of 8
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
doi:
10.1088/0004-637X/794/2/157
C

2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
THE XXL SURVEY. V. DETECTION OF THE SUNYAEV–ZEL’DOVICH EFFECT OF THE REDSHIFT 1.9
GALAXY CLUSTER XLSSU J021744.1
−
034536 WITH CARMA
A. B. Mantz
1
,
2
, Z. Abdulla
1
,
2
, J. E. Carlstrom
1
,
2
,
3
, C. H. Greer
4
, E. M. Leitch
1
,
2
, D. P. Marrone
4
, S. Muchovej
5
,
C. Adami
6
, M. Birkinshaw
7
, M. Bremer
7
, N. Clerc
8
,P.Giles
7
, C. Horellou
9
, B. Maughan
7
,
F. Pacaud
10
, M. Pierre
11
, and J. Willis
12
1
Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA;
amantz@kicp.uchicago.edu
2
Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
3
Department of Physics
/
Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
4
Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA
5
Owens Valley Radio Observatory, California Institute of Technology, Big Pine, CA 93513, USA
6
LAM, OAMP, Universit
́
e Aix-Marseille and CNRS, P
ˆ
ole de l’
́
Etoile, Site de Ch
ˆ
ateau Gombert, 38 rue Fr
́
ed
́
eric Joliot-Curie, F-13388 Marseille 13 Cedex, France
7
H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
8
Max-Planck Institut f
̈
ur Extraterrestrische Physik, Giessenbachstrasse 1, D-85748 Garching, Germany
9
Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, SE-439 92 Onsala, Sweden
10
Argelander-Institute for Astronomy, Auf dem H
̈
ugel 71, D-53121 Bonn, Germany
11
Service d’Astrophysique, Bt. 709, CEA Saclay, F-91191 Gif sur Yvette Cedex, France
12
Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road, Victoria, BC, Canada
Received 2014 January 9; accepted 2014 August 25; published 2014 October 7
ABSTRACT
We report the detection of the Sunyaev–Zel’dovich (SZ) effect of galaxy cluster XLSSU J021744.1
−
034536, using
30 GHz Combined Array for Research in Millimeter-wave Astronomy (CARMA) data. This cluster was discovered
via its extended X-ray emission in the
XMM-Newton
Large Scale Structure survey, the precursor to the XXL survey.
It has a photometrically determined redshift
z
=
1
.
91
+0
.
19
−
0
.
21
, making it among the most distant clusters known, and
nominally the most distant for which the SZ effect has been measured. The spherically integrated Comptonization
is
Y
500
=
(3
.
0
±
0
.
4)
×
10
−
12
, a measurement that is relatively insensitive to assumptions regarding the size and
redshift of the cluster, as well as the background cosmology. Using a variety of locally calibrated cluster scaling
relations extrapolated to
z
∼
2, we estimate a mass
M
500
∼
(1–2)
×
10
14
M

from the X-ray flux and SZ signal.
The measured properties of this cluster are in good agreement with the extrapolation of an X-ray luminosity–SZ
effect scaling relation calibrated from clusters discovered by the South Pole Telescope at higher masses and lower
redshifts. The full XXL–CARMA sample will provide a more complete, multi-wavelength census of distant clusters
in order to robustly extend the calibration of cluster scaling relations to these high redshifts.
Key words:
galaxies: clusters: individual (XLSSU J021744.1
−
034536) – galaxies: clusters: intracluster
medium – X-rays: galaxies: clusters
Online-only material:
color figures
1. INTRODUCTION
Building on the success of cosmological tests using the
number density and growth of galaxy clusters (e.g., Mantz
et al.
2008
,
2010b
; Vikhlinin et al.
2009b
; Rozo et al.
2010
;
Benson et al.
2013
; Hasselfield et al.
2013
) and cluster gas
mass fractions (e.g., Allen et al.
2004
,
2008
; LaRoque et al.
2006
; Ettori et al.
2009
; Mantz et al.
2014
; see also Allen et al.
2011
), a number of observational programs seek to extend the
census of the cluster population to redshifts
z

1. Efforts have
included searches for serendipitous detections (Fassbender et al.
2011a
; Mehrtens et al.
2012
) and controlled surveys (Eisenhardt
et al.
2008
; Muzzin et al.
2008
; Hasselfield et al.
2013
; Planck
Collaboration et al.
2013b
; Reichardt et al.
2013
). The number of
confirmed, high-redshift clusters has recently expanded rapidly,
including
z

1
.
5 discoveries at X-ray (Fassbender et al.
2011b
;
Santos et al.
2011
), millimeter (Bayliss et al.
2013
), and IR
(Papovich et al.
2010
; Gobat et al.
2011
; Brodwin et al.
2012
;
Stanford et al.
2012
; Zeimann et al.
2012
) wavelengths.
This paper concerns a cluster discovered via its extended
X-ray emission in the
XMM
-
Newton
Large Scale Structure
survey (
XMM
-LSS; Pierre et al.
2004
).
XMM
-LSS reaches a flux
detection limit for clusters of
∼
5
×
10
−
15
erg cm
−
2
s
−
1
in the
0.5–2.0 keV band over an 11 deg
2
footprint that has extensive,
complementary optical and IR photometry. Clusters discovered
by the survey reach redshifts as high as
z
∼
2 (Willis et al.
2013
,
hereafter
W13
; see also Valtchanov et al.
2004
; Willis et al.
2005
;Bremeretal.
2006
; Pierre et al.
2006
; Pacaud et al.
2007
;
Maughan et al.
2008
). An expanded survey footprint covering
50 deg
2
(XXL) has since been completed to similar depth, and a
number of cosmological and astrophysical investigations based
on these data are ongoing (Pierre et al.
2011
).
Among these investigations is an observing campaign with
the Combined Array for Research in Millimeter-wave Astron-
omy
13
(CARMA), targeting cluster detections in the northern
25 deg
2
field of XXL (which includes the
XMM
-LSS footprint)
at 30 GHz, with the aim of measuring the Sunyaev–Zel’dovich
(SZ) effect of the hot intracluster medium (ICM). Here we
present the first result from that program, the detection of
the SZ signal of cluster XLSSU J021744.1
−
034536 (here-
after XLSSU J0217
−
0345), which was obtained using the
CARMA sub-array of eight 3.5 m telescopes (formerly the
Sunyaev–Zel’dovich Array). This cluster is a “class 1” detec-
tion, meaning that it meets conservative criteria designed to
produce a pure sample of extended sources (see Pacaud et al.
2006
). The survey data imply an unabsorbed 0.5–2.0 keV flux
13
http://www.mmarray.org
1
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
of 1
.
08
×
10
−
14
erg cm
−
2
s
−
1
(
W13
). With a photometric red-
shift of
∼
1
.
9 (see below) and only
∼
100 net source photons
contributing to the detection, this cluster is representative of a
population of faint, distant X-ray sources detectable by XXL
(and by upcoming missions like eROSITA; Predehl et al.
2010
)
for which survey data cannot directly provide estimates of the
temperature or mass of the ICM. Observations of the SZ effect
provide a complementary probe, allowing independent confir-
mation of the presence of hot gas and estimates of the cluster
mass. The redshift independence of the SZ brightness makes it
particularly powerful for following up distant clusters.
W13
present 10 band (
ugrizYJK
,
3
.
6
μ
m
,
4
.
5
μ
m) photomet-
ric data covering XLSSU J0217
−
0345, and we summarize the
key results of that analysis here. The distribution of photomet-
ric redshifts for galaxies near the X-ray detection is bimodal,
with a peak at
z
∼
1
.
0 and another (larger) peak at
z
∼
1
.
9.
Galaxies associated with the
z
∼
1 peak display neither spatial
clustering associated with the X-ray source nor an identifiable
red sequence. In contrast, galaxies with photometric redshifts
1
.
7
<z<
2
.
1 are clustered around the location of the extended
X-ray emission (Figure
1
) and display a poorly populated yet
significant red sequence, whose color is consistent with that
anticipated from a passively evolving, solar metallicity stellar
population formed at
z
=
10 and observed at
z
=
1
.
9. On
this basis,
W13
conclude that the
z
∼
1 peak arises from an
unassociated foreground structure, and assign a cluster redshift
z
=
1
.
91
+0
.
19
−
0
.
21
. Note that the quoted uncertainty represents the
full width of the peak in the galaxy redshift histogram, not the
error on the mean of this peak. Spectroscopic confirmation of
this redshift is not yet available, though we note that compari-
son of the cluster’s X-ray flux with our CARMA data favors a
redshift
∼
1
.
9 compared with 1
.
0 (see Section
4.2
).
This paper is organized as follows. Sections
2
and
3
describe
the CARMA data and the determination of the cluster SZ signal,
the spherically integrated Compton
Y
parameter. In Section
4
,
we discuss estimates of the cluster mass based on the X-ray
and SZ data, and compare the measured X-ray and SZ signals
for XLSSU J0217
−
0345 to a scaling relation calibrated from
higher-mass and lower-redshift South Pole Telescope (SPT)
clusters. We summarize in Section
5
.
Throughout this work, we assume a concordance
Λ
CDM
cosmological model, with dark energy in the form of a cos-
mological constant, described by Hubble parameter
h
70
=
H
0
/
70 km s
−
1
Mpc
−
1
=
1, matter density
Ω
m
=
0
.
3, and dark
energy density
Ω
Λ
=
0
.
7. Quoted uncertainties refer to 68.3%
confidence intervals (with the exception of the photometric red-
shift estimate, noted above). We report dimensionless, spheri-
cally integrated Comptonization (
Y
) in units of steradians.
2. CARMA DATA
CARMA is a heterogeneous interferometric array comprised
of six 10.4 m, nine 6.1 m, and eight 3.5 m telescopes; our data
were obtained using the eight-element array of 3.5 m antennas
operating at a central frequency of 31 GHz. The data were
taken over two periods spanning 2012 March–July and 2013
September–November. The 3.5 m antennas were configured
with 6 elements in a compact array, providing 15 baselines
with sensitivity at arcminute scales, and 2 outlying elements
providing 13 baselines with sensitivity at higher resolution.
The compact and extended baselines respectively sample
uv
ranges of 0.35–2 k
λ
and 2–9.5 k
λ
with comparable flux
sensitivity, allowing emission from compact radio sources to
Table 1
CARMA Data
ID
UT Date
Config
a
t
int
b
c0927.3SL_31J02170.1
2012 Mar 6
SL
2.5
c0927.3SL_31J02170.2
2012 Mar 9
SL
3.5
c0927.3SL_31J02170.3
2012 Mar 10
SL
3.5
c0927.3SL_31J02170.4
2012 Mar 12
SL
2.2
c0927.3SL_31J02170.5
2012 Mar 13
SL
2.6
c0927.3SL_31J02170.6
2012 Mar 14
SL
2.3
c0927.3SL_31J02170.7
2012 Mar 15
SL
1.6
c0927.3SH_31J02170.1
2012 May 31
SH
3.6
c0927.3SH_31J02170.3
2012 Jun 4
SH
2.5
c0927.3SH_31J02170.4
2012 Jul 24
SH
1.9
c0927.3SH_31J02170.5
2012 Sep 1
SH
2.2
c1171.33SH_30s4.3
2013 Nov 1
SH
0.4
c1171.33SH_30s4.4
2013 Nov 2
SH
3.5
c1171.33SH_30s4.5
2013 Nov 3
SH
3.5
c1171.33SH_30s4.7
2013 Nov 4
SH
3.1
c1171.33SH_30s4.8
2013 Nov 5
SH
3.2
c1171.33SH_30s4.9
2013 Nov 6
SH
2.8
c1171.33SH_30s4.10
2013 Nov 8
SH
0.1
c1171V.35SH_30s6.7
2013 Nov 10
SH
1.7
c1171.33SH_30s4.11
2013 Nov 11
SH
3.1
c1171V.36SH_30s7.2
2013 Nov 12
SH
3.0
Notes.
a
Configuration of the 3.5 m CARMA dishes. The SH and SL configurations
provide similar baseline coverage, and are approximately equivalent for the
targets at the declination of XLSSU J0217
−
0345.
b
Effective on-source integration time after flagging (hours).
be distinguished from the extended SZ effect. The signals were
processed by the CARMA 8 GHz bandwidth digital correlator
in sixteen 500 MHz sub-bands, each consisting of 16 channels.
More details of the specific observations can be found in Table
1
.
Our data reduction procedure is described in Muchovej et al.
(
2007
). Briefly, the data are filtered for bad weather, shadowing,
and high system temperatures or other technical issues, and
bandpass and gain calibrations are applied based on periodic
observations of planets and radio-bright quasars. The absolute
flux calibration compares observations of Mars to the model
of Rudy (
1987
), which is accurate to better than 5%. The
reduced, calibrated data are equivalent to a total of 52.8 hr of
on-source integration time. At short baselines (
uv
radii
<
2k
λ
)
the rms noise level is 0.15 mJy beam
−
1
, with a 117

×
129

FWHM synthesized beam. At long baselines (
>
2k
λ
), the noise
is 0.13 mJy beam
−
1
, and the synthesized beam FWHM is
17
.

9
×
24
.

7.
The short-baseline map, after modeling and removing point
sources (Section
3
) and applying the CLEAN image deconvo-
lution algorithm of H
̈
ogbom (
1974
), is shown in the left panel
of Figure
1
. (Note that in our analysis of the cluster, detailed in
the next section, we do not use this map, but instead fit models
directly to the measured visibility data in the
uv
plane.) The
right panel of the figure shows an
iJK
color image of the cluster
from
W13
, with X-ray brightness and SZ significance contours
overlaid, and galaxies with photometric redshifts between 1.7
and 2.1 circled.
3. MEASUREMENTS OF COMPTONIZATION AND MASS
We use a Markov Chain Monte Carlo exploration of the
parameter space to fit models of the cluster SZ effect and
emission from unresolved radio sources directly to the
uv
data
at all baselines. To parameterize the SZ signal, we adopt the
2
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
−03:45:00
43:00
47:00
49:00
Declination
02:17:45
5
3
:
7
1
5
5
:
7
1
Right ascension
1 arcmin
−0.8
−0.4
0.0
0.4
0.8
flux density (mJy/beam)
Figure 1.
Left: short-baseline (
uv
radii
<
2k
λ
) 30 GHz map of XLSSU J0217
−
0345 after modeling and subtracting point sources and applying the CLEAN algorithm.
The position of the brighter point source in Table
2
is indicated by the “
×
” (the other lies outside the image). White contours show the extended X-ray emission
associated with the cluster detection. The gray ellipse in the lower-left corner shows the FWHM synthesized beam. Right:
iJK
image, with X-ray (white) and SZ
(blue) contours overlaid. The SZ contours correspond to
−
2
.
5,
−
3
.
5,
−
4
.
5, and
−
5
.
5 times the rms noise level of the short-baseline map. Galaxies with photometric
redshifts in the range 1
.
7
<z<
2
.
1 are circled in green.
(A color version of this figure is available in the online journal.)
Nagai et al. (
2007
) form for the shape of the three-dimensional,
spherically symmetric electron pressure profile of clusters:
P
(
x
)
=
P
0
x
γ
[
1+
x
α
]
(
β
−
γ
)
/α
,
(1)
and fix the parameters
α
=
0
.
86,
β
=
3
.
67, and
γ
=
0
.
67 as
prescribed by Sayers et al. (
2013
, hereafter S13). We discuss
the implications of using this particular measurement of the
parameters in Equation (
1
)inthe
Appendix
. The free parameters
of this model are the position of the cluster center; the scale
radius, which normalizes the radial coordinate (
x
=
r/r
s
,or
θ/θ
s
in units of angle); and an overall normalization, which we
take to be the line-of-sight Comptonization through the cluster
center:
y
0
=
2
σ
T
D
A
(
z
)
m
e
c
2
∫
∞
0
dθ P
(
θ/θ
s
)
,
(2)
where
σ
T
is the Thompson cross section,
m
e
is the electron
rest mass,
c
is the speed of light in vacuum, and
D
A
(
z
)isthe
angular diameter distance to the cluster.
14
The Comptonization
integrated in a sphere corresponding to angular radius
Θ
is
Y
(
Θ
)
=
σ
T
D
A
(
z
)
m
e
c
2
∫
Θ
0
4
πθ
2
dθ P
(
θ/θ
s
)
.
(3)
Given a prescription for determining
r
500
,
15
we thus can straight-
forwardly calculate
Y
500
=
Y
[
r
500
/D
A
(
z
)]. The closely related
quantity
D
A
(
z
)
2
Y
500
is proportional to the thermal energy of the
ICM, and should therefore scale with the total cluster mass.
The measured properties of unresolved radio sources in the
field are essentially independent of the cluster gas model because
14
Note that measuring
y
0
or
Y
does not require explicit assumptions about the
cluster redshift or the cosmic expansion history. The factors of
D
A
(
z
)
appearing in Equations (
2
)and(
3
) are only necessary to express these
quantities in terms of the electron pressure profile.
15
Defined as the cluster radius enclosing a mean density 500 times the critical
density of the universe at the cluster’s redshift:
M
500
=
(2000
/
3)
πρ
cr
(
z
)
r
3
500
.
Table 2
Properties of Unresolved Radio Sources
R.A.
Decl.
Offset
Flux
(mJy)
02:17:57.30
±
0
.

6
−
03:46:47.5
±
0
.

63
.

55
2
.
21
±
0
.
09
02:17:51.84
±
2
.

5
−
03:40:29.4
±
2
.

55
.

48
0
.
70
±
0
.
14
Note.
J2000 positions, angular distances from the XXL cluster position
(02:17:43.9
−
03:45:36), and 30 GHz flux densities (corrected for the primary
beam) of unresolved radio sources detected near XLSSU J0217
−
0345 in our
observations.
they are primarily constrained by the long-baseline data, where
signal from the cluster is negligible (
uv
radii

2k
λ
). There
are two compact, emissive sources detected in the data, both
several arcminutes from the cluster position, and we fit for
their positions and flux densities simultaneously with the cluster
model. The results appear in Table
2
; we find flux densities at
30 GHz of 2
.
21
±
0
.
09 and 0
.
70
±
0
.
14 mJy. The brighter of the
two has a 1.4 GHz counterpart in the NVSS and FIRST surveys
and is also the closest 1.4 GHz source to the cluster position
(i.e., there are no radio sources in projection with the cluster SZ
decrement in Figure
1
). There is negligible covariance between
the brightness of these sources and cluster parameters in our
fits. In particular, a factor of
∼
2 change to the flux density of
the brighter and closer point source would be required to force
a1
σ
shift in the normalization of the cluster model.
The scale radius of the cluster pressure profile is poorly
constrained by our data, leading to a strong degeneracy between
the scale radius and the normalization of the profile. In the
following sections, we consider three priors on the scale radius.
The first is based on a scaling relation between mass and
pressure, and directly links the scale radius with the measured
SZ signal. The second is a Gaussian prior based on the measured
X-ray flux from the cluster, and is independent of the SZ data.
The third case is simply a wide uniform prior, encompassing
values consistent with the other two approaches. In all cases,
3
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
Table 3
Cluster Properties
Section
3.1
Section
3.2
Section
3.3
Offset
E
(

)3
±
72
±
73
±
8
Offset
N
(

)
−
35
±
9
−
34
±
9
−
34
±
10
10
4
y
0
2
.
5
±
0
.
23
.
5
±
0
.
62
+4
−
1
θ
s
(

)0
.
652
±
0
.
017
0
.
58
±
0
.
07
0
.
4
+0
.
4
−
0
.
2
10
12
Y
500
2
.
8
±
0
.
43
.
0
±
0
.
42
.
2
+1
.
8
−
0
.
8
D
2
A
Y
500
(10
−
6
Mpc
2
)8
.
3
±
1
.
29
.
1
±
1
.
36
+5
−
2
r
500
(Mpc)
0
.
388
±
0
.
010
0
.
35
±
0
.
04
···
M
500
(10
14
M

)1
.
34
±
0
.
11
1
.
0
±
0
.
4
···
Notes.
Best-fitting values and 68.3% confidence intervals for the cluster
parameters of our SZ model. Offsets describe the position of the cluster model
center with respect to 02:17:43.9
−
03:45:36 in J2000 coordinates, and
y
0
is
the dimensionless line-of-sight Comptonization through the cluster center. Note
that there are different priors used in each set of results. In particular, the model
of Section
3.1
deterministically links
y
0
and
θ
s
, resulting in tight constraints
on those parameters, as well as on the mass. In Section
3.2
we instead apply a
Gaussian prior to
θ
s
, but do not impose a prior on
y
0
. In Section
3.3
,weuse
a uniform prior on
θ
s
. The basis of the mass constraints also differs; see the
indicated sections for details. The
D
2
A
Y
500
,
r
500
,
and
M
500
constraints assume a
cluster redshift
z
=
1
.
91.
the addition of the cluster model yields a significantly improved
fit compared to a point-source-only model, with
Δ
χ
2
min
∼
85 (for
55,005 degrees of freedom in the case of Section
3.1
, equivalent
to a 7
.
3
σ
significance). Statistically, the cluster models in
the following sections provide equally good fits to the data.
Their constraints on the integrated Comptonization,
Y
500
, agree
within measurement uncertainties. These analyses also produce
estimates of the cluster mass, which are more sensitive to a
priori assumptions than the
Y
500
constraints; we will discuss the
mass estimates further in Section
4.1
. Table
3
summarizes the
constraints on cluster parameters.
We note an offset of 34

±
9

between the nominal X-ray
detection position and the best-fitting centers of the SZ models
below, although the SZ centers still lie within the extended X-ray
emission and the distribution of photometrically selected
z
∼
1
.
9 galaxies (Figure
1
). While the X-ray
/
SZ offset is suggestive
of an asymmetry in the distribution of hot gas in the system, we
have no reliable information about the morphological state of
this cluster and firm conclusions cannot be drawn from the data
in hand. Such offsets are not unprecedented (Andersson et al.
2011
), nor necessarily unusual in the case of a major merger
(Zhang et al.
2014
).
3.1. Scale Radius from the Pressure–Mass Relation
We first consider a cluster model where the scale radius of the
pressure profile is self-consistently related to its normalization
and the cluster mass through a scaling relation linking pressure
and mass. In this case, the single free parameter describing the
pressure profile of the cluster is
M
500
, which determines the scale
radius through the fixed parameter
c
500
=
r
500
/r
s
=
1
.
18 (
S13
).
The normalization of the electron pressure profile is given by
P
0
(
M
500
)
=
(
0
.
0158
keV
cm
3
)
E
(
z
)
8
/
3
h
1
/
2
70
×
(
M
500
10
15
h
−
1
70
M

)
2
3
+
α
P
,
(4)
with
α
P
=
0
.
12, and where we have neglected a higher-order
correction in the exponent of
M
500
(see Arnaud et al.
2010
and
S13
). Here
E
(
z
)
=
H
(
z
)
/H
0
encodes the evolution of the
Hubble parameter.
This analysis yields a mass estimate of
M
500
=
(1
.
34
±
0
.
11)
×
10
14
M

, corresponding to scale radius
r
s
=
0
.
329
±
0
.
009 Mpc (statistical uncertainties only). Note that we have
simply extrapolated the
S13
scaling relation, calibrated at
z<
0
.
9, to
z
=
1
.
9. This
M
500
constraint, as with any
such extrapolated estimate, should therefore be treated with
extreme caution. The constraint on the spherically integrated
Comptonization is
Y
500
=
(2
.
8
±
0
.
4)
×
10
−
12
, consistent with
the results of the less constrained analyses in the following
sections.
3.2. Scale Radius from the X-Ray Flux
The
XMM
measurement of the X-ray luminosity of
XLSSU J0217
−
0345 can be used to define a loose prior on
the pressure scale radius, providing an approach to fitting the
SZ data that is less constraining than the one in Section
3.1
.This
procedure introduces a covariance between the measured values
of
L
X
and
Y
. In practice, however, this covariance is negligible
compared to the measurement uncertainties, as shown below.
The Kaiser (
1986
) self-similar model relating X-ray
luminosity and mass is
L
Δ
E
(
z
)
∝
[
E
(
z
)
M
Δ
]
a
,
(5)
with
a
=
4
/
3 for the bolometric luminosity, and where both
quantities are integrated within a fixed overdensity with respect
to critical (e.g.,
Δ
=
500). The factors of
E
(
z
) arise from
the critical density,
ρ
cr
(
z
)
∝
H
(
z
)
2
. For soft-band emission
from clusters (such as the 0.5–2.0 keV band used for XXL),
measured values of
a
span the range
∼
1
.
3–1
.
8 (e.g., Reiprich &
B
̈
ohringer
2002
; Allen et al.
2003
; Pratt et al.
2009
; Vikhlinin
et al.
2009a
; Mantz et al.
2010a
). For convenience, and because
the precise value within this range has a negligible effect on our
results (
<
1

in the estimate of
θ
s
), we take
a
=
4
/
3. Using that
M
Δ
∝
E
(
z
)
2
r
3
Δ
, the above relation thus yields
r
Δ
∝
L
1
3
a
Δ
E
(
z
)
−
3
a
+1
3
a
∝
L
1
/
4
Δ
E
(
z
)
−
5
/
4
.
(6)
We calibrate the normalization of this relation using other
XXL clusters, spanning redshifts 0
.
4
<z<
1
.
1, for which
deep X-ray observations provide estimates of mass and
r
500
(P.
Giles et al., in preparation).
16
Identifying the 0.5–2.0 keV
L
X
values estimated from the survey data with
L
500
for this purpose,
we find
r
500
Mpc
=
(1
.
035
±
0
.
021)
(
L
X
10
44
erg s
−
1
)
1
/
4
E
(
z
)
−
5
/
4
,
(7)
with a residual scatter of
∼
4%.
16
The calibration uses five clusters in the
XMM
-XXL sample with
comparable X-ray luminosity to XLSSU J0217
−
0345 (also detected by
CARMA, to be reported in future work). Luminosities are estimated directly
from the survey count rates, and masses from measurements of
Y
X
(the
product of gas mass and temperature) from either the survey data or deeper
XMM
data, assuming a reference
Y
X
–mass relation. More details, as well as a
more complete analysis of cluster scaling relations, will appear in P. Giles et al.
(in preparation). Note that the data used here are not powerful enough to
directly provide a meaningful constraint on the slope,
a
.
4
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
0.15
0.20
0.25
0.30
0.35
0.40
0.45
1234567
r
s
(
Mpc
)
10
4
y
0
0.15
0.20
0.25
0.30
0.35
0.40
0.45
12345
r
s
(
Mpc
)
10
12
Y
500
Figure 2.
Two-dimensional 68.3% and 95.4% confidence regions from our analysis in Section
3.2
. Left: scale radius and normalization of the pressure profile,
parameterized by the line-of-sight Comptonization through the cluster center. Right: scale radius vs. the spherically integrated Comptonization
within
r
500
.
(A color version of this figure is available in the online journal.)
Table 4
Mass Estimates
Proxy
Scaling Relation
M
500
(10
14
M

)
Y
Section
3.1
1
.
34
±
0
.
11
L
X
Section
3.2
1
.
0
±
0
.
2
Y
Andersson et al. (
2011
)1.4
Y
Planck Collaboration et al. (
2013a
)1.7
L
X
Pratt et al. (
2009
)2.0
L
X
Vikhlinin et al. (
2009a
)1.7
L
X
Mantzetal.(
2010a
)1.1
L
X
Andersson et al. (
2011
)1.3
Notes.
The evolution of cluster scaling relations out to
z
=
1
.
9 has not been
constrained by data, and so we have not attempted to quantify the systematic
uncertainties on these estimates due to extrapolation in redshift. For the estimates
obtained in Sections
3.1
and
3.2
, the table reproduces the uncertainties quoted in
each analysis; see those subsections for a discussion of exactly what is included
in the error bars.
Owing to the use of the luminosity–mass scaling in
Equation (
5
), we expect an additional uncertainty of
∼
11%
to apply to estimates of
r
500
, given an intrinsic scatter in
L
X
at fixed
M
500
of 40%–45% and an
L
X
–
M
500
slope of
∼
4
/
3. In
practice, we identify
r
s
=
r
500
/c
500
, with
c
500
=
1
.
18 from
S13
and
r
500
estimated from Equation (
7
), and marginalize over a
Gaussian prior with a standard deviation of 12%, accounting for
the systematic and statistical sources of uncertainty. Assuming
the nominal redshift of 1.91, this yields
r
s
=
0
.
30
±
0
.
04 Mpc,
implying a mass
M
500
=
(1
.
0
±
0
.
4)
×
10
14
M

.
Marginalizing over this
L
X
–motivated prior on the pressure
scale radius, we constrain the normalization and center of the
cluster model from the SZ data. Our constraints from this
analysis are summarized in Table
3
; we find
Y
500
=
(3
.
0
±
0
.
4)
×
10
−
12
, or equivalently
D
A
(
z
)
2
Y
500
=
(9
.
1
±
1
.
3)
×
10
−
6
Mpc
2
.
As described above, there is a strong degeneracy between
the scale radius and the pressure normalization, which can
be seen in the joint constraints on these parameters shown
in the left panel of Figure
2
. As the right panel of the figure
shows, the scale radius is also degenerate with the spherically
integrated Comptonization,
Y
500
(with a somewhat weaker
degree of correlation). Despite this degeneracy, however, our
results are not particularly sensitive to the cluster redshift given
an observationally motivated prior such as the one used in this
section. Varying the cluster redshift by
±
0
.
2, and adjusting the
prior on
θ
s
accordingly, we find that
Y
500
changes by only
∓
4%,
well within our statistical uncertainties.
While we performed the test above by repeating the entire
analysis assuming a different value for the cluster redshift, an
approximate estimate for the size of the effect can be obtained
as follows. Taking advantage of the fact that
Y
500
∝
∼
r
1
s
∝
r
500
in
Figure
2
, the fractional shift in
Y
500
with redshift follows from
converting Equation (
7
) into an expression for
θ
s
and accounting
straightforwardly for the luminosity–distance dependence of
L
X
. From this, we estimate that differences of
>
0
.
5 in redshift
would be necessary to change the measured value of
Y
500
by an
amount comparable to its statistical uncertainty (
∼
14%). Note
that this shift in
Y
500
partially cancels the explicitly redshift-
dependent factor
E
(
z
)
D
A
(
z
)
2
appearing in the scaling relation
analysis of Section
4.2
.
3.3. Uniform Prior on the Scale Radius
Without any external constraint, our data are unable to
meaningfully break the degeneracy between the scale radius and
normalization of the pressure profile, leading to significantly less
tight constraints compared to the previous sections (Table
3
).
However, it is worth noting that the scale radius constraint in
this case is consistent with the results of Sections
3.1
and
3.2
,
rather than preferring extremely low or high values, and that the
constraints on the cluster position are comparable.
4. DISCUSSION
4.1. Mass Estimates
Our analysis has produced two estimates of the mass of
XLSSU J0217
−
0345:
M
500
∼
1
.
3
×
10
14
M

from the SZ
data in combination with the pressure scaling relation of
S13
(Section
3.1
), and
M
500
∼
1
.
0
×
10
14
M

from the preliminary,
empirical
L
X
scaling for XXL clusters specifically (Section
3.2
;
P. Giles et al., in preparation). We stress that any such estimates
based on the extrapolation of scaling relations beyond the mass
and redshift regimes where they are calibrated must be regarded
skeptically. Nevertheless, for completeness, we collect in Table
4
a few more mass estimates based on the adopted cluster redshift
5
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
0.5
1.0
2.0
5.0
12 51020
E
(
z
)
−
2
3
L
0.5
−
2
keV
(
10
44
erg
s
−
1
)
E
(
z
)
D
A
(
z
)
2
Y
500
(
10
−
5
Mpc
2
)
SPT
J0217−0345
Figure 3.
X-ray
luminosity
and
SZ
effect
measurements
for
XLSSU J0217
−
0345 are compared with measurements of SPT clusters
from Andersson et al. (
2011
). Solid and dashed lines indicate the nominal
L
X
–
Y
500
relation fit to the SPT data and its 68.3% confidence predictive range
(Section
4.2
; the predictive range accounts for intrinsic scatter and uncertainty
in the slope of the scaling relation, but not uncertainty in its evolution). The
filled circle showing XLSSU J0217
−
0345 is from our analysis in Section
3.2
,
assuming a cluster redshift
z
=
1
.
91. Open circles show the nominal results
assuming
z
=
1
.
7and2
.
1, the limits of the likely redshift range identified
from photometric data (
W13
). The triangle shows our measurements if the
cluster redshift is assumed to be 1.0, where the photometric data show a local
maximum in the distribution of galaxy redshifts (although these galaxies are
not clustered about the X-ray emission). The combination of X-ray flux and SZ
data also disfavors a cluster redshift
z
=
1 compared with 1
.
9, assuming that
the adopted evolution of the scaling relation holds out to
z
∼
2. The red square
shows the best-fitting value, assuming
z
=
1
.
91, when the pressure profile
template of Planck Collaboration et al. (
2013c
) is used rather than that of
S13
;
the two agree at the
∼
1
σ
level(seethe
Appendix
).
(A color version of this figure is available in the online journal.)
of
z
=
1
.
91 and either the survey X-ray luminosity or our
measurement of
Y
500
from Section
3.2
. Given the large and
poorly quantified systematic uncertainties associated with the
extrapolation in redshift, we do not quote errors for these
estimates. Nevertheless, the overall consensus is a value of
M
500
roughly in the (1–2)
×
10
14
M

range, consistent with our own
estimates.
Any cosmological interpretation of the detection of
XLSSU J0217
−
0345 should account for the survey selection
function and take place in the context of appropriately cali-
brated scaling relations at
z>
1 (Allen et al.
2011
). However,
we note that the mass estimates here, taken at face value, are
entirely consistent with predictions of the concordance cosmo-
logical model (Harrison & Hotchkiss
2013
).
17
4.2. SZ–X-Ray Scaling
Figure
3
compares the
L
X
and
Y
500
values for XLSSU J0217
−
0345 with measurements of SPT clusters (spanning 0
.
3
<
z<
1
.
08) from Andersson et al. (
2011
, hereafter A11). Those
17
Specifically, we ran the Matlab code provided by Harrison & Hotchkiss
(
2013
) assuming a flat
Λ
CDM model with
h
=
0
.
7,
Ω
m
=
0
.
3, and matter
power spectrum amplitude
σ
8
=
0
.
8. The code calculates three measures of
rareness for a cluster with a given mass and redshift under a given
cosmological model. Using a nominal mass and redshift of
M
500
=
1
.
34
×
10
14
M

and
z
=
1
.
91, all three measures indicate that the
existence of XLSSU J0217
−
0345 within a 25 deg
2
search area is consistent
with the assumed cosmology. This conclusion does not change if the search
area is 11 deg
2
(corresponding to the precursor
XMM
-LSS survey).
authors did not explicitly fit the
L
X
–
Y
500
scaling relation, but
an approximate
L
X
–
Y
500
relation for the SPT clusters can be
constructed by algebraically combining their results for the
L
X
–
M
500
and
Y
500
–
M
500
relations. Including a unit conversion
from keV
M

to Mpc
2
,thisis
E
(
z
)
D
A
(
z
)
2
Y
500
10
−
5
Mpc
2
=
1
.
48
(
E
(
z
)
−
2
/
3
L
X
10
44
erg s
−
1
)
1
.
42
.
(8)
Here, for consistency, we have followed
A11
in assuming a small
departure from self-similar evolution in the
L
X
–
M
500
relation
(ultimately based on the work of Vikhlinin et al.
2009a
), leading
to the combination
E
−
2
/
3
L
X
rather than
E
−
1
L
X
. Equation (
8
)
appears as a solid line in Figure
3
, and qualitatively fits the SPT
clusters well. At the smallest luminosities shown, bias from the
SPT SZ selection will become increasingly important; the same
bias prevents us from straightforwardly fitting the published
A11
measurements. Note that the
A11
scaling relation fits did
approximately account for this selection bias.
Instead, we fit a power-law plus scatter model to the
L
X
/E
2
/
3
>
2
×
10
44
erg s
−
1
SPT data, with the slope fixed
to 1.42, finding an intrinsic scatter of 42
+18
−
12
%, marginally larger
than the expected
∼
30% (based on a
L
X
–
M
scatter of 40%–45%;
e.g., Mantz et al.
2010a
). Incorporating this 42% intrinsic scat-
ter, and adopting an uncertainty of
±
0
.
39 on the slope, based
on
A11
, yields the 68.3% confidence predictive range indicated
by the dashed lines in Figure
3
. With the assumed evolution,
XLSSU J0217
−
0345 is consistent with the SPT scaling relation.
Adopting self-similar evolution would reduce this consistency,
although not by a significant amount compared with the intrin-
sic scatter in the relation. Future work including a large sample
of XXL clusters followed up with CARMA, covering a range
of redshifts and luminosities, will provide better insight into the
evolution of the scaling relation and related astrophysics.
The placement of XLSSU J0217
−
0345 on this scaling dia-
gram is dependent on the cluster redshift. While there is good ev-
idence for a redshift
∼
1
.
9 from photometric data (
W13
), this has
not yet been spectroscopically confirmed. Section
3.2
showed
that our
Y
500
constraint has a relatively mild dependence on
the assumed redshift. In contrast, the rest-frame
L
X
value in-
ferred from the measured X-ray flux straightforwardly depends
on redshift through factors of the luminosity distance and, to a
lesser extent, the
K
-correction. Open circles in Figure
3
show
the nominal positions of XLSSU J0217
−
0345 in the scaling-
relation plot corresponding to cluster redshifts of 1
.
7 and 2
.
1,
the limits of the likely redshift range identified by
W13
; the dif-
ferences from
z
=
1
.
91 are small compared to the measurement
errors and intrinsic scatter, and do not change our conclusions
above.
Also shown in the figure (the triangular symbol) is the
result assuming
z
=
1
.
0, corresponding to a secondary peak
in the distribution of galaxy redshifts from
W13
. While the
photometric data disfavor this redshift in any case (the
z
∼
1
galaxies are not clustered around the X-ray emission), Figure
3
illustrates that requiring X-ray flux and SZ data to be consistent
with a well-calibrated scaling relation can in principle provide
complementary information on galaxy cluster redshifts. If we
assume that the adopted evolution of the scaling relation holds
precisely, this consistency requirement favors a redshift
z
=
1
.
9
over
z
=
1 by a factor of
∼
5, accounting for the measurement
uncertainties, the intrinsic scatter, and the statistical uncertainty
in the normalization and slope of the scaling relation. In practice,
data such as those we present here (with the addition of
6
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
spectroscopic redshift confirmation) should be used to better
constrain the slope and evolution of the
L
X
–
Y
500
scaling relation,
allowing this technique to be applied to new clusters discovered
in the future.
Within the measurement uncertainties and intrinsic scatter,
our conclusions in this section are robust against the particular
pressure profile template (
S13
) adopted in this work. The red
square in Figure
3
shows the results that would be obtained
(assuming
z
=
1
.
91) when adopting instead the template profile
of the Planck Collaboration et al. (
2013c
); see further discussion
in the
Appendix
.
5. SUMMARY
We have detected the SZ effect of XXL galaxy cluster
XLSSU J0217
−
0345, confirming the presence of a hot ICM.
With a photometrically determined redshift of
z
=
1
.
91
+0
.
19
−
0
.
21
(
W13
), XLSSU J0217
−
0345 is the most distant cluster for
which the SZ effect has been detected. Extrapolating a variety
of locally calibrated scaling relations, we estimate a mass in
the range
M
500
∼
(1–2)
×
10
14
M

from the X-ray and SZ
data, with the caveat that such estimates are heavily dependent
on the assumed evolution of the scaling relations. In contrast,
our measurement of the spherically integrated Comptonization,
Y
500
=
(3
.
0
±
0
.
4)
×
10
−
12
, is relatively insensitive to the
cluster’s redshift over a broad range.
For redshifts consistent with the photometric data, the mea-
sured
Y
500
and X-ray luminosity are in good agreement with
the extrapolation of a
Y
500
–
L
X
scaling relation calibrated from
higher-mass and lower-redshift SPT clusters (
A11
). In princi-
ple, requiring consistency with such a scaling relation provides a
way to constrain cluster redshifts based only on X-ray flux and
SZ measurements. At the moment, uncertainties in the slope
and especially in the evolution of the
Y
500
–
L
X
relation are large,
limiting the utility of this approach for relatively low-mass, high-
redshift clusters such as XLSSU J0217
−
0345. However, given
a scaling relation that has been calibrated at similar masses and
at redshifts
z>
1, SZ follow-up could provide confirmation and
redshift and mass information for the population of low signal-
to-noise, extended X-ray detections expected in new surveys
such as eROSITA.
We note that the SZ measurements presented here were made
using only the CARMA sub-array of eight 3.5 m antennas
operating at a wavelength of 1 cm. Using the new, low-noise
centimeter-wave receivers recently installed on all 23 antennas,
similar detection signal-to-noise could be achieved roughly one-
tenth of the time, while also providing sensitivity over a larger
range of angular scales.
XXL is an international project based around an
XMM
Very Large Program surveying two 25 deg
2
extragalactic fields
at a depth of
∼
5
×
10
−
15
erg cm
−
2
s
−
1
in the 0.5–2.0 keV
band. The XXL Web site is
http://irfu.cea.fr/xxl
. Multi-band
information and spectroscopic follow-up of the X-ray sources
are obtained through a number of survey programs, summarized
at
http://xxlmultiwave.pbworks.com/
.
Support for CARMA construction was derived from the states
of California, Illinois, and Maryland, the James S. McDon-
nell Foundation, the Gordon and Betty Moore Foundation, the
Kenneth T. and Eileen L. Norris Foundation, the University
of Chicago, the Associates of the California Institute of Tech-
nology, and the National Science Foundation (NSF). Ongoing
CARMA development and operations are supported by the
National Science Foundation under a cooperative agreement,
0.20
0.25
0.30
0.35
0.40
0.45
0.50
1234567
r
500
(
Mpc
)
10
12
Y
500
Arnaud 2010
Planck 2013
Sayers 2013
Figure 4.
Two-dimensional 68.3% and 95.4% confidence regions from an
analysis as in Section
3.2
, comparing results employing the pressure profile
templates given by Arnaud et al. (
2010
), the Planck Collaboration et al. (
2013c
),
and
S13
. Although the constraints are mutually consistent, the difference
between the template profiles (primarily in the slope at large radii) does have an
effect on our results.
(A color version of this figure is available in the online journal.)
and by the CARMA partner universities; the work at Chicago
was supported by NSF grant AST-1140019. Additional sup-
port was provided by PHY-0114422. F.P. acknowledges support
from BMBF
/
DLR grant 50 OR 1117 and the DfG Transregio
Programme TR33.
Facilities:
CARMA,
XMM
(EPIC)
APPENDIX
INFLUENCE OF THE PRESSURE PROFILE TEMPLATE
The CARMA sub-array of eight 3.5 m telescopes sample
a limited range of angular scales around
∼
1

that are well
matched to detecting the bulk SZ effect of distant clusters, but
not to measuring the detailed shape of cluster pressure profiles.
Consequently, some assumption about the shape of the profile
must be made in order to reconstruct the three-dimensional
Comptonization of a galaxy cluster from these data.
The parameterized form of the scaled pressure profile in
Equation (
1
) was proposed by Nagai et al. (
2007
), and its
parameters have been constrained from the combination of
X-ray data and hydrodynamical simulations (Arnaud et al.
2010
), X-ray and SZ data (Planck Collaboration et al.
2013c
),
and SZ data alone (
S13
). In this work, we adopt the
S13
template
because it has the advantage of being fit to SZ data at all radii
(rather than X-ray data at small radii and
/
or simulations at large
radii). In this Appendix, we compare results obtained employing
the
S13
template to those that assume templates from Arnaud
et al. (
2010
) and the Planck Collaboration et al. (
2013c
), in order
to estimate the impact of this choice.
Figure
4
shows constraints from the analysis described in
Section
3.2
, employing each of the pressure templates. (These
are displayed in terms of
r
500
rather than
r
s
because the templates
specify different values of
c
500
; hence, our X-ray prior on
r
500
translates to different values of the scale radius in each
case.) The primary difference between the templates is the
slope of the pressure profile at large radii, which is steepest
for the Arnaud et al. (
2010
) template and shallowest for the
7
The Astrophysical Journal
, 794:157 (8pp), 2014 October 20
Mantz et al.
S13
template (see
S13
). This is reflected straightforwardly
in a relatively smaller value of
Y
500
obtained from the
S13
template, since a larger fraction of the projected signal is
ascribed to pressure at radii
>r
500
. We note, however, that the
two-dimensional constraints shown remain consistent at the 1
σ
level. The marginalized constraints on 10
12
Y
500
are respectively
4
.
2
±
0
.
5 (for the Arnaud et al.
2010
template), 4
.
0
±
0
.
5 (for
Planck Collaboration et al.
2013c
), and 3
.
0
±
0
.
4(for
S13
). In
termsofFigure
3
, the values derived using all three templates
lie within the 1
σ
predictive interval of the SPT scaling relation,
i.e., XLSSU J0217
−
0345 is within the intrinsic scatter of the
extrapolated relation regardless of which template is used. Note
that the significance of the cluster detection, in terms of the
improvement in
χ
2
when a model for the cluster is included in
the fit, is similar across all three templates.
We next consider whether the

1
σ
discrepancy between the
constraints in Figure
4
might be reduced if uncertainty in each of
the template shapes is taken into account. For the Arnaud et al.
(
2010
) template there is effectively no measurement error, since
the profile at radii
r>r
500
is assumed to match simulations.
18
In contrast, both the Planck Collaboration et al. (
2013c
) and
S13
templates are based on SZ measurements of the pressure at large
radii. We were able to obtain the full posterior distribution of the
parameters determining the model in Equation (
1
)fromthe
S13
analysis (J. Sayers 2014, private communication). Marginalizing
over this multi-dimensional prior expands the
S13
-template
constraints to be consistent with the other templates at the
1
σ
level, as would be expected from the
∼
1
σ
consistency of
the templates themselves within these uncertainties (
S13
). We
cannot repeat this exercise for the Planck Collaboration et al.
(
2013c
) template, since the measurement uncertainties in that
case are not available to us. However, it seems reasonable to
conclude that the small discrepancy between these two templates
can be explained by measurement uncertainties affecting the
templates themselves.
Further study of the pressure in cluster outskirts, at and
beyond the virial radius, would help to settle this question.
We note that all of the works considered above include rela-
tively strong priors by virtue of adopting a parameterized model
(Equation (
1
)). A non-parametric approach such as the Gaussian
process model investigated by
S13
may provide a better alterna-
tive, given sufficiently precise data; that particular option has the
benefit of naturally including both measurement uncertainties
and intrinsic scatter among clusters as a function of radius.
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