The Serendipitous Observation of a Gravitationally Lensed Galaxy at z = 0.9057 from the Blanco Cosmology Survey: The Elliot Arc
ABSTRACT We report on the serendipitous discovery in the Blanco Cosmology Survey (BCS) imaging data of a z = 0.9057 galaxy that is being strongly lensed by a massive galaxy cluster at a redshift of z = 0.3838. The lens (BCS J2352–5452) was discovered while examining i- and z-band images being acquired in 2006 October during a BCS observing run. Follow-up spectroscopic observations with the Gemini Multi-Object Spectrograph instrument on the Gemini-South 8 m telescope confirmed the lensing nature of this system. Using weak-plus-strong lensing, velocity dispersion, cluster richness N 200, and fitting to a Navarro-Frenk-White (NFW) cluster mass density profile, we have made three independent estimates of the mass M 200 which are all very consistent with each other. The combination of the results from the three methods gives M 200 = (5.1 ± 1.3) × 1014 M ☉, which is fully consistent with the individual measurements. The final NFW concentration c 200 from the combined fit is c 200 = 5.4+1.4 – 1.1. We have compared our measurements of M 200 and c 200 with predictions for (1) clusters from ΛCDM simulations, (2) lensing-selected clusters from simulations, and (3) a real sample of cluster lenses. We find that we are most compatible with the predictions for ΛCDM simulations for lensing clusters, and we see no evidence based on this one system for an increased concentration compared to ΛCDM. Finally, using the flux measured from the [O II]3727 line we have determined the star formation rate of the source galaxy and find it to be rather modest given the assumed lens magnification.
- S. Desai, R. Armstrong, J. J. Mohr, D. R. Semler, J. Liu, E. Bertin, S. S. Alam, W. A. Barkhouse, G. Bazin, E. J. Buckley-Geer, M. C. Cooper, S. M. Hansen, F. W. High, H. Lin, Y. T. Lin, C. -C. Ngeow, A. Rest, J. Song, D. Tucker, A. Zenteno[Show abstract] [Hide abstract]
ABSTRACT: The Blanco Cosmology Survey (BCS) is a 60 night imaging survey of $\sim$80 deg$^2$ of the southern sky located in two fields: ($\alpha$,$\delta$)= (5 hr, $-55^{\circ}$) and (23 hr, $-55^{\circ}$). The survey was carried out between 2005 and 2008 in $griz$ bands with the Mosaic2 imager on the Blanco 4m telescope. The primary aim of the BCS survey is to provide the data required to optically confirm and measure photometric redshifts for Sunyaev-Zel'dovich effect selected galaxy clusters from the South Pole Telescope and the Atacama Cosmology Telescope. We process and calibrate the BCS data, carrying out PSF corrected model fitting photometry for all detected objects. The median 10$\sigma$ galaxy (point source) depths over the survey in $griz$ are approximately 23.3 (23.9), 23.4 (24.0), 23.0 (23.6) and 21.3 (22.1), respectively. The astrometric accuracy relative to the USNO-B survey is $\sim45$ milli-arcsec. We calibrate our absolute photometry using the stellar locus in $grizJ$ bands, and thus our absolute photometric scale derives from 2MASS which has $\sim2$% accuracy. The scatter of stars about the stellar locus indicates a systematics floor in the relative stellar photometric scatter in $griz$ that is $\sim$1.9%, $\sim$2.2%, $\sim$2.7% and$\sim$2.7%, respectively. A simple cut in the AstrOmatic star-galaxy classifier {\tt spread\_model} produces a star sample with good spatial uniformity. We use the resulting photometric catalogs to calibrate photometric redshifts for the survey and demonstrate scatter $\delta z/(1+z)=0.054$ with an outlier fraction $\eta<5$% to $z\sim1$. We highlight some selected science results to date and provide a full description of the released data products.The Astrophysical Journal 04/2012; 757(1). · 6.28 Impact Factor - SourceAvailable from: Risa WechslerL. E. Bleem, B. Stalder, M. Brodwin, M. T. Busha, M. D. Gladders, F. W. High, A. Rest, R. H. Wechsler[Show abstract] [Hide abstract]
ABSTRACT: The Blanco Cosmology Survey is 4-band (griz) optical-imaging survey that covers ~80 square degrees of the southern sky. The survey consists of two fields roughly centered at (RA,DEC) = (23h,-55d) and (5h30m,-53d) with imaging designed to reach depths sufficient for the detection of L* galaxies out to a redshift of one. In this paper we describe the reduction of the survey data, the creation of calibrated source catalogs and a new method for the separation of stars and galaxies. We search these catalogs for galaxy clusters at z< 0.75 by identifying spatial over-densities of red-sequence galaxies. We report the coordinates, redshift, and optical richness, Lambda, for 764 detected galaxy clusters at z < 0.75. This sample, >85% of which are new discoveries, has a median redshift of 0.52 and median richness Lambda(0.4L*) of 16.4. Accompanying this paper we also release data products including the reduced images and calibrated source catalogs. These products are available at http://data.rcc.uchicago.edu/dataset/blanco-cosmology-survey .03/2014; - SourceAvailable from: Laura MocanuJ. Song, A. Zenteno, B. Stalder, S. Desai, L. E. Bleem, K. A. Aird, R. Armstrong, M. L. N. Ashby, M. Bayliss, G. Bazin, [......], S. A. Stanford, Z. Staniszewski, A. A. Stark, K. Story, C. W. Stubbs, A. van Engelen, K. Vanderlinde, J. D. Vieira, R. Williamson, O. Zahn[Show abstract] [Hide abstract]
ABSTRACT: We present the results of the ground- and space-based optical and near-infrared (NIR) follow-up of 224 galaxy cluster candidates detected with the Sunyaev-Zel'dovich (SZ) effect in the 720 deg^2 of the South Pole Telescope (SPT) survey completed in the 2008 and 2009 observing seasons. We use the optical/NIR data to establish whether each candidate is associated with an overdensity of galaxies and to estimate the cluster redshift. Most photometric redshifts are derived through a combination of three different cluster redshift estimators using red-sequence galaxies, resulting in an accuracy of \Delta z/(1+z)=0.017, determined through comparison with a subsample of 57 clusters for which we have spectroscopic redshifts. We successfully measure redshifts for 158 systems and present redshift lower limits for the remaining candidates. The redshift distribution of the confirmed clusters extends to z=1.35 with a median of z_{med}=0.57. Approximately 18% of the sample with measured redshifts lies at z>0.8. We estimate a lower limit to the purity of this SPT SZ-selected sample by assuming that all unconfirmed clusters are noise fluctuations in the SPT data. We show that the cumulative purity at detection significance \xi>5 (\xi>4.5) is >= 95 (>= 70%). We present the red brightest cluster galaxy (rBCG) positions for the sample and examine the offsets between the SPT candidate position and the rBCG. The radial distribution of offsets is similar to that seen in X-ray-selected cluster samples, providing no evidence that SZ-selected cluster samples include a different fraction of recent mergers than X-ray-selected cluster samples.The Astrophysical Journal 07/2012; 761(1). · 6.28 Impact Factor
Page 1
arXiv:1108.4681v1 [astro-ph.CO] 23 Aug 2011
The serendipitous observation of a gravitationally lensed galaxy
at z = 0.9057 from the Blanco Cosmology Survey: The Elliot Arc
E. J. Buckley-Geer,1H. Lin,1E. R. Drabek,1,19S. S. Allam,1D. L. Tucker,1R. Armstrong,2
W. A. Barkhouse,3E. Bertin,4M. Brodwin,5,6S. Desai,15J. A. Frieman,1,7S. M. Hansen,8
F. W. High,7J. J. Mohr,9,10,11Y.-T. Lin,12,13C.-C. Ngeow,14,15A. Rest,16R. C. Smith,17
J. Song,18A. Zenteno,9,10
ABSTRACT
1Center for Particle Astrophysics, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL
60510
2National Center for Supercomputing Applications,University of Illinois, 1205 West Clark Street, Ur-
banan, IL 61801
3Department of Physics & Astrophysics,University of North Dakota, Grand Forks, ND 58202
4Institut d’Astrophysique de Paris, UMR 7095 CNRS, Universit´ e Pierre et Marie Curie, 98 bis boulevard
Arago, F-75014 Paris, France
5Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138
6W. M. Keck Postdoctoral Fellow at the Harvard-Smithsonian Center for Astrophysics
7University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637
8National Science Foundation Astronomy & Astrophysics Postdoctoral Fellow, University of California
Observatories & Department of Astronomy, University of California, Santa Cruz, CA 95064
9Department of Physics, Ludwig-Maximilians-Universit¨ at, Scheinerstr. 1, 81679 M¨ unchen, Germany
10Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching, Germany
11Max-Planck-Institut f¨ ur extraterrestrische Physik, Giessenbachstr. 85748 Garching, Germany
12Institute for Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwa-no-ha,
Kashiwa-shi, Chiba 277- 8568, Japan
13Institute of Astronomy & Astrophysics, Academia Sinica, Taipei, Taiwan
14Graduate Institute of Astronomy, National Central University, No. 300 Jonghda Rd, Jhongli City 32001
Taiwan
15Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801
16Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218
17Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, La Serena, Chile
18Department of Physics, University of Michigan, 450 Church St. Ann Arbor, MI 48109
19School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
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We report on the serendipitous discovery in the Blanco Cosmology Survey
(BCS) imaging data of a z = 0.9057 galaxy that is being strongly lensed by a
massive galaxy cluster at a redshift of z = 0.3838. The lens (BCS J2352-5452)
was discovered while examining i- and z-band images being acquired in October
2006 during a BCS observing run. Follow-up spectroscopic observations with
the GMOS instrument on the Gemini South 8m telescope confirmed the lensing
nature of this system. Using weak plus strong lensing, velocity dispersion, cluster
richness N200, and fitting to an NFW cluster mass density profile, we have made
three independent estimates of the mass M200which are all very consistent with
each other. The combination of the results from the three methods gives M200=
(5.1±1.3)×1014M⊙, which is fully consistent with the individual measurements.
The final NFW concentration c200from the combined fit is c200= 5.4+1.4
compared our measurements of M200 and c200 with predictions for (a) clusters
from ΛCDM simulations, (b) lensing selected clusters from simulations, and (c)
a real sample of cluster lenses. We find that we are most compatible with the
predictions for ΛCDM simulations for lensing clusters, and we see no evidence
based on this one system for an increased concentration compared to ΛCDM.
Finally, using the flux measured from the [OII]3727 line we have determined the
star formation rate (SFR) of the source galaxy and find it to be rather modest
given the assumed lens magnification.
−1.1. We have
Subject headings: gravitational lensing: strong — gravitational lensing: weak —
galaxies: high-redshift
1.Introduction
Strong gravitational lenses offer unique opportunities to study cosmology, dark mat-
ter, galactic structure, and galaxy evolution.
namely the lenses themselves, that are selected based on total mass rather than luminos-
ity or surface brightness. The majority of lenses discovered in the past decade were found
through dedicated surveys using a variety of techniques. For example, the Sloan Digital
Sky Survey (SDSS) data have been used to effectively select lens candidates from rich clus-
ters (Hennawi et al. 2008) through intermediate scale clusters (Allam et al. 2007; Lin et al.
2009) to individual galaxies (Bolton et al. 2008; Willis et al. 2006). Other searches using the
CFHTLS (Cabanac et al. 2007) and COSMOS fields (Faure et al. 2008; Jackson et al. 2008)
have yielded 40 and 70 lens candidates respectively. These searches cover the range of giant
arcs with Einstein radii θEIN> 10′′all the way to small arcs produced by single lens galaxies
They also provide a sample of galaxies,
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with θEIN< 3′′.
In this paper we report on the serendipitous discovery of a strongly lensed z = 0.9057
galaxy in the Blanco Cosmology Survey (BCS) imaging data. The lens is a rich cluster
containing a prominent central brightest cluster galaxy (BCG) and has a redshift of z =
0.3838. Cluster-scale lenses are particularly useful as they allow us to study the effects of
strong lensing in the core of the cluster and weak lensing in the outer regions. Strong lensing
provides constraints on the mass contained within the Einstein radius of the arcs whereas
weak lensing provides information on the mass profiles in the outer reaches of the cluster.
Combining the two measurements allows us to make tighter constraints on the mass M200and
the concentration c200, of an NFW (Navarro, Frenk, & White 1995) model of the cluster mass
density profile, over a wider range of radii than would be possible with either method alone
(Natarajan et al. 1998, 2002; Brada˘ c et al. 2006, 2008a,b; Diego et al. 2007; Limousin et al.
2007; Hicks et al. 2007; Deb et al. 2008; Merten et al. 2009; Oguri et al. 2009). In addition,
if one has spectroscopic redshifts for the member galaxies one can determine the cluster
velocity dispersion, assuming the cluster is virialized, and hence obtain an independent
estimate for M200(Becker et al. 2007). Finally one can also derive an M200estimate from
the maxBCG cluster richness N200(Hansen et al. 2005; Johnston et al. 2007). These three
different methods, strong plus weak lensing, cluster velocity dispersion, and optical richness,
provide independent estimates of M200 (M200 is defined as the mass within a sphere of
overdensity 200 times the critical density at the redshift z) and can then be combined to
obtain improved constraints on M200 and c200. Measurements of the concentration from
strong lensing clusters is of particular interest as recent publications suggest that they may
be more concentrated than one would expect from ΛCDM models (Broadhurst & Barkana
2008; Oguri & Blandford 2009).
The paper is organized as follows. In § 2 we describe the Blanco Cosmology Survey.
Then in § 3 we discuss the initial discovery and the spectroscopic follow-up that led to
confirmation of the system as a gravitational lens, the data reduction, the properties of the
cluster, the extraction of the redshifts, and finally the measurement of the cluster velocity
dispersion and estimate of the cluster mass. In § 4 we summarize the strong lensing features
of the system. In § 5 we describe the weak lensing measurements. In § 6 we present the results
of combining of the strong and weak lensing results and the final mass constraints derived
from combining the lensing results with the velocity dispersion and richness measurements.
We describe the source galaxy star formation rate measurements in § 7 and finally in § 8 we
conclude. We assume a flat cosmology with ΩM= 0.3, ΩΛ= 0.7, and H0= 70 km s−1Mpc−1,
unless otherwise noted.
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2. The BCS Survey
The Blanco Cosmology Survey (BCS) is a 60-night NOAO imaging survey program
(2005-2008), using the Mosaic-II camera on the Blanco 4m telescope at CTIO, that has
uniformly imaged 75deg2of the sky in the SDSS griz bands in preparation for cluster finding
with the South Pole Telescope (SPT) (Vanderlinde et al. 2010) and other millimeter-wave
experiments. The depths in each band were chosen to allow the estimation of photometric
redshifts for L ≥ L∗galaxies out to a redshift of z = 1 and to detect galaxies to 0.5L∗at
5σ to these same redshifts. The survey was divided into two fields to allow efficient use of
the allotted nights between October and December. Both fields lie near δ = −55◦which
allows for overlap with the SPT. One field is centered near α = 23.5 hr and the other is at
α = 5.5 hr. In addition to the large science fields, BCS also covers 7 small fields that overlap
large spectroscopic surveys so that photometric redshifts (photo-z’s) using BCS data can be
trained and tested using a sample of over 5,000 galaxies.
3.Discovery of the lens and spectroscopic follow-up
The lens BCS J2351-5452 was discovered serendipitously while examining i- and z-band
images being acquired in October 2006 during the yearly BCS observing run. The discoverer
(EJB-G) decided to name it “The Elliot Arc” in honor of her then 8 year old nephew. Table 1
lists the observed images along with seeing conditions. Fig. 1 shows a gri color image of the
source, lens and surrounding environment (the pixel scale is 0.268′′per pixel). The source
forms a purple ring-like structure of radius ∼ 7.5′′with multiple distinct bright regions. The
lens is the BCG at the center of a large galaxy cluster. Photometric measurements estimated
the redshift of the cluster at z ∼ 0.4, using the expected g −r and r −i red sequence colors,
and also provided a photo-z for the source of z ∼ 0.7, as described below.
We obtained Gemini Multi-Object Spectrograph (GMOS) spectra of the source and a
number of the neighboring galaxies (Lin et al. 2007). We targeted the regions of the source
labeled A1-A4 in Fig. 2, and photometric properties of these bright knots are summarized
in Table 2. In addition we selected 51 more objects for a total of 55 spectra. The additional
objects were selected using their colors in order to pick out likely cluster member galaxies.
Fig. 3 shows the r − i versus i color-magnitude diagram (top plot) and the g − r vs. r − i
color-color diagram (bottom plot) of the field. The blue squares in the bottom panel of Fig. 3
show the four targeted knots in the lensed arcs. The green curve is an Scd galaxy model
(Coleman, Wu, & Weedman 1980) with the green circles indicating a photometric redshift
for the arc of z ∼ 0.7. Note this is not a detailed photo-z fit, but is just a rough estimate
meant to show that the arc is likely at a redshift higher than the cluster redshift. Highest
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target priority was given to the arc knots and to the BCG. Then cluster red sequence galaxy
targets were selected using the simple color cuts 1.55 ≤ g − r ≤ 1.9 and 0.6 ≤ r − i ≤ 0.73
(also shown in the bottom panel of Fig. 3), which approximate the more detailed final
cluster membership criteria described below in §3.2. Red sequence galaxies with i < 21.6
(3′′-diameter SExtractor aperture magnitudes) were selected, with higher priority given to
brighter galaxies with i(3′′) ≤ 21. Additional non-cluster targets lying outside the cluster
color selection box were added at lowest priority.
We used the GMOS R150 grating + the GG455 filter in order obtain spectra with about
4600 – 9000˚ A wavelength coverage. This was designed to cover the [OII] 3727 emission line
expected at ∼ 6300˚ A, given the photo-z estimate of ∼ 0.7 for the arcs as well as the Mg
absorption features at ∼ 7000˚ A (and the 4000˚ A break at ∼ 5600˚ A) for the z ∼ 0.4 cluster
elliptical galaxies.
We used 2 MOS masks in order to fully target these cluster galaxies (along with the
arcs) for spectroscopy. Each mask had a 3600 second exposure time split into 4 900-second
exposures for cosmic ray removal. We also took standard Cu-Ar lamp spectra for wavelength
calibrations and standard star spectra for flux calibrations. All data were taken in queue
observing mode. A summary of the observations is given in Table 1.
3.1. Data Reduction
The BCS imaging data were processed using the Dark Energy Survey data management
system (DESDM V3) which is under development at UIUC/NCSA/Fermilab (Mohr et al.
2008; Ngeow et al. 2006; Zenteno et al. 2011). The images are corrected for instrumental
effects which include crosstalk correction, pupil ghost correction, overscan correction, trim-
ming, bias subtraction, flat fielding and illumination correction. The images are then astro-
metrically calibrated and remapped for later coaddition. For photometric data, a photomet-
ric calibration is applied to the single-epoch and coadd object photometry. The AstrOmatic
software1SExtractor (Bertin & Arnouts 1996), SCAMP (Bertin 2006) and SWarp (Bertin et al.
2002) are used for cataloging, astrometric refinement and remapping for coaddition over each
image. We have used the coadded images in the griz bands for this analysis.
The spectroscopic data were processed using the standard data reduction package pro-
vided by Gemini that runs in the IRAF framework2. We used version 1.9.1. This produced
1http://www.astromatic.net
2http://www.gemini.edu/sciops/data-and-results/processing-software
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flux- and wavelength-calibrated 1-D spectra for all the objects. Additional processing for
the source spectra was done using the IRAF task apall.
3.2.Cluster properties
We adopt the procedure used by the maxBCG cluster finder (Koester et al. 2007a,b) to
determine cluster membership and cluster richness and to derive a richness-based cluster mass
estimate. We first measure Ngal, the number of cluster red sequence galaxies, within a radius
1 h−1Mpc (= 4.55′) of the BCG, that are also brighter than 0.4L∗at the cluster redshift
z = 0.38. From Koester et al. (2007a), 0.4L∗corresponds to an i-band absolute magnitude
M = −20.25 + 5logh at z = 0, while at z = 0.38, 0.4L∗ corresponds to an apparent
magnitude i = 20.5 (specific value provided by J. Annis & J. Kubo, private communication),
after accounting for both K-correction and evolution (also as described in Koester et al.
2007a). We apply this magnitude cut using the SExtractor i-band MAG AUTO magnitude,
which provides a measure of a galaxy’s total light. (Note the 3′′-diameter aperture magnitude
used earlier for target selection in general measures less light cf. MAG AUTO, but is better
suited for roughly approximating the light entering a GMOS slit.) We set the red sequence
membership cuts to be g−r and r−i color both within 2σ of their respective central values
(g − r)0= 1.77 and (r − i)0= 0.65, where the latter are determined empirically based on
the peaks of the color histograms of galaxies within 1 h−1Mpc of the BCG. In applying
the color cuts we use the colors defined by SExtractor 3′′-diameter aperture magnitudes
(this provides higher S/N colors compared to using MAG AUTO), and for the uncertainty we
define σ =
?σ2
SExtractor aperture magnitude errors, and σintrinsicis the intrinsic red sequence color width,
taken to be 0.05 for g − r and 0.06 for r − i (Koester et al. 2007a).
color+ σ2
intrinsic, where σcoloris the color measurement error derived from the
Carrying out the above magnitude and color cuts, we obtain an initial richness estimate
Ngal = 44. Then, as discussed in Hansen et al. (2005), we define another radius rgal
0.156 N0.6
the BCG to obtain a final richness estimate N200 = 55. Finally, using the weak lensing
mass calibration of Johnston et al. (2007) for maxBCG clusters, we obtain a mass estimate
M200= (8.794 × 1013) × (N200/20)1.28h−1M⊙= (4.6 ± 2.1) × 1014M⊙(h = 0.7), where we
have also adopted the fractional error of 0.45 derived by Rozo et al. (2009) for this N200-based
estimate of M200for maxBCG clusters.
200=
200of
galh−1Mpc = 1.51 h−1Mpc (= 6.88′), and repeat the same cuts within rgal
We note that Rozo et al. (2010) apply a factor of 1.18 to correct the Johnston et al.
(2007) cluster masses upward, in order to account for a photo-z bias effect that is detailed
in Mandelbaum et al. (2008). We have not applied this correction as it makes only a 0.4σ
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difference, although we remark that the resulting mass M200= 5.4 × 1014M⊙does appear
to improve the (already good) agreement with our other mass estimates below (see §3.4 and
§6.1).
Fig. 3 shows color-magnitude and color-color plots of all galaxies that have i < 21
(SExtractor MAG AUTO) and that are within a radius rgal
BCG. Note we have extended the magnitude limit here down to i = 21, to match the
effective magnitude limit of our spectroscopic redshift sample (§3.3 below) In particular, we
find 86 maxBCG cluster members for i < 21, compared to the earlier N200= 55 for i < 20.5
(corresponding to 0.4L∗). These member galaxies are shown using red symbols in Fig. 3 and
their properties are given in Table 3.
200= 1.51 h−1Mpc (= 6.88′) of the
3.3.Redshift determinations
The redshift extraction was carried out using the xcsao and emsao routines in the
IRAF external package rvsao (Kurtz & Mink 1998). We obtained spectra for the 55 objects
that were targeted. Four of these spectra were of the source. Out of the remaining 51
spectra we had sufficient signal-to-noise in 42 of them to determine a redshift. Thirty of the
objects with redshifts between 0.377 and 0.393 constitute our spectroscopic sample of cluster
galaxies. Fig. 4 shows the spatial distribution of galaxies within a 6′×6′box centered on the
BCG, with maxBCG cluster members, arc knots, and objects with spectroscopic redshifts
indicated by different colors and symbols. Table 3 summarizes the properties of the 30 cluster
member galaxies with redshifts, and Table 4 summarizes the properties of the remaining 12
spectroscopic non-member galaxies. In Fig. 5 we show four examples of the flux-calibrated
cluster member spectra including the BCG.
Examination of Table 3 and Table 4 shows that our spectroscopic sample is effectively
limited at i ≈ 21, as 39 of the 42 non-arc redshifts have i < 21. Note that of the 30
spectroscopically defined cluster members, 22 are also maxBCG members, while another
7 lie close to the maxBCG color selection boundaries. Also, of the 12 spectroscopic non-
members, none meets the maxBCG criteria except the faintest one (with i = 21.58).
The redshift of the source was determined from a single emission line at 7100˚ A which is
present with varying signal-to-noise in each of the knots that were observed. We take this line
to be the [OII]3727˚ A line which yields a redshift of 0.9057±0.0005. The four flux-calibrated
source spectra are shown in Fig. 6. Knot A2 was observed under seeing conditions that were
a factor of two worse than for the other three knots (see Table 1).
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3.4. Velocity dispersion and cluster mass measurement
We used the 30 cluster galaxies to estimate the redshift and velocity dispersion of the
cluster using the biweight estimators of Beers et al. (1990). We first use the biweight location
estimator to determine the best estimate for cz. This yields a value of cz = 115151.1 ±
241.1 km s−1which translates to a redshift of zc = 0.3838 ± 0.0008. We then use this
estimate of the cluster redshift to determine the peculiar velocity vpfor each cluster member
relative to the cluster center of mass using
vp=(cz − czc)
(1 + zc)
(1)
We determine the biweight estimate of scale for vpwhich is equal to the velocity dispersion
of the cluster. We find a value for the velocity dispersion of σc = 855+108
uncertainties are obtained by doing a jackknife resampling. The redshift distribution is
shown in Fig. 7. The overlaid Gaussian has a mean of zcand a width of σc× (1 + zc). The
lines represent the individual peculiar velocities vpof the cluster members.
−96 km s−1. The
We can use the estimated velocity dispersion to derive an estimate for the cluster mass.
We use the results of Evrard et al. (2008) (see also Becker et al. 2007) which relates M200to
the dark matter velocity dispersion
M200= 1015M⊙
1
h(z)
?σDM
σ15
?1/α
,(2)
where h(z) = H(z)/100 km s−1Mpc−1is the dimensionless Hubble parameter. The values
of the parameters were found to be σ15 = 1082.9 ± 4 km s−1and α = 0.3361 ± 0.0026
(Evrard et al. 2008). Using the standard definition of velocity bias bv = σgal/σDM, where
σgalis the galaxy cluster velocity dispersion, we can rewrite Equation 2 as
b1/α
v
M200= 1015M⊙
1
h(z)
?σgal
σ15
?1/α
, (3)
where the quantity b1/α
stituting in the measured values for σgalwe obtain b1/α
v M200parameterizes our lack of knowledge about velocity bias. Sub-
v M200= 5.79+2.22
−1.99× 1014M⊙.
Bayliss et al. (2010, and references therein) discuss an “orientation bias” effect which
causes an upward bias in the measured velocity dispersions of lensing-selected clusters, due
to the higher likelihood of the alignment along the line of sight of the major axes of the
cluster halos, which are in general triaxial. Bayliss et al. (2010) estimate that on average
this will result in the dynamical mass estimate being biased high by 19-20%, using the same
relation between M200and velocity dispersion as we have used (Eqn. 2 above; Evrard et al.
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2008). Correcting for this orientation bias effect would result in b1/α
which is not a significant difference, as the change is well under 1σ. We therefore do not
apply this correction, but we do note that it would improve the already good agreement with
our other mass estimates in §3.2 and §6.1 (assuming no velocity bias, bv= 1.)
v M200= 4.8 × 1014M⊙,
4.Strong Lensing Properties
We use the coadded r-band image shown in Fig. 8 to study the strong lensing features
of the system as it has the best seeing and hence shows the most detail. To remove the
contribution to the arc fluxes from nearby objects we used GALFIT (Peng et al. 2002) to
model the profiles of these objects (galaxies and stars) and then subtracted the model from
the image. This was done for all four bands griz. These subtracted images are used for all
determinations of arc fluxes and positions. A number of individual knots can be observed
in the system along with the more elongated features. For example it appears that knot A1
is actually composed of two individual bright regions which are resolved by the Sextractor
object extraction described below. Knot A2 also appears to have two components although
these are not resolved by the object extraction so we treat them as one in the modeling. Even
though the cluster is fairly massive we do not see evidence for additional arc-like features
outside of the central circular feature. In this case we expect the mass of the lens to be well
constrained by the image positions.
We use the criteria that to obtain multiple images the average surface mass density
within the tangential critical curve must equal the critical surface mass density Σcrit. The
tangentially oriented arcs occur at approximately the tangential critical curves and so the
radius of the circle θarctraced by the arcs provides a measurement of the Einstein radius
θEIN (Narayan & Bartelmann 1996). The mass MEIN enclosed with the Einstein radius is
therfore given by
MEIN= Σcritπ(DlθEIN)2
(4)
Substituting for Σcritgives
MEIN=
c2
4G
DlDs
Dls
θ2
EIN
(5)
where Dsis the angular diameter distance to the source, Dlthe angular diameter distance
to the lens, and Dlsthe angular diameter distance between the lens and the source. These
values are Ds= 1610 Mpc, Dl= 1081 Mpc and Dls= 825 Mpc.
To determine the Einstein radius we ran Sextractor (Bertin & Arnouts 1996) on the r-
band image. This identified eight distinct objects in the image. We used the coordinates of
those eight objects and fit them to a circle. The radius of the circle gives us a measure of the
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Einstein radius. The Einstein radius we measure is θEIN= 7.53 ± 0.25′′which translates to
39.5±1.3 kpc. This yields a mass estimate of (1.5±0.1)×1013M⊙and a corresponding velocity
dispersion (assuming an isothermal model for the mass distribution) of σ = 694±12 km s−1.
The magnification of the lens flenscan be roughly estimated under the assumption that
the 1/2-light radius of a source at redshift z ∼ 0.9 is about 0.46′′(derived from the mock
galaxy catalog described in Jouvel et al. (2009)). The ratio of the area subtended by the
ring to that subtended by the source is ∼ 0.6 × (4R/δr), where R is the ring radius and δr
is the 1/2-light radius of the source. The 0.6 factor accounts for the fraction of the ring that
actually contains images. This gives a magnification of flens= 39.
To obtain a more quantitative value for the magnification we have used the PixeLens3
program (Saha & Williams 2004) to model the lens. PixeLens is a parametric modeling
program that reconstructs a pixelated mass map of the lens. It uses as input the coordinates
of the extracted image positions and their parities along with the lens and source redshifts.
It samples the solution space using a Markov Chain Monte Carlo method and generates an
ensemble of mass models that reproduce the image positions. We used the Sextractor image
positions obtained above and assigned the parities according to the prescription given in
Read (2007). In Saha & Williams (2004) they note that if one uses pixels that are too large
then the mass distribution is poorly resolved and not enough steep mass models are allowed.
We have chosen a pixel size such that this should not be a problem.
It is well known (see for example Saha & Williams (2006)) that changing the slope of
the mass profile changes the overall magnification, in particular a steeper slope produces
a smaller magnification but does not change the image positions. Therefore the quoted
magnification should be taken as a representative example rather than a definitive answer.
The magnification quoted is the sum over the average values of the magnification for each
image position for 100 models. We obtain a value of flens= 141 ± 39 where the error is
the quadrature sum of the RMS spreads of the individual image magnifications. PixeLens
can also determine the enclosed mass within a given radius. For the 100 models we obtain
MEIN= (1.4 ± 0.02) × 1013M⊙which is within 1σ of the mass obtained from the circle fit
described above.
In order to combine the strong lensing mass with the mass estimate from the weak
lensing analysis (in §6.1 below) we will need to estimate the mass within θEINthat is due to
dark matter alone (MDM). To do this we will need to subtract estimates of the stellar mass
(MS) and the hot gas mass (MG) from the total mass MEIN. To determine MSwe use the
GALAXEV (Bruzual & Charlot 2003) evolutionary stellar population synthesis code to fit
3Version 2.17: http://www.qgd.uzh.ch/programs/pixelens/
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galaxy spectral energy distribution models to the griz magnitudes of the BCG within the
Einstein radius. The BCG photometric data are taken from the GALFIT modeling described
above, and we sum up the light of the PSF-deconvolved GALFIT model inside the Einstein
radius. The GALAXEV models considered are simple stellar population (SSP) models which
have an initial, instantaneous burst of star formation; such models provide good fits to early-
type galaxies, such as those in clusters. In particular we find a good fit to the BCG, using a
SSP model with solar metallicity, a Chabrier (2003) stellar initial mass function (IMF), and
an age 9.25 Gyr (this age provided the best χ2over the range we considered, from 1 Gyr
to 9.3 Gyr, the latter being the age of the universe for our cosmology at the cluster redshift
z = 0.38). The resulting stellar mass (more precisely the total stellar mass integrated over
the IMF) is MS= 1.7 × 1012M⊙.
To estimate the gas mass MG we have looked at estimates of hot gas fraction fgas
in cluster cores from X-ray observations. Typical fgas measurements are of order 10%
(Maughan et al. 2004; Pointecouteau et al. 2004) which give us an MG estimate of 1.5 ×
1012M⊙.
Finally we calculate the total M/L ratio within θEINfor the i-band. This yields a value
of (M/L)i= 33.7 ± 4.4 (M/L)⊙.
5.Weak Lensing Measurements
5.1. Adaptive Moments
We used the program Ellipto (Smith et al. 2001) to compute adaptive moments (Bernstein & Jarvis
2002; Hirata et al. 2004) of an object’s light distribution, i.e., moments optimized for signal-
to-noise via weighting by an elliptical Gaussian function self-consistently matched to the the
object’s size. Ellipto computes adaptive moments using an iterative method and runs off
of an existing object catalog produced by SExtractor for the given image. Ellipto is also a
forerunner of the the adaptive moments measurement code used in the SDSS photometric
processing pipeline Photo.
We ran Ellipto on our coadded BCS images and corresponding SExtractor catalogs,
doing so independently in each of the griz filters to obtain four separate catalogs of adaptive
second moments:
Qxx =
?
?
x2w(x,y)I(x,y) dxdy
??
??
w(x,y)I(x,y) dxdy(6)
Qyy
=y2w(x,y)I(x,y) dxdyw(x,y)I(x,y) dxdy(7)
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Qxy
=
?
xy w(x,y)I(x,y) dxdy
??
w(x,y)I(x,y) dxdy ,(8)
where I(x,y) denotes the measured counts of an object at position x,y on the CCD image,
and w(x,y) is the elliptical Gaussian weighting function determined by Ellipto. The images
are oriented with the usual convention that North is up and East is to the left, i.e., right
ascension increases along the −x direction and declination increases along the +y direction.
We then computed the ellipticity components e1 and e2 of each object using one of the
standard definitions
e1 = (Qxx− Qyy)/(Qxx+ Qyy)(9)
e2 = 2Qxy/(Qxx+ Qyy) . (10)
5.2.PSF Modeling
For each filter, we then identified a set of bright but unsaturated stars to use for PSF
fitting. We chose the stars from the stellar locus on a plot of the size measure Qxx+ Qyy
from Ellipto vs. the magnitude MAG AUTO from SExtractor, using simple cuts on size and
magnitude to define the set of PSF stars. We then derived fits of the ellipticities e1,e2and
the size Qxx+Qyyof the stars vs. CCD x and y position, using polynomial functions of cubic
order in x and y (i.e., the highest order terms are x3,x2y,xy2, and y3). On each image, these
fits were done separately in each of 8 rectangular regions, defined by splitting the image area
into 2 parts along the x direction and into 4 parts along the y direction, corresponding to the
distribution of the 8 Mosaic-II CCDs over the image. This partitioning procedure was needed
in order to account for discontinuities in the PSF ellipticity and/or size as we cross CCD
boundaries in the Mosaic-II camera. Also note that the individual exposures comprising the
final coadded image in each filter were only slightly dithered, so that the CCD boundaries
were basically preserved in the coadd. To illustrate the PSF variation in our images, we
present in Figure 9 “whisker plots” that show the spatial variation of the magnitude and
orientation of the PSF ellipticity across our i- and r-band images . In addition, we also show
the residuals in the PSF whiskers remaining after our fitting procedure, showing that the
fits have done a good job of modeling the spatial variations of the PSF in our data.
We next used our PSF model to correct our galaxy sizes and ellipticities for the effects
of PSF convolution. Specifically, for the size measure Qxx+Qyywe used the simple relation
(cf. Hirata & Seljak 2003)
Qxx,true+ Qyy,true= (Qxx,observed+ Qyy,observed) − (Qxx,PSF+ Qyy,PSF)(11)
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to estimate the true size Qxx,true+ Qyy,trueof a galaxy from its observed size Qxx,observed+
Qyy,observed, where Qxx,PSF+ Qyy,PSF is obtained from the PSF model evaluated at the x,y
position of the galaxy. For the ellipticities we similarly used the related expressions
ei,true =
ei,observed
R2
+
?
1 −
1
R2
?
ei,PSF, i = 1,2(12)
R2 ≡ 1 −
Qxx,PSF+ Qyy,PSF
Qxx,observed+ Qyy,observed
(13)
The relations used in this simple correction procedure strictly hold only for unweighted
second moments, or for adaptive moments in the special case when both the galaxy and the
PSF are Gaussians. We have therefore also checked the results using the more sophisticated
“linear PSF correction” procedure of Hirata & Seljak (2003), which uses additional fourth
order adaptive moment measurements (also provided here by Ellipto) in the PSF correction
procedure. In particular, the linear PSF correction method is typically applied in weak
lensing analyses of SDSS data. However, we found nearly indistinguishable tangential shear
profiles from applying the two PSF correction methods, and we therefore adopted the simpler
correction method for our final results.
5.3.Shear Profiles and Mass Measurements
Given the estimates of the true galaxy ellipticities from Equation (12), we then computed
the tangential (eT) and B-mode or cross (e×) ellipticity components, in a local reference frame
defined for each galaxy relative to the BCG:
eT
= e1cos(2φ) − e2sin(2φ)(14)
e× = e1sin(2φ) + e2cos(2φ)(15)
where φ is the position angle (defined West of North) of a vector connecting the BCG to the
galaxy in question. Here we have dropped the subscript true for brevity. The ellipticities
were then converted to shears γ using γ = e/R, where R is the responsivity, for which we
adopted the value R = 2(1 − σ2
noise as done in previous SDSS cluster weak lensing analyses (e.g., Kubo et al. 2007, 2009).
SN) = 1.73, using σSN = 0.37 as the intrinsic galaxy shape
We then fit our galaxy shear measurements to an NFW profile by minimizing the fol-
lowing expression for χ2:
χ2=
N
?
i=1
[γi− γNFW(ri;M200,c200)]2
σ2
γ
(16)
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where the index i refers to each of the N galaxies in a given sample, riis a galaxy’s pro-
jected physical radius from the BCG (at the redshift of the cluster), σγ is the measured
standard deviation of the galaxy shears, and γNFW is the shear given by Equations (14-16)
of Wright & Brainerd (2000) for an NFW profile with mass M200and concentration c200. We
used a standard Levenberg-Marquardt nonlinear least-squares routine to minimize χ2and
obtain best-fitting values and errors for the parameters M200and c200of the NFW profile.
Similar fits of the weak lensing radial shear profile to a parameterized NFW model have of-
ten been used to constrain the mass distributions of galaxy clusters (e.g., King & Schneider
2001; Clowe & Schneider 2001; Kubo et al. 2009; Oguri et al. 2009; Okabe et al. 2010). Note
that we chose the above expression for χ2since it does not require us to do any binning in
radius, but for presentation purposes below we will have to show binned radial shear profiles
compared to the NFW shear profiles obtained from our binning-independent fitting method.
For the shear fitting analysis, we defined galaxy samples separately in each of the four
griz filters using cuts on the magnitude MAG AUTO and on the size Qxx,observed+ Qyy,observed,
as detailed in Table 5. The bright magnitude cut was chosen to exclude brighter galaxies
which would tend to lie in the foreground of the cluster and hence not be lensed, while the
faint magnitude cuts were set to the photometric completeness limit in each filter, as defined
by the turnover magnitude in the histogram of SExtractor MAG AUTO values. For the size
cut, we set it so that only galaxies larger than about 1.5 times the PSF size would be used,
as has been typically done in SDSS cluster weak lensing analyses (e.g., Kubo et al. 2007,
2009). Note that in order to properly normalize the NFW shear profile to the measure-
ments, we also need to calculate the critical surface mass density Σcrit, which depends on
the redshifts of the lensed source galaxies as well as the redshift of the lensing cluster; see
Equations (9,14) of Wright & Brainerd (2000). To do this, we did not use any individual
redshift estimates for the source galaxies in our analysis, but instead we calculated an ef-
fective value of 1/Σcritvia an integral over the source galaxy redshift distribution published
for the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS; Ilbert et al. 2006), as
appropriate to the magnitude cuts we applied in each of the griz filters.
Our NFW fitting results are shown in Figures 10-11 and detailed in Table 5. We show
results for both the tangential and B-mode shear components. As lensing does not produce
an B-mode shear signal, these results provide a check on systematic errors and should be
consistent with zero in the absence of significant systematics. For all of our filters, our
B-mode shear results are indeed consistent with no detected mass, as the best-fit M200is
within about 1σ of zero. On the other hand, for the tangential shear results in the r, i,
and z filters, we do indeed obtain detections of non-zero M200at the better than 1.5σ level.
In the g filter we do not detect a non-zero M200. Comparing the weak lensing results from
the different filters serves as a useful check of the robustness of our lensing-based cluster
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mass measurement, in particular as the images in the different filters are subject to quite
different PSF patterns, as shown earlier in Fig. 9. Though the mass errors are large, the M200
values from the r-, i-, and z-band weak lensing NFW fits are nonetheless consistent with
each other and with the masses derived earlier from the velocity dispersion and maxBCG
richness analyses. Moreover, independent of the NFW fits, we have also derived probabilities
(of exceeding the observed χ2) that our binned shear profiles are consistent with the null
hypothesis of zero shear. As shown in Table 5, we see that the B-mode profiles are in all
cases consistent with zero, as expected, but that the tangential profiles for the r and i filters
are not consistent with the null hypothesis at about the 2σ level (probabilities ≈ 0.06), thus
providing model-independent evidence for a weak lensing detection of the cluster mass.
5.4.Combining Weak Lensing Constraints from Different Filters
Here we will combine the weak lensing shear profile information from the different
filters griz in order to improve the constraints on the NFW parameters, in particular on
M200. The main complication here is that although the ellipticity measurement errors are
independent among the different filters, the most important error for the shear measurement
is the intrinsic galaxy shape noise, which is correlated among filters because a subset of the
galaxies is common to two or more filters, and for these galaxies we expect their shapes to
be fairly similar in the different filters. In particular we find that the covariance of the true
galaxy ellipticities between filters is large, for example, the covariance of e1between the i
and r filters, Cov(e1,i,e1,r) =
N
?(e1,i− ¯ e1,i)(e1,r− ¯ e1,r), is about 0.9 times the variance of
e1in the i and r filters individually. The same holds true for e2and for the other filters as
well. We will not attempt to use a full covariance matrix approach to deal with the galaxy
shape correlations when we combine the data from two or more filters. Instead, we take
a simpler approach of scaling the measured standard deviation of the shear (the σγ used
to calculate χ2in Equation 16) by
?N/Nunique, where N is the total number of galaxies
in a given multi-filter sample, and Nunique is the number of unique galaxies in the same
sample. This is equivalent to rescaling χ2in the NFW fit to correspond to Nuniquedegrees of
freedom instead of N. We have verified using least-squares fits to Monte Carlo simulations of
NFW shear profiles that this simple approach gives the correct fit uncertainties on M200and
c200when the mock galaxy data contain duplicate galaxies, with identical e1and e2values,
simulating the case of completely correlated intrinsic galaxy shapes among filters. Note that
our approach is conservative and will slightly overestimate the errors, because the galaxy
shapes in the real data are about 90% correlated, not fully correlated, among filters.
1
Before fitting the combined shear data from multiple filters, we make one additional
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