA
5Institute of Theoretical Physics, University of Z¨ urich, Winterthurerstrasse 190, 8057 Z¨ urich, Switzerland
6Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge MA 02138, USA
Received 31 March 2008 / Accepted 7 July 2008
ABSTRACT
Gravitationally lensed quasars can be used to map the mass distribution in lensing galaxies and to estimate the Hubble constant H0
by measuring the time delays between the quasar images. Here we report the measurement of two independent time delays in the
quadruply imaged quasar WFI J2033–4723 (z = 1.66). Our data consist of R-band images obtained with the Swiss 1.2m EULER
telescope located at La Silla and with the 1.3m SMARTS telescope located at Cerro Tololo. The light curves have 218 independent
epochs spanning 3 full years of monitoring between March 2004 and May 2007, with a mean temporal sampling of one observation
every 4th day. We measure the time delays using three different techniques, and we obtain ∆tB−A = 35.5 ± 1.4 days (3.8%) and
∆tB−C = 62.6+4.1
find R-band flux ratios of FA/FB= 2.88 ± 0.04, FA/FC= 3.38 ± 0.06, and FA1/FA2= 1.37 ± 0.05 with no evidence for microlensing
variability over a time scale of three years. However, these flux ratios do not agree with those measured in the quasar emission
lines, suggesting that longer term microlensing is present. Our estimate of H0agrees with the concordance value: non-parametric
modeling of the lensing galaxy predicts H0= 67+13
km s−1Mpc−1(68% confidence level). More complex lens models using a composite de Vaucouleurs plus NFW galaxy mass profile
show twisting of the mass isocontours in the lensing galaxy, as do the non-parametric models. As all models also require a significant
external shear, this suggests that the lens is a member of the group of galaxies seen in field of view of WFI J2033–4723.
−2.3days (+6.5%
−3.7%), where A is a composite of the close, merging image pair. After correcting for the time delays, we
−10km s−1Mpc−1, while the Single Isothermal Sphere model yields H0= 63+7
−3
Key words. Gravitational lensing: quasar, time delay, microlensing – Cosmology: cosmological parameters, Hubble constant, dark
matter – quasars: individual (WFI J2033–4723).
1. Introduction
When a quasar is gravitationally lensed and we observe multi-
ple images of the source there are light travel time differences
between the images. Any intrinsic variation of the quasar is ob-
served at different times in each image with a measurable “time
delay” between them. Refsdal (1964) first showed that time de-
lays provide a means of determining the Hubble constant H0
independent of any local distance calibrator, provided a mass
model can be inferred for the lensing galaxy. Conversely, one
⋆Based on observations obtained with the 1.2m EULER Swiss
Telescope, the 1.3m Small and Moderate Aperture Research Telescope
System (SMARTS) which is operated by the SMARTS Consortium,
and the NASA/ESA Hubble Space Telescope as part of program HST-
GO-9744 of theSpace TelescopeScience Institute, whichisoperated by
the Association of Universities for Research in Astronomy, Inc., under
NASA contract NAS 5-26555.
⋆⋆Research Fellow, Belgian National Fund for Scientific Research
(FNRS)
can also assume H0in order to study the distribution of the total
mass in the lensing galaxy.
During the past 25 years, time delays have been measured in
only 17 systems, at various accuracy levels (see Oguri 2007, for
a review). As the error in the time delay propagates directly into
H0, it is importantto make it as small as possible. Unfortunately,
most existing time delays have uncertainties of the order of 10%
that are comparable to the current uncertainties in H0. This un-
certainty can be reduced by increasing the sample of lenses with
knowntimedelays,andbysimultaneouslyfittingalllensesinthe
sample with a common value for H0(Saha et al. 2006b,a; Coles
2008).
COSMOGRAILis anopticalmonitoringcampaignthat aims
to measure time delays for a large number of gravitationally
lensed quasars to accuracies of a few percent using a network
of 1- and 2-m class telescopes. The first result of this campaign
was the measurement of the time delay in the doubly imaged
quasar SDSS J1650+4251 to an accuracy of 3.8% based on two
observingseasons ofdata (Vuissoz et al.2007). COSMOGRAIL

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2C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
Fig.1. The 6.3′× 6.3′field of view around WFI J2033–4723.This image is the central part of a combination of 418 R-band frames
obtained with the 1.2m EULER Telescope with a total exposuretime of 48 hours and a mean seeing of 1.3′′. The three stars PSF1–3
used to model the Point Spread Function (PSF) and the 7 reference stars S4–10 used for frame alignment and flux calibration are
indicated.
complements a second monitoring group whose most recent re-
sults are a delay for HE 1104-1805 (Poindexter et al. 2007). In
this paper we present time-delay measurements for the quadru-
ply imaged quasar WFI J2033–4723 based on merging 3 years
of optical monitoring data from the two groups. In a compan-
ion effort, Morgan et al. (2008) analyzed the mergeddata for the
two-image lens QJ0158–4325,succeeding in measuring the size
of the source accretion disk but failing to measure a time delay
due to the high amplitude of the microlensing variability in this
system.
WFI J2033–4723(20h33m42.s08, –47◦23′43.′′0; J2000.0)was
discovered by Morgan et al. (2004) and consists of 4 images of
a z = 1.66 quasar with a maximum separation of 2.5′′. The lens
galaxy was identified by Morgan et al. (2004) and has a spectro-
scopic redshift of zlens= 0.661 ± 0.001 (Eigenbrod et al. 2006).
The lens appears to be the member of a group, with at least 6
galaxieswithin 20′′of the lens (Morgan et al. 2004), and we will
have to account for this environment in any lens model.
We describe the monitoring data and its analysis in Sect. 2
In Sect. 3 we present the near-IR Hubble SpaceTelescope (HST)
observations that we used to obtain accurate differential astrom-
etry of the lens components and surface photometry of the lens
galaxy. We estimate the time delays in Sect. 4 and model them
using parametric (Sect. 5) and non-parametric (Sect. 6) models
for the mass distribution of the lens galaxy. We summarize our
results in Sec. 7.
2. Photometric monitoring
Our3-yearphotometricmonitoringofWFI J2033–4723wascar-
ried out from March 2004 to May 2007 with the 1.2m EULER
telescope and the 1.3m SMARTS telescope located in Chile
at La Silla and the Cerro Tololo Interamerican Observatory
(CTIO), respectively. WFI J2033–4723 was monitored from
both sites for three years during its visibility window from early
March to mid-December.
The 1.2m EULER telescope is equipped with a 2048×2048
CCD camera which has 0.344′′pixels and produces an image
with an 11′field of view. The mean sampling of the EULER
data is one epoch every five days, where each epoch consists of
five dithered 360s images taken with an R-band filter. The worst
gaps due to weather or technical problems are 2–3 weeks. The
EULERdataset consists of141epochsofdataobtainedbetween
May2004andMay2007.Theimagequalityvariesbetween0.9′′
and 2.0′′FWHM over 3 years, with a median of 1.4′′.
The 1.3m SMARTS telescope is equipped with the dual-
beamANDICAM (DePoy et al. 2003) camera.Here we use only
the optical channelwhich has 0.369′′pixels and a 6.5′×6.3′field
of view. The mean sampling of the SMARTS data is one epoch
every eight days, with three 300s exposures at each epoch. The
SMARTS data set consists of 77 epochs of data obtained be-
tween March 2004 and December 2006. The seeing on the im-
ages varies between 0.5′′and 2.0′′, with a median of 1.4′′.

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C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–47233
Fig.2. Result of the simultaneous deconvolution of the 956
R-band images (EULER+SMARTS) of WFI J2033–4723. The
pixel size of this image is half the pixel size of the EULER
detector, i.e., 0.172′′, and the resolution is 2 pixels Full-Width-
Half-Maximum, i.e., 0.344′′. The field of view is 22′′on a side.
Two galaxies G2 and G3 are seen to the West and North of the
main lensing galaxy G1. G3 is part of a group included in the
lens modeling, while G1 and G2 are modeled individually (see
Sect. 5).
The combined data set consists of 218 observing epochs
comprising 956 images covering the common field of view
shown in Fig. 1. The average temporal sampling when
WFI J2033–4723 was visible is one observation every 4 days
over a period of three years, one of the best sets of monitoring
data available for a lensed quasar.
The EULER data are reduced using the automated pipeline
described in Vuissoz et al. (2007) and the SMARTS data with
the SMARTS pipeline, using standard methods. The reduced
frames are then aligned and interpolated to a common refer-
ence frame, one of the best-seeing (1′′) EULER images, taken
on the night of 5 April 2006. The 10 stars (PSF1–3 and S4–10)
shown in Fig. 1 are used to determine the geometric transforma-
tion needed for each EULER and SMARTS image to match the
reference frame. The transformationincludes image parity, rota-
tion, shifting and rescaling. These 10 stars are also used to de-
termine the photometric zero point of each image relative to the
reference image. After interpolation, cosmic rays are removed
using the L.A.Cosmic algorithm (van Dokkum 2001). We check
that no data pixels are mistakenly removed by this process.
The light curves of the quasars are measured by simulta-
neously deconvolving all the images using the MCS algorithm
(Magain et al. 1998). This method has already been successfully
applied to the monitoring data of several lensed quasars (e.g.
Vuissoz et al. 2007; Hjorth et al. 2002; Burud et al. 2002a,b).
The deconvolved images have a pixel scale of 0.172′′(one-half
the pixel scale of the EULER data) and are constructed to have a
Gaussian PSF with a 2 pixel (0.344′′) FWHM. The Point Spread
Function (PSF) for each of the 956 images is constructed from
the three stars PSF1–3 (see Fig. 1). During the deconvolution
process,the relativepositions ofthe quasarimages are held fixed
to the values derived from fitting the HST images in Sect. 3,
while their fluxes are allowed to vary from frame to frame. The
flux, position and shape of the lensing galaxy are the same for
all frames, but the values vary freely as part of the fit.
Fig. 2 shows an example of a deconvolved image. It is clear
that we will have no difficulty estimating the fluxes of compo-
nents B and C separately. Components A1and A2, however, are
separated by only 0.724′′, which is only twice the resolution of
our deconvolved images, and remain partially blended after de-
convolution. Since the delay between these images should be
very small, we will sum the fluxes of the two images and con-
sider only the light curve of the total flux A = A1+ A2. The
resulting R-band light curves are displayed in Fig. 3.
We also display in Fig. 3 the deconvolved light curve of
the isolated star S6, which has roughly the same color as
WFI J2033–4723. Each point is the mean of the images taken
at a given epoch and the error bar is the 1σ standard error of
the mean. The light curve is flat, with a standard deviation over
the 3 years of monitoring of σtot = 0.010mag about its av-
erage, which is roughly consistent with the mean error bar of
σmean= 0.006mag of the individual epochs.
The dispersion of the points in the star’s light curve reflects
bothstatistical errors andsystematic errorsfromthe photometric
calibrations and the construction of the PSF. To the extent that
all the light curves suffer from the same systematic errors, we
can correct the quasar’s light curves by subtracting the residu-
als of the star’s light curve from each of them. We then define
the uncertainty in a quasar’s light curve as the quadrature sum
of the uncertainties in the two light curves. This procedure will
increase the photon noise but should minimize the systematic
errors.
3. HST Near-IR Imaging
We determine the relative positions of the lens components and
thelightprofileforthemainlensgalaxyG1andits closestneigh-
bor G2 (see Fig. 2) by analyzing our HST images of the system.
These data were obtained in the framework of the CASTLES
program (Cfa-Arizona Space Telescope LEns Survey), which
provides HST images for all known gravitationally lensed
quasars. We deconvolve these images using a modified ver-
sion of the MCS deconvolution algorithm for images with poor
knowledge of the PSF (Magain et al. 2007). We previously used
this approach to unveil the faint Einstein ring and the lensing
galaxy hidden in the glare of the quasar images of the so-called
“cloverleaf” HE1413+117 (Chantry & Magain 2007). We ana-
lyze the Near Infrared Camera and Multi-Object Spectrometer
(NICMOS) F160W (H-band) images obtained with the NIC2
camera. The data consist of four dithered MULTIACCUM im-
ages with a total exposure time of 2752 s and a mean pixel scale
of 0.07568′′(Krist & Hook 2004). We calibrate the images us-
ing CALNICA, the HST image reduction pipeline, subtract con-
stants for each quadrant of NIC2 to give each image a mean
background of zero, and create a noise map for each frame.
The images are simultaneously deconvolved in a manner
similar to that used for the EULER and SMARTS data. The
NICMOS frames lack any PSF stars, so we construct the PSF
using the quasar images themselves in the iterative method of
Chantry & Magain (2007). We first estimate the PSF of each
frame using Tiny Tim (Krist & Hook 2004) and then we decon-
volve them to have the final Gaussian PSF. During the decon-
volution, each image is decomposed into a set of point sources
and any extendedflux. The latter is then reconvolvedto the reso-
lution of the original data and subtracted from the four initial

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4C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
30003000 320032003400 340036003600 38003800 4000 400042004200
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
2
star +1
B
A +0.8
C +0.3
Fig.3. Our R-band light curves obtained for WFI J2033–4723 as well as for the reference star S6 (see Fig. 1). The magnitudes are
given in relative units. The filled symbols correspond to the EULER observations while the SMARTS data points are marked by
open symbols. Components A1and A2were summed into one single component A. The curves have been shifted in magnitude for
visibility, as indicated in the figure.
frames, leading to images with far less contamination by ex-
tended structures. Four new PSFs are estimated from these new
images,andwe carryouta newdeconvolution.Theprocessis re-
peated until the residual maps are close to being consistent with
the estimated noise (e.g. Courbin et al. 1998). In this case, con-
vergence is reached after three iterations and the final reduced
χ2is 3.59. The final deconvolvedimage shown in Fig. 4 has half
the pixel scale of the initial images and a Gaussian PSF with a
FWHM of 0.075′′.
As partoftheMCS deconvolutionwealsofit analyticalmod-
els to the main lens galaxy (G1) and its nearby companion G2.
The main lens is an early-typegalaxy (Eigenbrod et al. 2006), as
its companionis likely to be, so we use elliptical de Vaucouleurs
profilesforboth.Theuncertaintiesareestimatedbythescatterof
the measurements from a separate set of fits to each independent
image. We also estimate that there are systematic errors in the
astrometry from the NICMOS pixel scale and focal plane distor-
tions of order 2 milli-arcseconds based on our earlier fits to the
NICMOS data of H1413+117 (Chantry & Magain 2007). These
systematic errors are compatible with the Leh´ ar et al. (2000)
comparison of NICMOS and VLBI astrometry for radio lenses.
The relative astrometry and photometry of the lens compo-
nents and of the lensing galaxiesG1 andG2 are givenin Table 1.
Coordinates are relative to image B, in the same orientation as
Fig 4. The photometry is in the Vega system. For each measure-
ment, we give the 1σ internal error bars, to which a systematic
error of 2 milli-arcsec should be added. The models for G1 and
G2 are presented in Table 2, with the effective semi-major and
semi-minor axes of the light distribution a0and b0. Each mea-
surement is accompanied by its 1σ error bar.
4. Time delay measurement
We measure the time delays between the blended light curve of
A1/A2and images B andC using three different techniques: i the
minimum dispersion method of Pelt et al. (1996); ii the polyno-
mial method of Kochanek et al. (2006); and iii the method of
Burud et al. (2001). Since WFI J2033–4723 shows well-defined
variations(see Fig. 3), it is alreadyclear byvisualinspectionthat
∆tB−A∼ 35 days and ∆tB−C∼ 65 days.

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C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–47235
Fig.4. Left: Deep NICMOS2 image,taken in the F160W-band.This image is a combinationof 4 frames, fora total exposuretime of
46 minutes. North is up and East to the left. The field of view is 4′′on a side. Middle: Simultaneous deconvolutionof the individual
NICMOS images (see text), using the MCS deconvolutionalgorithm. The PSF in this image is an analytical Gaussian with 2 pixels
Full-Width-at-Half-Maximum(FWHM), i.e., the resolution is 0.075′′. The pixel size is 0.035′′, i.e., oversampled by a factor of two
compared to the original pixel size. Right: Residual map of the deconvolution, with the cut levels set to ±5σ. Only minor structures
are seen in the center of the sharpest objects, which is acceptable given the quality of the NICMOS PSF.
Table 1. Relative astrometry and photometry for the four com-
ponents of WFI J2033–4723and for the lensing galaxiesG1 and
G2.
ID
B
A1
A2
C
G1
G2
∆α (′′)
0.
∆δ (′′)
0.
Magnitude
17.77 ± 0.02
17.16 ± 0.02
17.52 ± 0.02
17.88 ± 0.02
18.59 ± 0.03
18.14 ± 0.02
−2.1946 ± 0.0004
−1.4809 ± 0.0004
−2.1128 ± 0.0003
−1.4388 ± 0.0019
−5.4100 ± 0.0006
1.2601 ± 0.0003
1.3756 ± 0.0005
−0.2778 ± 0.0003
0.3113 ± 0.0008
0.2850 ± 0.0003
Table 2. Shape parameters for the main and secondary lensing
galaxies.
Obj.
G1
G2
PA (◦)
27.8 ± 4.3
6.4 ± 3.1
Ellipticity
0.18 ± 0.03
0.15 ± 0.02
a0(′′)
b0(′′)
0.665 ± 0.036
0.389 ± 0.004
0.556 ± 0.025
0.334 ± 0.005
4.1. Minimum dispersion method
In the minimum dispersion method, time delays are computed
for pairs of light curves using a cross-correlation technique that
takes into account irregular sampling. The two light curves are
first normalized to have zero mean. Then, one of the light curves
is used as a referenceand the secondcurveis shifted relativeto it
by a range of time delays. For each delay, we calculate the mean
dispersion between the shifted points and their nearest temporal
neighbors in the reference light curve. The best time-delay es-
timate is the one that minimizes this dispersion function. Since
the mean sampling of our curves is one epoch every four days
and since there is a limit to the number of time delays that can
be tested independently, we test time delays in steps of 2 days.
Fig. 5 shows an example of a dispersion curve where we have
then fit a parabola and set the best time delay to be the one cor-
responding to the minimum of the parabola.
There is, however, a complication in the step of normalizing
the light curves, arising from sampling the light curve of each
lensed image over a different time period of the intrinsic source
variability (Vuissoz et al. 2007). We solve this problem by com-
puting the dispersions as a function of a small magnitude shift
Fig.5. Example of a dispersion curve as obtained from the min-
imum dispersion method, for components B and A. The posi-
tion of the parabola minimum gives the time delay. Each point
is separated by 2 days, i.e. about half the data mean sampling.
The time delay indicated here is for only one realization of the
boot-strap procedure (see text).
∆m in the normalization, measuring both the minimum disper-
sion Dmin(∆m) and the best fitting time delay ∆t(∆m) as shown
in Fig. 6. Our final value for the delay is the one corresponding
to the shift ∆m that minimizes the overall dispersion.
We then estimate the uncertainties by randomly perturbing
the data points, based on a Gaussian distribution with the width
of the measurement errors, and computing the dispersions and
time delays again. We define the uncertainties by the 1σ disper-
sion in the results for 100,000 trials (Vuissoz et al. 2007). The
resulting uncertainty estimates are symmetric about the mean,

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6C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
Fig.6. Variation of the dispersion function minimum Dmin(red
solid curves), as a function of the magnitude shift used for the
normalization (see Sect. 4.1). Each Dmincorresponds to a dif-
ferent estimate of the time delay, indicated on the blue dotted
curves. The final time delay is the one with the lowest Dmin. The
top panel is for the B-A time delay, the bottom one for B-C.
Time delays indicated here are for only one realization of the
boot-strap procedure (see text).
so our final estimates based on this method are
∆tB−A= 35.6 ± 1.3 days (3.6%)
∆tB−C= 64.6 ± 3.4 days (5.3%)(1)
While we have not taken microlensing effects into account
for this analysis, it should matter little, as the method is not very
sensitive (Eigenbrod et al. 2005) to the very low amplitude mi-
crolensing variability observed for this system (see Sect. 4.2).
Fig.7. Top: Best polynomial fit to the light curves, which are
shifted vertically for display purpose. Bottom: The residuals of
the fit.
4.2. Polynomial fit of the light curves
In the polynomial method (Kochanek et al. 2006), the intrinsic
light curve of the source is modeled as a polynomial that is si-
multaneously fit to all three light curves. Each quasar image has
an additional low order polynomial to model slow, uncorrelated
variability due to microlensing. We increase the source poly-
nomial order for each season until the improvement in the χ2
statistics of the fits cease to be significant. This results in us-
ing polynomial orders of 11, 10, 17 and 4 for the four seasons
of data. The low amplitude microlensing variations are modeled
with a simple linear function for the four seasons. Fig. 7 shows
the best fits to the data and the residuals from the model. The
effects of microlensing in this system are very small, with varia-
tions of only ∼ 0.01 mag over three years. As with the minimum

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C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–47237
Fig.8. Top: The light curves of the quasar images shown along
with the best numerical model. Bottom: The residuals of the fit.
dispersion method, we estimate the uncertainties by randomly
perturbingthe light curves 100,000 times and using the standard
deviation of the trials as the error estimates to find that
∆tB−A= 35.0 ± 1.1 days (3.0%)
∆tB−C= 61.2 ± 1.5 days (2.4%) (2)
4.3. Numerical modeling of the light curves
Our last approach is based on the method described in
Burud et al. (2001), which determines the time delay between
a pair of light curves using a gridded numerical model for the
sourcelightcurve.Foraseriesoftimedelays,wefitthedatawith
a flux ratio between the two curves, and a linear trend for mi-
crolensing on each full light curve. The numerical source model
Fig.9. Light curves of the three quasar images, shifted by their
respective time delay and flux ratio. The blue circles correspond
to image A, the red triangles to B and the green squares to C.
is smoothed on the scale of the temporal sampling, based on a
smoothing functionweighted by a Lagrange multiplier. The best
time delay is the one that minimizes the χ2between the model
and data points.
This method has several advantages: first, none of the data
light curves is taken as a reference: they are all treated on an
equal basis. Furthermore, as the model is purely numerical, no
assumption is made on the shape of the quasar’s intrinsic light
curve(exceptthatitissufficientlysmooth).Finally,amodellight
curve is obtained for the intrinsic variations of the quasar, as for
the polynomial fit method (see Sect. 4.2).
We have applied this method to the two pairs of light curves
of WFI J2033–4723. The resulting fits to the light curves and
their residuals are shown in Fig. 8. Using a Monte Carlo method
to estimate the uncertainties, we find from 7,000 trials (adding
normallydistributedrandomerrorswiththeappropriatestandard
deviation on each data point) :
∆tB−A= 36.0 ± 1.5 days (4.2%)
∆tB−C= 61.9+6.7
−0.5days (+11%
−1%)(3)
We notea secondarypeakin the ∆tB−CMonte Carlo distribu-
tion, around 69 days, in addition to the main peak at 61.9 days.
There is, however, no evidence of such a secondary peak in
the results of the minimum dispersion method and the polyno-
mial fitting technique. This translates into an asymmetrical error
bar on the result obtained with the numerical fitting of the light
curves, and is taken into account in our final estimate of the time
delay between quasar images B and C.
4.4. Final time delays
Forthefinaldelayestimateweadopttheunweightedmeanofthe
three methods, and we take as uncertainties the quadrature sum
of the average statistical error and the dispersion of the results
fromthe individualmethodsabouttheirmean.Ourfinal estimate

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8C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
WFI 2033-4723
G6
G5
G4
G3
G2
G1
E
N
5 arcsec
Fig.10. Environment of WFI J2033–4723 as seen in an
HST/ACS F814 (I-band) image. The main lens galaxy G1 and
the close companion G2 were included in our analysis of the
NICMOS image, and here we have labeled additional group
members as G3-G6.
of the time delays is
∆tB−A= 35.5 ± 1.4 days (3.8%)
∆tB−C= 62.6+4.1
−2.3days (+6.5%
−3.7%)(4)
We cannot measure the time delay between the individual A1
and A2light curves, but values larger than ∆tA1−A2= 2 days are
incompatible with any of the models we consider in the follow-
ing section. We can nevertheless estimate the flux ratio between
A1and A2. After correcting for the time delays, we find that the
R-band flux ratios between the images are
FA
FB
= 2.88 ± 0.04,
FA
FC
= 3.38 ± 0.06,
FA1
FA2
= 1.37 ± 0.05 (5)
Fig. 9 displays the light curves obtained for the three quasar
images, after shifting by the time delays and flux ratios. Note
thatthese fluxratiosdifferfromthosemeasuredbyMorgan et al.
(2004) from the MgII broad emission lines, probably due to
long-term microlensing (on a longer scale than our monitoring
3-year baseline), as discussed in the next section.
5. Parametric modeling
5.1. Observational constraints
We constrain the mass models of WFI J2033–4723 using the
positions of the four lensed images, the position of the lens
galaxy G1 and the two delay measurements, for a total of 12
constrains. Except when indicated, we do not use the image flux
ratios because they can be affected by extinction (Falco et al.
1999; Jean & Surdej 1998) and milli-lensing by substructures
(Mao & Schneider 1998). We can also constrain the structure of
G1 given its ellipticity e, position angle θeand effective radius
Reto the extent that these properties are correlated with those
of its dark matter halo. Although a possible mismatch between
the light and mass distributions is not impossible, we adopt the
formal errors of 0.002′′on the position of the lens G1 (Table 2).
This is motivatedby the small offset betweenthe centers ofmass
and light found by Yoo et al. (2006) in a sample of four lensing
galaxies.
Finally, WFI J2033–4723 is located in a group of galaxies,
labeledG2-G6inFig.10.WeincludeG2asasingularisothermal
sphere(SIS) in all our modelssince it is close (4′′) and of similar
luminositytoG1. As Morgan et al. (2004), we are unableto suc-
cessfully model the system without includingG2. When enough
observational constraints are available we further add galaxies
G3-G6as a SIS mass distributionlocatedat the barycenterGgroup
of the group. In all models we include an external shear of am-
plitude γ and position angle θγthat represents the gravitational
perturbationsduetomassunaccountedforexplicitly.We alsoex-
periment with including mass at the position of object X (Fig. 4,
2′′North of G1) and find that doing so does not improve the
models.
We consider a sequence of standard mass models for G1, in-
cluding a singular isothermal ellipsoid (SIE), a de Vaucouleurs
(dVC) model and a NFW model (Navarro et al. 1997), and we
fit the data using LENSMODEL (v1.99g) (Keeton 2001). The re-
sults are summarized in Table 3, where columns #1 and #2 de-
scribe the model family, and #3 the mass parameter (either the
Einstein radius b in arcseconds or the mean mass surface density
κs, as defined in Keeton 2001). Column #4 is for the elliptic-
ity e and PA θeof the lens G1. Note that the measured PA of
G1 is θ = 27.8◦(Table 2). Column #5 gives the external shear
amplitude γ and PA θγ, #6 the number of degrees of freedom
for each model, and #7 the resulting reduced χ2. Column #8 fi-
nally shows the best estimate for h =H0/100. A minus sign in
this column means that time delays are not used as constraints.
All angles are given positive East of North, and values given
in parentheses are fitted to the observations. All models assume
∆tA1−A2= 2 days and include the companion galaxy G2, with a
resulting mass 0.1mG1< mG2< mG1.
5.2. SIE Models
Our first model consists of an SIE for G1, an SIS for G2 and
an external shear. When we fit only the image positions but in-
clude a prior on the position angle θe(from Table 1) we do not
find a good fit unless the constraint on the position of the lens-
ing galaxy is relaxed. The prior on the position angle is justified
by statistical studies finding correlations between the position
angles but not the axis ratios of the visible and total mass dis-
tributions (Ferreras et al. 2008; Keeton et al. 1997). With the in-
clusion of the time delays we have enough constraints to add
the group halo to the model. With the position angle of G1 con-
strained,we obtainpoorfits to thedata with reducedχ2= 3.6for
Ndof = 2. When we leave the position angle free, we find good
fits but the model PA is 55◦from the observed. These models
have Hubble parameters of h ≃ 0.63+0.07
nated by the degeneracies between the ellipticity and the shear.
−0.03with the spread domi-
5.3. De Vaucouleurs Models
Nextwe considera constantmass-to-lightratiomodelofthe lens
galaxy based on a De Vaucouleurs model. The position angle
and the effective radius Re= 0.608′′(the geometric mean of the
semi-axes in Table 1, corresponding to 4 kpc for h = 0.72) are
constrained by the values measured for the galaxy. This model
does not fit well the lens configuration (χ2∼ 34.4), mainly due
to the small uncertainty on the lens galaxy position. When we
include the time delays we find a good fit (χ2≃ 0.01) as long
as we allow G1 to be misaligned with respect to the observed

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C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–47239
Table 3. Result of the parametric lens modeling.
Name
SIE+γ
SIE+γ
SIE+γ
dVC+γ
dVC+γ
NFW+γ
NFW+γ
NFW+γ
dVC+NFW+γ
Comp.mass
b=0.96
b=0.94
b=0.97
b=2.71
b=2.83
κs=0.20
κs=0.21
κs=0.09
b=1.56
κs=0.082
b=1.53
κs=0.10
e, θe
γ, θγ
#d.o.f.
1
2
1
1
1
1
1
1
-
1
-
3
χ2
15.3
3.6
0.30
34.4
0.01
0.38
0.06
0.01
-
6.33
-
3.2
h
-
Comments
Time delays not used
Ggroupincluded
Ggroupincluded
Time delays not used
Ggroupincluded
rs=10′′(fixed); time delays not used
rs=10′′(fixed); Ggroupincluded
rs=1′′(fixed); Ggroupincluded
Re= 0.608′′(fixed)
rs=10′′(fixed); Ggroupincluded
same model as above, with
flux ratios included
0.21, (20.8)
0.13, (30.5)
0.16, 84.4
0.20, (20.1)
0.18, 83.1
0.16, (27.4)
0.15, 85.7
0.15, 85.4
(0.17), (29.3)
0.065, (29.3)
(0.16), (26.4)
0.43, 89.8
0.187, 7.4
0.063, 24.6
0.059, 46.9
0.305, 9.7
0.116, 64.5
0.070, -3.6
0.079, 9.5
0.076, 30.6
0.057, 37.0
0.79+0.04
0.63+0.07
-
0.92+0.06
-
0.29+0.03
0.63+0.10
-
0.78+0.12
-
0.69+0.20
−0.02
−0.03
−0.03
−0.03
−0.08
Light
Halo
Light
Halo
−0.10
dVC+NFW+γ
0.075, 27.5
−0.10
galaxy. As expected from the reduced surface density compared
to the SIE model (Kochanek 2002), we find a much higher value
for the Hubble parameter, h = 0.92.
5.4. NFW Models
We use an NFW model with a fixed break radius of rs = 10′′
(40 kpc), where the break radius is related to the virial radius
through the concentration c = Rvir/rs. Since rslies well outside
the Einstein radius of the lens, its particular value is not impor-
tant. This model is not realistic by itself because the shallow
ρ ∝ 1/r central density cusp of the model will lead to a visible
central image. We again find that we can fit the astrometry well
even when the position angle of the lens is constrained, but we
cannot do so after including the time delays unless we allow the
model of G1 to be misaligned relative to the light. In any case,
this model leads to a fifth image about 3 mag fainter than A that
should be visible on our NICMOS data. This NFW model has a
higher surface density near the Einstein ring than the SIE model,
so we find a lower value for the Hubble parameter of h ≃ 0.29.
Using an unphysically small break radius of rs= 1′′raises the
density and hence the Hubble parameter to h ≃ 0.63.
5.5. De Vaucouleurs plus NFW Models
As our final, and most realistic, parametrizedmodelwe combine
a dVC model constrained by the visible galaxy with an NFW
model for the halo. The two components are first constrained to
have the same position and position angle, the parameters of the
dVC model are constrained by the observations, and the NFW
model has a fixed rs= 10′′break radius. This model leads to a
poor fit, with χ2= 6.33 for Ndof = 1. When we free the PA of
the NFW model, we find an acceptable fit for Ndof = 0, but the
misalignment of the NFW model relative to the optical is 40◦.
We can further constrain the model by including the three
MgII emission line flux ratios from Morgan et al. (2004). We
use the line flux ratios instead of those obtained from the light
curves, because they should be insensitive to microlensing.With
these three additional constraints we still find that the 89.8◦po-
sition angle of the NFW model is strongly misaligned from the
26.4◦position angle of the dVc model, indicating a twisting
of the mass isocontours. The model has a reduced χ2of 3.2
for Ndof = 3. The model flux ratios are significantly different
from the constraints. We find FA/FB = 2.81, FA/FC = 5.01,
and FA1FA2= 1.26 while Morgan et al. (2004) report FA/FB=
2.55 ± 0.60, FA/FC= 2.02 ± 0.35, and FA1/FA2= 1.61 ± 0.35.
The match of the flux ratios is better if we do not include the
20
40
60
80
100
102030
50100
Hubble time (Gyr)
Hubble constant (local units)
number of models
Fig.11. Distribution of H0from 1000 non-parametric models.
The bottom-axis gives the Hubble time, the top-axis H0in km
s−1Mpc−1.
constraints from the time delays. In all cases, FB/FCis the most
“anomalous” flux ratio, as also found by Morgan et al. (2004).
While the differences between the line and continuum flux ra-
tios suggests the presence of long-term microlensing, we see no
evidence for the time variability in the flux ratios expected from
microlensing. We also note that the broad line flux ratios vary
with wavelength (Morgan et al. 2004), which suggests that dust
extinction may as well be affecting the flux ratios.
6. Non-parametric modeling
We use the non-parametricPixeLens (Saha & Williams 2004)
method as our second probe of the mass distribution. This ap-
proach has the advantage that it makes fewer assumptions about
the shape of the G1 than the ellipsoidal parametric models. The
models include priors on the steepness of the radial mass pro-
file, imposes smoothness criteria on the profile and we restrict to
models symmetric about the lens center. We include two point
masses to represent G2 and the group. We run 1000 trial mod-
els at a resolution of ∼ 0.23′′/pixel which are constrained to fit
the image positions and the time delays exactly. For each model
we vary the Einstein radii of G2 and the group over the ranges
0.03′′< RE(G2) < 3′′and 0.3′′< RE(group) < 5′′, respectively.
Apart from the inclusion of these additional point masses, the
method and priors are as explained in detail in Coles (2008). A
test, where the technique is used to infer H0from a N-body and
hydro simulated lens, and an additional discussion of the priors
are described in Read et al. (2007). Fig. 11 shows the resulting

Page 10

10C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
Fig.12. Mean mass distribution from 1000 pixellated lens mod-
els. The red dots are the quasar images and the blue dot the
source position. The thick solid line indicates the observed ma-
jor axis of the lensing galaxy. Each tick-mark measures 1′′. The
third contour from the outside traces the critical mass density
Σcrit= 1.191011M⊙arcsec−2, and the others are drawn logarith-
mically from the critical one (each contour is 2.5 larger/smaller
than the previous one). North is to the top and East to the left.
probability distribution for H0from the 1000 models. The me-
dian value of the distribution is
H0= 67.1+13.0
−9.9
km s−1Mpc−1
(6)
where the error bars are at 68% confidence. As already illus-
trated by our parametric modeling, the predicted H0value de-
pends on the density gradient of the models. Fig. 12 shows the
mean surface density contoursof the models,and we see a twist-
ing of the contours away from that of the visible galaxy in the
outer regions.
7. Conclusions
By combining data from COSMOGRAIL and the SMARTS
1.3m telescope we measure two independent time delays in
the quadruply imaged quasar WFI J2033–4723 (Morgan et al.
2004). The fractional uncertainties of ∼ 4% are among the best
obtained so far from an optical monitoring. We obtain the light
curves of the quasar images using the MCS deconvolution pho-
tometry algorithm (Magain et al. 1998) and then measure time
delays using three different approaches with a final estimate of
∆tB−A= 35.5 ± 1.4 days (3.8%)
∆tB−C= 62.6+4.1
−2.3days (+6.5%
−3.7%) (7)
where A is the mean light curve of the blended of quasar im-
ages A1and A2. We find little evidence of microlensing in this
system, which makes WFI J2033–4723 a very good system for
measuring clean time delays.
The parametric models are consistent with concordance
value of H0when the lens galaxy has an isothermal mass pro-
file out to the radius of the Einstein ring. As expected, the mod-
els allow higher (lower) values as the mass distribution is more
centrally concentrated (extended) using de Vaucouleurs (NFW)
mass distribution. The non-parametric models predict H0= 67.1
+13.0
−9.9km s−1Mpc−1.
The addition of the time delays as a constraint on the lens
models does not alter the mismatch between the observed and
predicted image flux ratios. The largest flux ratio anomaly is the
45% difference between the MgII flux ratios found for images
B/C. Morgan et al. (2004) also noted that the FB/FCflux ratio
varies with wavelength, suggesting the presence of chromatic
microlensing. The lack of significant variability in the flux ra-
tio over our three year monitoringperiod suggests either that the
effective source velocities in this lens are very low or that the
affected images lie in one of the broad demagnified valleys typi-
cal of microlensingmagnificationpatterns forlow stellar surface
densities.
Several galaxies close to the line of sight have a significant
impact on the mass modeling. We generally model the potential
as the sum of a main lensing galaxy G1, a companion galaxy
G2 (∼ 4′′West of G1), and a nearby group (∼ 9′′North of G1).
Both the parametric and non-parametricmodels suggest that the
isodensity contours of G1 itself must be twisted, with some ev-
idence that the outer regions are aligned with the tidal field of
the group rather than the luminous galaxy. This could indicate
that G1 is a satellite rather than the central galaxy of the group
(e.g. Kuhlen et al. 2007). The twisting seems to be requiredeven
though the angular structure of the potential can be adjusted
through the companion galaxy G2, an external tidal shear, and
in some cases a group halo. Clarifying this issue requires more
constraints such as detailed imaging of the Einstein ring image
of the quasar host, measuring the redshifts of the nearby galax-
ies, and measuring the velocity dispersion of G1.
Acknowledgements. We would like to thank all the observers at the EULER
telescope for the acquisition of these monitoring data. We also thank Profs. G.
Burki and M. Mayor for their help in the flexible scheduling of the observing
runs, improving the necessary regular temporal sampling. We are very grate-
ful to Prof. A. Blecha and the technical team of the Geneva Observatory for
their efficient help with the electronics of the CCD camera. Many thanks also
to Sandrine Sohy for her commitment in the programming part of the deconvo-
lution techniques. Finally, we would like to thank Chuck Keeton for his advice
on the use of LENSMODEL. This work is supported by ESA and the Belgian
Federal Science Policy Office under contract PRODEX 90195. CSK is funded
by National Science Foundation grant AST-0708082. COSMOGRAIL is finan-
cially supported by the Swiss National Science Foundation (SNSF).
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12C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
Table 4. Photometry of WFI J2033–4723, as in Fig. 3. The Julian date corresponds to HJD-2450000 days.
HJD
3112.86
3124.85
3125.84
3131.83
3146.90
3149.34
3150.32
3151.35
3152.29
3154.30
3154.84
3156.27
3157.39
3158.36
3159.29
3160.32
3161.37
3162.33
3163.22
3168.93
3183.37
3184.78
3194.30
3195.28
3196.36
3197.18
3202.41
3202.76
3203.41
3211.74
3241.31
3258.72
3270.73
3279.64
3282.63
3287.60
3291.56
3292.57
3295.62
3296.15
3298.57
3301.62
3302.09
3303.06
3303.58
3307.59
3309.08
3310.13
3310.55
3320.55
3324.56
3328.52
3329.07
3338.51
3347.06
3432.39
3434.40
3442.37
3450.39
3458.40
seeing [”]
1.55
1.58
1.71
1.38
1.45
1.69
1.22
1.64
1.47
1.42
1.42
1.36
1.23
1.59
1.40
1.23
1.37
1.11
1.34
1.62
1.78
1.28
1.12
1.12
1.32
1.26
1.81
1.40
1.12
1.20
1.24
1.36
1.87
1.53
1.25
1.66
1.60
1.89
1.10
1.50
1.20
1.65
1.48
1.45
1.71
1.62
1.24
1.03
1.22
1.27
1.32
1.49
1.05
1.64
1.18
1.30
1.20
1.92
1.08
1.29
mag A
1.330
1.350
1.352
1.392
1.409
1.430
1.425
1.421
1.432
1.439
1.443
1.434
1.444
1.454
1.453
1.446
1.451
1.464
1.460
1.471
1.491
1.498
1.516
1.501
1.504
1.495
1.511
1.520
1.508
1.491
1.481
1.493
1.490
1.502
1.494
1.505
1.497
1.489
1.483
1.512
1.508
1.464
1.486
1.496
1.477
1.444
1.492
1.473
1.473
1.499
1.485
1.485
1.499
1.492
1.518
1.475
1.477
1.465
1.481
1.477
σA
0.006
0.017
0.006
0.022
0.018
0.005
0.009
0.006
0.009
0.006
0.022
0.007
0.012
0.008
0.012
0.009
0.015
0.009
0.008
0.020
0.007
0.006
0.016
0.006
0.008
0.006
0.015
0.020
0.009
0.006
0.004
0.008
0.035
0.011
0.011
0.016
0.025
0.023
0.016
0.008
0.014
0.036
0.011
0.015
0.018
0.016
0.002
0.007
0.033
0.013
0.010
0.019
0.011
0.021
0.006
0.010
0.006
0.015
0.005
0.013
mag B
1.752
1.783
1.769
1.823
1.834
1.859
1.874
1.866
1.864
1.876
1.847
1.853
1.867
1.887
1.915
1.889
1.841
1.871
1.853
1.846
1.848
1.845
1.863
1.845
1.837
1.843
1.849
1.818
1.841
1.814
1.846
1.844
1.838
1.794
1.821
1.840
1.800
1.872
1.835
1.857
1.840
1.831
1.854
1.870
1.837
1.776
1.873
1.863
1.874
1.891
1.870
1.834
1.857
1.760
1.847
1.824
1.809
1.854
1.850
1.823
σB
0.016
0.045
0.019
0.061
0.053
0.015
0.014
0.016
0.029
0.011
0.055
0.017
0.026
0.037
0.040
0.026
0.043
0.024
0.021
0.043
0.022
0.029
0.046
0.018
0.018
0.015
0.031
0.051
0.017
0.023
0.007
0.023
0.088
0.045
0.025
0.019
0.050
0.050
0.045
0.022
0.016
0.094
0.033
0.030
0.052
0.047
0.012
0.019
0.101
0.041
0.030
0.045
0.031
0.047
0.016
0.028
0.017
0.020
0.010
0.040
mag C
2.155
2.183
2.169
2.190
2.173
2.221
2.202
2.211
2.214
2.210
2.168
2.238
2.196
2.208
2.240
2.246
2.211
2.236
2.217
2.235
2.280
2.260
2.282
2.264
2.273
2.281
2.282
2.275
2.267
2.231
2.293
2.310
2.341
2.270
2.296
2.300
2.290
2.349
2.297
2.302
2.312
2.329
2.309
2.330
2.324
2.223
2.309
2.293
2.319
2.317
2.294
2.267
2.269
2.254
2.293
2.266
2.270
2.300
2.265
2.257
σC
0.027
0.063
0.036
0.041
0.056
0.013
0.016
0.017
0.031
0.014
0.056
0.016
0.026
0.037
0.043
0.024
0.049
0.029
0.025
0.060
0.014
0.021
0.050
0.020
0.017
0.018
0.037
0.056
0.017
0.040
0.007
0.042
0.111
0.034
0.035
0.037
0.066
0.061
0.060
0.023
0.023
0.136
0.051
0.035
0.069
0.078
0.010
0.022
0.112
0.037
0.046
0.047
0.033
0.080
0.019
0.025
0.029
0.024
0.012
0.043
telescope
SMARTS
SMARTS
SMARTS
SMARTS
SMARTS
EULER
EULER
EULER
EULER
EULER
SMARTS
EULER
EULER
EULER
EULER
EULER
EULER
EULER
EULER
SMARTS
EULER
SMARTS
EULER
EULER
EULER
EULER
EULER
SMARTS
EULER
SMARTS
EULER
SMARTS
SMARTS
SMARTS
SMARTS
SMARTS
SMARTS
SMARTS
SMARTS
EULER
SMARTS
SMARTS
EULER
EULER
SMARTS
SMARTS
EULER
EULER
SMARTS
SMARTS
SMARTS
SMARTS
EULER
SMARTS
EULER
EULER
EULER
EULER
EULER
EULER

Page 13

C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–472313
Table 4. continued.
HJD
3480.38
3483.86
3500.40
3508.85
3511.34
3516.36
3520.41
3520.87
3522.41
3524.38
3528.83
3547.35
3558.23
3562.86
3585.76
3586.27
3592.04
3601.19
3602.21
3603.27
3606.21
3606.72
3607.18
3608.17
3614.32
3614.70
3620.69
3633.64
3638.66
3640.24
3641.58
3643.61
3648.60
3650.11
3651.55
3654.58
3665.55
3668.06
3668.52
3672.10
3673.52
3675.05
3675.52
3676.07
3677.11
3678.07
3680.07
3680.51
3681.10
3682.12
3682.51
3684.07
3685.10
3686.07
3687.07
3687.51
3688.10
3689.06
3690.08
3691.05
3692.03
seeing [”]
1.58
1.27
1.62
1.53
1.41
1.18
1.40
1.13
1.00
1.34
1.16
1.26
1.38
1.37
1.22
1.61
1.05
0.97
1.42
1.24
1.91
1.75
1.22
1.34
1.41
1.07
1.27
1.58
1.64
1.47
1.53
1.57
0.96
1.18
1.05
1.60
1.29
1.43
1.50
1.43
1.53
1.19
1.12
1.53
1.50
1.46
1.43
1.49
1.78
1.86
1.70
1.63
1.22
1.44
1.45
1.50
1.10
1.33
1.65
1.65
1.64
mag A
1.493
1.491
1.482
1.496
1.533
1.549
1.545
1.556
1.545
1.560
1.558
1.596
1.587
1.611
1.580
1.546
1.537
1.512
1.497
1.507
1.490
1.487
1.477
1.475
1.461
1.476
1.475
1.460
1.454
1.454
1.450
1.434
1.428
1.421
1.412
1.417
1.420
1.433
1.415
1.432
1.411
1.432
1.395
1.406
1.408
1.402
1.394
1.388
1.395
1.387
1.389
1.365
1.391
1.380
1.362
1.375
1.386
1.379
1.380
1.383
1.382
σA
0.015
0.022
0.008
0.030
0.005
0.011
0.012
0.014
0.006
0.029
0.010
0.006
0.005
0.051
0.013
0.005
0.011
0.009
0.006
0.008
0.013
0.016
0.008
0.006
0.015
0.003
0.004
0.032
0.013
0.039
0.022
0.011
0.048
0.006
0.027
0.015
0.020
0.010
0.014
0.007
0.014
0.009
0.011
0.014
0.011
0.012
0.007
0.021
0.018
0.023
0.023
0.013
0.010
0.008
0.011
0.009
0.012
0.018
0.021
0.029
0.011
mag B
1.871
1.871
1.942
1.939
1.983
2.019
1.965
1.955
1.970
2.024
1.948
1.928
1.887
1.877
1.825
1.804
1.822
1.788
1.760
1.784
1.757
1.763
1.766
1.760
1.771
1.761
1.753
1.721
1.736
1.747
1.737
1.768
1.686
1.709
1.678
1.687
1.729
1.722
1.690
1.732
1.669
1.745
1.686
1.707
1.697
1.716
1.712
1.701
1.706
1.729
1.673
1.694
1.710
1.695
1.682
1.705
1.733
1.713
1.711
1.719
1.762
σB
0.040
0.028
0.022
0.066
0.020
0.026
0.025
0.036
0.014
0.074
0.016
0.019
0.019
0.142
0.035
0.008
0.024
0.024
0.030
0.024
0.035
0.041
0.018
0.012
0.036
0.023
0.012
0.054
0.034
0.098
0.057
0.014
0.118
0.015
0.064
0.040
0.025
0.020
0.031
0.014
0.039
0.017
0.034
0.038
0.024
0.026
0.023
0.043
0.037
0.052
0.064
0.031
0.028
0.024
0.026
0.031
0.030
0.031
0.056
0.072
0.031
mag C
2.302
2.266
2.305
2.311
2.320
2.301
2.293
2.249
2.287
2.361
2.314
2.336
2.377
2.371
2.409
2.395
2.384
2.362
2.333
2.387
2.363
2.355
2.395
2.366
2.403
2.383
2.346
2.311
2.359
2.331
2.359
2.315
2.348
2.298
2.293
2.326
2.289
2.271
2.276
2.302
2.253
2.296
2.271
2.293
2.281
2.283
2.290
2.240
2.289
2.303
2.218
2.273
2.292
2.305
2.286
2.262
2.270
2.305
2.273
2.302
2.279
σC
0.042
0.027
0.029
0.072
0.022
0.019
0.025
0.030
0.018
0.073
0.018
0.021
0.015
0.173
0.052
0.015
0.029
0.029
0.030
0.027
0.039
0.068
0.020
0.019
0.043
0.009
0.021
0.063
0.052
0.129
0.077
0.069
0.218
0.016
0.085
0.055
0.042
0.023
0.062
0.018
0.053
0.026
0.042
0.046
0.033
0.027
0.034
0.051
0.032
0.056
0.069
0.042
0.032
0.032
0.029
0.083
0.029
0.037
0.100
0.079
0.041
telescope
EULER
SMARTS
EULER
SMARTS
EULER
EULER
EULER
SMARTS
EULER
EULER
SMARTS
EULER
EULER
SMARTS
SMARTS
EULER
EULER
EULER
EULER
EULER
EULER
SMARTS
EULER
EULER
EULER
SMARTS
SMARTS
SMARTS
SMARTS
EULER
SMARTS
SMARTS
SMARTS
EULER
SMARTS
SMARTS
SMARTS
EULER
SMARTS
EULER
SMARTS
EULER
SMARTS
EULER
EULER
EULER
EULER
SMARTS
EULER
EULER
SMARTS
EULER
EULER
EULER
EULER
SMARTS
EULER
EULER
EULER
EULER
EULER

Page 14

14C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–4723
Table 4. continued.
HJD
3693.06
3694.06
3695.06
3696.07
3699.52
3700.07
3701.53
3707.07
3806.39
3819.38
3820.34
3824.39
3826.89
3829.37
3831.39
3832.41
3839.87
3844.41
3847.40
3848.39
3849.39
3850.37
3851.34
3852.35
3852.87
3863.79
3869.36
3877.88
3886.86
3887.42
3889.40
3891.42
3892.40
3896.88
3900.39
3903.79
3908.33
3913.28
3917.12
3918.84
3919.33
3932.40
3937.73
3944.22
3944.78
3945.35
3946.32
3946.63
3950.27
3952.24
3961.31
3964.09
3964.75
3967.78
3968.76
3970.22
3971.75
3979.17
3979.75
3980.27
3981.25
seeing [”]
1.17
1.22
1.72
1.55
1.30
1.60
1.58
1.79
1.42
1.19
1.28
1.32
1.25
1.24
1.09
1.18
1.79
1.21
1.37
1.54
1.16
1.46
1.28
1.18
1.19
1.07
1.23
1.15
0.84
1.29
1.12
1.32
1.19
1.72
1.09
1.23
1.10
1.08
1.72
0.60
1.11
1.53
1.18
1.63
1.58
1.35
1.33
1.39
1.35
1.20
1.57
1.11
0.74
0.67
1.24
1.48
1.02
1.35
1.66
1.56
1.10
mag A
1.378
1.378
1.370
1.367
1.370
1.376
1.365
1.394
1.370
1.353
1.377
1.384
1.371
1.358
1.366
1.370
1.393
1.353
1.352
1.350
1.351
1.354
1.339
1.352
1.383
1.371
1.368
1.390
1.422
1.406
1.415
1.424
1.412
1.463
1.430
1.460
1.455
1.476
1.477
1.521
1.474
1.526
1.537
1.522
1.544
1.510
1.517
1.531
1.489
1.488
1.463
1.449
1.474
1.450
1.448
1.447
1.453
1.426
1.452
1.435
1.415
σA
0.007
0.004
0.008
0.013
0.017
0.012
0.006
0.015
0.010
0.010
0.011
0.004
0.017
0.007
0.006
0.005
0.011
0.011
0.005
0.009
0.005
0.008
0.007
0.006
0.007
0.011
0.015
0.010
0.015
0.006
0.005
0.005
0.009
0.024
0.006
0.015
0.008
0.007
0.010
0.020
0.006
0.020
0.008
0.022
0.005
0.007
0.007
0.010
0.006
0.047
0.009
0.004
0.021
0.011
0.020
0.011
0.013
0.003
0.018
0.018
0.010
mag B
1.729
1.730
1.724
1.742
1.727
1.762
1.692
1.763
1.717
1.686
1.710
1.712
1.679
1.697
1.720
1.723
1.714
1.739
1.732
1.725
1.746
1.744
1.757
1.767
1.787
1.809
1.824
1.858
1.893
1.861
1.884
1.881
1.841
1.892
1.883
1.922
1.882
1.891
1.841
1.851
1.860
1.812
1.802
1.797
1.765
1.764
1.758
1.768
1.737
1.780
1.755
1.752
1.719
1.738
1.761
1.778
1.776
1.778
1.840
1.774
1.786
σB
0.020
0.014
0.021
0.020
0.048
0.028
0.066
0.035
0.023
0.026
0.024
0.012
0.042
0.017
0.020
0.011
0.026
0.030
0.010
0.020
0.015
0.032
0.020
0.018
0.019
0.029
0.036
0.037
0.040
0.014
0.017
0.017
0.043
0.078
0.020
0.053
0.015
0.017
0.026
0.048
0.034
0.049
0.015
0.040
0.017
0.015
0.015
0.030
0.017
0.102
0.019
0.011
0.055
0.029
0.038
0.037
0.029
0.013
0.031
0.031
0.024
mag C
2.268
2.256
2.297
2.230
2.246
2.246
2.183
2.253
2.234
2.225
2.222
2.219
2.218
2.177
2.185
2.178
2.153
2.216
2.188
2.204
2.199
2.200
2.187
2.184
2.230
2.181
2.168
2.219
2.207
2.199
2.204
2.199
2.177
2.236
2.187
2.217
2.202
2.222
2.244
2.182
2.209
2.297
2.301
2.343
2.330
2.269
2.291
2.278
2.296
2.377
2.342
2.322
2.331
2.340
2.317
2.293
2.325
2.313
2.248
2.291
2.293
σC
0.021
0.012
0.021
0.026
0.057
0.032
0.047
0.048
0.030
0.037
0.027
0.013
0.046
0.020
0.019
0.013
0.069
0.031
0.011
0.025
0.017
0.027
0.025
0.018
0.027
0.038
0.039
0.028
0.043
0.023
0.017
0.014
0.029
0.116
0.016
0.067
0.018
0.015
0.023
0.091
0.013
0.061
0.006
0.073
0.022
0.016
0.017
0.025
0.025
0.125
0.026
0.018
0.070
0.033
0.048
0.041
0.036
0.017
0.050
0.035
0.036
telescope
EULER
EULER
EULER
EULER
SMARTS
EULER
SMARTS
EULER
EULER
EULER
EULER
EULER
SMARTS
EULER
EULER
EULER
SMARTS
EULER
EULER
EULER
EULER
EULER
EULER
EULER
SMARTS
SMARTS
EULER
SMARTS
SMARTS
EULER
EULER
EULER
EULER
SMARTS
EULER
SMARTS
EULER
EULER
EULER
SMARTS
EULER
EULER
SMARTS
EULER
SMARTS
EULER
EULER
SMARTS
EULER
EULER
EULER
EULER
SMARTS
SMARTS
SMARTS
EULER
SMARTS
EULER
SMARTS
EULER
EULER

Page 15

C. Vuissoz et al.: COSMOGRAIL VII: time delays and H0from WFI J2033–472315
Table 4. continued.
HJD
3982.25
3987.55
3994.14
3994.64
3998.12
3999.11
4002.57
4003.10
4005.10
4007.62
4008.17
4014.53
4021.58
4024.15
4025.10
4027.09
4028.57
4032.06
4036.07
4036.53
4039.05
4042.04
4046.04
4057.05
4065.06
4072.06
4174.40
4183.40
4191.40
4197.36
4203.39
4204.39
4207.37
4213.41
4228.34
4230.31
seeing [”]
1.63
1.34
1.38
1.03
1.88
1.22
0.91
1.00
1.37
1.26
1.18
1.43
1.12
1.60
1.72
1.84
1.09
1.81
1.45
1.07
1.67
1.34
1.52
1.90
1.29
1.87
1.58
1.43
1.61
1.42
1.13
1.43
1.60
1.63
1.71
1.22
mag A
1.417
1.421
1.396
1.400
1.404
1.401
1.416
1.405
1.414
1.429
1.407
1.440
1.439
1.435
1.442
1.463
1.456
1.446
1.452
1.478
1.470
1.475
1.492
1.507
1.499
1.514
1.436
1.397
1.404
1.402
1.400
1.400
1.411
1.404
1.397
1.392
σA
0.013
0.021
0.007
0.017
0.010
0.008
0.010
0.005
0.011
0.011
0.007
0.014
0.011
0.009
0.007
0.008
0.006
0.015
0.007
0.014
0.012
0.008
0.007
0.010
0.006
0.011
0.022
0.010
0.015
0.017
0.011
0.011
0.009
0.007
0.020
0.008
mag B
1.767
1.818
1.805
1.776
1.798
1.800
1.837
1.817
1.831
1.834
1.820
1.829
1.894
1.852
1.882
1.876
1.844
1.850
1.849
1.828
1.877
1.839
1.830
1.776
1.774
1.774
1.730
1.709
1.737
1.740
1.734
1.756
1.739
1.748
1.697
1.697
σB
0.031
0.068
0.024
0.022
0.025
0.015
0.024
0.015
0.032
0.011
0.016
0.067
0.038
0.020
0.022
0.030
0.024
0.037
0.022
0.026
0.030
0.027
0.023
0.034
0.022
0.023
0.058
0.031
0.026
0.035
0.025
0.030
0.031
0.019
0.047
0.024
mag C
2.303
2.351
2.265
2.272
2.258
2.263
2.279
2.271
2.248
2.273
2.248
2.241
2.256
2.272
2.266
2.254
2.295
2.271
2.258
2.295
2.237
2.283
2.283
2.261
2.313
2.359
2.277
2.279
2.226
2.230
2.223
2.256
2.236
2.229
2.198
2.240
σC
0.048
0.083
0.025
0.021
0.068
0.013
0.035
0.013
0.031
0.017
0.022
0.069
0.038
0.023
0.025
0.029
0.019
0.046
0.022
0.016
0.034
0.025
0.023
0.034
0.027
0.064
0.080
0.037
0.036
0.042
0.031
0.034
0.034
0.027
0.055
0.025
telescope
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