# Weak lensing measurement of galaxy clusters in the CFHTLS-Wide survey

HuanYuan Shan$\dagger$1$\dagger$1affiliationmark:  22affiliation: Laboratoire
d’Astrophysique de Marseille, CNRS-Université de Provence, 38 rue Frédéric
Joliot-Curie, 13 388 Marseille Cedex 13, France 33affiliation: Centre de
Physique des Particules de Marseille, CNRS/IN2P3-Luminy and Université de la
Méditerranée, Case 907, F-13288 Marseille Cedex 9, France , Jean-Paul
Kneib22affiliation: Laboratoire d’Astrophysique de Marseille, CNRS-Université
de Provence, 38 rue Frédéric Joliot-Curie, 13 388 Marseille Cedex 13, France ,
Charling Tao11affiliation: Department of Physics and Tsinghua Center for
Astrophysics, Tsinghua University, Beijing, 100084, China 33affiliation:
Centre de Physique des Particules de Marseille, CNRS/IN2P3-Luminy and
Université de la Méditerranée, Case 907, F-13288 Marseille Cedex 9, France ,
Zuhui Fan44affiliation: Department of Astronomy, Peking University, Beijing,
100871, China , Mathilde Jauzac22affiliation: Laboratoire d’Astrophysique de
Marseille, CNRS-Université de Provence, 38 rue Frédéric Joliot-Curie, 13 388
Marseille Cedex 13, France , Marceau Limousin22affiliation: Laboratoire
d’Astrophysique de Marseille, CNRS-Université de Provence, 38 rue Frédéric
Joliot-Curie, 13 388 Marseille Cedex 13, France 5 5affiliationmark:  , Richard
Massey66affiliation: Institute for Astronomy, Royal Observatory, Blackford
Hill, Edinburgh EH9 3HJ, UK , Jason Rhodes77affiliation: California Institute
of Technology, MC 350-17, 1200 East California Boulevard, Pasadena, CA 91125,
USA 88affiliation: Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA 91109, USA , Karun Thanjavur99affiliation: Canada
France Hawaii Telescope, 65-1238 Mamalahoa Hwy, Kamuela, HI 96743, USA
1010affiliation: Department of Physics & Astronomy, University of Victoria,
Victoria, BC, V8P 1A1, Canada 1111affiliation: National Research Council of
Canada, Herzberg Institute of Astrophysics, 5071 West Saanich Road, Victoria,
BC, V9E 2E7, Canada and Henry J. McCracken1212affiliation: Institude
d’Astrophysique de Paris, UMR 7095, 98 bis Boulevard Arago, 75014 Paris,
France

###### Abstract

We present the first weak gravitational lensing analysis of the completed
Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). We study the $64~{}{\rm
deg}^{2}$ W1 field, the largest of the CFHTLS-Wide survey fields, and present
the largest contiguous weak lensing convergence “mass map” yet made.

2.66 million galaxy shapes are measured, using a Kaiser, Squires and
Broadhurst (KSB) pipeline verified against high-resolution Hubble Space
Telescope imaging that covers part of the CFHTLS. Our $i^{\prime}$-band
measurements are also consistent with an analysis of independent
$r^{\prime}$-band imaging. The reconstructed lensing convergence map contains
$301$ peaks with signal-to-noise ratio $\nu>3.5$, consistent with predictions
of a $\Lambda$CDM model. Of these peaks, $126$ lie within $3\arcmin.0$ of a
brightest central galaxy identified from multicolor optical imaging in an
independent, red sequence survey. We also identify seven counterparts for
massive clusters previously seen in X-ray emission within $6~{}\rm deg^{2}$
XMM-LSS survey.

With photometric redshift estimates for the source galaxies, we use a
tomographic lensing method to fit the redshift and mass of each convergence
peak. Matching these to the optical observations, we confirm $85$
groups/clusters with $\chi^{2}_{\mathrm{reduced}}<3.0$, at a mean redshift
$\langle z_{c}\rangle=0.36$ and velocity dispersion
$\langle\sigma_{c}\rangle=658.8~{}\rm km~{}s^{-1}$. Future surveys, such as
DES, LSST, KDUST and EUCLID, will be able to apply these techniques to map
clusters in much larger volumes and thus tightly constrain cosmological
models.

###### Subject headings:

cosmology: observations, - galaxies: clusters: general, -gravitational
lensing: weak, -X-rays: galaxies: clusters

55affiliationtext: Dark Cosmology Centre, Niels Bohr Institute, University of
Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen,
Denmark$\dagger$$\dagger$affiliationtext: Email address<EMAIL_ADDRESS>
##  1\. Introduction

Clusters of galaxies are the largest gravitationally bound structures in the
universe. The number and mass of the biggest clusters are highly sensitive to
cosmological parameters including the mass density $\Omega_{m}$, the
normalization of the mass power spectrum $\sigma_{8}$ (e.g., Press & Schechter
1974; Frenk et al. 1990; Eke et al. 1996; Sheth & Tormen 1999), and the
dynamics of dark energy (e.g., Bartelmann et al. 2006; Francis et al. 2009;
Grossi & Springel 2009). Understanding the properties of clusters is vital to
test theories of structure formation and to map the distribution of cosmic
matter on scales of $\sim$1–10 Mpc.

Theoretical predictions of structure formation deal directly with the total
mass of clusters; measurements are restricted to indirect proxies that can be
observed. Contaminating the translation between theory and observation are
large uncertainties in the interpretation of galaxy richness, X-ray
luminosity/temperature and the Sunyaev-Zeldovich decrement (e.g. Bode et al.
2007; Leauthaud et al. 2010). Weak gravitational lensing, the coherent
distortion of galaxies behind a cluster, can potentially provide direct
measurements of the total mass regardless of its baryon content, dynamical
state, and star formation history.

By measuring the shear (coherent elongation) of many background galaxies, we
can reconstruct the two-dimensional (2D) weak lensing convergence map, which
is proportional to density projected along each line of sight. Peaks in the
convergence map with high signal-to-noise ratio $\nu$ generally correspond to
massive clusters (Hamana et al. 2004; Haiman et al. 2004). Since the three-
dimensional (3D) shear signal should increase behind those clusters in a
predictable way that depends upon only the lens-source geometry, we can also
use photometric redshift estimates of the background galaxies (from multi-band
imaging) to measure the redshift and mass of each foreground cluster (Wittman
et al. 2001, 2003; Hennawi & Spergel 2005; Gavazzi & Soucail 2007).

Systematic weak lensing cluster searches have only recently become
practicable. Miyazaki et al. (2002) used Subaru/Suprime-Cam in excellent
seeing conditions to find an excess of $4.9\pm 2.3$ convergence peaks with
$\nu>5$ in an area of $2.1~{}\rm deg^{2}$. Dahle et al. (2003) and Schirmer et
al. (2003) each identified several shear-selected clusters with redshifts
$z\sim 0.5$ determined from two-color photometry. Hetterscheidt et al. (2005)
reported the detection of five cluster candidates over a set of $50$
disconnected Very Large Telescope/FORS images covering an effective area of
$0.64~{}\rm deg^{2}$, while Wittman et al. (2006) found eight detections in
the first $8.6~{}\rm deg^{2}$ of the Blanco Deep Lens Survey. Gavazzi &
Soucail (2007) presented a weak lensing analysis of initial Canada-France-
Hawaii Telescope Legacy Survey (CFHTLS) Deep data covering $4~{}\rm deg^{2}$.
They demonstrated that the image quality at CFHT is easily sufficient for
cluster finding. Miyazaki et al. (2007) presented the first large sample of
weak lensing-selected clusters in the Subaru weak lensing survey, with $100$
significant convergence peaks in a $16.7~{}\rm deg^{2}$ effective survey area.
Hamana et al. (2009) reported results from a multi-object spectroscopic
campaign to target $36$ of these cluster candidates, of which $28$ were
confirmed (and $6$ were projections along a line of sight of multiple, small
groups).

The main astrophysical systematic effect afflicting weak lensing cluster
surveys is the projection of large-scale structure along the line of sight.
Random noise is also added due to the finite density of resolved source
galaxies and the scatter of their intrinsic shapes. Numerical studies (White
et al. 2002; Hamana et al. 2004) show that these contaminants significantly
reduce the purity of cluster detection. To improve our analysis, we shall
combine our weak lensing results with multi-wavelength imaging. Simultaneous
detection of a weak lensing signature plus an overdensity of galaxies with a
single red sequence provides an unambiguous cluster identification.
Furthermore, 3D lensing tomography using photometric redshifts from the multi-
wavelength data can remove the other potential hurdles of: lensing signal
dilution by cluster member galaxies, and identifying the redshift of weak
lensing peaks when no corresponding galaxy overdensity is apparent.

Here we present a weak gravitational lensing analysis of the $64~{}\rm
deg^{2}$ CFHTLS-Wide W1 field, which is sufficiently large to contain several
hundred galaxy clusters. Compared to the analysis of the CFHTLS-Deep survey by
Gavazzi & Soucail (2007), our shallower CFHTLS-Wide imaging (and lower source
galaxy density) will favor the detection of higher mass, nearby clusters. The
huge increase in survey area over any previous survey is expected to yield
many more systems overall. In this paper, we shall primarily study the
properties of the detected clusters, rather than the cosmology in which they
are embedded. For this purpose, we adopt a default cosmological model with
$\Omega_{m}=0.27$, $\Omega_{\Lambda}=0.73$, $\sigma_{8}=0.809$,
$H_{0}=100~{}h~{}\mathrm{km}~{}{\mathrm{s}}^{-1}~{}\mathrm{Mpc}^{-1}$, and
$h=0.71$.

This paper is organized in the following way. In Section 2, we describe the
CFHT and Hubble Space Telescope (HST) data used. In Section 3, we present the
measurement of galaxy shapes in the CFHT imaging, and their calibration
against measurements of the same galaxies in the HST imaging. In Section 4, we
reconstruct the 2D lensing convergence “mass map” signal, and extract a
catalog of local maxima that represent cluster candidates. In Section 5, we
search for optical counterparts of these candidates, dramatically cleaning the
catalog. In Section 6, we investigate the full 3D lensing signal around each
cluster, further cleaning the catalog when the lensing signal behind spurious
peaks does not increase as expected with redshift - but obtaining an
independent estimate of the cluster redshift when it does. We finally explore
global scaling relations between cluster mass observables, then conclude in
Section 7.

##  2\. Data

###  2.1. CFHTLS-Wide T0006 imaging

The CFHT Legacy Survey is a joint Canadian-French program to make efficient
use of the CFHT wide field imager MegaPrime, simultaneously addressing several
fundamental questions in astronomy. Each MegaPrime/MegaCam image consists of
an array of $9\times 4$ e2v CCDs with a pixel scale of $0\arcsec.187$ and a
total field of view of $\sim 1~{}\mathrm{deg}^{2}$. The survey used most of
the telescope dark and gray time from 2003 to 2008. We analyze CFHTLS-Wide
imaging from the Terapix T0006 processing run, which is the first to include
the complete survey and was publicly released on 2010 November 15 (Goranova et
al. 2009). These data cover $\sim 171~{}\rm deg^{2}$ in four fields (W1, W2,
W3, and W4) of which the $72$-pointing, $\sim 64~{}\rm deg^{2}$ W1 field is
the largest, and in five passbands
($u^{\prime},g^{\prime},r^{\prime},i^{\prime}$,and $z^{\prime}$) down to
$i\sim 24.5$ and $r\sim 25.0$.

Fu et al. (2008) showed that the $i^{\prime}$-band exposures, taken in sub-
arcsecond seeing conditions, provide the best image quality and resolve the
galaxy population with highest median redshift. Resolving the shapes of more
distant galaxies is vital for weak lensing analysis, since the strength of the
shear signal is proportional to the ratio of the Lens–Source and
Observer–Source distances. We therefore choose to analyze the
$i^{\prime}$-band images (mean seeing $0".73$) in the contiguous W1 field. We
also analyze the independent $r^{\prime}$-band imaging to check the
calibration of our shear measurements. We also use photometric redshift
estimates for source galaxies obtained from the multicolor imaging (Ilbert et
al. 2006; Coupon et al. 2009; Arnouts et al. 2010).

Early releases of smaller regions of the CFHTLS have also been used to measure
the weak lensing cosmic shear signal (Semboloni et al. 2006; Hoekstra et al.
2006; Fu et al. 2008). As the survey size has increased, the statistical
errors have shrunk, and difficulty measuring shapes at a precision better than
the statistical error has so far prevented publication of a cosmic shear
analysis of the complete survey. However, weak lensing cluster searches are
restricted by construction to regions of the survey where the signal is
strongest, and the circular symmetry of our analysis removes the negative
impact of additive shear measurement errors (cf. Mandelbaum et al. 2005).

###  2.2. HST COSMOS Imaging

The HST COSMOS survey (Scoville et al. 2007) is the largest contiguous optical
imaging survey ever conducted from space. High resolution ($0\arcsec.12$)
imaging in the $I_{F814W}$ band was obtained during 2003–2005 across an area
of 1.64 $\rm deg^{2}$ that also corresponds to the CFHTLS D2 deep field. Any
galaxies resolved by CFHT are very easily resolved by HST, which therefore
provides highly accurate shape measurements almost without the need for point-
spread function (PSF) correction. We shall calibrate our CFHTLS shape
measurements against those from COSMOS by Leauthaud et al. (2010).

Note that measurements of the shapes of individual galaxies from ground-based
and space-based observations need not necessarily match exactly, even without
shape measurement errors, because the different noise properties of the data
sets may make them most sensitive to different isophotes, which can be twisted
relative to each other. The slightly different passbands may also emphasize
different regions of a galaxy’s morphology. However, across a large population
of galaxies, these differences should average out, and a comparison of
successful shear measurements between the two data sets should agree.

##  3\. Galaxy Shape Measurement

Table 1SExtractor Configuration Parameters Parameter | Value
---|---
DETECT_MINAREA | 3
DETECT_THRESH | 1.0
DEBLEND_NTHRESH | 32
DEBLEND_MINCONT | 0.002
CLEAN_PARAM | 1.0
BACK_SIZE | 512
BACK_FILTERSIZE | 9
BACKPHOTO_TYPE | local
BACKPHOTO_THICK | 30

###  3.1. Object Detection and Masking

Figure 1.— “W1+2+3” pointing from the CFHTLS-Wide W1 field in $i^{\prime}$
band, showing masked regions. This pointing is representative of those with
fairly poor image quality: the seeing of $0\arcsec.78$ is worse in only 24 of
72 (1 in 3) pointings. In our automated algorithm for masking diffraction
spikes around bright stars, the basic shape of the star mask is predefined,
and its size is scaled with the observed major axis of each star.

We conduct shape measurement in both CFHTLS $i^{\prime}$ and $r^{\prime}$
bands. We detect astronomical sources in the images using SExtractor (Bertin &
Arnouts 1996). Our choice of the main SExtractor parameters is listed in Table
LABEL:tab:tab1, and the data are filtered prior to detection by a $3$ pixel
Gaussian kernel.

Figure 2.— Star selection (red points) in the planes of magnitude vs. flux
radius (top) and magnitude vs. peak surface brightness (bottom). We find the
latter more robust. The red points denote objects selected as stars for PSF
modeling. The blue objects are spurious detection.

Near saturated stars, many spurious objects are found due to detector effects
and optical ghosting. It would also be difficult to measure the shapes of real
stars or galaxies in these regions, because of the steep background gradients.
We have developed an automatic pipeline to define polygonal-shaped masks
around saturated stars, and all objects inside the masks are removed from our
catalog. The masks in all images are then visually inspected; our automated
pipeline fails in a few cases (mainly very saturated stars for which the
centroid of the star measured by SExtractor was widely offset from the
diffraction spikes) and those stellar masks are corrected by hand. An example
of the masks for one CFHT pointing is shown in Figure 1. This pointing has
slightly worse than average image quality, so we shall use it throughout this
paper as a conservative representation of our analysis. After applying all of
our masks across the entire survey, the final effective sky coverage drops
from $64~{}\rm deg^{2}$ to $\sim 51.3~{}\rm deg^{2}$ and $55.0~{}\rm deg^{2}$
for $i^{\prime}$ and $r^{\prime}$ bands, respectively.

We shall employ the popular KSB method for galaxy shear measurement (Kaiser et
al. 1995; Luppino & Kaiser 1997; Hoekstra et al. 1998). In this method, the
observed galaxy shape is modeled as a convolution of the (sheared) galaxy with
the PSF, which is modeled as an isotropic, circular profile convolved with a
small anisotropy.

###  3.2. PSF Modelling

Figure 3.— Spatial variation of measured stellar ellipticities in the
representative CFHTLS-Wide W1+2+3 field, before (top) and after (bottom) PSF
anisotropy correction. The longest tick marks represent ellipticities of $\sim
11\%$. The mean absolute ellipticity after correction is $0.62\%$.

To measure the shapes of galaxies, it is first necessary to correct them for
convolution with the PSF imposed by the telescope optics and Earth’s
atmosphere. The changing size and shape of the PSF across the field of view
and between exposures can be traced from stars, which are intrinsically point
sources. We identify stars from their constrained locus within the size-
magnitude plane (Figure 2(a)). Heymans et al. (2006) suggest using the full
width at half maximum (FWHM). However, we find that FWHM is not robustly
measured by SExtractor, so we instead use the $\mu_{\rm max}$-magnitude plane
(Bardeau et al. 2005, 2007; Leauthaud et al. 2007), where $\mu_{\rm max}$ is
the peak surface brightness (Figure 2(b)). The red points in Figure 2 indicate
the selected stars; our chosen locus reflects a careful balance between
obtaining sufficient stars to model the small-scale variations that we observe
in the PSF pattern, and introducing spurious noise by including faint stars.
The blue points are spurious detections of noise, cosmic rays, etc. (cf.
Leauthaud et al. 2007).

Figure 4.— Projection of the stellar ellipticities in the $(e_{1},e_{2})$
plane before (black) and after (red) PSF anisotropy correction. The post-
correction residuals are consistent with featureless white noise.

We then measure the Gaussian-weighted shape moments of the stars, and
construct their ellipticity. In addition to cuts in $\mu_{\mathrm{max}}$ and
magnitude, we also exclude noisy outliers with signal-to-noise $\nu<100$ or
absolute ellipticity $e^{*}$ more than $2\sigma$ away from the mean local
value, and we iteratively remove objects very different from neighboring
stars. In 15 pointings with the worst image quality, including W1+2+3, the PSF
becomes larger than $r_{g}\sim 0\arcsec.5$ in the corners of the field of
view, so we finally add these regions to the survey mask (and exclude galaxies
in them from our weak lensing analysis).

Having obtained our clean sample of stars, we construct a spatially varying
model of the PSF across the field of view. In most pointings, we fit the $\sim
30$ stars in each of the $36$ individual CCDs composing the MegaCam focal
plane, using a polynomial of second order in $x$ and $y$. For stacked data
with large dithers, we use a higher order polynomial. Figures 3 and 4 show the
stellar ellipticity before and after correction for the W1+2+3 pointing, using
a weight function of default size $r_{g}$ to measure the PSF shape moments.
The residual stellar ellipticity after correction is a consistent random
scatter around zero, of width $\sigma_{e_{i}}\sim 0.01$.

Figure 5.— Ellipticity of the PSF changes from the core to the wings. This
shows the mean PSF ellipticity in the $i^{\prime}$-band of the CFHTLS-Wide W1
pointing W1+2+3 as a function of the size of the Gaussian weight function with
which it is measured, before (black) and after (red) PSF anisotropy
correction. The error bars show the rms scatter throughout that pointing.

The ellipticity of the PSF changes from the core to the wings. We measure the
PSF shape using differently-sized weight functions and, when correcting each
galaxy, use the same size weight function to measure both the PSF and galaxy
shapes. Figure 5 shows the variation of mean stellar ellipticity as a function
of the weight function size $r_{g}$, before and after PSF anisotropy
correction.

###  3.3. Galaxy Shape Measurement

Figure 6.— Galaxy magnitude and redshift distributions. Top: number counts of
galaxies per magnitude bin immediately after star-galaxy separation (solid
histograms) and after all the lensing cuts (dotted histograms) for imaging in
$i^{\prime}$ (black lines) and $r^{\prime}$ (red lines) bands. Bottom: the
redshift distribution of galaxies used from the $i^{\prime}$ (black lines) and
$r^{\prime}$ (red lines) bands.

Galaxies are selected as those objects with half light radius
$1.1r^{\mathrm{PSF}}_{h}<r_{h}<4$ pixels, where $r^{\mathrm{PSF}}_{h}$ is the
size of the largest star, signal-to-noise $\nu>10$, magnitude
$21.5<i^{\prime}<24.5$ and SExtractor flag $\rm{\tt FLAGS=0}$. To also exclude
blended or close pairs that could bias ellipticity measurements, we also cut
objects with corrected ellipticity $|e_{\rm cor}|>1$ and pairs of galaxies
within $3\arcsec$. After survey masking and catalog cuts, the galaxy number
density is $n_{g}\sim 11.5~{}{\rm arcmin}^{-2}$ in an area of
$A_{i^{\prime}}\sim 51.3~{}\rm deg^{2}$ of $i^{\prime}$-band imaging; and
$n_{g}\sim 7.9~{}{\rm arcmin}^{-2}$ in $A_{r^{\prime}}\sim 55.0~{}\rm deg^{2}$
of $r^{\prime}$-band data. Note that both are lower than the galaxy density
$n_{g}\sim 38~{}{\rm arcmin}^{-2}$ obtained in CFHTLS-Deep imaging by Gavazzi
& Soucail (2007). This will restrict our detections to generally more massive
clusters. Figure 6 shows the magnitude distribution of the galaxies, and the
redshift distribution of the $72~{}\%$ ($76~{}\%$) of galaxies selected in the
$i^{\prime}$ ($r^{\prime}$) bands that also have photometric redshift
estimates by Arnouts et al. (2010).

We then measure the shapes of all the selected galaxies. Our implementation of
KSB is based on the KSBf90111http://www.roe.ac.uk/ heymans/KSBf90/Home.html
pipeline (Heymans et al. 2006). This has been generically tested on simulated
images containing a known shear signal as part of the Shear Testing Programme
(STEP; Heymans et al. 2006; Massey et al. 2007) and the Gravitational lensing
Accuracy Testing (GREAT08; Bridle et al. 2010) challenge. In all cases, the
method was found to have small and repeatable systematic errors.

If the PSF anisotropy is small, the shear $\gamma$ can be recovered to first-
order from the observed ellipticity $e^{\rm obs}$ of each galaxies via

$\gamma=P_{\gamma}^{-1}\left(e^{\rm obs}-\frac{P^{\rm sm}}{P^{\rm
sm*}}e^{*}\right),$ (1)

where asterisks indicate quantities that should be measured from the PSF model
interpolated to the position of the galaxy, $P^{\rm sm}$ is the smear
polarizability, and $P_{\gamma}$ is the correction to the shear polarizability
that includes smearing with the isotropic component of the PSF. The
ellipticities are constructed from a combination of each object’s weighted
quadrupole moments, and the other quantities involve higher order shape
moments. All definitions are taken from Luppino & Kaiser (1997). Note that we
approximate the matrix $P_{\gamma}$ by a scalar equal to half its trace. Since
measurements of $\mathrm{Tr}~{}P_{\gamma}$ from individual galaxies are noisy,
we follow Fu et al. (2008) and fit it as a function of galaxy size and
magnitude, which are more robustly observable galaxy properties.

Following Hoekstra et al. (2000), we weight the shear contribution from each
galaxy as

$w=\frac{1}{\sigma_{e,i}^{2}}=\frac{P_{\gamma}^{2}}{\sigma_{0}^{2}P_{\gamma}^{2}+\sigma_{e,i}^{2}},$
(2)

where $\sigma_{e,i}$ is the error in an individual ellipticity measurement
obtained via the formula in Appendix A of Hoekstra et al. (2000), and
$\sigma_{0}\sim 0.278$ is the dispersion in galaxies’ intrinsic ellipticities.

###  3.4. Calibration of Multiplicative Shear Measurement Biases

Figure 7.— Choices for the way shear polarizability $P_{\gamma}$ can be fitted
to a galaxy population in the CFHT KSBf90 pipeline, to reduce noise and bias
in individual measurements. Linearly spaced contours compare our shear
measurements of galaxies in a subset of the CFHTLS-Deep imaging, stacked to
the depth of the CFHTLS-Wide survey, against measurements from the Hubble
Space Telescope. Dashed lines show the best-fit relation
$\gamma_{1}^{\mathrm{CFHT}}=(m-1)\gamma_{1}^{\mathrm{HST}}+c$. The four panels
illustrate various fitting schemes. Top-left: raw (noisy) $P_{\gamma}$
measurements from each galaxy, without fitting. Top-right: fitted as a
polynomial in galaxy size $P_{\gamma}(r_{h})$. Bottom-left: fitting function
$P_{\gamma}(r_{h},\mathrm{mag})$ from Fu et al. (2008). Bottom-right: best-fit
rational function $P_{\gamma}(r_{h},\mathrm{mag})$, as described in the text.
Figure 8.— Robustness of the calibration of our shear measurement as a
function of image quality. Linearly-spaced contours compare our shear
measurements of galaxies in subsets of CFHTLS-Deep imaging with varying mean
seeing (black solid: $0\arcsec.90$, red dashed: $0\arcsec.69$, blue dotted:
$0\arcsec.57$) to measurements from the Hubble Space Telescope. Shears are
consistently underestimated by our pipeline, but the calibration is remarkably
robust.

We exploit the opportunity that the CFHTLS-Deep D2 field includes the HST
COSMOS survey field, and verify the calibration of our shear measurement
pipeline for ground-based data against an independent analysis of the much
higher resolution space-based data (Leauthaud et al. 2007, 2010). We stack
subsets of the CFHTLS-Deep D2 imaging to the same depth as the CFHTLS-Wide
survey and analyze it using the same pipeline applied to the CFHTLS-Wide W1
field. Since any galaxy seen by CFHT is very well resolved by HST, and imaged
to very high signal-to-noise ratio by the COSMOS survey, the space-based shear
measurements require only negligible PSF correction and suffer from only
negligible shot noise. A consistent shear measurement between ground and space
for this subset of galaxies would therefore indicate a robust shear
measurement across the CFHTLS.

Multiplicative shear measurement biases $m$ are the most problematic for
circularly-symmetric cluster measurements. Multiplicative biases cannot be
internally diagnosed within a shear catalog, so our comparison against
external data is most useful for checking that $m$ is sufficiently small that
it corresponds to a bias smaller than our statistical errors. Within the KSB
framework, difficulties in shear calibration mainly rest in measurement of the
shear polarizability $P_{\gamma}$, so we first investigate different
possibilities for fitting $P_{\gamma}$ across a galaxy population. Figure 7
compares shear measurements from a subset of the CFHTLS-Deep imaging with mean
seeing $0\arcsec.69$ (similar to the mean seeing in our survey) stacked to the
depth of the CFHTLS-Wide imaging against shear measurements obtained from HST.
The dashed lines show the best-fit linear relations
$\gamma_{1}^{\mathrm{CFHT}}=(1+m)\gamma_{1}^{\mathrm{HST}}+c$, which are
obtained using a total least-squares fitting method (e.g. Kasliwal et al.
2008) that accounts for the noise present in both shear catalogs. The top-left
panel shows the CFHT shear measurements with $P_{\gamma}$ naïvely obtained
from each raw, noisy galaxy without any fitting. This results in a large bias
on shear measurements and a large amount of extra noise. The top-right panel
shows the shear measurements if $P_{\gamma}$ is fitted as a function of galaxy
size, $P_{\gamma}(r_{h})=a_{0}+a_{1}r_{h}+a_{2}r_{h}^{2}$. The bottom-left
panel shows shears if
$P_{\gamma}(r_{h},\mathrm{mag})=a_{0}+a_{1}r_{h}+a_{2}r_{h}^{2}+a_{3}m_{\nu}$
(Fu et al. 2008). The bottom-right panel shows the matched shear with
$P_{\gamma}(r_{h},\mathrm{mag})$ the best-fit rational function

$P_{\gamma}=\frac{a_{0}+a_{1}m_{\nu}+a_{2}m_{\nu}^{2}+a_{3}r_{h}}{1+a_{4}m_{\nu}+a_{5}m_{\nu}^{2}+a_{6}r_{h}+a_{7}r_{h}^{2}}~{}.$
(3)

In this example, the coefficients are $a_{0}=25.07$, $a_{1}=-2.19$,
$a_{2}=0.045$, $a_{3}=0.53$, $a_{4}=0.58$, $a_{5}=-0.022$, $a_{6}=-0.85$, and
$a_{7}=0.14$. The more sophisticated fits produce a shear catalog that is a
marginally better match to the reliable HST measurements, and this is even
more true if we redo the analysis using the full CFHTLS-Deep depth, in which
galaxies are fainter and smaller. We henceforth choose to adopt the rational
function fit to $P_{\gamma}$ for all subsequent analyses, obtaining new best-
fit coefficients for each pointing.

To quantify the performance of our shear measurement pipeline as a function of
image quality, we stack subsets of the CFHTLS-Deep D2 imaging with low-,
medium-, and high-seeing to the same depth as the CFHTLS-Wide survey, and
analyze each separately (Figure 8). We find that our CFHTLS pipeline
consistently underestimates shear, but that the calibration is remarkably
robust to seeing conditions. We can therefore simply recalibrate our pipeline
for all images by multiplying all measured shears by $1/(1-0.21)$.

###  3.5. Assessment of Residual Additive Shear Systematics

Figure 9.— Mean shear measurements from galaxies in $i^{\prime}$-band
observations of the entire CFHTLS-Wide W1 field. In the absence of additive
systematics, these should be consistent with zero. In practice, they always
remain within the dashed lines than indicate an order of magnitude lower than
the $1\%$–$10\%$ shear signal around clusters. Upper and lower panels show
components $\gamma_{1}$ and $\gamma_{2}$, respectively. Left, middle, and
right panels show trends as a function of galaxy magnitude, size, and
detection signal-to-noise.

Additive shear measurement systematics $c$ generally cancel out in circularly-
symmetric cluster measurements (Mandelbaum et al. 2006). However, to double-
check for significant additive systematics, we first measure the mean shears
$\langle\gamma\rangle$ across all $72$ pointings of the CFHTLS-Wide W1 field.
Figure 9 demonstrates that the mean shear is consistent with zero as expected,
for galaxies of all sizes, magnitudes, and signal-to-noise ratios.

Figure 10.— The cross-correlation between shear measurements and stellar
ellipticities, as a function of the separation between galaxies and stars,
averaged throughout the CFHTLS-Wide W1 field. If all residual influence of the
observational PSF has been successfully removed from the galaxy shape
measurements, the red (lower) points should be consistent with zero.

We also look for residual systematics left in the weak lensing cosmic shear
signal due to imperfect PSF correction. Figure 10 shows the correlation
$\xi_{\mathrm{sys}}$ between the corrected shapes of galaxies and the
uncorrected shapes of stars. Following Bacon et al. (2003) and Massey et al.
(2005), we normalize the star-galaxy ellipticity correlation by the
uncorrected star-star ellipticity correlation to assess its impact on shear
measurements

$\xi_{\rm
sys}(\theta)=\frac{<e^{*}(\mathbf{x})\,\gamma(\mathbf{x}+\mathbf{\theta})>^{2}}{<e^{*}(\mathbf{x})\,e^{*}(\mathbf{x}+\mathbf{\theta})>},$
(4)

where $e^{*}$ is the ellipticity of the stars before PSF correction and
$\gamma$ is the shear estimate from galaxies. We find that our PSF correction
is well within requirements for our analysis because on cluster scales $1$–$5$
$\rm arcmin$, the amplitude of $\xi_{\rm sys}$ is at least one order of
magnitude smaller than the cosmic shear signal

$\xi_{\pm}=\xi_{\rm tt}(\theta)\pm\xi_{\rm
xx}(\theta)=\frac{1}{2\pi}\int_{0}^{\infty}\ell\,P_{\kappa}(\ell)\,{\rm
J}_{0,4}(\ell\theta)\,\mathrm{d}\ell~{},$ (5)

where $\xi_{\rm tt}(\theta)$ ($\xi_{\rm xx}(\theta)$) are the correlation
functions between components of shear rotated tangentially (at $45^{\circ}$)
to the line between pairs of galaxies separated by an angle $\theta$ and $\rm
J_{0}$, $\rm J_{4}$ are Bessel functions of the first kind.

Figure 11.— Gravitational lensing is achromatic, so measurements of galaxy
shapes from imaging in different colors should on average be consistent. This
shows a comparison of shear measurements obtained from CFHTLS-Wide
$r^{\prime}$-band and $i^{\prime}$-band imaging of the whole W1 field. The
dashed line shows the best-fit linear relation
$\gamma_{1}^{i}=(m-1)\gamma_{1}^{r}+c$.

Figure 12.— Distribution of foreground mass in the W1+2+3 pointing,
reconstructed from shear measurements via the KS93 method. Left: the physical
$E$-mode convergence signal. Right: the $B$-mode systematics signal, created
by rotating the shears by $45^{\circ}$ then remaking the map. Contours are
drawn at detection significances of $3\sigma$, $4\sigma$, and $5\sigma$, with
dashed lines for negative values.  Figure 13.— Reconstructed “dark matter
mass” convergence map for the entire $64$ $\rm deg^{2}$ CFHTLS-Wide W1 field.
This has been smoothed by a Gaussian filter of width $\theta_{G}=1\arcmin$.
Black contours are drawn at detection signal-to-noise ratios $\nu=3.0$, $3.5$,
$4.0$, and red contours continue this sequence from $\nu\geq 4.5$.

Figure 14.— Reconstructed “dark matter mass” convergence map for the entire
$64$ $\rm deg^{2}$ CFHTLS-Wide W1 field showing the same data as Figure 13,
but smoothed with a Gaussian filter of width $\theta_{G}=6\arcmin$ (left) and
multi-scale wavelet filtering (right) to highlight the large-scale features.

Figure 15.— Numbers of local maxima (solid line) and minima (dashed line) in
our $E$-mode (black) and $B$-mode (red) convergence map of the CFHTLS-Wide W1
field, with smoothing scales $\theta_{G}=1\arcmin$ (top-panel) and
$\theta_{G}=2\arcmin$ (bottom-panel). Local maxima can still have a slightly
negative peak height if they occur along the same line of sight as a negative
noise fluctuation (or a huge void), and local minima can similarly have a
slightly positive peak height. To eliminate spurious noise peaks, we shall
mainly consider maxima or minima with $|\nu|>3.5$. In this regime, there is an
excess of local maxima over local minima, and an excess of $E$-mode peaks over
$B$-mode peaks (see Table 2).

Figure 16.— Cumulative density of local maxima $N(>\nu)$ (solid line) and
corresponding density of local minima $N(<-\nu)$ (dashed line) in the CFHTLS-
Wide W1 $E$-mode (black) and $B$-mode (red) convergence map with smoothing
scale $\theta_{G}=1\arcmin$ (top-panel) and $\theta_{G}=2\arcmin$ (bottom-
panel). Error bars are simply $1\sigma$ uncertainties assuming Poisson shot
noise. The dot-dashed line shows the prediction from Gaussian random field
theory (van Waerbeke 2000). Circles with additional error bars and the dotted
curves show an analytical prediction in a $\Lambda$CDM universe (Fan et al.
2010), with and without the influence of random noise. The excess of positive
maxima over negative minima demonstrates the non-Gaussianity of the
convergence field.  Figure 17.— Reconstructed lensing convergence signal-to
noise map for the W1+2+3 pointing, plus overlays showing optically and X-ray
selected cluster counterparts. The smoothing scale of the background map is
$\theta_{G}=1\arcmin$. Symbols indicate the positions of
$+$: lensing peaks detected with $\nu>3.5$ in the $\theta_{G}=1\arcmin$ map,
$\square$: lensing peaks detected with $\nu>3.5$ in the $\theta_{G}=2\arcmin$
map,
$\triangle$: optically-detected clusters in the K2 catalog, and
$\times$: X-ray selected clusters found in XMM-LSS (Adami et al. 2011).

Figure 18.— Distribution of the offsets between matched pairs of weak lensing
peaks and K2-detected clusters. Left: offsets for all peaks in maps with
smoothing scales of $0\arcmin.5$ (solid black), $1\arcmin$ (dotted red), and
$2\arcmin$ (dashed blue). Right: offsets for peaks with $\nu>3$ (solid black
histograms), $\nu>3.5$ (dotted red histograms) and $\nu>4$ (dashed blue
histograms), all with the smoothing scale $\theta=1~{}\rm arcmin$.  Figure
19.— Cluster redshift distribution for the matched clusters of weak lensing
and K2 (black solid histogram) and the total K2 detected clusters with K2
detection significance $(r-i)>3$ (red dashed histogram).

Because gravitational lensing is achromatic while systematics are typically
not, we can also assess the robustness of our measurements by comparing shears
measured from independent imaging acquired in multiple bands. The first
attempt at comparing multicolor shear measurements was made by Kaiser et al.
(2000) using the CFHT12K camera. The $I$ and $V$ bands showed significantly
different signals that were inconsistent with the change in redshift
distribution between the two filters. After a great deal of algorithmic
progress, Semboloni et al. (2006) obtained consistent shear measurements from
$i^{\prime}$-band and $r^{\prime}$-band CFHTLS-Deep data. Gavazzi & Soucail
(2007) extracted consistent shear from the $g^{\prime}$, $r^{\prime}$,
$z^{\prime}$ and $i^{\prime}$ bands of CFHTLS-Deep. Gavazzi et al. (2009) also
measured consistent values of the PSF-corrected ellipticities of central Coma
cluster galaxies in MegaCam-$u^{*}$ and CFH12k-$I$ bands. Our analysis
pipeline measures shears in the independent CFHTLS $r^{\prime}$-band and
$i^{\prime}$-band imaging that are consistent within the $\sim 0.1$ rms noise
(Figure 11). To maximize the total number of galaxies in our shear catalog, we
therefore combine $r^{\prime}$-band and $i^{\prime}$-band measurements. Only
the unique $r^{\prime}$-band galaxies are added to the $i^{\prime}$-band
catalog. The combined catalog includes $\sim 2.66$ million galaxies, with
$n_{g}\sim 14.5~{}{\rm arcmin}^{-2}$ for lensing measurements.

We shall continue testing for systematics at each stage of our analysis, by
checking that the shear signal behaves as expected, and is consistent with
external data sets. An important example of this is the (nonphysical) $B$-mode
signal, which we shall compute wherever we reconstruct the (physical)
$E$-mode. Pure gravitational fields produce zero $B$-mode for isolated
clusters and only tiny $B$-modes through coupling between multiple systems
along adjacent lines of sight (Schneider et al. 2002). The $B$-mode signal
corresponds to the imaginary component of $P_{\kappa}(\ell)$; it can be
conveniently measured by rotating all galaxy shears through $45^{\circ}$ then
remeasuring the $E$-mode signal (Crittenden et al. 2002).

##  4\. Mass reconstructions

###  4.1. Kaiser-Squires Inversion and Masking

The shear field $\gamma_{i}(\mathbf{\theta})$ is sparsely and noisily sampled
by measurements of the shapes of galaxies at positions $\mathbf{\theta}$. The
smooth, underlying shear field $\gamma_{i}(\mathbf{\theta})$ can be written in
terms of the lensing potential $\phi(\mathbf{\theta})$ as

$\gamma_{1}=\frac{1}{2}(\partial_{1}^{2}-\partial_{2}^{2})\phi,$ (6)
$\gamma_{2}=\partial_{1}\partial_{2}\phi,$ (7)

where the partial derivatives $\partial_{i}$ are with respect to $\theta_{i}$.
The convergence field $\kappa(\mathbf{\theta})$, which is proportional to the
mass projected along a line of sight, can also be expressed in terms of the
lensing potential as

$\kappa=\frac{1}{2}(\partial_{1}^{2}+\partial_{2}^{2})\phi.$ (8)

We shall reconstruct the convergence field from our shear measurements via the
Kaiser & Squires (1993) (KS93) method. This is obtained by inverting Equations
(6) and (7) in Fourier space:

$\hat{\gamma}_{i}=\hat{P}_{i}\hat{\kappa}$ (9)

for $i=1,2$, where the hat symbol denotes Fourier transforms, we define
$k^{2}=k_{1}^{2}+k_{2}^{2}$ and

$\hat{P}_{1}(k)=\frac{k_{1}^{2}-k_{2}^{2}}{k^{2}},$ (10)
$\hat{P}_{2}(k)=\frac{2k_{1}k_{2}}{k^{2}}.$ (11)

This inversion is non-local, so we deal with masked regions of the shear field
by masking out the same area in the convergence field, plus a $1\arcmin.5$
border. We shall ignore any signal within these regions, and set the
convergence to zero in relevant figures.

For the finite density of source galaxies resolved by CFHT, the scatter of
their intrinsic ellipticities means that a raw, unsmoothed convergence map
$\kappa(\mathbf{\theta})$ will be very noisy. Following Miyazaki et al.
(2002), we smooth the convergence map by convolving it (while still in Fourier
space) with a Gaussian window function,

$W_{G}(\theta)=\frac{1}{\pi\theta_{G}^{2}}{\rm
exp}\left(-\frac{\theta^{2}}{\theta_{G}^{2}}\right),$ (12)

As shown by van Waerbeke (2000), if different galaxies’ intrinsic
ellipticities are uncorrelated, the statistical properties of the resulting
noise field can be described by Gaussian random field theory (Bardeen et al.
1986; Bond & Efstathiou 1987) on scales where the discreteness effect of
source galaxies can be ignored. The Gaussian field is uniquely specified by
the variance of the noise, which is in turn controlled by the number of
galaxies within a smoothing aperture (Kaiser & Squires 1993; Van Waerbeke
2000)

$\sigma_{\rm
noise}^{2}=\frac{\sigma_{e}^{2}}{2}\frac{1}{2\pi\theta_{G}^{2}n_{g}},$ (13)

where $\sigma_{e}$ is the rms amplitude of the intrinsic ellipticity
distribution and $n_{g}$ is the density of source galaxies. We define the
signal-to-noise ratio for weak lensing detections by

$\nu\equiv\frac{\kappa}{\sigma_{\rm noise}}.$ (14)

To define the noise level in theoretical calculations of $\nu$, we adopt a
constant effective density of galaxies equal to the mean within our survey.
For observational calculations of $\nu$, we use the mean galaxy density in
each pointing — but do not consider the non-uniformity of the density within
each field due to masks or galaxy clustering.

It turns out that a simple Gaussian filter of width $\theta_{G}\approx
1\arcmin$ is close to the optimal linear filter for cluster detection, and
this choice has been extensively studied in simulations (White et al. 2002;
Hamana et al. 2004; Tang & Fan 2005). Because of our relatively low source
galaxy density, the galaxies’ random intrinsic shapes will produce spurious
noise peaks, degrading the completeness and purity of our cluster detection.
To reduce contamination, we repeat our mass reconstruction using two smoothing
scales $\theta_{G}=1\arcmin$ and $\theta_{G}=2\arcmin$. The map with greater
smoothing will be less noisy; to help remove spurious peaks from the higher
resolution map, we consider only those peaks detected above a signal-to-noise
threshold in both maps.

Figure 12 shows the reconstructed convergence field corresponding to
foreground mass in the W1+2+3 pointing. The left panel shows the $E$-mode
reconstruction with KS93 method after smoothing by a $1\rm arcmin$ Gaussian
kernel. This contains several high signal-to-noise ratio peaks, while the
associated $B$-mode systematics measurement in the right panel is
statistically consistent with zero, with fewer peaks. As weak lensing produces
only curl-free or $E$-mode distortions, a detection (significant above
statistical noise) of curl or $B$-mode signal would have indicated
contamination from residual systematics, e.g. imperfect PSF correction.

###  4.2. Large-scale Lensing Mass Map

A reconstructed “dark matter mass” convergence map for the entire $64~{}{\rm
deg}^{2}$ CFHTLS-Wide W1 field is presented in Figure 13. We detect $301$
peaks with $\nu>3.5$ in maps with both smoothing scales $\theta_{G}=1\arcmin$
and $\theta_{G}=2\arcmin$. The same information is reproduced in Figure 14,
with $\theta_{G}=6\arcmin$ and after multi-scale entropy restoration filtering
(MRLens; Starck et al. 2006), to better display large-scale features. The
MRLens filtering effectively suppresses noise peaks, but results in non-
Gaussian noise that complicates the peak selection (Jiao et al. 2011), so we
shall not use it further.

Table 2The Number of Local Maxima and Minima in the Convergence Map of the CFHTLS-Wide W1 Field, as a Function of Smoothing Scale. Smoothing |  $E$-mode |  $E$-mode |  $B$-mode |  $B$-mode
---|---|---|---|---
Scale $\theta_{G}$ | $\nu>3.5$ | $\nu<-3.5$ | $\nu>3.5$ | $\nu<-3.5$
$0\arcmin.5$ | $1512$ | $1270$ | $1244$ | $1033$
$1\arcmin.0$ | $543$ | $445$ | $361$ | $282$
$2\arcmin.0$ | $281$ | $233$ | $148$ | $126$

To assess the reliability of this map, we shall first investigate the
statistical properties of local maxima and minima. Figure 15 shows the
distribution of peak heights, as a function of detection signal-to-noise. The
bimodal distribution in both the $B$-mode and $E$-mode signals is dominated by
positive and negative noise fluctuations, but an asymmetric excess in the
$E$-mode signal is apparent at both $\nu>3.5$ and, at lower significance,
$\nu<-3.5$. The amplitude, slope and non-Gaussianity of this excess are all
powerful discriminators between values of parameters in cosmological models
(Pires et al. 2009). Positive peaks correspond mainly to dark matter halos
around galaxy clusters. Local minima could correspond to voids (Jain & van
Waerbeke 2000; Miyazaki et al. 2002), but the large size of voids is ill-
matched to our $\theta_{G}=1\arcmin$ filter width, and their density contrast
can never be greater than unity, so this aspect of our data is likely just
noise.

Figure 16 recasts the peak distribution into a cumulative density of positive
maxima or negative minima. As expected, we find a non-Gaussian mass
distribution with more highly significant positive maxima (corresponding to
mass overdensities) than highly significant negative minima (see Table 2).
Analytic predictions of peak counts are also overlaid. Following van Waerbeke
(2000), dot-dashed lines show the expected density of pure noise peaks, and
dotted lines show the expected number of true dark matter halos. Predictions
from Fan et al. (2010), which also take into account the effect of noise on
the heights of true peaks and the clustering of noise peaks near dark matter
halos, are shown as circles with error bars. In these theoretical
calculations, we model the population of background galaxies as having an
intrinsic ellipticity dispersion $\sigma_{e}=0.278$, density $n_{g}=14.5~{}\rm
arcmin^{-2}$ and the redshift distribution from Fu et al. (2008) in a
$\Lambda$CDM universe. At $\nu>4.5$, it appears that theory may begin to
predict more peaks than are observed. However, these are very small number
statistics, and our observations are consistent with analytical predictions
within Poisson noise. At very low $\nu$, the number of peaks is washed out and
actually decreases when noise is superimposed, because it is impossible to
extract very low-$\nu$ peaks. However, if larger and deeper surveys still find
fewer low-$\nu$ or high-$\nu$ peaks than expected, and systematic effects such
as the consequences of masked regions are more fully understood, it may
indicate a cosmology with, e.g., lower $\Omega_{m}$ and $\sigma_{8}$ than the
values used for our predictions.

Our main conclusions about the distribution of convergence peaks are as
follows.

  * •

Peak counts detected in CFHTLS-Wide are consistent with predictions from a
$\Lambda$CDM cosmological model, once noise effects are properly included (van
Waerbeke 2000; Fan et al. 2010).

  * •

The convergence field is non-Gaussian. The excess of local maxima with
$\nu>3.5$ compared to local minima with $\nu<-3.5$ is also consistent with
models (Miyazaki et al. 2002; Gavazzi & Soucail 2007).

  * •

Noise peaks dominate the expected peak counts due to cosmological weak lensing
below $|\nu|\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}3$.

We expect that weak lensing peak counts will become reliably employed to
constrain cosmological parameters in future lensing analyses. Although it is
difficult to remove the contributions of noise from intrinsic galaxy shapes
and the projection of large scale structures, these effects can be
analytically predicted. Pushing these predictions into the low signal-to-noise
regime might also allow constraints to use a much higher number density of
less massive peaks, tightening predictions by reducing Poisson noise.

##  5\. Optical/X-ray counterparts

We shall now compare our weak lensing peak detections with catalogs of
overdensities detected via optical or X-ray emission. We adopt the K2 optical
cluster catalog constructed using photometric redshifts from the same CFHTLS-
Wide W1 imaging (Thanjavur et al. 2009), and the XMM-LSS X-ray selected
cluster catalog (Adami et al. 2011), which partially overlaps our survey
field.

Table 3The Detection Purity of Various Weak Lensing Cluster Surveys Described in the Literature. | Weak Lensing Cluster Sample | Comparison Sample | Purity
---|---|---|---
Hamana et al. (2004) |  $n_{\mathrm{gal}}=30$ arcmin-2, $\nu>4$ | Halos (simulations) | $60\%$
Dietrich et al. (2007) |  $n_{\mathrm{gal}}=18$ arcmin-2, | Halos (simulations) | $75\%$
Miyazaki et al. (2007) | $\nu>3.69$ | X-ray clusters (XMM-LSS) | $80\%$
Gavazzi & Soucail (2007) |  $n_{\mathrm{gal}}\sim 35$ arcmin-2, $\nu>3.5$ | Photometric clusters | $\sim 65\%$
Schirmer et al. (2007) | $\nu>4$ | BCG | $\sim 45\%$
Geller et al. (2010) | $\nu>3.5$ | Spectroscopic clusters (SHELS) | $\sim 33\%$

We define the purity $f_{p}$ of our blind weak lensing cluster search as the
fraction of peaks above a given detection threshold $\nu_{\rm th}$ that are
associated with an optically detected cluster

$f_{p}=\frac{N_{\rm matched}(\nu>\nu_{\rm th})}{N(\nu>\nu_{\rm th})}~{}.$ (15)

The expected purity depends upon the survey depth (galaxy density),
systematics, and the extent of multiband or spectroscopic follow-up. Using
numerical simulations with $n_{\mathrm{gal}}=30$ arcmin-2, Hamana et al.
(2004) predict a purity of more than $60\%$ for convergence peaks with
$\nu>4$. The Bonn Lensing, Optical, and X-ray selected galaxy clusters (BLOX)
simulations by Dietrich et al. (2007) with $n_{\mathrm{gal}}=18$ arcmin-2 also
predict that $75\%$ of matches between convergence map peaks and massive halos
are within $2\arcmin.15$. In practice, Miyazaki et al. (2007) achieve $80\%$
purity for the $\sim 100$ peaks in Subaru convergence maps with $\nu>3.69$.
Gavazzi & Soucail (2007) obtain $\sim 65\%$ purity from $14$ peaks in CFHTLS-
Deep with $\nu>3.5$. Schirmer et al. (2007) obtain $\sim 45\%$ purity for the
$158$ possible mass concentrations identified in the Garching-Bonn Deep Survey
(GaBoDS) at $\nu>4$, consistent with an earlier evaluation of a subsample of
the survey (Maturi et al. 2007). Geller et al. (2010) find only $\sim 33\%$
purity by combining the Deep Lens Survey with the Smithsonian Hectospec
Lensing Survey (SHELS) (see Table 3).

Figure 17 shows a subset of our cluster search in the representative W1+2+3
pointing, which also overlaps with the XMM-LSS survey (Pacaud et al. 2007;
Adami et al. 2011). The observed weak lensing peak positions may not coincide
exactly with cluster centers defined from optical emission, because of a
combination of noise, substructure, and physical processes associated with
cluster mergers (Fan et al. 2010; Hamana et al. 2004). We therefore search for
matched pair candidates in K2 within a $3\arcmin.0$ radius of peaks that
appear in both the $\theta_{G}=1\arcmin$ and $\theta_{G}=2\arcmin$ lensing
map. This search radius is chosen to be larger than the smoothing scale, but
smaller than the angular virial radius of a massive cluster at $0.1<z<0.9$
(Hamana et al. 2004). If more than one pair exists within $3\arcmin.0$, we
adopt the closest match as the primary candidate.

Table 4Cluster Search Purity as a Function of Peak Height Threshold $\nu_{\rm th}$. $\nu_{\rm th}$ | $N(\nu>\nu_{\rm th})$ | $N_{\rm matched}(\nu>\nu_{\rm th},\rm K2)$ | $f_{p}$
---|---|---|---
3.5 | 301 | 126 | 42%
4.0 | 125 | 67 | 54%
4.5 | 51 | 30 | 59%

We obtain $126$ matches between weak lensing peaks with $\nu>3.5$ and optical
K2 clusters: corresponding to a purity of $42\%$. This is lower than in
CFHTLS-Deep (Gavazzi & Soucail 2007) because of the much lower source galaxy
density. The purity is listed as a function of detection threshold $\nu_{\rm
th}$ in Table 4, and the complete catalog of matched pairs is presented in
Table LABEL:tab:matchpeaks. Figure 18 shows the separations between the
matched weak lensing peaks and K2 centers. The left panel shows the offsets
for peaks with $\nu>0$ in maps with various smoothing scales; the separation
between peaks typically matches the smoothing scale. The right panel shows the
offsets for only the reliably-detected peaks with high $\nu$; the finite
number of clusters is too low to draw solid conclusions about the typical
separation. Figure 19 shows the redshift distribution of matched clusters,
relative to the overall K2 sample. Our lensing selection preferentially
detects clusters at $0.2<z<0.4$, and becomes inefficient above $z>0.5$.

We also compare our $\nu>3.5$ lensing peaks with X-ray observations from the
XMM-LSS survey. Adami et al. (2011) present $66$ spectroscopically confirmed
clusters $(0.05<z<1.5)$ within the $6~{}\rm deg^{2}$ XMM-LSS survey. This
partially overlaps with the CFHTLS-W1 field ($53$ X-ray clusters are within
W1). In this overlap region, we find $31$ lensing peaks, $7$ of which are
within $5\arcmin.0$ of X-ray clusters. Note that we increase the distance
threshold for matches because of additional noise in the X-ray centers and the
common phenomenon of separation between the gravitational field and X-ray gas
— Shan et al. (2010) found that $45\%$ of a sample of $38$ clusters had X-ray
offsets $>10\arcsec$. Indeed, in our new sample, we also find that the offsets
between weak lensing and X-ray centers are always comparable to or much larger
than the offset between weak lensing and optical centers.

Miyazaki et al. (2007) also perform a weak lensing analysis of
$0.5~{}\mathrm{deg}^{2}$ of the XMM-LSS survey. They find $15$ lensing peaks
with optical counterparts, of which $10$ match X-ray selected clusters (Adami
et al. 2011). Many of the X-ray clusters are simply at too high a redshift to
be detected by the CFHTLS lensing data. However, three of these clusters are
detected in both our analysis (c77, c92 and c93 in Table LABEL:tab:matchxray)
and that of Miyazaki et al. (2007).

##  6\. Tomographic analysis of lensing peaks

Since multi-band photometric redshift estimates are available for $76\%$ of
the source galaxies, we shall now perform a 3D, tomographic shear analysis
around all $\nu>3.5$ cluster candidates with an optical or X-ray counterpart.
This process yields an estimate of the cluster redshift (and mass)
independently of its visible emission. It also further cleans the cluster
catalog of spurious peaks created by either noise or the projection of
multiple small systems along a single line of sight.

We fit the 3D shear signal around each cluster candidate to both a singular
isothermal sphere (SIS) and a Navarro et al. (1996; NFW) model, with the
cluster lens as an additional free parameter. We assume that the center of
each cluster candidate is at the position of the brightest central galaxy
(BCG). This may not be optimal (Johnston et al. 2007), but it is much more
precisely known than the peak of the lensing signal (Fan et al. 2010). For
each source galaxy, we adopt the best-fit redshift from the cleaned Arnouts et
al. (2010) catalog. Following Gavazzi & Soucail (2007), we measure the mean
tangential shear in a $1\arcmin$–$5\arcmin$ annulus from the cluster center,
excluding the core to minimize dilution of the signal from any cluster member
galaxies with incorrect photometric redshifts.

For an SIS model, the component of shear tangential to the cluster center is

$\gamma_{t}(\theta,z_{s};z_{l})=\frac{D_{ls}}{D_{s}}\frac{4\pi\sigma^{2}_{v}}{c^{2}}\frac{1\arcsec}{2\theta}~{},$
(16)

where $\theta$ is the angular distance from the center. We simultaneously fit
the unknown lens redshift and characteristic cluster velocity dispersion
$\sigma_{v}$ by minimizing

$\chi_{\rm
SIS}^{2}(z_{l},\sigma_{v})=\sum_{i}\frac{\big{(}\gamma_{t,i}-\gamma_{{\rm
SIS},i}(z_{l},\sigma_{\rm tomo})\big{)}^{2}}{\sigma_{e,i}^{2}}~{},$ (17)

where $w_{i}=w(z_{l},z_{s,i})$ and $\sigma_{e,i}^{2}$ is given by Equation.
(2).

The full NFW model has two free parameters, but we assume the Bullock et al.
(2001) relation between concentration $c$ and virial mass $M_{\rm vir}$ seen
in numerical simulations

$c_{\rm NFW}(M_{\rm vir},z)=\frac{c_{*}}{1+z}\left(\frac{M_{\rm
vir}}{10^{14}h^{-1}M_{\odot}}\right)^{-0.13},$ (18)

where $c_{*}=8$. As for the SIS model, there is then only one free parameter,
and we fit the shear field for lens redshift and halo mass by minimizing

$\chi_{\rm NFW}^{2}(z_{l},M_{\rm
vir})=\sum_{i}\frac{\big{(}\gamma_{t,i}-\gamma_{\rm NFW}(z_{l},M_{\rm
vir})\big{)}^{2}}{\sigma_{e,i}^{2}}.$ (19)

To aid comparison with other work, for each cluster we calculate both the
virial mass $M_{\rm vir}$ and the mass $M_{\rm 200}$ enclosed within a radius
$r_{\rm 200}$ in which the mean density of the halo is $200$ times the
critical density at the redshift of the cluster.

Figure 20.— Results of a tomographic weak lensing analysis around one example
peak (c3 in our catalog), which has an optical counterpart at redshift
$z=0.28$. The solid and dashed lines are the best-fit SIS and NFW models. Top:
projection in the redshift direction showing the characteristic increase with
redshift of a real signal. The best-fit lens redshift is
$0.26^{+0.11}_{-0.10}$ for an SIS model and $0.26^{+0.12}_{-0.12}$ for an NFW
model. Middle: radial profile projected onto the plane of the sky. Black
circles show the $E$-mode tangential shear signal. Red circles (triangles)
show positive (negative) values of the $B$-mode systematic signal, which
oscillates about zero. Bottom: joint redshift-mass constraints from the best
fit NFW model. Contours show 68%, 95% and 99% confidence limits.  Figure 21.—
Composite $3\times 3$ arcmin2 CFHTLS $g^{\prime}$, $r^{\prime}$, $i^{\prime}$
color images for four clusters detected in both weak lensing and the K2
optical catalog. Contours show signal-to-noise in reconstructed convergence,
starting at $\nu=3.0$ and increasing in steps of $0.5$ and the images are
centered on the convergence peak. Top-left: cluster c3 with $\nu=5.395$. Top-
right: cluster c49 with $\nu=4.728$. Bottom-left: cluster c21 with
$\nu=4.142$. Bottom-right: cluster c103 with $\nu=3.725$. Candidate c21 is
included here as an example of a 2D lensing peak that is probably spurious: it
does not appear obviously associated with an overdensity of galaxies in the
optical imaging, and is not well-fit by a 3D shear signal.

Figure 20 illustrates our 3D tomographic results on one cluster
(identification c3). The mean tangential shear is consistent with zero for
$z_{s}\leq 0.26$. The subsequent increase with redshift is clear and allows
for an unambiguous identification of the lens redshift. Error bars are derived
from the scatter in observed ellipticities (intrinsic+measurement error), as
determined by Equation (1). The observed tangential shear profile is
consistent with either an SIS or NFW model. Due to our low density of source
galaxies and our exclusion of galaxies within the central $1\arcmin$, we have
insufficient signal-to-noise for individual clusters to distinguish between
the two models, which differ most noticeably near the core. The amplitude of
the systematic $B$-mode signal, computed by rotating all shear estimates by
$45^{\circ}$, is always at least one order of magnitude smaller than the
tangential shear, and it oscillates about zero.

Figure 21 shows the signal-to-noise contours of the convergence signal
reconstructed around four clusters from the 3D shear signal.

Figure 22.— Comparison between cluster redshifts derived directly from the
photometric redshifts of cluster member galaxies $z_{\rm opt}$ and from weak
lensing tomography $z_{\rm tomo}$. This figure includes all $85$ $\nu>3.5$
weak lensing peaks with optical counterparts, whose 3D shear signal is
consistent at $\chi^{2}_{\mathrm{red}}<3$ with the expected increase as a
function of redshift.

Our tomographic analysis confirms the identification of $85$ clusters with
$\chi^{2}_{\mathrm{red}}=\chi^{2}/{\rm dof}<3$. The mean redshift and velocity
dispersion of these clusters are $\langle z_{c}\rangle=0.36$ and
$\langle\sigma_{v}\rangle=658.8\rm km~{}s^{-1}$. Their full properties are
listed in Table LABEL:tab:matchpeaks. Reassuringly, we find that the inferred
lens redshifts are effectively identical for either SIS or NFW profile fits,
and are consistent (although noisy) with the (independent) photometric
redshifts of the cluster member galaxies. Figure 22 compares the redshift
estimates from tomographic gravitational lensing and optical spectroscopy of
member galaxies for these $85$ clusters.

At the faint end of our source galaxy sample, photo-$z$ estimates will be
unreliable because of noise in the photometry and degeneracies in the broad-
band colors of galaxies with different spectral energy distributions at
different redshifts. This will show up as a “double peak” in the posterior
probability of the redshift distribution. Using only the best-fit peak might
be randomly picking whichever of these peaks is higher because of noise. This
often biases lensing analyses because the expected lensing signal may be much
higher at one redshift than the other. To check for such an effect, we redo
the tomographic analysis without any photo-$z$s that have a double peak
(Arnouts et al. 2010). For cluster c3 in our catalog, we get very similar fit
results: $z_{\rm SIS}=0.26^{+0.13}_{-0.12}$ and
$\sigma_{v}=724.0^{+128.3}_{-131.5}$ for the SIS model, and $z_{\rm
NFW}=0.26^{+0.09}_{-0.11}$ and $m_{\rm NFW}=4.14^{+0.81}_{-0.76}$ for the NFW
model. This suggests that the fit is not very sensitive to that population of
galaxies with “double peaks” in photometric redshifts.

In cases where the data are poorly fit ($\chi^{2}_{\mathrm{red}}>3$) by a 3D
lensing signal, the inferred velocity dispersion or virial mass are typically
very small (often consistent with zero). These systems are probably spurious
peaks due to noise or projection effects. In addition, two peaks (c71 and
c104) have an unphysically high velocity dispersion $\sigma_{\rm
tomo}>1300~{}\rm km~{}s^{-1}$. After careful examination of the image data, we
found that they lie near two strongly saturated stars whose flux extends
beyond the masked regions, possibly degrading galaxy shape measurements.

One important goal of cluster lensing is to measure the total mass of systems,
which can also be estimated from the velocity dispersion of its member
galaxies or from its X-ray emission, under various assumptions about the state
of the intra-cluster medium and hydrostatic equilibrium (e.g., Bahcall et al.
1995; Carlberg et al. 1996; Carlstrom et al. 2002).

Figure 23.— Scaling relation between X-ray and weak lensing tomographic
measurements of the velocity dispersion of clusters. Black filled circles show
our data for four lensing-selected clusters. Red filled squares show the
lensing-selected clusters of Hamana et al. (2009). Blue open circles and green
open squares denote the X-ray selected clusters from Cypriano et al. (2004)
and Hoekstra (2007) respectively.

Figure 23 shows the relation between one mass proxy obtained from X-ray
observations and another obtained from weak lensing, for the $4$ of $7$
clusters in our sample with an X-ray counterpart and an SIS velocity
dispersion parameter well constrained by lensing. These are overlaid on the
results of another lensing-selected cluster sample (Hamana et al. 2009) and
two X-ray selected cluster samples (Cypriano et al. 2004; Hoekstra 2007). Even
combining these samples, the scatter is large. However, the consistency of the
scatter between the four samples suggests that neither detection method
produces a strong selection bias. Note that, since the density (and shear)
profile of real cluster is not necessarily a single power law, the best-fit
SIS model may depend on details of the fitting method, and the range over
which data are fit. Our results therefore are somewhat method-dependent. A
corollary of this issue is that it might also be possible to minimize scatter
in the $\sigma_{\rm xray}$-$\sigma_{\rm tomo}$ relation by optimizing the
tomographic lens fitting method.

##  7\. Conclusions

We have presented a tomographic weak gravitational lensing analysis of the
completed $64~{}\rm deg^{2}$ CFHTLS-Wide W1 field, demonstrating some of the
power of lensing to probe mass in galaxy clusters. We measured the shapes of
distant galaxies using the KSB shape measurement method, which we verified
against shape measurements from high-resolution HST imaging of an overlapping
sky area. We also obtained consistent shape measurements using two independent
imaging bands. The level of residual shape measurement systematics is an order
of magnitude lower than the $1\%$–$10\%$ shear signal expected in galaxy
clusters, so this analysis is acceptable for cluster studies.

We have reconstructed the largest contiguous “dark matter map” convergence
field to date, using two different smoothing scales to help remove spurious
noise peaks. From this map, we performed the largest lensing-selected blind
cluster search to date, finding $301$ local maxima in the lensing map with
detection significance $\nu>3.5$. Once sources of noise are properly modeled
from the intrinsic shapes of galaxies and substructure, this is consistent
with predictions from a $\Lambda$CDM cosmology. Note that our theoretical
calculations (Fan et al. 2010) do not consider projection effects of
structures along the line of sight.

To identify counterparts of the weak lensing peaks, we match our cluster
candidates to the K2 galaxy cluster catalog, created using photometric
redshift estimates across the CFHTLS-Wide W1 field (Thanjavur et al. 2009). Of
the $301$ peaks with $\nu>3.5$, $126$ have a corresponding optically-detected
BCG within $3\arcmin.0$. In the (much smaller) survey area that overlaps the
XMM-LSS survey, we also find matches for seven lensing peaks with X-ray
selected clusters. Thus, many of the candidate peaks are indeed likely just
noise.

Tomographic weak lensing techniques dramatically improve standard 2D
algorithms. In a full 3D lensing analysis of the $\nu>3.5$ peaks, we further
distinguish real clusters from noise fluctuations, and confirm (at
$\chi^{2}_{\rm red}<3$) the identification of $85$ clusters. Importantly, we
obtain independent measurements of the cluster lens redshifts, which are
consistent with the redshifts of their previously-identified optical
counterparts. For each cluster, we fit NFW and SIS radial profiles to the
lensing data to measure the mass or velocity dispersion $\sigma_{\rm tomo}$.
The clusters’ mean redshift and velocity dispersion is $\langle
z_{c}\rangle=0.36$ and $\langle\sigma_{c}\rangle=658.8~{}\rm km~{}s^{-1}$.
Weak lensing measurements of the total mass in the four of our clusters with
X-ray counterparts are also in reasonable agreement with mass estimates
obtained from X-ray emission. Future surveys, such as DES, LSST, KDUST and
EUCLID, will be able to apply these techniques to map clusters in much larger
volumes. Such large catalogs will also be able to tightly constrain
cosmological models (Takada & Bridle 2007; Dietrich & Hartlap 2010).

## Acknowledgments

The authors thank Bernard Fort, Liping Fu, Bo Qin, Catherine Heymans, and
Ludovic Van Waerbeke for useful discussions. H.Y.S. acknowledges support from
Sino French laboratories FCPPL and Origins and CPPM hospitality during stays
in France. H.Y.S. acknowledges the support from NSFC of China under grants
11103011 and China Postdoctoral Science Foundation. J.P.K. acknowledges
supports from CNRS as well as PNCG and CNES. Z.H.F. acknowledges the support
from NSFC of China under grants 10773001, 11033005, and 973 program
2007CB815401. M.L. acknowledges the Centre National de la Recherche
Scientifique (CNRS) for its support. The Dark Cosmology Centre is funded by
the Danish National Research Foundation.

This work is based on observations obtained with MegaPrime/MegaCam, a joint
project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT)
which is operated by the National Research Council (NRC) of Canada, the
Institut National des Science de l’Univers of the Centre National de la
Recherche Scientifique (CNRS) of France, and the University of Hawaii. This
work is based in part on data products produced at TERAPIX and the Canadian
Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy
Survey, a collaborative project of NRC and CNRS.

This work also uses observations obtained with the Hubble Space Telescope. The
HST COSMOS Treasury program was supported through NASA grant HST-GO-09822. We
thank Tony Roman, Denise Taylor, and David Soderblom for their assistance in
planning and scheduling the extensive COSMOS observations. We thank the NASA
IPAC/IRSA staff (Anastasia Laity, Anastasia Alexov, Bruce Berriman, and John
Good) for providing online archive and server capabilities for the COSMOS data
sets. It is also our pleasure to gratefully acknowledge the contributions of
the entire COSMOS collaboration, consisting of more than 70 scientists. More
information on the COSMOS survey is available at
http://www.astro.caltech.edu/~cosmos.

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Table 5Catalog of the Matching Groups/Clusters between $\nu>3.5$ Convergence Peaks and K2-detected Groups/Clusters in CFHTLS-Wide W1 Fields. K2 redshift denotes the median redshift of bright ($i\leq 20$) cluster members ID | $z_{\rm K2}$ | $\alpha_{\rm K2}$ | $\delta_{\rm K2}$ | $\rm sig_{r-i}$ | $\alpha$ | $\delta$ | d | $z_{\rm SIS}$ | $\sigma_{v}$ | $\chi^{2}_{\rm SIS}$ | $z_{\rm NFW}$ | $m_{\rm NFW}$ | $m_{200}$ | $\chi^{2}_{\rm NFW}$ | $\nu$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | arcsec |  | $\rm km/s$ |  |  | $10^{14}M_{\odot}/h$ | $10^{14}M_{\odot}/h$ |  |
c1-w1 | 0.18 | 30.990 | -4.223 | 3.19 | 30.976 | -4.231 | 59.2 | $0.28^{+0.17}_{-0.10}$ | $829.7^{+225.1}_{-308.9}$ | 0.42 | $0.29^{+0.16}_{-0.14}$ | $2.88^{+6.22}_{-2.15}$ | $2.50^{+5.39}_{-1.86}$ | 0.41 | 4.458
c2-w1 | 0.48 | 30.625 | -3.966 | 4.09 | 30.619 | -3.970 | 29.6 | $0.26^{+0.08}_{-0.10}$ | $945.5^{+173.8}_{-212.5}$ | 1.52 | $0.26^{+0.07}_{-0.08}$ | $11.0^{+17.8}_{-7.20}$ | $9.32^{+15.1}_{-6.10}$ | 1.50 | 4.113
c3-w1 | 0.28 | 30.421 | -5.030 | 7.45 | 30.420 | -5.030 | 1.62 | $0.26^{+0.11}_{-0.10}$ | $701.6^{+134.2}_{-132.8}$ | 0.85 | $0.26^{+0.12}_{-0.12}$ | $3.51^{+0.63}_{-0.66}$ | $3.02^{+0.54}_{-0.57}$ | 0.88 | 5.395
c4-w1 | 0.72 | 30.296 | -6.089 | 9.85 | 30.260 | -6.088 | 128.5 | $0.69^{+0.21}_{-0.22}$ | $\sim 0$ | 4.33 | $0.69^{+0.23}_{-0.20}$ | $\sim 0$ | $\sim 0$ | 4.25 | 3.732
c5-w1 | 0.38 | 30.860 | -5.925 | 4.72 | 30.867 | -5.945 | 74.3 | $0.41^{+0.10}_{-0.09}$ | $503.1^{+102.5}_{-104.1}$ | 1.37 | $0.40^{+0.10}_{-0.11}$ | $0.78^{+0.16}_{-0.17}$ | $0.70^{+0.14}_{-0.15}$ | 1.37 | 3.510
c6-w1 | 0.27 | 30.840 | -7.331 | 3.68 | 30.836 | -7.341 | 38.2 | $0.20^{+0.09}_{-0.12}$ | $559.8^{+131.8}_{-139.6}$ | 0.68 | $0.22^{+0.11}_{-0.10}$ | $0.79^{+0.18}_{-0.17}$ | $0.69^{+0.16}_{-0.15}$ | 0.51 | 4.184
c7-w1 | 0.33 | 31.077 | -7.213 | 3.20 | 31.080 | -7.216 | 15.5 | $0.39^{+0.30}_{-0.23}$ | $646.1^{+183.9}_{-222.3}$ | 1.05 | $0.40^{+0.25}_{-0.35}$ | $1.38^{+2.09}_{-1.18}$ | $1.23^{+1.86}_{-1.05}$ | 1.03 | 3.677
c8-w1 | -99.0 | 30.779 | -7.142 | 4.28 | 30.785 | -7.141 | 20.1 | $0.76^{+0.15}_{-0.19}$ | $162.3^{+137.0}_{-125.4}$ | 0.78 | $0.80^{+0.16}_{-0.17}$ | $0.11^{+0.08}_{-0.09}$ | $0.10^{+0.07}_{-0.08}$ | 0.73 | 4.586
c9-w1 | 0.81 | 30.884 | -6.736 | 5.78 | 30.882 | -6.749 | 46.8 | $0.77^{+0.25}_{-0.26}$ | $892.1^{+274.1}_{-291.7}$ | 1.25 | $0.78^{+0.24}_{-0.26}$ | $4.07^{+0.98}_{-1.04}$ | $3.82^{+0.92}_{-0.97}$ | 1.21 | 3.722
c10-w1 | 0.36 | 30.628 | -6.524 | 5.11 | 30.649 | -6.536 | 85.3 | $0.41^{+0.13}_{-0.12}$ | $\sim 0$ | 9.34 | $0.41^{+0.12}_{-0.11}$ | $\sim 0$ | $\sim 0$ | 8.30 | 3.897
c11-w1 | 0.31 | 30.364 | -8.283 | 4.20 | 30.369 | -8.275 | 35.2 | $0.35^{+0.16}_{-0.13}$ | $\sim 0$ | 5.22 | $0.35^{+0.15}_{-0.17}$ | $\sim 0$ | $\sim 0$ | 4.28 | 3.710
c12-w1 | 0.14 | 30.325 | -7.651 | 4.43 | 30.346 | -7.659 | 81.9 | $0.22^{+0.12}_{-0.11}$ | $396.6^{+128.6}_{-102.1}$ | 1.96 | $0.42^{+0.15}_{-0.14}$ | $0.28^{+0.07}_{-0.06}$ | $0.25^{+0.06}_{-0.05}$ | 1.59 | 4.728
c13-w1 | 0.23 | 30.708 | -9.337 | 4.83 | 30.704 | -9.356 | 69.7 | $0.21^{+0.16}_{-0.10}$ | $473.8^{+221.3}_{-239.5}$ | 2.15 | $0.21^{+0.13}_{-0.11}$ | $0.16^{+0.08}_{-0.09}$ | $0.14^{+0.07}_{-0.08}$ | 2.01 | 4.084
c14-w1 | 0.40 | 30.534 | -8.437 | 7.52 | 30.537 | -8.417 | 71.4 | $0.43^{+0.09}_{-0.08}$ | $691.1^{+102.1}_{-97.8}$ | 0.14 | $0.43^{+0.09}_{-0.11}$ | $1.50^{+0.19}_{-0.17}$ | $1.34^{+0.17}_{-0.15}$ | 0.14 | 4.045
c15-w1 | 0.32 | 30.870 | -9.817 | 18.02 | 30.881 | -9.838 | 86.2 | $0.36^{+0.14}_{-0.13}$ | $483.9^{+120.9}_{-112.7}$ | 0.68 | $0.36^{+0.13}_{-0.15}$ | $0.70^{+0.16}_{-0.18}$ | $0.62^{+0.14}_{-0.16}$ | 0.59 | 4.835
c16-w1 | 0.66 | 30.452 | -10.853 | 5.81 | 30.463 | -10.840 | 59.6 | $0.62^{+0.08}_{-0.09}$ | $747.7^{+114.3}_{-117.2}$ | 1.15 | $0.62^{+0.10}_{-0.08}$ | $2.24^{+0.33}_{-0.35}$ | $2.06^{+0.30}_{-0.32}$ | 1.07 | 3.511
c17-w1 | 0.32 | 32.021 | -4.583 | 3.85 | 32.045 | -4.542 | 171.4 | $0.35^{+0.10}_{-0.09}$ | $931.9^{+218.7}_{-239.2}$ | 1.12 | $0.35^{+0.11}_{-0.14}$ | $5.52^{+5.32}_{-3.20}$ | $4.81^{+4.63}_{-2.79}$ | 0.93 | 3.628
c18-w1 | 0.25 | 31.797 | -4.002 | 3.04 | 31.772 | -3.963 | 165.9 | $0.51^{+0.45}_{-0.17}$ | $874.1^{+175.9}_{-340.5}$ | 0.69 | $0.50^{+0.21}_{-0.14}$ | $5.09^{+6.41}_{-3.42}$ | $4.56^{+5.75}_{-3.07}$ | 0.61 | 5.011
c19-w1 | 0.29 | 31.793 | -3.894 | 4.37 | 31.792 | -3.854 | 142.4 | $0.39^{+0.19}_{-0.18}$ | $\sim 0$ | 6.94 | $0.38^{+0.20}_{-0.17}$ | $\sim 0$ | $\sim 0$ | 5.82 | 4.540
c20-w1 | 0.19 | 31.283 | -4.972 | 3.17 | 31.308 | -4.993 | 118.5 | $0.12^{+0.12}_{-0.13}$ | $\sim 0$ | 5.12 | $0.11^{+0.11}_{-0.12}$ | $\sim 0$ | $\sim 0$ | 4.64 | 3.899
c21-w1 | 0.42 | 31.558 | -6.167 | 4.34 | 31.538 | -6.167 | 70.2 | $0.32^{+0.14}_{-0.16}$ | $\sim 0$ | 3.73 | $0.31^{+0.13}_{-0.11}$ | $\sim 0$ | $\sim 0$ | 4.16 | 4.142
c22-w1 | 0.41 | 31.272 | -5.923 | 4.63 | 31.254 | -5.943 | 95.4 | $0.51^{+0.26}_{-0.25}$ | $273.0^{+164.5}_{-157.3}$ | 1.51 | $0.49^{+0.15}_{-0.18}$ | $0.24^{+0.16}_{-0.15}$ | $0.22^{+0.15}_{-0.14}$ | 1.22 | 3.860
c23-w1 | 0.35 | 31.667 | -7.384 | 4.89 | 31.665 | -7.400 | 57.0 | $0.26^{+0.21}_{-0.22}$ | $\sim 0$ | 3.14 | $0.26^{+0.19}_{-0.20}$ | $\sim 0$ | $\sim 0$ | 3.30 | 4.211
c24-w1 | 0.40 | 31.358 | -7.588 | 10.03 | 31.353 | -7.589 | 20.6 | $0.88^{+0.55}_{-0.80}$ | $659.3^{+141.3}_{-181.0}$ | 0.82 | $0.88^{+0.11}_{-0.12}$ | $1.16^{+0.70}_{-0.45}$ | $1.11^{+0.67}_{-0.43}$ | 0.71 | 5.311
c25-w1 | 0.42 | 31.927 | -7.502 | 3.33 | 31.953 | -7.489 | 101.7 | $0.32^{+0.31}_{-0.28}$ | $\sim 0$ | 3.48 | $0.32^{+0.29}_{-0.27}$ | $\sim 0$ | $\sim 0$ | 3.48 | 3.860
c26-w1 | 0.24 | 31.320 | -7.680 | 3.00 | 31.326 | -7.664 | 63.5 | $0.22^{+0.13}_{-0.12}$ | $417.4^{+138.7}_{-131.5}$ | 0.86 | $0.22^{+0.12}_{-0.12}$ | $0.49^{+0.17}_{-0.16}$ | $0.43^{+0.15}_{-0.14}$ | 0.66 | 4.430
c27-w1 | 0.26 | 31.595 | -8.807 | 4.22 | 31.617 | -8.806 | 75.8 | $0.17^{+0.09}_{-0.14}$ | $646.2^{+103.0}_{-135.1}$ | 1.07 | $0.19^{+0.11}_{-0.16}$ | $1.95^{+1.54}_{-1.27}$ | $1.67^{+1.32}_{-1.09}$ | 1.12 | 4.423
c28-w1 | 0.08 | 31.769 | -8.495 | 3.43 | 31.724 | -8.512 | 171.6 | $0.06^{+0.10}_{-0.11}$ | $426.0^{+153.1}_{-166.8}$ | 2.41 | $0.08^{+0.12}_{-0.10}$ | $0.65^{+0.21}_{-0.18}$ | $0.55^{+0.18}_{-0.15}$ | 1.54 | 3.651
c29-w1 | 0.27 | 31.230 | -10.400 | 14.90 | 31.230 | -10.407 | 24.4 | $0.21^{+0.16}_{-0.18}$ | $\sim 0$ | 5.94 | $0.22^{+0.13}_{-0.15}$ | $\sim 0$ | $\sim 0$ | 4.60 | 4.104
c30-w1 | 0.19 | 32.773 | -4.129 | 3.19 | 32.758 | -4.151 | 96.1 | $0.37^{+0.13}_{-0.15}$ | $455.5^{+132.6}_{-138.9}$ | 0.34 | $0.40^{+0.14}_{-0.15}$ | $0.48^{+0.11}_{-0.13}$ | $0.43^{+0.10}_{-0.12}$ | 0.43 | 4.674
c31-w1 | 0.34 | 32.634 | -4.123 | 6.94 | 32.653 | -4.132 | 76.5 | $0.28^{+0.12}_{-0.11}$ | $1134.9^{+243.1}_{-237.0}$ | 1.38 | $0.28^{+0.12}_{-0.12}$ | $12.3^{+2.41}_{-2.35}$ | $10.5^{+2.05}_{-2.00}$ | 1.17 | 4.899
c32-w1 | 0.28 | 32.981 | -4.688 | 3.95 | 32.957 | -4.652 | 157.7 | $0.22^{+0.17}_{-0.14}$ | $\sim 0$ | 3.59 | $0.23^{+0.16}_{-0.17}$ | $\sim 0$ | $\sim 0$ | 3.15 | 3.737
c33-w1 | 0.23 | 32.435 | -5.730 | 3.36 | 32.456 | -5.726 | 77.9 | $0.21^{+0.07}_{-0.10}$ | $599.6^{+97.8}_{-117.5}$ | 1.04 | $0.22^{+0.11}_{-0.14}$ | $1.09^{+0.12}_{-0.13}$ | $0.94^{+0.10}_{-0.11}$ | 1.11 | 3.576
c34-w1 | 0.48 | 32.669 | -7.455 | 5.61 | 32.675 | -7.449 | 31.3 | $0.36^{+0.14}_{-0.11}$ | $703.7^{+150.7}_{-193.7}$ | 0.73 | $0.39^{+0.25}_{-0.17}$ | $1.71^{+2.27}_{-1.28}$ | $1.52^{+2.02}_{-1.14}$ | 0.68 | 4.474
c35-w1 | 0.45 | 32.986 | -7.123 | 3.48 | 32.941 | -7.132 | 163.9 | $0.41^{+0.24}_{-0.23}$ | $1071.5^{+262.2}_{-239.6}$ | 1.89 | $0.42^{+0.17}_{-0.18}$ | $6.89^{+1.07}_{-1.13}$ | $6.10^{+0.95}_{-1.00}$ | 1.81 | 3.911
c36-w1 | 0.40 | 32.865 | -6.694 | 3.31 | 32.839 | -6.726 | 145.2 | $0.36^{+0.15}_{-0.16}$ | $580.5^{+121.5}_{-124.3}$ | 1.51 | $0.36^{+0.16}_{-0.17}$ | $1.27^{+0.23}_{-0.25}$ | $1.13^{+0.20}_{-0.22}$ | 1.28 | 4.430
c37-w1 | 0.62 | 32.599 | -6.543 | 6.99 | 32.575 | -6.541 | 85.3 | $0.51^{+0.29}_{-0.27}$ | $\sim 0$ | 4.12 | $0.51^{+0.28}_{-0.27}$ | $\sim 0$ | $\sim 0$ | 4.54 | 3.504
c38-w1 | 0.33 | 32.837 | -8.396 | 8.91 | 32.824 | -8.403 | 55.2 | $0.39^{+0.10}_{-0.10}$ | $\sim 0$ | 3.28 | $0.41^{+0.11}_{-0.10}$ | $\sim 0$ | $\sim 0$ | 3.17 | 3.774
c39-w1 | 0.34 | 32.135 | -7.730 | 3.54 | 32.167 | -7.750 | 133.5 | $0.37^{+0.17}_{-0.19}$ | $682.9^{+225.9}_{-241.1}$ | 1.34 | $0.36^{+0.16}_{-0.18}$ | $2.50^{+2.01}_{-1.67}$ | $2.19^{+1.76}_{-1.46}$ | 1.13 | 3.632
c40-w1 | 0.46 | 33.012 | -7.676 | 9.58 | 33.020 | -7.659 | 69.4 | $0.76^{+0.13}_{-0.13}$ | $1101.3^{+261.1}_{-263.8}$ | 1.21 | $0.83^{+0.13}_{-0.15}$ | $4.49^{+1.18}_{-1.26}$ | $4.23^{+1.11}_{-1.19}$ | 1.05 | 4.486
c41-w1 | 0.51 | 32.658 | -7.471 | 6.09 | 32.655 | -7.445 | 93.5 | $0.55^{+0.21}_{-0.18}$ | $\sim 0$ | 4.11 | $0.55^{+0.17}_{-0.16}$ | $\sim 0$ | $\sim 0$ | 3.65 | 4.157
c42-w1 | 0.71 | 32.313 | -9.244 | 15.30 | 32.324 | -9.237 | 44.9 | $0.78^{+2.12}_{-0.32}$ | $530.9^{+138.9}_{-208.4}$ | 1.68 | $0.77^{+0.13}_{-0.12}$ | $1.10^{+0.60}_{-0.40}$ | $1.04^{+0.57}_{-0.38}$ | 1.31 | 3.792
c43-w1 | 0.65 | 32.795 | -9.139 | 6.56 | 32.815 | -9.157 | 95.8 | $0.61^{+0.20}_{-0.12}$ | $678.1^{+112.3}_{-143.9}$ | 0.83 | $0.66^{+0.11}_{-0.09}$ | $1.80^{+1.15}_{-0.95}$ | $1.67^{+1.07}_{-0.88}$ | 0.66 | 3.815
c44-w1 | 0.29 | 32.553 | -8.562 | 11.58 | 32.575 | -8.560 | 78.4 | $0.25^{+0.12}_{-0.11}$ | $971.1^{+342.1}_{-382.5}$ | 0.74 | $0.26^{+0.09}_{-0.08}$ | $10.9^{+5.61}_{-6.85}$ | $6.85^{+9.30}_{-4.78}$ | 0.71 | 4.367
c45-w1 | 0.30 | 32.961 | -9.994 | 4.98 | 32.971 | -9.978 | 68.7 | $0.35^{+0.15}_{-0.16}$ | $\sim 0$ | 3.51 | $0.34^{+0.19}_{-0.17}$ | $\sim 0$ | $\sim 0$ | 3.38 | 4.109
c46-w1 | 0.62 | 32.847 | -9.875 | 3.04 | 32.883 | -9.877 | 129.3 | $0.67^{+0.17}_{-0.16}$ | $521.8^{+133.9}_{-129.1}$ | 1.67 | $0.67^{+0.16}_{-0.18}$ | $0.66^{+0.12}_{-0.14}$ | $0.62^{+0.11}_{-0.13}$ | 1.56 | 4.238
c47-w1 | 0.28 | 33.607 | -6.461 | 9.74 | 33.596 | -6.454 | 47.5 | $0.24^{+0.11}_{-0.10}$ | $698.8^{+198.2}_{-211.7}$ | 1.41 | $0.25^{+0.10}_{-0.10}$ | $2.35^{+1.12}_{-1.09}$ | $2.04^{+0.97}_{-0.95}$ | 1.28 | 3.562
c48-w1 | 0.65 | 34.017 | -6.137 | 11.48 | 34.001 | -6.095 | 161.7 | $0.64^{+0.29}_{-0.14}$ | $152.8^{+162.4}_{-139.6}$ | 0.65 | $0.64^{+0.19}_{-0.15}$ | $0.07^{+0.11}_{-0.10}$ | $0.06^{+0.10}_{-0.09}$ | 0.63 | 3.930
c49-w1 | 0.30 | 33.780 | -5.981 | 7.22 | 33.779 | -5.978 | 11.9 | $0.25^{+0.13}_{-0.13}$ | $547.5^{+120.8}_{-117.9}$ | 2.59 | $0.27^{+0.14}_{-0.11}$ | $0.78^{+0.18}_{-0.16}$ | $0.69^{+0.16}_{-0.14}$ | 1.83 | 4.728
c50-w1 | 0.19 | 33.941 | -5.930 | 3.46 | 33.956 | -5.976 | 174.8 | $0.37^{+0.16}_{-0.17}$ | $667.4^{+156.3}_{-198.7}$ | 1.28 | $0.37^{+0.12}_{-0.14}$ | $2.49^{+2.22}_{-1.55}$ | $2.20^{+1.96}_{-1.37}$ | 1.18 | 3.579
c51-w1 | 0.35 | 33.293 | -5.625 | 4.20 | 33.295 | -5.613 | 40.8 | $0.25^{+0.07}_{-0.10}$ | $629.1^{+98.4}_{-118.7}$ | 1.96 | $0.25^{+0.11}_{-0.13}$ | $1.86^{+2.20}_{-1.44}$ | $1.61^{+1.90}_{-1.25}$ | 1.70 | 4.205
c52-w1 | 0.69 | 33.528 | -7.145 | 5.13 | 33.509 | -7.148 | 67.8 | $0.31^{+0.29}_{-0.30}$ | $\sim 0$ | 7.76 | $0.33^{+0.21}_{-0.22}$ | $\sim 0$ | $\sim 0$ | 6.81 | 3.739
c53-w1 | 0.28 | 33.402 | -6.953 | 3.15 | 33.384 | -6.944 | 70.6 | $0.23^{+0.12}_{-0.11}$ | $694.7^{+133.5}_{-129.8}$ | 0.86 | $0.22^{+0.11}_{-0.11}$ | $1.65^{+0.29}_{-0.21}$ | $1.44^{+0.25}_{-0.18}$ | 0.61 | 4.166
c54-w1 | 0.31 | 33.728 | -6.539 | 4.65 | 33.748 | -6.495 | 171.4 | $0.38^{+0.14}_{-0.15}$ | $193.1^{+109.6}_{-101.3}$ | 1.77 | $0.37^{+0.16}_{-0.14}$ | $0.19^{+0.10}_{-0.11}$ | $0.17^{+0.09}_{-0.10}$ | 1.73 | 3.590
c55-w1 | 0.32 | 33.113 | -9.926 | 9.79 | 33.130 | -9.950 | 106.0 | $0.83^{+2.07}_{-0.30}$ | $606.1^{+163.2}_{-231.8}$ | 1.63 | $0.84^{+0.14}_{-0.13}$ | $0.97^{+0.33}_{-0.29}$ | $0.92^{+0.31}_{-0.28}$ | 1.58 | 3.809
c56-w1 | 0.34 | 33.720 | -9.936 | 3.35 | 33.737 | -9.908 | 118.3 | $0.50^{+0.21}_{-0.19}$ | $597.4^{+147.1}_{-138.2}$ | 0.93 | $0.49^{+0.19}_{-0.19}$ | $1.09^{+0.19}_{-0.20}$ | $0.99^{+0.17}_{-0.18}$ | 0.94 | 3.872
c57-w1 | 0.39 | 33.427 | -9.769 | 4.34 | 33.426 | -9.770 | 4.689 | $0.42^{+0.15}_{-0.14}$ | $514.7^{+128.7}_{-123.5}$ | 0.16 | $0.43^{+0.13}_{-0.15}$ | $0.74^{+0.16}_{-0.18}$ | $0.66^{+0.14}_{-0.16}$ | 0.16 | 3.570
c58-w1 | 0.51 | 34.244 | -4.554 | 6.43 | 34.233 | -4.585 | 118.0 | $0.56^{+0.25}_{-0.16}$ | $449.3^{+211.9}_{-163.0}$ | 1.34 | $0.55^{+0.21}_{-0.18}$ | $0.45^{+0.20}_{-0.14}$ | $0.42^{+0.18}_{-0.13}$ | 1.21 | 6.448
c59-w1 | 0.75 | 34.071 | -4.157 | 9.06 | 34.030 | -4.131 | 174.9 | $0.82^{+0.22}_{-0.23}$ | $\sim 0$ | 3.87 | $0.85^{+0.21}_{-0.21}$ | $\sim 0$ | $\sim 0$ | 3.70 | 3.564
c60-w1 | 0.62 | 34.400 | -3.946 | 13.75 | 34.436 | -3.978 | 176.1 | $0.65^{+0.19}_{-0.17}$ | $830.3^{+196.8}_{-225.4}$ | 1.32 | $0.64^{+0.16}_{-0.17}$ | $4.63^{+1.15}_{-1.17}$ | $4.24^{+1.05}_{-1.07}$ | 1.23 | 4.363
c61-w1 | 0.37 | 34.327 | -3.772 | 3.13 | 34.311 | -3.749 | 100.0 | $0.27^{+0.12}_{-0.14}$ | $\sim 0$ | 3.56 | $0.29^{+0.13}_{-0.12}$ | $\sim 0$ | $\sim 0$ | 3.21 | 3.791
c62-w1 | 0.36 | 34.657 | -5.570 | 4.17 | 34.684 | -5.572 | 98.4 | $0.57^{+0.13}_{-0.14}$ | $909.7^{+61.5}_{-60.1}$ | 1.55 | $0.55^{+0.15}_{-0.13}$ | $5.31^{+0.32}_{-0.30}$ | $4.82^{+0.29}_{-0.27}$ | 1.47 | 4.194
c63-w1 | 0.79 | 34.511 | -6.743 | 15.30 | 34.531 | -6.488 | 89.8 | $0.70^{+0.31}_{-0.28}$ | $\sim 0$ | 4.33 | $0.71^{+0.26}_{-0.25}$ | $\sim 0$ | $\sim 0$ | 4.09 | 3.931
c64-w1 | 0.33 | 34.655 | -5.674 | 9.59 | 34.653 | -5.626 | 170.7 | $0.42^{+0.14}_{-0.11}$ | $\sim 0$ | 4.18 | $0.41^{+0.13}_{-0.10}$ | $\sim 0$ | $\sim 0$ | 3.87 | 4.186
c65-w1 | 0.35 | 34.092 | -7.369 | 5.17 | 34.070 | -7.380 | 87.7 | $0.27^{+0.12}_{-0.12}$ | $\sim 0$ | 4.28 | $0.26^{+0.10}_{-0.09}$ | $\sim 0$ | $\sim 0$ | 4.09 | 5.230
c66-w1 | 0.33 | 34.483 | -6.755 | 3.35 | 34.449 | -6.742 | 129.5 | $0.31^{+0.10}_{-0.19}$ | $\sim 0$ | 3.26 | $0.31^{+0.11}_{-0.10}$ | $\sim 0$ | $\sim 0$ | 3.13 | 4.692
c67-w1 | 0.22 | 34.350 | -6.687 | 3.84 | 34.390 | -6.717 | 180.0 | $0.37^{+0.26}_{-0.19}$ | $794.7^{+235.7}_{-340.1}$ | 1.72 | $0.39^{+0.06}_{-0.05}$ | $3.63^{+0.90}_{-1.71}$ | $3.20^{+0.79}_{-1.51}$ | 1.51 | 4.515
c68-w1 | 0.33 | 34.219 | -8.229 | 7.14 | 34.219 | -8.223 | 21.6 | $0.38^{+0.16}_{-0.17}$ | $\sim 0$ | 3.09 | $0.37^{+0.15}_{-0.16}$ | $\sim 0$ | $\sim 0$ | 3.06 | 3.967
c69-w1 | 0.71 | 34.948 | -8.120 | 13.80 | 34.965 | -8.091 | 117.5 | $0.75^{+0.21}_{-0.18}$ | $514.0^{+123.4}_{-109.9}$ | 1.27 | $0.74^{+0.19}_{-0.18}$ | $0.63^{+0.15}_{-0.14}$ | $0.59^{+0.14}_{-0.13}$ | 1.22 | 3.737
c70-w1 | 0.70 | 34.837 | -7.585 | 13.38 | 34.829 | -7.570 | 59.7 | $0.76^{+0.07}_{-0.08}$ | $545.4^{+94.2}_{-98.4}$ | 0.62 | $0.76^{+0.06}_{-0.08}$ | $0.90^{+0.13}_{-0.17}$ | $0.85^{+0.12}_{-0.16}$ | 0.58 | 4.497
c71-w1 | 0.28 | 34.415 | -9.099 | 6.19 | 34.419 | -9.104 | 21.4 | $0.43^{+0.05}_{-0.06}$ | $1342.7^{+242.7}_{-249.2}$ | 0.95 | $0.44^{+0.06}_{-0.06}$ | $33.1^{+5.21}_{-5.32}$ | $28.7^{+4.51}_{-4.61}$ | 0.85 | 5.520
c72-w1 | 0.31 | 34.476 | -9.849 | 4.14 | 34.439 | -9.837 | 138.6 | $0.31^{+0.13}_{-0.14}$ | $1079.6^{+251.6}_{-266.8}$ | 1.24 | $0.27^{+0.16}_{-0.14}$ | $13.2^{+2.86}_{-2.73}$ | $11.3^{+2.44}_{-2.33}$ | 1.23 | 3.705
c73-w1 | 0.32 | 34.692 | -9.463 | 3.50 | 34.729 | -9.454 | 132.6 | $0.22^{+0.11}_{-0.15}$ | $\sim 0$ | 3.61 | $0.22^{+0.13}_{-0.15}$ | $\sim 0$ | $\sim 0$ | 3.58 | 3.800
c74-w1 | 0.41 | 34.280 | -9.354 | 15.23 | 34.290 | -9.367 | 60.1 | $0.47^{+0.17}_{-0.18}$ | $\sim 0$ | 3.33 | $0.49^{+0.16}_{-0.17}$ | $\sim 0$ | $\sim 0$ | 3.30 | 3.990
c75-w1 | 0.21 | 34.029 | -10.419 | 3.37 | 34.055 | -10.421 | 92.8 | $0.53^{+0.97}_{-0.17}$ | $506.9^{+140.8}_{-207.8}$ | 1.45 | $0.57^{+0.92}_{-0.18}$ | $0.57^{+0.82}_{-0.45}$ | $0.53^{+0.76}_{-0.42}$ | 1.42 | 4.841
c76-w1 | -99.0 | 35.401 | -4.420 | 3.72 | 35.374 | -4.391 | 140.7 | $0.50^{+0.23}_{-0.25}$ | $\sim 0$ | 6.14 | $0.42^{+0.23}_{-0.21}$ | $\sim 0$ | $\sim 0$ | 5.80 | 4.355
c77-w1 | 0.43 | 35.441 | -3.772 | 22.39 | 35.456 | -3.768 | 57.2 | $0.34^{+0.11}_{-0.12}$ | $766.1^{+182.5}_{-229.9}$ | 0.86 | $0.35^{+0.15}_{-0.15}$ | $2.04^{+2.78}_{-1.54}$ | $1.79^{+2.44}_{-1.35}$ | 0.82 | 4.209
c78-w1 | 0.44 | 35.595 | -4.890 | 3.26 | 35.601 | -4.892 | 23.0 | $0.31^{+0.15}_{-0.13}$ | $\sim 0$ | 4.45 | $0.31^{+0.14}_{-0.15}$ | $\sim 0$ | $\sim 0$ | 4.17 | 3.788
c79-w1 | 0.04 | 35.216 | -4.782 | 3.08 | 35.229 | -4.743 | 150.3 | $0.06^{+0.12}_{-0.11}$ | $573.8^{+113.9}_{-108.7}$ | 1.16 | $0.07^{+0.11}_{-0.10}$ | $2.78^{+0.33}_{-0.31}$ | $2.30^{+0.27}_{-0.26}$ | 1.09 | 4.204
c80-w1 | 0.59 | 35.436 | -6.358 | 6.80 | 35.436 | -6.354 | 14.1 | $0.45^{+0.19}_{-0.17}$ | $\sim 0$ | 6.63 | $0.43^{+0.20}_{-0.19}$ | $\sim 0$ | $\sim 0$ | 5.90 | 4.710
c81-w1 | 0.22 | 35.590 | -5.682 | 3.09 | 35.569 | -5.723 | 164.9 | $0.59^{+0.11}_{-0.12}$ | $1266.7^{+108.9}_{-117.3}$ | 1.35 | $0.67^{+0.13}_{-0.11}$ | $10.9^{+1.70}_{-1.50}$ | $9.97^{+1.56}_{-1.37}$ | 1.29 | 4.870
c82-w1 | 0.37 | 35.650 | -7.270 | 3.34 | 35.680 | -7.281 | 112.4 | $0.32^{+0.13}_{-0.11}$ | $628.4^{+106.1}_{-104.6}$ | 1.22 | $0.33^{+0.12}_{-0.10}$ | $1.80^{+0.22}_{-0.25}$ | $1.59^{+0.19}_{-0.22}$ | 1.21 | 3.923
c83-w1 | 0.32 | 35.830 | -7.997 | 5.21 | 35.826 | -7.992 | 21.4 | $0.08^{+0.07}_{-0.09}$ | $954.6^{120.0}_{132.6}$ | 1.68 | $0.10^{+0.04}_{-0.05}$ | $11.1^{+1.26}_{-1.30}$ | $9.10^{+1.03}_{-1.07}$ | 1.67 | 4.287
c84-w1 | 0.02 | 35.924 | -7.989 | 3.40 | 35.931 | -7.994 | 31.5 | $0.16^{+0.04}_{-0.05}$ | $789.9^{+64.3}_{-69.1}$ | 0.15 | $0.12^{+0.02}_{-0.01}$ | $7.50^{+0.82}_{-0.77}$ | $6.21^{+0.68}_{-0.64}$ | 0.19 | 4.127
c85-w1 | 0.35 | 35.486 | -8.950 | 7.92 | 35.486 | -8.937 | 48.4 | $0.25^{+0.15}_{-0.18}$ | $\sim 0$ | 3.98 | $0.24^{+0.17}_{-0.19}$ | $\sim 0$ | $\sim 0$ | 3.91 | 4.372
c86-w1 | 0.27 | 35.868 | -8.865 | 5.82 | 35.883 | -8.864 | 55.4 | $0.34^{+0.16}_{-0.14}$ | $523.9^{+122.8}_{-118.9}$ | 0.65 | $0.36^{+0.15}_{-0.16}$ | $0.79^{+0.12}_{-0.13}$ | $0.70^{+0.11}_{-0.12}$ | 0.41 | 4.779
c87-w1 | 0.32 | 35.821 | -9.347 | 6.25 | 35.805 | -9.344 | 61.1 | $0.38^{+0.19}_{-0.22}$ | $\sim 0$ | 3.52 | $0.39^{+0.18}_{-0.20}$ | $\sim 0$ | $\sim 0$ | 2.94 | 3.690
c88-w1 | 0.24 | 35.941 | -10.924 | 5.53 | 35.935 | -10.888 | 129.8 | $0.26^{+0.08}_{-0.09}$ | $538.0^{+112.3}_{-107.2}$ | 0.27 | $0.25^{+0.10}_{-0.08}$ | $0.90^{+0.15}_{-0.16}$ | $0.78^{+0.13}_{-0.14}$ | 0.22 | 3.543
c89-w1 | 0.34 | 35.827 | -10.399 | 3.79 | 35.828 | -10.406 | 26.4 | $0.43^{+0.17}_{-0.12}$ | $\sim 0$ | 4.77 | $0.42^{+0.16}_{-0.13}$ | $\sim 0$ | $\sim 0$ | 3.70 | 5.260
c90-w1 | 0.19 | 35.520 | -10.346 | 4.55 | 35.488 | -10.353 | 118.1 | $0.08^{+0.11}_{-0.10}$ | $\sim 0$ | 2.96 | $0.10^{+0.12}_{-0.10}$ | $\sim 0$ | $\sim 0$ | 3.11 | 3.640
c91-w1 | 0.20 | 35.284 | -10.330 | 4.14 | 35.317 | -10.305 | 149.6 | $0.28^{+0.13}_{-0.14}$ | $\sim 0$ | 4.19 | $0.26^{+0.14}_{-0.12}$ | $\sim 0$ | $\sim 0$ | 3.72 | 4.422
c92-w1 | 0.65 | 36.372 | -4.258 | 4.79 | 36.372 | -4.248 | 36.9 | $0.65^{+0.26}_{-0.26}$ | $\sim 0$ | 5.69 | $0.66^{+0.22}_{-0.20}$ | $\sim 0$ | $\sim 0$ | 4.63 | 4.548
c93-w1 | 0.30 | 36.121 | -4.165 | 3.36 | 36.097 | -4.167 | 87.5 | $0.26^{+0.13}_{-0.12}$ | $359.6^{+131.2}_{-121.7}$ | 0.25 | $0.25^{+0.11}_{-0.11}$ | $0.77^{+0.17}_{-0.18}$ | $0.67^{+0.15}_{-0.16}$ | 0.20 | 4.063
c94-w1 | 0.55 | 36.108 | -5.088 | 3.13 | 36.077 | -5.102 | 122.2 | $0.20^{+0.17}_{-0.15}$ | $344.8^{+97.5}_{-89.1}$ | 0.78 | $0.20^{+0.18}_{-0.16}$ | $0.23^{+0.06}_{-0.04}$ | $0.20^{+0.05}_{-0.04}$ | 0.81 | 3.521
c95-w1 | 0.35 | 36.617 | -4.998 | 10.12 | 36.636 | -4.990 | 72.8 | $0.22^{+0.14}_{-0.15}$ | $\sim 0$ | 4.55 | $0.21^{+0.13}_{-0.14}$ | $\sim 0$ | $\sim 0$ | 4.15 | 3.948
c96-w1 | 0.50 | 36.121 | -4.821 | 8.92 | 36.116 | -4.852 | 114.5 | $0.47^{+0.12}_{-0.14}$ | $701.3^{+131.3}_{-129.0}$ | 0.61 | $0.47^{+0.13}_{-0.12}$ | $2.10^{+0.31}_{-0.27}$ | $1.89^{+0.28}_{-0.24}$ | 0.57 | 4.211
c97-w1 | 0.29 | 36.455 | -5.896 | 10.48 | 36.465 | -5.892 | 38.6 | $0.35^{+0.11}_{-0.12}$ | $430.4^{+116.3}_{-120.2}$ | 0.79 | $0.35^{+0.13}_{-0.12}$ | $0.53^{+0.12}_{-0.11}$ | $0.47^{+0.11}_{-0.10}$ | 0.76 | 4.505
c98-w1 | 0.32 | 36.631 | -5.695 | 3.81 | 36.635 | -5.692 | 17.3 | $0.23^{+0.10}_{-0.11}$ | $\sim 0$ | 4.40 | $0.24^{+0.12}_{-0.15}$ | $\sim 0$ | $\sim 0$ | 4.36 | 4.147
c99-w1 | 0.51 | 36.890 | -7.462 | 3.34 | 36.903 | -7.483 | 88.4 | $0.48^{+0.13}_{-0.19}$ | $1055.6^{+263.4}_{-305.1}$ | 1.73 | $0.49^{+0.14}_{-0.18}$ | $6.03^{+1.27}_{-1.32}$ | $5.41^{+1.14}_{-1.18}$ | 1.51 | 3.546
c100-w1 | 0.31 | 35.996 | -8.595 | 18.74 | 36.008 | -8.599 | 45.3 | $0.36^{+0.16}_{-0.14}$ | $905.3^{+182.9}_{-193.5}$ | 0.87 | $0.35^{+0.15}_{-0.16}$ | $4.53^{+0.85}_{-0.91}$ | $3.92^{+0.74}_{-0.79}$ | 0.73 | 4.631
c101-w1 | 0.34 | 36.405 | -9.775 | 5.22 | 36.415 | -9.758 | 72.7 | $0.30^{+0.09}_{-0.07}$ | $670.8^{+103.7}_{-92.8}$ | 1.36 | $0.31^{+0.07}_{-0.06}$ | $1.26^{+0.19}_{-0.22}$ | $1.11^{+0.17}_{-0.19}$ | 1.23 | 3.856
c102-w1 | 0.33 | 36.402 | -11.158 | 6.97 | 36.398 | -11.166 | 30.2 | $0.24^{+0.11}_{-0.19}$ | $\sim 0$ | 2.95 | $0.27^{+0.12}_{-0.11}$ | $\sim 0$ | $\sim 0$ | 3.08 | 4.075
c103-w1 | 0.27 | 36.785 | -11.058 | 4.54 | 36.791 | -11.053 | 27.7 | $0.29^{+0.12}_{-0.15}$ | $301.5^{+152.2}_{-158.7}$ | 0.59 | $0.29^{+0.14}_{-0.13}$ | $0.15^{+0.09}_{-0.11}$ | $0.13^{+0.08}_{-0.10}$ | 0.50 | 3.725
c104-w1 | 0.29 | 36.473 | -10.992 | 3.88 | 36.476 | -10.988 | 15.2 | $0.23^{+0.05}_{-0.05}$ | $1567.2^{+188.5}_{-185.9}$ | 0.96 | $0.24^{+0.06}_{-0.05}$ | $46.6^{+3.32}_{-2.45}$ | $38.9^{+2.77}_{-2.04}$ | 0.90 | 3.838
c105-w1 | 0.29 | 37.199 | -5.589 | 6.37 | 37.200 | -5.618 | 103.7 | $0.32^{+0.07}_{-0.08}$ | $729.8^{+93.6}_{-89.8}$ | 0.19 | $0.33^{+0.08}_{-0.08}$ | $3.43^{+0.31}_{-0.22}$ | $2.97^{+0.27}_{-0.19}$ | 0.18 | 3.713
c106-w1 | 0.32 | 37.662 | -4.991 | 10.71 | 37.670 | -4.988 | 36.7 | $0.79^{+3.20}_{-0.26}$ | $700.2^{+231.9}_{-322.5}$ | 1.53 | $0.75^{+1.23}_{-0.22}$ | $1.77^{+2.77}_{-1.56}$ | $1.66^{+2.60}_{-1.47}$ | 1.60 | 4.449
c107-w1 | 0.34 | 37.720 | -4.855 | 7.63 | 37.724 | -4.863 | 30.6 | $0.27^{+0.08}_{-0.06}$ | $324.6^{+92.8}_{-83.7}$ | 0.69 | $0.26^{+0.08}_{-0.07}$ | $0.26^{+0.10}_{-0.11}$ | $0.23^{+0.09}_{-0.10}$ | 0.62 | 4.784
c108-w1 | 0.30 | 37.358 | -4.816 | 3.08 | 37.359 | -4.835 | 71.2 | $0.33^{+0.13}_{-0.09}$ | $348.6^{+113.3}_{-104.2}$ | 0.56 | $0.33^{+0.12}_{-0.10}$ | $0.24^{+0.07}_{-0.09}$ | $0.21^{+0.06}_{-0.08}$ | 0.53 | 3.655
c109-w1 | -99.0 | 37.000 | -6.397 | 3.17 | 37.022 | -6.429 | 117.5 | $0.46^{+0.16}_{-0.09}$ | $741.4^{+152.6}_{-194.8}$ | 1.72 | $0.43^{+0.16}_{-0.11}$ | $3.17^{+3.32}_{-2.07}$ | $2.82^{+2.95}_{-1.84}$ | 1.25 | 3.946
c110-w1 | 0.49 | 37.812 | -5.572 | 3.10 | 37.784 | -5.587 | 116.9 | $0.52^{+0.17}_{-0.15}$ | $303.5^{+141.2}_{-133.1}$ | 0.89 | $0.52^{+0.15}_{-0.13}$ | $0.16^{+0.10}_{-0.07}$ | $0.15^{+0.09}_{-0.06}$ | 0.83 | 4.335
c111-w1 | 0.28 | 37.767 | -7.269 | 10.60 | 37.776 | -7.272 | 33.9 | $0.37^{+0.12}_{-0.10}$ | $\sim 0$ | 3.17 | $0.36^{+0.11}_{-0.11}$ | $\sim 0$ | $\sim 0$ | 3.18 | 3.708
c112-w1 | 0.36 | 37.541 | -7.536 | 3.04 | 37.540 | -7.513 | 81.0 | $0.42^{+0.16}_{-0.18}$ | $817.2^{+164.2}_{-177.0}$ | 0.87 | $0.43^{+0.17}_{-0.17}$ | $3.76^{+0.72}_{-0.74}$ | $3.34^{+0.64}_{-0.66}$ | 0.81 | 4.646
c113-w1 | 0.19 | 37.354 | -7.494 | 5.18 | 37.340 | -7.486 | 58.8 | $0.39^{+0.09}_{-0.10}$ | $\sim 0$ | 4.83 | $0.38^{+0.10}_{-0.10}$ | $\sim 0$ | $\sim 0$ | 4.41 | 3.725
c114-w1 | 0.37 | 37.088 | -9.226 | 3.35 | 37.096 | -9.242 | 62.4 | $0.35^{+0.11}_{-0.13}$ | $672.0^{+114.3}_{-119.5}$ | 1.21 | $0.35^{+0.12}_{-0.13}$ | $2.71^{+0.56}_{-0.51}$ | $2.39^{+0.49}_{-0.45}$ | 1.10 | 3.616
c115-w1 | 0.27 | 37.299 | -8.901 | 3.48 | 37.294 | -8.892 | 35.3 | $0.31^{+0.12}_{-0.14}$ | $947.2^{+155.7}_{-168.3}$ | 2.47 | $0.32^{+0.13}_{-0.14}$ | $5.55^{+0.72}_{-0.75}$ | $4.77^{+0.62}_{-0.64}$ | 2.44 | 4.734
c116-w1 | 0.28 | 37.355 | -8.841 | 5.10 | 37.347 | -8.835 | 34.1 | $0.26^{+0.16}_{-0.15}$ | $174.9^{+194.5}_{-189.3}$ | 2.81 | $0.25^{+0.16}_{-0.17}$ | $0.08^{+0.13}_{-0.14}$ | $0.07^{+0.12}_{-0.13}$ | 2.67 | 4.513
c117-w1 | 0.64 | 37.828 | -11.147 | 5.49 | 37.802 | -11.140 | 93.2 | $0.77^{+0.27}_{-0.25}$ | $\sim 0$ | 5.64 | $0.74^{+0.24}_{-0.25}$ | $\sim 0$ | $\sim 0$ | 5.46 | 3.684
c118-w1 | 0.27 | 37.922 | -4.883 | 12.07 | 37.936 | -4.880 | 54.2 | $0.29^{+0.13}_{-0.12}$ | $311.2^{+103.4}_{-97.4}$ | 0.56 | $0.30^{+0.11}_{-0.12}$ | $0.14^{+0.05}_{-0.06}$ | $0.12^{+0.04}_{-0.05}$ | 0.53 | 3.555
c119-w1 | 0.49 | 38.525 | -4.728 | 3.14 | 38.483 | -4.737 | 153.6 | $0.46^{+0.14}_{-0.11}$ | $422.1^{+126.1}_{-135.6}$ | 0.48 | $0.46^{+0.13}_{-0.14}$ | $0.24^{+0.11}_{-0.08}$ | $0.22^{+0.10}_{-0.07}$ | 0.43 | 3.567
c120-w1 | 0.31 | 38.048 | -6.491 | 5.70 | 38.022 | -6.501 | 102.0 | $0.12^{+0.11}_{-0.12}$ | $\sim 0$ | 3.77 | $0.16^{+0.12}_{-0.11}$ | $\sim 0$ | $\sim 0$ | 3.71 | 3.850
c121-w1 | 0.33 | 37.925 | -7.790 | 3.65 | 37.938 | -7.828 | 145.0 | $0.37^{+0.12}_{-0.11}$ | $725.9^{+152.9}_{-143.8}$ | 0.16 | $0.37^{+0.14}_{-0.12}$ | $2.12^{+0.39}_{-0.43}$ | $1.86^{+0.34}_{-0.38}$ | 0.16 | 3.853
c122-w1 | 0.43 | 37.998 | -7.624 | 3.44 | 37.986 | -7.658 | 130.0 | $0.33^{+0.15}_{-0.17}$ | $\sim 0$ | 3.83 | $0.32^{+0.16}_{-0.15}$ | $\sim 0$ | $\sim 0$ | 3.74 | 3.725
c123-w1 | 0.37 | 38.688 | -8.801 | 3.62 | 38.737 | -8.797 | 172.1 | $0.41^{+0.13}_{-0.13}$ | $547.5^{+117.8}_{-102.7}$ | 1.19 | $0.40^{+0.12}_{-0.13}$ | $1.81^{+0.29}_{-0.31}$ | $1.60^{+0.26}_{-0.27}$ | 1.13 | 3.563
c124-w1 | 0.23 | 38.669 | -9.835 | 3.70 | 38.630 | -9.843 | 141.1 | $0.26^{+0.15}_{-0.15}$ | $756.0^{+143.0}_{-139.6}$ | 0.57 | $0.26^{+0.15}_{-0.14}$ | $7.14^{+1.32}_{-1.27}$ | $6.09^{+1.13}_{-1.08}$ | 0.56 | 4.467
c125-w1 | 0.63 | 37.902 | -9.562 | 4.82 | 37.907 | -9.595 | 117.5 | $0.59^{+0.29}_{-0.18}$ | $814.3^{+313.2}_{-187.3}$ | 1.53 | $0.57^{+0.33}_{-0.15}$ | $3.00^{+3.14}_{-1.90}$ | $2.74^{+2.86}_{-1.73}$ | 1.47 | 4.915
c126-w1 | 0.26 | 38.639 | -10.472 | 5.31 | 38.647 | -10.458 | 57.3 | $0.44^{+0.10}_{-0.10}$ | $536.5^{+102.1}_{-108.7}$ | 1.62 | $0.40^{+0.11}_{-0.10}$ | $0.96^{+0.15}_{-0.13}$ | $0.86^{+0.13}_{-0.12}$ | 1.16 | 4.764

Table 6Catalog of the Matching Groups/Clusters between $\nu>3.5$ Convergence Peaks and X-Ray/K2-detected Groups/Clusters in CFHTLS-Wide W1 Fields. K2 redshift denotes the median redshift of bright ($i\leq 20$) cluster members. X-ray redshift denotes the photometric redshifts of X-ray clusters (Adami et al. 2011). The parameters $d_{\rm xray}$ and $d_{\rm k2}$ are the offset between X-ray/optical and weak lensing center, respectively.  ID | $\alpha_{\rm xray}$ | $\delta_{\rm xray}$ | $\alpha_{\rm K2}$ | $\delta_{\rm K2}$ | $\alpha$ | $\delta$ | $d_{\rm xray}$ | $d_{\rm k2}$ | $\nu$ | $z_{\rm K2}$ | $z_{\rm xray}$ | $\sigma_{v-xray}$ | $z_{\rm SIS}$ | $\sigma_{v}$ | $\chi^{2}_{\rm SIS}$ | $z_{\rm NFW}$ | $m_{\rm NFW}$ | $m_{200}$ | $\chi^{2}_{\rm NFW}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | $\rm arcsec$ | $\rm arcsec$ |  |  |  | $\rm km/s$ |  | $\rm km/s$ |  |  | $10^{14}M_{\odot}/h$ | $10^{14}M_{\odot}/h$ |
J022145.2-034617 | 35.438 | -3.772 | 35.441 | -3.772 | 35.456 | -3.768 | 66.5 | 57.2 | 4.209 | 0.43 | 0.429$\pm$0.001 | 977$\pm$157 | $0.34^{+0.11}_{-0.12}$ | $766.1^{+182.5}_{-229.9}$ | 0.86 | $0.35^{+0.15}_{-0.15}$ | $2.04^{+2.78}_{-1.54}$ | $1.79^{+2.44}_{-1.35}$ | 0.82
J022402.0-050525 | 36.008 | -5.090 | 36.108 | -5.088 | 36.077 | -5.101 | 251.1 | 122.2 | 3.521 | 0.55 | 0.324$\pm$0.001 | 364$\pm$69 | $0.20^{+0.17}_{-0.15}$ | $344.8^{+97.5}_{-89.1}$ | 0.78 | $0.20^{+0.18}_{-0.16}$ | $0.23^{+0.06}_{-0.04}$ | $0.20^{+0.05}_{-0.04}$ | 0.81
J022433.8-041405 | 36.141 | -4.234 | 36.121 | -4.165 | 36.097 | -4.161 | 289.1 | 87.5 | 4.063 | 0.30 | 0.262$\pm$0.001 | 483$\pm$100 | $0.26^{+0.13}_{-0.12}$ | $359.6^{+131.2}_{-121.7}$ | 0.25 | $0.25^{+0.11}_{-0.11}$ | $0.77^{+0.17}_{-0.18}$ | $0.67^{+0.15}_{-0.16}$ | 0.20
J022530.6-041420 | 36.377 | -4.239 | 36.372 | -4.258 | 36.372 | -4.248 | 36.3 | 36.9 | 4.548 | 0.65 | 0.14$\pm$0.002 | 899$\pm$218 | $0.65^{+0.26}_{-0.26}$ | $\sim 0$ | 5.69 | $0.66^{+0.22}_{-0.20}$ | $\sim 0$ | $\sim 0$ | 4.63
J021837.0-054028 | 34.654 | -5.675 | 34.655 | -5.674 | 34.653 | -5.626 | 175.7 | 170.7 | 4.186 | 0.33 | 0.275$\pm$0.0 | - | $0.31^{+0.14}_{-0.11}$ | $\sim 0$ | 4.18 | $0.32^{+0.13}_{-0.10}$ | $\sim 0$ | $\sim 0$ | 3.87
J021842.8-053254 | 34.678 | -5.548 | 34.657 | -5.570 | 34.684 | -5.572 | 91.1 | 98.4 | 4.194 | 0.36 | 0.38$\pm$0.001 | 847$\pm$279 | $0.57^{+0.13}_{-0.14}$ | $909.7^{+61.5}_{-60.1}$ | 1.55 | $0.55^{+0.15}_{-0.13}$ | $5.31^{+0.32}_{-0.30}$ | $4.82^{+0.29}_{-0.27}$ | 1.47
J022632.4-050003 | 36.638 | -5.007 | 36.678 | -4.950 | 36.643 | -4.959 | 62.6 | 72.8 | 3.156 | 0.22 | 0.494$\pm$0.0 | - | $0.23^{+0.19}_{-0.17}$ | $\sim 0$ | 3.80 | $0.25^{+0.16}_{-0.21}$ | $\sim 0$ | $\sim 0$ | 3.81