A&A 467, 427-436 (2007)
DOI: 10.1051/0004-6361:20066994
S. Paulin-Henriksson1 - V. Antonuccio-Delogu1 - C. P. Haines2 - M. Radovich2 - A. Mercurio2 - U. Becciani1
1 -
INAF / Osservatorio Astrofisico di Catania
via S. Sofia, 78, 95123 Catania, Italy
2 -
INAF, Osservatorio Astronomico di Capodimonte,
Salita Moiariello 16, 80131 Napoli, Italy
Received 21 December 2006 / Accepted 5 February 2007
Abstract
Context. Weak lensing applied to deep optical images of clusters of galaxies provides a powerful tool to reconstruct the distribution of the gravitating mass associated to these structures.
Aims. We use the shear signal extracted by an analysis of deep exposures of a region centered around the galaxy cluster ABCG 209, at redshift ,
to derive both a map of the projected mass distribution and an estimate of the total mass within a characteristic radius.
Methods. We use a series of deep archival R-band images from CFHT-12k, covering an area of 0.3 deg2. We determine the shear of background galaxy images using a new implementation of the modified Kaiser-Squires-Broadhurst KSB+ pipeline for shear determination, which we has been tested against the "Shear TEsting Program 1 and 2'' simulations. We use mass aperture statistics to produce maps of the 2 dimensional density distribution, and parametric fits using both Navarro-Frenk-White and singular-isothermal-sphere profiles to constrain the total mass.
Results. The projected mass distribution shows a pronounced asymmetry, with an elongated structure extending from the SE to the NW. This is in general agreement with the optical distribution previously found by other authors. A similar elongation was previously detected in the X-ray emission map, and in the distribution of galaxy colours. The circular NFW mass profile fit gives a total mass of
inside the virial radius
Mpc.
Conclusions. The weak lensing profile reinforces the evidence for an elongated structure of ABCG 209, as previously suggested by studies of the galaxy distribution and velocities.
Key words: gravitational lensing - galaxies: clusters: individual: Abell 209
Cluster masses have traditionally been derived through the virial analysis
of the velocity dispersion of cluster galaxies, with the assumption of
dynamical equilibrium
(e.g. Girardi et al. 1998; Girardi & Mezzetti 2001), and/or from the X-ray temperature of the hot
intracluster gas, assuming hydrostatic equilibrium (Rosati et al. 2002, and references therein). Since using these methods one has to
assume the dynamical and hydrostatic equilibrium, these mass
estimates are affected by the ignorance about the dynamical state of the cluster.
Weak lensing analysis offers a unique opportunity to determine the cluster
mass distribution without such assumptions on its equilibrium, as the effect
is due to the gravitational deflection of the light that is dependent solely on the
distribution of matter. In particular, one application of weak lensing
analysis is the detection of the weak shear around galaxy clusters,
yielding an estimate of the total cluster mass and allowing a full
mass reconstruction of mainly low (
)
redshift clusters (Bardeau et al. 2005; Clowe et al. 2006,2004). As a possible target for a weak lensing
analysis the galaxy cluster ABCG 209 is particularly interesting, because the photometric and
evolutionary properties of its galaxy populations have been already
thoroughly studied
(Mercurio et al. 2003a,2004; Haines et al. 2004).
In this paper we present the weak lensing mass reconstruction of the
galaxy cluster ABCG 209 at z=0.21 (Mercurio et al. 2003b, and references therein) using archival wide-field R-band imaging. ABCG 209
is a rich (richness class R=3, Abell et al. 1989), X-ray
luminous
(
keV
erg s-1, Ebeling et al. 1996), moderately hot
(
keV, Rizza et al. 1998) and massive cluster (Mercurio et al. 2003b; Dahle et al. 2002). It is
characterized by the presence of substructures, which is shown by an elongation and asymmetry in the X-ray emission maps, with
two main clumps (Rizza et al. 1998). Moreover, the young dynamical state is indicated by the
presence of a radio halo
(Venturi et al. 2006; Giovannini et al. 1999), which has been suggested to
be the result of a recent cluster merger, through the acceleration of
relativistic particles by the merger shocks (Feretti 2002).
The plan of the paper is as follows. In Sect. 2 we will shortly review the data reduction procedures. In Sect. 3 we will present the software pipeline which we have developed to perform this analysis, based on the KSB+ algorithm (Luppino & Kaiser 1997; Kaiser et al. 1995). There exist many variants of this algorithm (see Massey et al. 2006; Heymans et al. 2006, for a presentation and comparison of some implementations), so we will describe in some detail our particular implementation (the OACt pipeline). In Sect. 4 we will describe the preparation of the galaxy catalogue, and the technique adopted to extract the shear information. Section 5 will be devoted to present the mass estimated and a mass aperture reconstruction obtained from the shear maps. In Sect. 6 we will compare the mass maps with the galaxy distributions and the X-ray maps. Section 7 will present the conclusions.
A detailed description of the data and reduction techniques has been
given elsewhere (Haines et al. 2004), so here we will only
summarize the main steps. The data were obtained from the Canada-France-Hawaii telescope (CFHT)
science archive (PI J.-P. Kneib), and comprise a wide-field R-band image centered on the cluster. The observations were made on 14-16 November 1999, using the CFHT12K mosaic camera, an instrument made up of
12
CCDs, set at the prime focus of the 3.6-m CFHT. The
CCDs have a pixel scale of
,
resulting in a total
field of view of
,
corresponding to
at the cluster redshift. The
total exposure time is 7200 s, made up of twelve 600 s exposures, jittered to cover
the gaps between the CCDs.
Standard IRAF tools were used to bias-subtract the images, using bias
exposures and the overscan regions of each CCD, before flat-fielding using
a superflat made up of all science images from the same observing run,
registering and Co-adding the images. The resultant images have a median
seeing of
.
The photometric calibration was performed in the the Johnson-Kron-Cousins
photometric system, using observations of 300 secondary standard
stars (14<R<17) in fields 6 and 7 of Galadi-Enriquez et al. (2000),
resulting in a zero-point uncertainty of 0.005 mag.
For the weak lensing analysis we have masked: (i) saturated stars and
hot pixels; (ii) a
(i.e. 300 pixels) border all
around the field, where the point-spread function (hereafter PSF) is too
complex to be properly modelled (e.g. concave and/or varying too
rapidly on small scales); (iii) CCD gaps (i.e. area covered by
several CCD on stacked images), where the PSF is also too complex.
The data set does also contain B-band imaging of the field with seeing and depth significantly lower than on the R-band image. On this B-band image, the bright star density is too low to interpolate the PSF, so it is not used to compute the shape parameters, but to help distinguish between cluster, foreground and background galaxies. Using an algorithm which takes into account the R-band magnitude, B-R colour and the local density, Haines et al. (2004) attribute to each galaxy a probability of belonging to the cluster. Given the lack of spectroscopic information, this probability is the most accurate information we have to discriminate among cluster and field galaxies.
We extract the shear signal from observed polarisation of background
galaxies, corrected for the effects of the PSF, via the standard KSB+ method (Luppino & Kaiser 1997; Kaiser et al. 1995), improved as described in the following sections.
We have blind tested our pipeline on the Shear-TEsting-Program (STEP)
simulated data (Massey et al. 2006; Heymans et al. 2006), where
altogether 16 different weak lensing pipelines have been tested and compared. For reasonable PSFs, as the one sampled by the images presented in
this paper turned out to be, the shear we measure
is a linear function of the true (i.e. simulated) one
:
We present in Sects. 3.1 and 3.2 the basic KSB+ formalism, and in Sect. 3.3 the details specific to the OACt pipeline.
The observed polarisation of a galaxy offers an estimate of the local
gravitational shear, and can be defined using the weighted quadrupole
moments of the brightness distribution (Kaiser et al. 1995):
The current KSB+ method is the result of a series of successive
improvements (Luppino & Kaiser 1997; Hoekstra et al. 1998) of the
original method proposed by Kaiser et al. (1995). It provides a
gravitational shear estimate by first-order subtraction of the PSF
smearing and shearing from the galaxy polarisation. The 2D vector KSB+ shear estimator of a single galaxy
is given by:
The actual prescription to estimate ,
and the PSF-subscripted tensors, the choice of the window function W in Eq. (3), the algorithm of pixelised summations, and finally the approximations, vary from one implementation of the method to another. Our algorithm is described in the following section.
We determine the significance
and the optimal smoothing
radius
of each object.
and
are defined as usual in weak lensing: when convolving
the image with a Mexican-hat filter, the radius
is the smoothing
radius for which the object has the best signal-to-noise ratio, and
the significance
is this best signal-to-noise ratio.
The window function W of Eq. (3) is
taken to be a circular Gaussian centered on the weighted centroid,
having a standard deviation equal to .
The weighted centroid, computed iteratively, is the point for which weighted dipoles are equal to zero:
After computation of the shape parameters and shear estimator, we discard the objects for which: (i) the standard deviation on the centroid is larger than 0.2 pixel; (ii) the polarisation
is greater than 1; (iii) the shear estimator
is greater than 2; (iv) the trace of the
tensor is lower than 0.2. For the current data set, this corresponds to 5% of the background galaxies. Even on noisier data sets this usually corresponds to less than 10%.
The corrective factors of a given galaxy are all computed in the bin corresponding to the
of the galaxy itself. In other words,
we interpolate PSF properties from stars in every single
bin
independently for each galaxy.
In all the
and
tensors of stars, the off-diagonal terms are completely dominated by
shot-noise, and typically they are more than one order of magnitude
smaller than the diagonal terms. For this reason, following similar
implementations (Hoekstra et al. 2000), we systematically neglect these off-diagonal terms.
Also the non-diagonal terms of the tensor
are
extremely noisy, and we then approximate this tensor
as a scalar equal to half its trace.
These approximations imply that the vector
of
Eq. (6) (i.e. the anisotropic component of the
PSF) is the interpolation of:
As we will see in the following, in order to keep a
relatively high star density, we use a
rather permissive star selection criterion. As a consequence, our star
catalogue is contaminated by small galaxies. In order to reject these small galaxies when fitting PSF properties, the fits are iterative: after the first fit is performed, we
reject all objects with at least one residual at more than ,
and we continue to iteratively perform new fits until
convergence. Typically, this procedure converges after 2 or 3 iterations.
To extract the weak shear information from the reduced and calibrated CHFT12k images presented in Sect. 2, we first build the star-field and the background-galaxy-field catalogues. Background galaxies contain the weak lensing signal, smeared and sheared by the PSF, while stars are measures of the local PSF. We first detect all the objects within the field and then select those relevant for weak lensing. Stars are selected according to their sizes and their magnitudes, while the background galaxies are selected by cross-checking our relevant object catalogue with the galaxy catalogue of Haines et al. (2004). The latter contains all galaxies within the field and assigns to each a probability of belonging to the field rather than to the cluster itself. All these steps are described in Sect. 4.1. We then compute shape parameters of stars and background galaxies (Sect. 3.3.2), using the stars to map the PSF (as described in Sect. 3.3.4), and finally compute a shear estimator for each background galaxy.
We detect all the objects on the image using SExtractor, with very low thresholds. We also get a large proportion ()
of spurious detections but these are rejected later. We demand detected objects to have at least 5 pixels above
,
where
is the standard deviation of the local background (i.e. DETECT_THRESH and ANALYSIS_THRESH set to 1.5, DETECT_MINAREA set to 5), where the local background is estimated with keywords BACK_SIZE set to 70 and BACK_FILTERIZE set to 5.
SExtractor is also used
to measure the flux and the half-light-radius
of each object.
We then compute
and
,
as described in Sect. 3.3.
We then successively remove from the catalogues :
(i) the objects with
;
(ii) the objects with at
least one neighbor nearer than
;
(iii) the objects with at least one pixel belonging to the
masked area within an aperture of
(the masked area is
described in Sect. 2); (iv) the
objects with
lower than the local smoothing radius of
stars. Finally, we compute the shapes of the remaining objects and
apply shape cuts, as described in Sect. 3.3.2. After having performed these steps, we
have a catalogue of
30 000 detections, containing all the
weak-lensing-relevant background galaxies but also stars, cluster
galaxies and a large proportion of spurious events due to the low
thresholds used with SExtractor.
We build a star catalogue with a loose selection based on 5 parameters:
the significance ;
the magnitude R; the surface brightness in
the central pixel
;
the half-light-radius
,
and the
smoothing radius
.
We demand:
;
;
;
;
.
This returns
1588 objects (
1.5 objects arcmin-2) uniformly
distributed in the field. We define this catalogue loose because
,
and
of stars show variations of
through the field with the PSF (while we apply these constant
cuts). Thus, these cuts result in a star catalogue which contains
of non-stellar detections, most of them being small
galaxies. These fake stars are iteratively rejected during the PSF
property fits, as described in Sect. 3.3.4. At the
end of iterations, we are left with
0.9 stars arcmin-2, as shown in Fig. 2.
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Figure 1:
Top ( bottom respectively) panel: magnitude - central magnitude (optimal smoothing radius ![]() |
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Figure 2:
Star polarisations in the field. Top panel: before any
correction (i.e. measured polarisations). Bottom panel: after the
anisotropic correction. In both panels, the vectors are oriented
along the major axis of the ellipsoid, their length being
proportional to the polarisation:
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These cuts are optimised to give a background galaxy catalogue with low foreground contamination, while keeping almost all the relevant
background galaxies. They are illustrated in Fig. 1, where the star sequence is clearly visible in
red, while background galaxies are in blue. The final background
galaxy catalogue contains 16 708 galaxies (16.7 galaxies arcmin-2).
When combining individual galaxy shears to produce shear maps, mass
reconstructions or density profile fits (see Sects. 4.3 and 5), we weight galaxies
according to their significance, as proposed by
Clowe et al. (2006): we do not consider objects with ,
while for
the weight is set equal to
.
In other words, for a given galaxy i, the weight wi is defined as:
Figure 2 shows the star polarisations over the
field before and after the anisotropic correction (i.e. the subtraction
of
in Eq. (11)). One can notice the lack of large scale
correlations due to the PSF anisotropies, after the subtraction. The
correction also reduces the average amplitude and anisotropy of the PSF, as
it is clear from Fig. 3. The corrected
distribution of ellipticities is more isotropic, and has also a smaller
scatter dispersion.
To get a shear map, we divide the field into
square cells
with an overlap of 50% (i.e. 50% of the galaxies in one cell belong only to this cell, while
the remaining 50% belong also to at least one of the 8 neighbouring
cells). In each cell we average
according to the weighting scheme described in
Sect. 4.1. The resulting shear map is shown in Fig. 4. One can see a characteristic pattern of increased
tangential shear, which coincides with the central region of the
cluster, as defined by the optical distribution of galaxies. This
visual impression is confirmed by the mass aperture map, as we will
see in the following sections.
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Figure 3:
Distribution of stellar polarisations. Upper panel: e1 against e2 of stars before (black) and after (red) the anisotropic correction. Bottom panel: ![]() |
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Figure 4:
Shear map of the whole field obtained with an overlap of 50% (i.e. 50% of the field area is accounted into more than one cell). The scale is given by the thick line in the upper right corners:
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There are quite a few different methods to deduce the mass distribution from the individual shears of background galaxies (see e.g. Bartelmann & Schneider 2001, for a review). A class of these methods makes use of the 2D smoothed shear maps to get the projected surface density distribution: examples of this class are the mass reconstruction method (Seitz & Schneider 2001,1995; Schneider & Seitz 1995), or the mass aperture technique (Schneider 1996). These methods suffer from the sheet mass degeneracy: they provide a reliable reconstruction of the surface density, but this is known except for a constant value. The alternative is to assume a priori a given mass profile, so that the degeneracy is removed, then attempt a parametric fitting. These latter methods are useful to get an estimate of the total mass of the cluster. Both methods suffer from possible systematic effects, for instance the contamination from background sources.
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Figure 5:
Total mass inside the radius R for the two models SIS (in blue) and NFW (in red).
Dashed lines are the 66% confidence level regions.
The black vertical lines show the virial radius
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In Sect. 5.1, we fit two different parametric spherical density profiles: a Singular Isothermal Sphere (SIS) and a Navarro-Frenk-White (NFW) (Navarro et al. 1996). In Sect. 5.2, we map the mass distribution using mass aperture statistics.
In order to derive actual values of the mass from the shear parametric, we have to know the critical surface density:
For both profiles we have performed a
minimization of the
tangential shear:
For the NFW fit we have either assumed that each galaxy provides an estimate of the underlying shear field, (so the summation in Eq. (15) extends to the full sample) or we have binned the data and minimised over the averages in the bins. We have verified that both procedures give compatible results.
We exclude from the fits galaxies lying within an inner central
region of the cluster, where the weak lensing approximation (
)
is not everywhere valid, and outside an outer region, where the
statistics are very weak.
The actual fitted region lies within the following bounds:
(
)
around the cluster center of mass.
The NFW profile has often been used as a good fit of numerically
simulated halos (Navarro et al. 1997,1995).
Although this fit was originally made only for simulated halos in
standard CDM models, it turned out to be a good fit for
halos which formed in CDM models.
The mass density of the NFW profile is described by:
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= | ![]() |
(17) |
![]() |
= | ![]() |
(18) |
![]() |
= | ![]() |
(19) |
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|||
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(22) |
For a SIS model, the density and shear profiles are respectively given by:
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(23) | ||
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(24) |
In Fig. 5 we show the total mass inside the
radius R, according to the two different fits we find.
Note that the
region of NFW is much larger than in the SIS case. This is a direct consequence of Eqs. (20) and (25): in the SIS model M(<R) is proportional to
and so the confidence region has a width of
,
while in the NFW model M(<R) depends on
.
This makes the
region to have a minimum
width for
Mpc.
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Figure 6:
Comparison of the weak lensing mass reconstruction with the
galaxy distribution for ABCG 209. The black contours represent the isodensity
contours from the
![]() ![]() ![]() ![]() |
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The mass within an aperture radius r can be obtained directly from the shear
using the aperture densitometry statistics ,
defined as
in Fahlman et al. (1994):
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Figure 7:
Comparison of the weak lensing mass reconstruction with the
X-ray emission for ABCG 209. The red contours represent the isodensity
contours from the
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Following the approach of Schneider (1996), we build the
(2D) mass aperture statistics by computing the aperture densitometry at each point of a grid on the field. The mass density
at a given point is given by:
The internal dynamics of the cluster was studied by Mercurio et al. (2003a) through a spectroscopic survey of 112 cluster members. A
high value of the line-of-sight velocity dispersion was found, with
km s-1 after removing
seven interlopers. Assuming dynamical equilibrium, this value of
leads to a
virial radius of
Mpc and a virial mass of
in a
CDM model,
with
and
.
We report this value
in Fig. 5, for a direct comparison with the results of the NFW and SIS analyses showed in this paper. The
difference in the estimates of the virial mass and the virial radius
obtained by the kinematics and weak lensing could be due to the presence
of substructures which results in an over estimate of the velocity
dispersion. Another source of uncertainties in the kinematics could be the
anisotropy parameter of the cluster velocity distribution. On the other
hand, the lensing values could be biased because of the elongation of the
cluster mass distribution (see Sect. 7).
Evidence in favour of the cluster undergoing a dynamical evolution is found in the form of a velocity gradient acting along a SE-NW axis, which is the same preferential direction found from the elongation in the spatial distribution of galaxies, as well as that of the cD galaxy. There is also significant deviation of the velocity distribution from a Gaussian, with evidence for two secondary clumps at z=0.199 and z=0.215, which appear spatially segregated from the main cluster. These all indicate that ABCG 209 is undergoing strong dynamic evolution with the merging of two or more sub-clumps along the SE-NW direction.
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Figure 8:
Comparison of the weak lensing mass reconstruction with the
mean colours of galaxies across ABCG 209. The black contours represent the isodensity
contours from the
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The X-ray data are taken from the XMM science archive (Prop #8423,
PI. J.-P. Kneib, see Marty et al. (2003) for an analysis). The observations were made in Jan 2001, with an
exposure time of 20 ks. The EPIC MOS1, MOS2 and pn images were
combined over the temperature range 0.5-12 keV and the resulting spatial
distribution of the X-ray emission is shown in Fig. 7 by the
grayscale-filled contours. The X-ray emission is centered on the cD
galaxy (h31m52.5s,
,
z=0.2097), making
it slightly offset (
)
from the center of mass determined from the weak
lensing by Eq. (16). The X-ray emission is
elongated along the same SE-NW direction as seen for the weak lensing reconstructed
mass distribution, the emission being most extended
towards the NW. There is no evidence of excess X-ray emission from the
substructure seen in the weak-lensing reconstruction
to the North of the cluster center.
From an analysis of a 10 ks Chandra ACIS-I (0.3-10 keV) X-ray observation of the
cluster, Mercurio et al. (2003a) obtained a best-fitting temperature of
keV which, assuming
,
would
correspond to
km s-1, and is consistent with the high value of
keV
erg s-1 (Ebeling et al. 1996). This value of the
velocity dispersion produces a virial mass estimate of
.
The mass estimates obtained through our weak lensing analysis are lower than those based on the X-ray temperature and
galaxy velocity dispersions. In a weak lensing analysis of 35 X-ray
luminous clusters at
0.15<z<0.30, Dahle (2006) finds a large
scatter in the relation between the weak lensing mass estimates and
the X-ray luminosity, producing a mass uncertainty of
dex. In a weak lensing study of 24 X-ray luminous
clusters at
0.05<z<0.31, Cypriano et al. (2004) found that on average the mass estimates
based on X-ray temperatures and velocity dispersions were 13-27%
higher than those from the weak lensing analysis. In particular they
found the discrepancy to be much greater for the most massive clusters
(
keV or
km s-1), where the mass
excess from the X-ray temperatues or velocity dispersions were
40-75%. They found that the discrepancy was largest for the two
clusters with the largest X-ray temperatures (
keV) and
velocity dispersions, which were known to be undergoing a merging
event, and are far from equilibrium. The high X-ray temperatures would
then be probably due to recent shocks, and the high velocity
dispersions due to substructures and the complex dynamical situation.
The star-formation history of galaxies is known to correlate strongly with their local environment. In Fig. 8 we compare the mass distribution with the mean B-R colour of the R<21 cluster galaxy population as a function of spatial position. Each galaxy is weighted according to the probability that it belongs to the cluster, and then the mean colour of cluster galaxies calculated as a function of spatial position using an adaptive kernel method. This analysis is described in details in Haines et al. (2004): the mean galaxy colours (and hence their star-formation histories) are strongly correlated with the dynamical state of the cluster, with an alignment of the colours with the main SE-NW axis. The region with the reddest mean galaxy colours, and hence the oldest stellar populations, is found at the cluster center of mass. There are also two regions of red galaxies outside the cluster core that are aligned with the dark matter distribution, confirming that galaxy evolution is strongly dependent on the hierarchical build up of clusters through mergers. Given the uncertain effects cluster dynamics have on the X-ray emission and galaxy velocity distributions, maps of the mass distribution based on weak lensing analyses provide an important tool for understanding the relation between galaxy evolution and the underlying dark matter distribution (Gray et al. 2004).
We have performed a weak lensing analysis of the galaxy cluster ABCG 209 through a new implementation of the KSB+ algorithm (the OACt pipeline), and we have also performed a mass reconstruction using Mass Aperture and parametric statistics. We clearly find a measurable weak lensing signal, and the comparison with optical and X-ray data for this cluster brings some interesting conlusions.
First, the centers of the X-ray emission, dark matter, and galaxy distribution all appear offset from one another, with the center of mass found from the weak lensing analysis lying between that of the X-ray and galaxy distributions, and all the three centers of mass aligned on the main SE-NW axis of the cluster. Such an effect is seen for the more extreme Bullet cluster (Clowe et al. 2004), and appears to reflect the different responses of the gas and dark matter components to the merger, briging a further hint at a cluster merging scenario for ABCG 209.
Second, we confirm that ABCG 209 is a massive cluster, although the mass estimated by weak lensing is lower than the estimates obtained by Mercurio et al. (2003a) from the analysis of the dynamical properties of the galactic population (assuming the dynamical equilibrium). On the weak lensing side, there are two sources of error not taken into account in this analysis, that could explain this discrepancy. First, the 2D-mass distribution of the cluster is not circular and this fit of a circular profile is possibly not accurate. Second, we have not taken into account the uncertainty on the critical surface density (Eqs. (13) and (14)), which has been computed according to the single-source plane approximation at z=1. Considering these uncertainties, the agreement we find among the different mass estimates should be regarded as satisfactory.
Acknowledgements
The work of S. Paulin-Henriksson, V. Antonuccio-Delogu and U. Becciani has been partially supported through the EC Transfer of Knowledge Marie Curie grant MTKD-CT-002995, project: COSMOCT, EC-VI Framework Programme for R&D. C. P. Haines acknowledges the financial supports provided through the European Community's Human Potential Program, under contract HPRN-CT-2002-0031 SISCO. This work is partially supported by the Italian Ministry of Education, University and Research (MIUR) grant COFIN200420323 and by the INAF grant "PRIN 2005''. S. Paulin and V. Antonuccio-Delogu would like to thank N. Kaiser for the online version of IMCAT, A. Réfrégier and D. Clowe for useful suggestions.