SPT-CL J0546-5345: A MASSIVE z >1 GALAXY CLUSTER SELECTED VIA THE SUNYAEV-ZEL’DOVICH EFFECT WITH THE SOUTH POLE TELESCOPE

Abstract

We report the spectroscopic confirmation of SPT-CL J0546-5345 at 〈z〉 = 1.067. To date this is the most distant cluster to be spectroscopically confirmed from the 2008 South Pole Telescope (SPT) catalog, and indeed the first z>1 cluster discovered by the Sunyaev–Zel'dovich Effect (SZE). We identify 21 secure spectroscopic members within 0.9 Mpc of the SPT cluster position, 18 of which are quiescent, early-type galaxies. From these quiescent galaxies we obtain a velocity dispersion of 1179[superscript +232 subscript −167] km s[superscript −1], ranking SPT-CL J0546-5345 as the most dynamically massive cluster yet discovered at z>1. Assuming that SPT-CL J0546-5345 is virialized, this implies a dynamical mass of M[subscript 200] = 1.0[superscript +0.6 subscript −0.4] × 10[superscript 15] M[subscript ☉], in agreement with the X-ray and SZE mass measurements. Combining masses from several independent measures leads to a best-estimate mass of M[subscript 200] = (7.95 ± 0.92) × 10[superscript 14] M[subscript ☉]. The spectroscopic confirmation of SPT-CL J0546-5345, discovered in the wide-angle, mass-selected SPT cluster survey, marks the onset of the high-redshift SZE-selected galaxy cluster era.

Full text

The Astrophysical Journal, 721:90–97, 2010 September 20 doi:10.1088/0004-637X/721/1/90
C
2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
SPT-CL J0546-5345: A MASSIVE z>1 GALAXY CLUSTER SELECTED VIA THE SUNYAEV–ZEL’DOVICH
EFFECT WITH THE SOUTH POLE TELESCOPE
M. Brodwin1,25,26 , J. Ruel2,P.A.R.Ade
3,K.A.Aird
4, K. Andersson5,M.L.N.Ashby
1, M. Bautz5, G. Bazin6,7,
B. A. Benson8,9, L. E. Bleem8,10, J. E. Carlstrom8,9,10 ,11, C. L. Chang8,9, T. M. Crawford8,11 ,A.T.Crites
8,11,T.deHaan
12,
S. Desai13, M. A. Dobbs12 , J. P. Dudley12, G. G. Fazio1, R. J. Foley1,27 , W. R. Forman1, G. Garmire14, E. M. George15 ,
M. D. Gladders8,11, A. H. Gonzalez16 , N. W. Halverson17,F.W.High
2, G. P. Holder12, W. L. Holzapfel15 ,J.D.Hrubes
4,
C. Jones1,M.Joy
18, R. Keisler8,10 ,L.Knox
19,A.T.Lee
15,20 , E. M. Leitch8,11, M. Lueker15 , D. P. Marrone4,8,
J. J. McMahon8,9,21,J.Mehl
8,11, S. S. Meyer8,9,10,11 ,J.J.Mohr
6,7,22,26 , T. E. Montroy23, S. S. Murray1, S. Padin8,11 ,
T. Plagge11,15 , C. Pryke8,9,11, C. L. Reichardt15 ,A.Rest
2, J. E. Ruhl23, K. K. Schaffer8,9,L.Shaw
12,24 , E. Shirokoff15,
J. Song13, H. G. Spieler20 , B. Stalder1, S. A. Stanford19, Z. Staniszewski23 , A. A. Stark1, C. W. Stubbs1,2,
K. Vanderlinde12,J.D.Vieira
8,10, A. Vikhlinin1, R. Williamson8,11 ,Y.Yang
13,O.Zahn
15, and A. Zenteno6,7
1Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
2Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
3Department of Physics and Astronomy, Cardiff University, CF24 3YB, UK
4University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
5Kavli Institute for Astrophysics and Space Research, MIT, Cambridge, MA 02139, USA
6Department of Physics, Ludwig-Maximilians-Universit¨
at, Scheinerstr. 1, 81679 M¨
unchen, Germany
7Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching, Germany
8Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
9Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
10 Department of Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
11 Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
12 Department of Physics, McGill University, 3600 Rue University, Montreal, Quebec H3A 2T8, Canada
13 Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801, USA
14 Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA
15 Department of Physics, University of California, Berkeley, CA 94720, USA
16 Department of Astronomy, University of Florida, Gainesville, FL 32611, USA
17 Department of Astrophysical and Planetary Sciences and Department of Physics, University of Colorado, Boulder, CO 80309, USA
18 Department of Space Science, VP62, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
19 Department of Physics, University of California, One Shields Avenue, Davis, CA 95616, USA
20 Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
21 Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, MI, 48109, USA
22 Max-Planck-Institut f¨
ur extraterrestrische Physik, Giessenbachstr. 85748 Garching, Germany
23 Physics Department and CERCA, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106, USA
24 Department of Physics, Yale University, P.O. Box 208210, New Haven, CT 06520-8120, USA
Received 2010 July 12; accepted 2010 July 24; published 2010 August 26
ABSTRACT
We report the spectroscopic confirmation of SPT-CL J0546-5345 at z=1.067. To date this is the most distant
cluster to be spectroscopically confirmed from the 2008 South Pole Telescope (SPT) catalog, and indeed the first
z>1 cluster discovered by the Sunyaev–Zel’dovich Effect (SZE). We identify 21 secure spectroscopic members
within 0.9 Mpc of the SPT cluster position, 18 of which are quiescent, early-type galaxies. From these quiescent
galaxies we obtain a velocity dispersion of 1179 +232
−167 km s−1, ranking SPT-CL J0546-5345 as the most dynamically
massive cluster yet discovered at z>1. Assuming that SPT-CL J0546-5345 is virialized, this implies a dynamical
mass of M200 =1.0+0.6
−0.4×1015 M, in agreement with the X-ray and SZE mass measurements. Combining masses
from several independent measures leads to a best-estimate mass of M200 =(7.95 ±0.92) ×1014 M. The spec-
troscopic confirmation of SPT-CL J0546-5345, discovered in the wide-angle, mass-selected SPT cluster survey,
marks the onset of the high-redshift SZE-selected galaxy cluster era.
Key words: galaxies: clusters: individual (SPT-CL J0546-5345) – galaxies: distances and redshifts – galaxies:
evolution
Online-only material: color figure
1. INTRODUCTION
Formed from the extreme peaks of the primordial density
field, galaxy clusters are both a sensitive probe of cosmology
25 W. M. Keck Postdoctoral Fellow at the Harvard-Smithsonian Center for
Astrophysics
26 Visiting astronomer, Cerro Tololo Inter-American Observatory, National
Optical Astronomy Observatory, under contract with the National Science
Foundation
27 Clay Fellow
and an excellent laboratory for galaxy evolution studies. Al-
though massive galaxy clusters are easy to identify in the local
universe, finding such objects at large lookback times has been
extremely challenging. A patchwork of optical, infrared, and
X-ray techniques has led to a heterogeneous sample of distant
galaxy clusters (e.g., Stanford et al. 1997; Rosati et al. 2004;
Gladders & Yee 2005; Mullis et al. 2005; Brodwin et al. 2006;
Elston et al. 2006; Stanford et al. 2006; Eisenhardt et al. 2008;
Muzzin et al. 2009; Papovich et al. 2010). While each technique
90

No. 1, 2010 SPT-CL J0546-5345: MASSIVE z>1 GALAXY CLUSTER SELECTED VIA THE SZE 91
offers unique advantages, namely, observational efficiency
(optical), redshift reach and mass sensitivity (IR), and a direct
mass observable (X-ray), none produce purely mass-selected,
nearly redshift independent cluster samples.
A long-awaited advance is the arrival of Sunyaev–Zel’dovich
Effect (SZE) cluster surveys. The SZE is a small distortion
in the cosmic microwave background (CMB) spectrum caused
by the inverse Compton scattering of CMB photons with the
hot intracluster medium (ICM; Sunyaev & Zel’dovich 1972).
The surface brightness of the SZE does not depend on a
cluster’s distance, which makes it a nearly redshift-independent
method for finding massive galaxy clusters (e.g., Carlstrom et al.
2002). A new generation of dedicated millimeter-wave (mm-
wave) experiments to search for galaxy clusters are currently
surveying large areas of sky, including the Atacama Cosmology
Telescope (Fowler et al. 2007) and the South Pole Telescope
(SPT; Carlstrom et al. 2009).
Taking advantage of the excellent conditions for mm-wave
observations at the South Pole, the 10 m SPT (Carlstrom
et al. 2009) is midway through a 2000 deg2survey sensitive
to galaxy clusters above ≈5×1014 Mat all redshifts. The
first three clusters discovered by the SZE were reported by
Staniszewski et al. (2009, hereafter S09). The complete 5σ
cluster catalog from the 2008 SPT season, a study of the optical
properties of these clusters, and a description of the survey
strategy and goals are given in Vanderlinde et al. (2010, hereafter
V10) and High et al. (2010, hereafter H10).
Here we report the spectroscopic confirmation, velocity
dispersion, and dynamical mass of the first z>1 SZE-
selected cluster, SPT-CL J0546-5345, at z=1.067. In
converting from r500 to r200 and M500 to M200 throughout,
we assume a Navarro–Frenk–White (NFW) density profile and
the mass-concentration relation of Duffy et al. (2008). Unless
otherwise indicated, we use Vega magnitudes and adopt a
WMAP5 cosmology (Dunkley et al. 2009), with ΩM=0.264,
ΩΛ=0.736, σ8=0.80,and H0=71 km s−1Mpc−1.
2. OBSERVATIONS
2.1. SPT-SZE
In 2008, the SPT survey observed a 196 deg2area (178 deg2
after point-source and non-uniform coverage masking) for
∼1500 hr (V10), reaching a 5σpoint source sensitivity of
∼7 mJy at 150 GHz (2.0 mm). Details of the data processing,
map-making, cluster extraction, and significance estimates are
given in S09 and V10. SPT-CL J0546-5345, first reported in
S09, has an SZE decrement of S/N=7.69 at 150 GHz. It is
among the most significant of the 2008 cluster candidates with
az1 optical red sequence (H10). SZE significance contours
at 150 GHz are shown in Figure 1(left).
2.2. Spitzer/IRAC and Optical Imaging
Mid-infrared Spitzer/Infrared Array Camera (IRAC) imaging
was obtained in 2009 September as part of a larger program to
follow up clusters identified in the SPT survey (PID 60099; PI
Brodwin). The on-target observations consisted of 8×100 s and
6×30 s dithered exposures at 3.6 and 4.5μm, respectively. The
deep 3.6 μm observations are sensitive to passively evolving
cluster galaxies down to 0.1 L∗at z=1.5. The data were
reduced following the method of Ashby et al. (2009). Briefly, we
correct for column pulldown, mosaic the individual exposures,
resample to 0.
86 pixels (half the solid angle of the native IRAC
pixels), and reject cosmic rays.
Optical data were provided by the Blanco Cosmology Survey
(BCS), an NOAO survey program with deep griz imaging over
100 deg2in a subset of the SPT 05 hr and 23 hr fields (Ngeow
et al. 2009). The Stellar Locus Regression method of High et al.
(2009) was used for photometric calibration, extinction correc-
tion, and Galactic de-reddening. The independent calibration
from the DES data management system (Mohr et al. 2008)gave
consistent results. The BCS data typically reach 5σAB depths
of 24.75, 24.65, 24.35, and 23.5 in griz. See S09 and H10 for a
more detailed description of the optical data.
Along with the rand iBCS photometry, the IRAC 3.6 μm
data were used to select promising cluster member candidates
for spectroscopy as described below. A false-color optical
(ri) + IRAC (3.6μm) image is shown in Figure 1(right). The
optical-only (grz) image (Figure 1, left) indicates how optically
(rest-frame UV) faint the cluster members are, and highlights the
importance of Spitzer/IRAC imaging for high-redshift cluster
detection and study.
2.3. Chandra
SPT-CL J0546-5345 was observed with Chandra/ACIS-I on
four separate occasions, for a total exposure time of 55.6 ks
(PID 09800046; PI Garmire, PID 11800471; PI Mohr). This
yielded 1304 source counts in the 0.5–7.0 keV energy range
within 0.5r500. Background was subtracted using blank sky
data normalized to the flux in the 9.5–12 keV energy band. The
cluster luminosity is LX(0.5–2 keV) =(6.4±0.4)×1044 erg s−1,
and the temperature, estimated in the (0.15–1) r500 annulus,
is TX=7.5+1.7
−1.1keV. The gas mass was estimated to be
Mg,500 =7.3+0.4
−0.3×1013 Mfrom the X-ray surface brightness
in the 0.5–2.0 keV band following the analysis method described
in Vikhlinin et al. (2006), where the gas density is assumed to
follow a modified β-model (Cavaliere & Fusco-Femiano 1978)
that is allowed to steepen at large radii and to have a power-
law cusp at the cluster center. The Chandra X-ray contours are
overlaid in Figure 1(right). The reader is referred to Andersson
et al. (2010, hereafter A10) for a full description of the X-
ray analysis of SPT-CL J0546-5345, as well as a study of the
X-ray properties of 15 of the SZE-selected clusters from the
V10 sample.
2.4. Optical Spectroscopy
Multislit spectroscopic observations were acquired on the
6.5 meter Magellan Baade telescope on UT 2010 February
11. We used the Gladders Image-Slicing Multi-Slit Option
(GISMO28; M. D. Gladders et al. 2010, in preparation) module
on the Inamori Magellan Areal Camera and Spectrograph
(IMACS; Dressler et al. 2006). GISMO optically remaps the
central region of the IMACS field of view (roughly 3.
5×3.
2)
to 16 evenly spaced regions of the focal plane, allowing for a
large density of slitlets in the cluster core while minimizing trace
overlaps on the CCD. We used the f/2 camera for its greater red
sensitivity, the 300 l/mm “red” grism, and the WB6300-9500
filter. The seeing was excellent (0.
5) throughout the six 30
minute exposures.
In designing the multislit mask, galaxies were assigned
a weight proportional to their i-band brightness and their
proximity to the cluster center, and inversely proportional to
their distance in color space, in both r−iand i−[3.6], from
the predicted color from a Bruzual & Charlot (2003, hereafter
28 http://www.lco.cl/telescopes-information/magellan/instruments/
imacs/gismo

92 BRODWIN ET AL. Vol. 721
Figure 1. Left: optical 4×4color image (grz) of SPT-CL J0546-5345, with SZE significance contours overlaid (S/N=2, 4, and 6). Right: false color optical
(ri) + IRAC (3.6μm) image of SPT-CL J0546-5345, with Chandra X-ray contours overlaid (0.25, 0.4, 0.85, and 1.6 counts per 2 ×2 pixel per 55.6 ks in the
0.5–2 keV band). North is up, east is to the left. Due to its high angular resolution, Chandra is able to resolve substructure to the SW, which may be evidence of a
possible merger. These images highlight the importance of IRAC imaging in studying the galaxies in high-redshift, optically faint clusters. Spectroscopic early-type
(late-type) members are indicated with yellow (cyan) circles. Green squares show the spectroscopic non-members.
BC03) passively evolving 100 Myr burst model with formation
redshift zf=3.
The COSMOS reduction package29 was used for stan-
dard CCD processing, resulting in wavelength-calibrated two-
dimensional spectra. The one-dimensional spectra were then
extracted from the sum of the reduced data. We flux calibrated
the data and removed telluric absorption using the continuum
of a spectrophotometric standard (Foley et al. 2003).
3. RESULTS
3.1. Redshifts
Redshifts for galaxy spectra exhibiting significant absorption
features were found through cross-correlation using the RVSAO
package in IRAF30 (Kurtz & Mink 1998). The validity of the
cross-correlation redshift was checked by visual inspection and
judged by the presence of visible absorption lines; most of these
displayed clear Ca HK lines. For three members the redshift
was determined from a strong, unresolved [O ii] emission line.
Redshift uncertainties were estimated as twice those given by
RVSAO (Quintana et al. 2000). An independent extraction and
visual redshift determination yielded identical redshifts for all
cluster members within the errors.
From these Magellan observations we obtained 28 secure
redshifts, of which 21 are spectroscopic cluster members within
r<0.9 Mpc of the SPT cluster position. This high success rate
validates our spectroscopic selection algorithm. Representative
spectra are shown in Figure 2. The majority of the members (18)
are quiescent, with redshifts determined from Ca HK absorption,
as expected given their red-sequence selection, central location,
and the extreme mass of the cluster.
3.2. Velocity Dispersion
An iterative 3σclipping algorithm was used to identify cluster
members. We list the 21 secure cluster members in Table 1, and
29 http://obs.carnegiescience.edu/Code/cosmos/
30 IRAF is distributed by the National Optical Astronomy Observatory, which
is operated by the Association of Universities for Research in Astronomy, Inc.,
under cooperative agreement with the National Science Foundation.
Figure 2. Representative spectra of cluster member galaxies for SPT-CL J0546-
5345. Vertical dotted lines indicate [O ii] and Ca HK features. Most (18/21)
confirmed members are passive, early-type galaxies.
plot the redshift histogram in Figure 3(left). In this figure the 18
passive members, for which the redshift was obtained from Ca
HK absorption lines, are shaded red. Redshifts of the remaining
three members, shaded blue, were secured from strong [O ii]
emission. Spectroscopic non-members are unshaded. From the
spectroscopic redshift histogram, SPT-CL J0546-5345 appears
to be a single massive halo, with no evidence of substructure
or merger activity. We note, however, that the X-ray image
(Figure 1) shows a substructure extending to the SW indicating
that a minor merger may be taking place (A10).
We use the robust biweight estimator of Beers et al. (1990)
to estimate the mean velocity and velocity dispersion, applying
the relativistic correction and the usual correction for velocity

No. 1, 2010 SPT-CL J0546-5345: MASSIVE z>1 GALAXY CLUSTER SELECTED VIA THE SZE 93
16 17 18 19
[3.6]
3
4
5
6
7
i - [3.6]
1.02 1.04 1.06 1.08 1.10 1.12
Redshift
0
2
4
6
8
Number
0.4 0.6 0.8 1.0 1.2
Redshift
0
2
4
6
8
10
12
Number
Figure 3. Left: histogram of spectroscopic redshifts obtained for SPT-CL J0546-5345, showing a very broad peak consisting of 21 members (shaded regions) centered
at z=1.0665 (dotted line). The passive galaxies used in the dynamical analysis are shaded red. Galaxies for which redshifts were determined from [O ii] emission
are shaded blue. Spectroscopic non-members are unshaded. The inset shows all the secure redshifts obtained toward this cluster. Right: color–magnitude diagram in
i−[3.6] within a 2.
5 radius around SPT-CL J0546-5345. The red (blue) squares are the spectroscopically confirmed passive ([O ii]) members. The passive members
form a rich red sequence. Spectroscopic non-members are marked with X symbols. The 5σcolor–magnitude limit is indicated by the dashed line. One member is
omitted due to low-S/N photometry. The red line is the rest-frame Coma CMR, in the approximately (U−H) color probed by our filters, normalized to match a BC03
passively evolving L∗galaxy.
(A color version of this figure is available in the online journal.)
Tab l e 1
Spectroscopic Members of SPT-CL J0546-5345
ID R.A. Decl. zδz
aPrincipal
(J2000) (J2000) Spectral Feature
J054637.2-534525 05:46:37.23 −53:45:25.6 1.0647 0.0002 Ca HK/D4000
J054636.2-534413 05:46:36.22 −53:44:13.4 1.0656 0.0004 Ca HK/D4000
J054642.3-534554 05:46:42.36 −53:45:54.5 1.0548 0.0003 Ca HK/D4000
J054633.6-534540 05:46:33.67 −53:45:40.5 1.0775 0.0005 Ca HK/D4000
J054635.1-534502 05:46:35.14 −53:45:02.0 1.0676 0.0003 Ca HK/D4000
J054638.9-534356 05:46:38.90 −53:43:56.2 1.0743 0.0003 Ca HK/D4000
J054634.8-534555 05:46:34.81 −53:45:55.6 1.0567 0.0002 Ca HK/D4000
J054635.8-534542 05:46:35.82 −53:45:42.0 1.0710 0.0003 Ca HK/D4000
J054638.6-534513 05:46:38.68 −53:45:13.7 1.0692 0.0003 Ca HK/D4000
J054644.3-534538 05:46:44.36 −53:45:38.4 1.0619 0.0002 Ca HK/D4000
J054645.0-534625 05:46:45.04 −53:46:25.9 1.0662 0.0003 Ca HK/D4000
J054641.8-534613 05:46:41.84 −53:46:13.5 1.0712 0.0004 Ca HK/D4000
J054630.3-534425 05:46:30.37 −53:44:25.3 1.0502 0.0005 Ca HK/D4000
J054638.8-534620 05:46:38.80 −53:46:20.2 1.0681 0.0004 Ca HK/D4000
J054633.8-534409 05:46:33.86 −53:44:09.3 1.0586 0.0005 Ca HK/D4000
J054646.8-534610 05:46:46.89 −53:46:10.9 1.0625 0.0005 Ca HK/D4000
J054634.9-534437 05:46:34.92 −53:44:37.5 1.0705 0.0005 Ca HK/D4000
J054636.4-534619 05:46:36.43 −53:46:19.5 1.0805 0.0007 Ca HK/D4000
J054644.4-534502 05:46:44.42 −53:45:02.7 1.0661 0.0025 [O ii]
J054646.8-534557 05:46:46.87 −53:45:57.6 1.0686 0.0002 [O ii]
J054642.0-534543 05:46:42.08 −53:45:43.9 1.0524 0.0002 [O ii]
Note. aRedshift errors are twice those given by RVSAO.
errors (Danese et al. 1980). For the full membership, we find
a mean redshift and velocity dispersion of z=1.0661 +0.0018
−0.0022
and σ=1181 +215
−186 km s−1, respectively. The errors in both
quantities, obtained from bootstrap resampling, represent the
68% confidence interval.
Since late-type members are often infalling, they tend to
yield broader dispersions than early types (e.g., Girardi et al.
1996; Fadda et al. 1996; Mohr et al. 1996; Koranyi & Geller
2000). We therefore explore limiting our analysis to the 18
early-type members, as these are expected to better reflect the
cluster potential. This approach yields nearly identical results,
with a mean redshift of z=1.0665 +0.0019
−0.0021 and a dispersion
of σ=1179 +232
−167 km s−1. Although the biweight estimator is
optimal, we also compute dispersions for these 18 members
using both the gapper method (Beers et al. 1990) and the
simple standard deviation. These yield σgap =1170 +240
−128 km s−1
and σSD =1138 +205
−132 km s−1, respectively, both in excellent
agreement with the biweight dispersion. There is no evidence
of merger activity in SPT-CL J0546-5345 from the line-of-
sight velocities, in either the appearance of Figure 3or in
the dispersion measures, although our redshift sampling is too
sparse to rule it out.

94 BRODWIN ET AL. Vol. 721
Tab l e 2
Comparison of Mass Measurements for SPT-CL J0546-5345
Mass Type Proxy Measurement Units Mass Scaling M200a,b
Relation (1014 M)
Dispersion Biweight 1179 +232
−167 km s−1σ–M200(Evrard et al. 2008)10.4+6.1
−4.4
Gapper 1170 +240
−128 km s−1σ–M200 (Evrard et al. 2008)10.1+6.2
−3.3
Std deviation 1138 +205
−132 km s−1σ–M200 (Evrard et al. 2008)9.3+5.0
−3.2
X-ray YX5.3±1.0×1014 MkeV YX–M500 (Vikhlinin et al. 2009)8.23 ±1.21
TX7.5+1.7
−1.1keV TX–M500 (Vikhlinin et al. 2009)8.11 ±1.89
SZE YSZ 3.5±0.6×1014 MkeV YSZ–M500 (A10) 7.19 ±1.51
S/N at 150 GHz 7.69 ξ–M500 (V10) 5.03 ±1.13 ±0.77
Richness N200 80 ±31 Galaxies N200–M200 (H10) 8.5±5.7±2.5
Ngal 66 ±7 Galaxies Ngal–M200 (H10) 9.2±4.9±2.7
Best Combined 7.95 ±0.92
Notes.
aM500 masses were scaled to M200 masses assuming an NFW density profile and the mass-concentration relation of Duffy et al.
(2008).
bWe do not correct the dynamical masses for the small potential bias in the dispersion discussed in Section 3.4.
3.3. Color–Magnitude Relation
We plot the i−[3.6] color–magnitude diagram for galax-
ies within a 2.
5 (1.22 Mpc) radius of SPT-CL J0546-5345 in
Figure 3(right). The spectroscopically confirmed passive galax-
ies define a rich red sequence, indicative of a cluster that is
already well evolved at z=1.067. The dashed line indicates
the 5σcolor–magnitude limit; one confirmed member is not
detected robustly enough in the optical for inclusion in this
plot. The solid red line indicates the slope of the rest-frame
color–magnitude relation (CMR) of Coma (Eisenhardt et al.
2007), normalized to L∗at 3.6 μm in the passively evolving
zf=3 BC03 model described above.
3.4. Dynamical Mass
There are several approaches in the literature for calculating
the dynamical mass. Perhaps the most widely adopted is
that of Carlberg et al. (1997), who use the simple definition
M200 =4/3πr
3
200 200 ρc, where r200 =√3σ/10 H(z) and
ρcis the critical density. Although this approach provides a
convenient basis for comparison with other studies, it relies on
the simplifying assumption that clusters are singular isothermal
spheres. We therefore prefer to use the simulation-based σ–M200
relation of Evrard et al. (2008),
M200 =1015
h(z)σDM
σDM,15 1/α
,(1)
where σDM,15 =1082.9kms
−1,α=0.3361, and σDM,the
dark matter velocity dispersion, is related to the observed galaxy
velocity dispersion by the velocity bias parameter, bv≡σ/σDM.
Simulations generally suggest that 0.9<b
v<1.1, and the
most recent numerical results (Evrard et al. 2008, and references
therein) indicate that galaxies are essentially unbiased tracers of
the dark matter potential (i.e., bv=1). Adopting this value,
we obtain M200 =1.04 +0.61
−0.44 ×1015 M. Dynamical masses
corresponding to the various velocity dispersion measures
reported in Section 3.2 are tabulated in Table 2. The Carlberg
et al. (1997) relation yields masses a factor of ≈1.5 larger.
Detailed studies of the velocity dispersion profile (e.g.,
Girardi et al. 1993; Fadda et al. 1996) indicate that dispersions
measured within radii less than r200 may be biased high. In A10,
r200 for SPT-CL J0546-5345 is estimated to be ≈1.57 Mpc,
and we are therefore probing an aperture of ≈0.57r200.
Numerical (Biviano et al. 2006) and observational (Rines &
Diaferio 2006; Katgert et al. 1996,1998) studies suggest that
for our early-type galaxy sample and the clustercentric radius
probed, the bias is expected to be small. For example, Biviano
et al. (2006) report the expected bias in the dispersion as a
function of the fractional virial radius probed; for our dispersion
measurement the expected upward bias is 2.5%. This implies
a corresponding bias in the dynamical mass of 7%, which
would lower the dynamical mass to ∼9.6×1014 M. While
this may well be a more accurate value, the bias correction is
both uncertain and small. We therefore defer a more extensive
analysis to a future paper, when a larger sample of spectroscopic
members out to r200 is available.
Finally, we note that no other z>1 cluster with 10
spectroscopically confirmed members has σ>1000 km s−1.
With a dispersion of σ=1179 km s−1, SPT-CL J0546-5345
is unambiguously the most dynamically massive cluster yet
identified at z>1.
4. DISCUSSION
4.1. σ–TXRelation
At TX=7.5+1.7
−1.1keV, SPT-CL J0546-5345 is among the
hottest clusters yet observed in the X-ray at z>1(Rosati
et al. 2009). Figure 4shows the well-known correlation between
X-ray temperature and galaxy velocity dispersion (Lubin &
Bahcall 1993; Bird et al. 1995; Girardi et al. 1996; Horner et al.
1999;Xue&Wu2000; Ortiz-Gil et al. 2004). The clusters shown
are the subset of the well-studied, low-redshift X-ray cluster
sample of Vikhlinin et al. (2009) for which accurate velocity
dispersion measurements, from at least 40 galaxies, are available
from Girardi et al. (1996). The temperatures are measured in an
identical manner to that of SPT-CL J0546-5345, which is plotted
as the large red circle. The dashed line is the best-fit relation
Girardietal.(1996) obtained using previous temperatures from
the literature, and the solid line is our own fit using the Vikhlinin
et al. (2009) temperatures. Both fits exclude SPT-CL J0546-
5345, and are consistent with typical measurements (e.g., Lubin
& Bahcall 1993; Horner et al. 1999). Although the comparison
clusters are all at low redshift (z<0.1), there is no expectation
of, nor evidence for, evolution in this relation to z∼1 (e.g.,
Wu et al. 1998;Tranetal.1999). The measured dispersion

No. 1, 2010 SPT-CL J0546-5345: MASSIVE z>1 GALAXY CLUSTER SELECTED VIA THE SZE 95
10
kT [keV]
1000
σ [km s-1]
Figure 4. Empirical σ–TXcorrelation for the X-ray clusters from Vikhlinin
et al. (2009), with velocity dispersions taken from Girardi et al. (1996).
The temperatures are measured exactly as for SPT-CL J0546-5345. The fits,
described in the text, are typical of those found by other authors (e.g., Lubin &
Bahcall 1993; Horner et al. 1999). SPT-CL J0546-5345 (red circle) falls right
on this relation.
and X-ray temperature for SPT-CL J0546-5345 fall right on the
σ–TXrelation, offering strong corroboration of the very large
dynamical mass presented here.
4.2. X-ray, SZE, and Optical Mass Measures
We now compare the dynamical mass with several other mass
measures available for SPT-CL J0546-5345, all reported in terms
of M200(ρc). A summary of these mass measures is given in
Table 2.
In A10, the cluster mass within r500 is measured using
the YX–M500 relation (Vikhlinin et al. 2009)tobeM500,YX=
(5.33 ±0.62) ×1014 M. The systematic uncertainty of this
scaling relation calibration was estimated by Vikhlinin et al.
(2009)tobe±9% by comparing X-ray mass estimates to
weak lensing mass measurements for a representative sample
of clusters. We include this uncertainty in quadrature when
converting to M200,YX, and we estimate that M200,YX=(8.23 ±
1.21) ×1014 M. This X-ray mass is consistent with the
measured dynamical mass within the errors. Although the
X-ray image shows evidence of a possible merger, the YX
estimator is expected to be robust to such events (Vikhlinin
et al. 2009). Indeed, the majority of high-redshift clusters
have asymmetrical X-ray morphologies (e.g., Vikhlinin et al.
2009; A10), so the inferred X-ray mass of SPT-CL J0546-5345
should be of comparable accuracy to other clusters at similar
redshifts. We also estimate the mass from the temperature, via
the TX–M500 relation of Vikhlinin et al. (2009), to be M200,TX=
(8.11 ±1.89) ×1014M.
The SZE measurement of the integrated Comptonization,
YSZ, is expected to be the most accurate Sunyaev–Zel’dovich
(SZ) mass proxy (Motl et al. 2005; Nagai 2006). In A10,
they measure a spherically deprojected Comptonization of
YSZ =(3.5±0.6) ×1014 MkeV, where the uncertainty is
estimated from the quadrature sum of statistical errors and the
uncertainty in the assumed gas profile. From this measurement,
we use the YSZ–M500 relation reported in A10 to estimate a mass,
where we marginalize over the allowed range of normalization
and slope parameters from their fit. We include an additional
±9% uncertainty to account for the systematic uncertainty of
the YX-based masses used to calibrate their relation.31 Using this
method, we infer a mass of M200,YSZ =(7.19 ±1.51) ×1014 M,
in agreement with the X-ray and dynamical mass estimates.
Another SZ mass estimate can be inferred from the SZE
significance-mass scaling relation established via WMAP7-
constrained simulations in V10. A10 compared this SZE
significance-based mass proxy with X-ray-inferred masses for
their sample of 15 SZE-selected clusters, finding that the
significance-based SZE masses may be biased low, with an av-
erage ratio of the SZE to X-ray masses of 0.89 ±0.06. The re-
sult for SPT-CL J0546-5345, M200,SZ =(5.03 ±1.13 ±0.77) ×
1014 M, where the uncertainties are statistical followed by sys-
tematic, is indeed ∼1.6σbelow the 68% confidence interval of
the more precise X-ray mass, although it is in agreement with
the dynamical mass within the errors. Accounting for the bias
quantified in A10 brings the significance-based mass estimate
into agreement with the X-ray mass.
H10 present a scaling relation between SZE-derived mass
and two optical richness measures, Ngal and N200. These
richness measures count the number of galaxies on the red
sequence at the cluster redshift within clustercentric radii
of 1 h−1Mpc and r200, respectively. The derived masses,
M200(Ngal )=(9.2±4.9±2.7) ×1014 Mand M200(N200 )=
(8.5±5.7±2.5)×1014 M, are consistent with the independent
richness-based mass estimate of Menanteau & Hughes (2009)
for this cluster. Although noisy mass proxies, these richness
measures offer independent evidence of the high mass of SPT-
CL J0546-5345.
4.3. Combined Mass for SPT-CL J0546-5345
Table 2lists total mass measures for SPT-CL J0546-5345
from dynamical, X-ray, SZE, and optical richness mass proxies.
For each physical probe, the bold entries indicate the specific
proxy expected to yield the most robust mass. For dispersions,
this is the biweight measure, which is optimal for the number of
spectroscopic members we have (Beers et al. 1990). For the X-
ray, the YXestimator is chosen over the TXestimator because it is
expected to be significantly less biased for mergers and to have
less intrinsic scatter with mass (Kravtsov et al. 2006; Vikhlinin
et al. 2009). For the SZE, the YSZ estimator is chosen over the
S/N estimator because its scaling relations have been calibrated
directly from external observations rather than simulations and
it is expected to have less intrinsic scatter with mass (Kravtsov
et al. 2006; V10). Finally, the N200 estimator is the best-tested
optical richness measure.
We optimally combine these independent measurements,
weighting them by their errors. We symmetrize the errors on
the dynamical mass and add the statistical and systematic errors
in quadrature for the richness. The combined mass is insensitive
to these details since these are the least constrained measures.
The resulting mass is M200 =(7.95 ±0.92) ×1014 M, which
we take as our best estimate of the mass of SPT-CL J0546-5345.
31 The SZ and X-ray mass estimates are not completely independent. We
expect that their largest correlation will be from the mass calibration of the
YX–M500 and YSZ–M500 relations, which are based on the same X-ray
measurements from Vikhlinin et al. (2009). We add the 9% uncertainty to the
YSZ mass estimate to account for this, and assume that any other correlated
uncertainty is negligible.

96 BRODWIN ET AL. Vol. 721
4.4. SPT-CL J0546-5345 in a Cosmological Context
Using the Tinker et al. (2008) mass function we calculate that
SPT-CL J0546-5345, which at z=1.067 is already almost as
massive as the Coma cluster, will increase in mass by a factor
of ∼4 over the next 8 Gyr. It should therefore grow into one of
the most massive clusters in the universe by the present day.
Historically, the existence of individual massive galaxy clus-
ters at high redshift has been used to constrain cosmological
models (e.g., Donahue et al. 1998). While we are entering an
era where large samples of SZ clusters will soon be available
in addressing such questions, it is interesting to ask whether
the existence of SPT-CL J0546-5345 is expected in our survey
volume for a concordance ΛCDM cosmology. Convolving the
Tinker et al. (2008) mass function with a Gaussian mass prob-
ability function for the best-estimate mass of SPT-CL J0546-
5345, we find that ΛCDM predicts the existence of 0.18 clusters
of this mass or higher at z>1 in 178 deg2. We note that the
M500–YXrelation was calibrated at lower redshifts (z0.6)
than SPT-CL J0546-5345, and the accuracy of this relation has
not been verified at z1. Given the caveats and uncertainties
inherent in this calculation, we conclude that the existence of
SPT-CL J0546-5345 in our survey volume is unsurprising. The
complete SPT sample, combined with improved mass scaling
relations based on complementary mass measures, will permit
ΛCDM predictions for the high end of the cluster mass function
to be robustly tested at high redshift.
5. CONCLUSIONS
We report the spectroscopic confirmation SPT-CL J0546-
5345 at z=1.067, the first SZE-selected galaxy cluster at
z>1. We measure a robust velocity dispersion from 18 early-
type members of σ=1179 +232
−167 km s−1, corresponding to a
dynamical mass of M200 =1.0+0.6
−0.4×1015 M. SPT-CL J0546-
5345 is the most dynamically massive cluster yet identified,
from any method, at z>1.
We find excellent consistency across several independent
mass measures. The measured dispersion and X-ray temperature
of SPT-CL J0546-5345 fall right on the σ–TXrelation. The X-
ray, SZE, and richness-based mass estimates are all consistent
with the dynamical mass, and with each other, within the errors.
Combining all the mass measures, we derive a best-estimate
mass for SPT-CL J0546-5345 of M200 =(7.95 ±0.92) ×
1014 M.
In ΛCDM, we expect 0.18 clusters consistent with this mass
above z>1 in our survey area. Given the uncertainties in X-ray
scaling relations at high redshift, we conclude that the existence
of SPT-CL J0546-5345 in our survey volume is unsurprising.
The complete SPT sample will provide the large sample of
clusters required to robustly test the high redshift, high mass
end of the cluster mass function.
The SPT is supported by the National Science Foundation
through grant ANT-0638937. Partial support is also provided
by the NSF Physics Frontier Center grant PHY-0114422 to the
Kavli Institute of Cosmological Physics at the University of
Chicago, the Kavli Foundation, and the Gordon and Betty Moore
Foundation. This work is based in part on observations made
with the Spitzer Space Telescope, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology under
a contract with NASA. Support for this work was provided by
NASA through an award issued by JPL/Caltech. This paper
includes data gathered with the 6.5 meter Magellan Telescopes
located at Las Campanas Observatory, Chile. This work is
based in part on observations obtained with the Chandra X-
ray Observatory, under contract SV4-74018, A31 with the
Smithsonian Astrophysical Observatory which operates the
Chandra for NASA. We are very grateful for the efforts of the
Spitzer,Chandra, Magellan, and CTIO support staff without
whom this paper would not be possible. Support for M.B. was
provided by the W. M. Keck Foundation. B.S. acknowledges
support from the Brinson Foundation.
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