1401.2087v2.pdf

Submitted January 9, 2014; accepted August 25, 2014

Preprint typeset using L

X style emulateapj v. 5/2/11

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,

E. M. Leitch,

1,2

D. P. Marrone,

S. Muchovej,

C. Adami,

M. Birkinshaw,

M. Bremer,

N. Clerc,

P. Giles,

C. Horellou,

B. Maughan,

F. Pacaud,

M. Pierre,

J. Willis

Submitted January 9, 2014; accepted August 25, 2014

ABSTRACT

report

the

detection

the

Sunyaev-Zel’dovich

(SZ)

effect

galaxy

cluster

XLSSU J021744.1

−

034536, using 30 GHz 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

= 1

−

, 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

500

= (3

−

, a measurement which 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

∼

2, we

estimate a mass

500

∼

(1–2)

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.

Subject headings:

galaxies: clusters: individual (XLSSU J021744.1

−

034536) – galaxies: clusters: intr-

acluster medium – X-rays: galaxies: clusters

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, Evrard, & Mantz 2011), a number

of observational programs seek to extend the census of

the cluster population to redshifts

≥

1. Efforts have in-

cluded searches for serendipitous detections (Fassbender

Department of Astronomy and Astrophysics, University of

Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

Kavli Institute for Cosmological Physics, University of

Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

Department of Physics/Enrico Fermi Institute, University of

Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

Steward Observatory, University of Arizona, 933 North

Cherry Avenue, Tucson, AZ 85721, USA

Owens Valley Radio Observatory, California Institute of

Technology, Big Pine, CA 93513, USA

LAM, OAMP, Universit ́e Aix-Marseille & CNRS, Pˆole de

l’

Etoile, Site de Chˆateau Gombert, 38 rue Fr ́ed ́eric Joliot-Curie,

F-13388, Marseille 13 Cedex, France

H. H. Wills Physics Laboratory, University of Bristol, Tyn-

dall Avenue, Bristol BS8 1TL, UK

Max-Planck Institut f ̈ur Extraterrestrische Physik, Giessen-

bachstrasse 1, D-85748 Garching, Germany

Department of Earth and Space Sciences, Chalmers Univer-

sity of Technology, Onsala Space Observatory, SE-439 92 Onsala,

Sweden

Argelander-Institute for Astronomy, Auf dem H ̈ugel 71, D-

53121 Bonn, Germany

Service d’Astrophysique, Bt. 709, CEA Saclay, F-91191 Gif

sur Yvette Cedex, France

Department of Physics and Astronomy, University of Vic-

toria, 3800 Finnerty Road, Victoria, BC, Canada

E-mail:

amantz@kicp.uchicago.edu

et al. 2011a; Mehrtens et al. 2012), and controlled surveys

(Eisenhardt et al. 2008; Muzzin et al. 2008; Hasselfield

et al. 2013; Planck Collaboration 2013b; Reichardt et al.

2013). The number of confirmed, high-redshift clusters

has recently expanded rapidly, including

∼

5 discover-

ies 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 ex-

tended 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

∼

−

erg cm

−

in the 0.5–2.0 keV band over an

11 sq. deg. footprint that has extensive, complementary

optical and IR photometry. Clusters discovered by the

survey reach redshifts as high as

∼

2 (Willis et al.

2013, hereafter W13; see also Valtchanov et al. 2004;

Willis et al. 2005; Bremer et al. 2006; Pierre et al. 2006;

Pacaud et al. 2007; Maughan et al. 2008). An expanded

survey footprint covering 50 sq. deg. (XXL) has since

been completed to similar depth, and a number of cos-

mological 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 Astronomy

(CARMA), targeting cluster detec-

tions in the northern 25 sq. deg. 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

http://www.mmarray.org

arXiv:1401.2087v2 [astro-ph.CO] 12 Sep 2014

A. B. Mantz et al.

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 SZA). This cluster is a “class 1” detection, 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 of 1

−

erg cm

−

(W13). With a pho-

tometric redshift

∼

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 confirma-

tion 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 (

ugrizY JK,

m) pho-

tometric data covering XLSSU J0217

−

0345, and we sum-

marize the key results of that analysis here. The dis-

tribution of photometric redshifts for galaxies near the

X-ray detection is bimodal, with a peak at

∼

0 and

another (larger) peak at

∼

9. Galaxies associated

with the

∼

1 peak display neither spatial clustering

associated with the X-ray source nor an identifiable red

sequence. In contrast, galaxies with photometric red-

shifts 1

< z <

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

= 10 and observed at

= 1

9. On this basis, W13

conclude that the

∼

1 peak arises from an unassoci-

ated foreground structure, and assign a cluster redshift

= 1

−

. Note that the quoted uncertainty repre-

sents the full width of the peak in the galaxy redshift

histogram, not the error on the mean of this peak. Spec-

troscopic confirmation of this redshift is not yet available,

though we note that comparison of the cluster’s X-ray

flux with our CARMA data favors a redshift

∼

9 com-

pared 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 Comp-

ton

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

ΛCDM cosmological model, with dark energy in the form

of a cosmological constant, described by Hubble param-

eter

70 km s

−

Mpc

−

= 1, matter density

Ω

= 0

3 and dark energy density Ω

= 0

7. Quoted

uncertainties refer to 68.3% confidence intervals (with

the exception of the photometric redshift estimate, noted

above). We report dimensionless, spherically integrated

Comptonization (

) in units of steradians.

Table 1

CARMA Data

UT date

config

int

c0927.3SL

31J02170.1

2012-03-06

2.5

c0927.3SL

31J02170.2

2012-03-09

3.5

c0927.3SL

31J02170.3

2012-03-10

3.5

c0927.3SL

31J02170.4

2012-03-12

2.2

c0927.3SL

31J02170.5

2012-03-13

2.6

c0927.3SL

31J02170.6

2012-03-14

2.3

c0927.3SL

31J02170.7

2012-03-15

1.6

c0927.3SH

31J02170.1

2012-05-31

3.6

c0927.3SH

31J02170.3

2012-06-04

2.5

c0927.3SH

31J02170.4

2012-07-24

1.9

c0927.3SH

31J02170.5

2012-09-01

2.2

c1171.33SH

30s4.3

2013-11-01

0.4

c1171.33SH

30s4.4

2013-11-02

3.5

c1171.33SH

30s4.5

2013-11-03

3.5

c1171.33SH

30s4.7

2013-11-04

3.1

c1171.33SH

30s4.8

2013-11-05

3.2

c1171.33SH

30s4.9

2013-11-06

2.8

c1171.33SH

30s4.10

2013-11-08

0.1

c1171V.35SH

30s6.7

2013-11-10

1.7

c1171.33SH

30s4.11

2013-11-11

3.1

c1171V.36SH

30s7.2

2013-11-12

3.0

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.

Effective on-source integration time after flagging (hours).

CARMA DATA

CARMA is a heterogeneous interferometric array com-

prised of six 10.4 m, nine 6.1 m, and eight 3.5 m tele-

scopes; 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 span-

ning 2012 March–July and 2013 September–November.

The 3.5 m antennas were configured with six elements

in a compact array, providing 15 baselines with sensitiv-

ity at arcminute scales, and two outlying elements pro-

viding 13 baselines with sensitivity at higher resolution.

The compact and extended baselines respectively sam-

ple

ranges of 0.35–2 k

and 2–9.5 k

with compara-

ble flux sensitivity, allowing emission from compact radio

sources to be distinguished from the extended SZ effect.

The signals were processed by the CARMA 8 GHz band-

width digital correlator in sixteen 500 MHz sub-bands,

each consisting of 16 channels. More details of the spe-

cific observations can be found in Table 1.

Our data reduction procedure is described in Mu-

chovej et al. (2007). Briefly, the data are filtered for

bad weather, shadowing, and high system temperatures

or other technical issues, and bandpass and gain cali-

brations are applied based on periodic observations of

planets and radio-bright quasars. The absolute flux cal-

ibration 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 to-

tal of 52.8 hours of on-source integration time.

short baselines (

radii

2 k

) the rms noise level

is 0.15 mJy

beam, with a 117

129 arcsec full-width-

at-half-maximum (FWHM) synthesized beam. At long

baselines (

2 k

) , the noise is 0.13 mJy

beam, and the

synthesized beam FWHM is 17

7 arcsec.

SZ Effect of a

= 1

9 Galaxy Cluster

−03:45:00

43:00

47:00

49:00

Declination

02:17:45

17:55

17:35

Right ascension

1 arcmin

−0.8

−0.4

0.0

0.4

0.8

flux density (mJy/beam)

Figure 1.

Left: Short-baseline (

radii

) 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

−

5, and

−

5 times the rms noise level of the short-baseline map. Galaxies with photometric redshifts in the range

< z <

1 are circled in green.

The short-baseline map, after modeling and removing

point sources (Section 3) and applying the CLEAN im-

age deconvolution 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

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 over-

laid, and galaxies with photometric redshifts between 1.7

and 2.1 circled.

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

data at all baselines. To parametrize the SZ sig-

nal, we adopt the Nagai et al. (2007) form for the shape

of the three-dimensional, spherically symmetric electron

pressure profile of clusters,

(

) =

[1 +

]

(

−

)

/α

(1)

and fix the parameters

= 0

86,

= 3

67 and

= 0

as prescribed by Sayers et al. (2013, hereafter S13). We

discuss the implications of using this particular measure-

ment of the parameters in Equation 1 in Appendix A.

The free parameters of this model are the position of

the cluster center; the scale radius, which normalizes the

radial coordinate (

r/r

, or

θ/θ

in units of angle);

and an overall normalization, which we take to be the

line-of-sight Comptonization through the cluster center,

(

)

∫

∞

dθP

(

θ/θ

)

(2)

where

is the Thompson cross section,

is the elec-

tron rest mass,

is the speed of light in vacuum, and

(

) is the angular diameter distance to the cluster.

The Comptonization integrated in a sphere correspond-

ing to angular radius Θ is

(Θ) =

(

)

∫

π θ

dθP

(

θ/θ

)

(3)

Given a prescription for determining

500

we thus can

straightforwardly calculate

500

[

500

(

)]. The

closely related quantity

(

)

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 they are primarily constrained by the long

baseline data, where signal from the cluster is negligible

(

radii

∼

2 k

). There are two compact, emissive

sources detected in the data, both several arcmin from

the cluster position, and we fit for their positions and flux

densities simultaneously with the cluster model. The re-

sults appear in Table 2; we find flux densities at 30 GHz

of 2

09 and 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 clus-

ter position (i.e., there are no radio sources in projection

with the cluster SZ decrement in Figure 1). There is neg-

ligible covariance between the brightness of these sources

and cluster parameters in our fits. In particular, a fac-

tor of

∼

2 change to the flux density of the brighter and

closer point source would be required to force a 1

shift

Note that measuring

does not require explicit assump-

tions about the cluster redshift or the cosmic expansion history.

The factors of

(

) appearing in Equations 2–3 are only neces-

sary to express these quantities in terms of the electron pressure

profile.

Defined as the cluster radius enclosing a mean density 500

times the critical density of the Universe at the cluster’s redshift:

500

= (2000

πρ

(

)

500

A. B. Mantz et al.

Table 2

Properties of Unresolved Radio Sources

Dec

Offset

flux (mJy)

02:17:57.30

′′

−

03:46:47.5

′′

3.55

′

02:17:51.84

′′

−

03:40:29.4

′′

5.48

′

Note

. — J2000 positions, angular distances from the XXL clus-

ter position (02:17:43.9

−

03:45:36), and 30 GHz flux densities (cor-

rected for the primary beam) of unresolved radio sources detected

near XLSSU J0217

−

0345 in our observations.

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 re-

lation 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,

the addition of the cluster model yields a significantly im-

proved fit compared to a point-source-only model, with

∆

min

∼

85 (for 55 005 degrees of freedom in the case of

Section 3.1, equivalent to a 7

significance). Statisti-

cally, the cluster models in the following sections provide

equally good fits to the data. Their constraints on the

integrated Comptonization,

500

, agree within measure-

ment uncertainties. These analyses also produce esti-

mates of the cluster mass, which are more sensitive to a

priori assumptions than the

500

constraints; we will dis-

cuss the mass estimates further in Section 4.1. Table 3

summarizes the constraints on cluster parameters.

We note an offset of 34

9 arcsec 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

∼

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 ra-

dius of the pressure profile is self-consistently related to

its normalization and the cluster mass through a scal-

ing relation linking pressure and mass. In this case, the

single free parameter describing the pressure profile of

the cluster is

500

, which determines the scale radius

through the fixed parameter

500

= 1

18 (S13).

The normalization of the electron pressure profile is given

(

500

) =

(

0158

keV

)

(

)

(

500

−

)

(4)

Table 3

Cluster Properties

Section 3.1

Section 3.2

Section 3.3

Offset E (

′′

)

Offset N (

′′

)

−

(

′

)

652

017

−

500

−

500

(10

−

Mpc

)

−

500

(Mpc)

388

010

—

500

(10

)

—

Note

. — Best fitting values and 68.3% confidence intervals for

the cluster parameters of our SZ model. Offsets describe the posi-

tion of the cluster model center with respect to 02:17:43.9

−

03:45:36

in J2000 coordinates, and

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

and

, resulting in tight

constraints on those parameters, as well as on the mass. In Sec-

tion 3.2 we instead apply a Gaussian prior to

, but do not impose

a prior on

. In Section 3.3, we use a uniform prior on

. The ba-

sis of the mass constraints also differs; see the indicated sections for

details. The

500

and

500

constraints assume a cluster

redshift

= 1

91.

with

= 0

12, and where we have neglected a higher-

order correction in the exponent of

500

(see Arnaud

et al. 2010 and S13). Here

(

) =

(

)

encodes the

evolution of the Hubble parameter.

This analysis yields a mass estimate of

500

= (1

11)

, corresponding to scale radius

329

009 Mpc (statistical uncertainties only). Note

that we have simply extrapolated the S13 scaling rela-

tion, calibrated at

z <

9, to

= 1

9. This

500

con-

straint, as with any such extrapolated estimate, should

therefore be treated with extreme caution. The con-

straint on the spherically integrated Comptonization is

500

= (2

−

, 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 fit-

ting the SZ data which is less constraining than the one

in Section 3.1. This procedure introduces a covariance

between the measured values of

and

. In practice,

however, this covariance is negligible compared to the

measurement uncertainties, as shown below.

The Kaiser (1986) self-similar model relating X-ray lu-

minosity and mass is

∆

(

)

∝

[

(

)

∆

]

(5)

with

= 4

3 for the bolometric luminosity, and where

both quantities are integrated within a fixed overdensity

with respect to critical (e.g., ∆ = 500). The factors

(

) arise from the critical density,

(

)

∝

(

)

For soft-band emission from clusters (such as the 0.5–

2.0 keV band used for XXL), measured values of

span

the range

∼

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

SZ Effect of a

= 1

9 Galaxy Cluster

0.15

0.20

0.25

0.30

0.35

0.40

0.45

(

)

0.15

0.20

0.25

0.30

0.35

0.40

0.45

(

)

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, parametrized by the line-of-sight Comptonization through the cluster center. Right: scale radius versus the spherically

integrated Comptonization within

500

precise value within this range has a negligible effect on

our results (

1 arcsec in the estimate of

), we take

= 4

3. Using that

∆

∝

(

)

∆

, the above relation

thus yields

∆

∝

∆

(

)

−

∝

∆

(

)

−

(6)

We calibrate the normalization of this relation using

other XXL clusters, spanning redshifts 0

< z <

1, for

which deep X-ray observations provide estimates of mass

and

500

(Giles et al., in preparation).

Identifying the

0.5–2.0 keV

values estimated from the survey data

with

500

for this purpose, we find

500

Mpc

= (1

035

021)

(

erg s

−

)

(

)

−

(7)

with a residual scatter of

∼

4%.

Owing to the use of the luminosity–mass scaling in

Equation 5, we expect an additional uncertainty of

∼

11% to apply to estimates of

500

, given an intrinsic scat-

ter in

at fixed

500

of 40–45% and an

–

500

slope

∼

3. In practice, we identify

500

, with

500

= 1

18 from S13 and

500

estimated from Equation 7,

and marginalize over a Gaussian prior with a standard

deviation of 12%, accounting for the systematic and sta-

tistical sources of uncertainty. Assuming the nominal

redshift of 1.91, this yields

= 0

04 Mpc, imply-

ing a mass

500

= (1

Marginalizing over this

–motivated prior on the

pressure scale radius, we constrain the normalization

and center of the cluster model from the SZ data. Our

The calibration uses 5 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 es-

timated directly from the survey count rates, and masses from

measurements of

(the product of gas mass and temperature)

from either the survey data or deeper XMM data, assuming a ref-

erence

–mass relation. More details, as well as a more complete

analysis of cluster scaling relations, will appear in Giles et al. (in

prep). Note that the data used here are not powerful enough to

directly provide a meaningful constraint on the slope,

constraints from this analysis are summarized in Ta-

ble 3; we find

500

= (3

−

, or equivalently

(

)

500

= (9

−

Mpc

As described above, there is a strong degeneracy be-

tween the scale radius and the pressure normalization,

which can be seen in the joint constraints on these pa-

rameters 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 Comptoniza-

tion,

500

(with a somewhat weaker degree of correla-

tion). 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

2, and

adjusting the prior on

accordingly, we find that

500

changes by only

∓

4%, well within our statistical uncer-

tainties.

While we performed the test above by repeating the

entire analysis assuming a different value for the clus-

ter redshift, an approximate estimate for the size of the

effect can be obtained as follows. Taking advantage of

the fact that

500

∝

∼

∝

500

in Figure 2, the frac-

tional shift in

500

with redshift follows from convert-

ing Equation 7 into an expression for

and accounting

straightforwardly for the luminosity-distance dependence

. From this, we estimate that differences of

in redshift would be necessary to change the measured

value of

500

by an amount comparable to its statisti-

cal uncertainty (

∼

14%). Note that this shift in

500

partially cancels the explicitly redshift-dependent factor

(

)

(

)

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 pre-

vious 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

A. B. Mantz et al.

Table 4

Mass Estimates

Proxy

Scaling relation

500

(10

)

Section 3.1

Section 3.2

Andersson et al. (2011)

1.4

Planck Collaboration (2013a)

1.7

Pratt et al. (2009)

2.0

Vikhlinin et al. (2009a)

1.7

Mantz et al. (2010a)

1.1

Andersson et al. (2011)

1.3

Note

. — The evolution of cluster scaling relations out to

= 1

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 Sec-

tions 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.

extremely low or high values, and that the constraints

on the cluster position are comparable.

DISCUSSION

4.1.

Mass Estimates

Our analysis has produced two estimates of the mass

of XLSSU J0217

−

0345:

500

∼

from the

SZ data in combination with the pressure scaling rela-

tion of S13 (Section 3.1), and

500

∼

from the preliminary, empirical

scaling for XXL clus-

ters specifically (Section 3.2; Giles et al. in preparation).

We stress that any such estimates based on the extrapo-

lation of scaling relations beyond the mass and redshift

regimes where they are calibrated must be regarded skep-

tically. Nevertheless, for completeness, we collect in Ta-

ble 4 a few more mass estimates based on the adopted

cluster redshift of

= 1

91 and either the survey X-ray

luminosity or our measurement of

500

from Section 3.2.

Given the large and poorly quantified systematic uncer-

tainties associated with the extrapolation in redshift, we

do not quote errors for these estimates. Nevertheless, the

overall consensus is a value of

500

roughly in the (1–

range, consistent with our own estimates.

Any cosmological interpretation of the detection of

XLSSU J0217

−

0345 should account for the survey selec-

tion function and take place in the context of appropri-

ately calibrated 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 predic-

tions of the concordance cosmological model (Harrison &

Hotchkiss 2013).

4.2.

SZ–X-ray Scaling

Figure 3 compares the

and

500

values for

XLSSU J0217

−

0345 with measurements of SPT clusters

Specifically, we ran the Matlab code provided by Harrison &

Hotchkiss (2013) assuming a flat ΛCDM model with

= 0

7, Ω

3 and matter power spectrum amplitude

= 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

500

= 1

and

= 1

91, all three

measures indicate that the existence of XLSSU J0217

−

0345 within

a 25 sq. deg. search area is consistent with the assumed cosmology.

This conclusion does not change if the search area is 11 sq. deg.

(corresponding to the precursor XMM-LSS survey).

0.5

1.0

2.0

5.0

(

)

−

0.5

−

(

−

)

(

)

(

)

500

(

−

)

SPT

J0217−0345

Figure 3.

X-ray luminosity and SZ effect measurements for

XLSSU J0217

−

0345 are compared with measurements of SPT clus-

ters from Andersson et al. (2011). Solid and dashed lines indicate

the nominal

–

500

relation fit to the SPT data and its 68.3%

confidence predictive range (Section 4.2; the predictive range ac-

counts for intrinsic scatter and uncertainty in the slope of the scal-

ing relation, but not uncertainty in its evolution). The filled circle

showing XLSSU J0217

−

0345 is from our analysis in Section 3.2, as-

suming a cluster redshift

= 1

91. Open circles show the nominal

results assuming

= 1

7 and 2

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

= 1 compared with 1

9, assum-

ing that the adopted evolution of the scaling relation holds out

∼

2. The red square shows the best-fitting value, assuming

= 1

91, when the pressure profile template of Planck Collabora-

tion (2013c) is used rather than that of S13; the two agree at the

∼

level (see Appendix A).

(spanning 0

< z <

08) from Andersson et al. (2011,

hereafter A11). Those authors did not explicitly fit the

–

500

scaling relation, but an approximate

–

500

relation for the SPT clusters can be constructed by al-

gebraically combining their results for the

–

500

and

500

–

500

relations. Including a unit conversion from

keV

to Mpc

, this is

(

)

(

)

500

−

Mpc

= 1

(

)

−

erg s

−

)

(8)

Here, for consistency, we have followed A11 in assuming

a small departure from self-similar evolution in the

–

500

relation (ultimately based on the work of Vikhlinin

et al. 2009a), leading to the combination

−

rather

than

−

. Equation 8 appears as a solid line in Fig-

ure 3, and qualitatively fits the SPT clusters well. At the

smallest luminosities shown, bias from the SPT SZ selec-

tion 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

erg s

−

SPT data, with the slope

fixed to 1.42, finding an intrinsic scatter of 42

+18

−

marginally larger than the expected

∼

30% (based on a

–

scatter of 40–45%; e.g., Mantz et al. 2010a). In-

SZ Effect of a

= 1

9 Galaxy Cluster

corporating this 42% intrinsic scatter, and adopting an

uncertainty of

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 intrinsic scatter in the relation. Fu-

ture work including a large sample of XXL clusters fol-

lowed 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

diagram is dependent on the cluster redshift. While there

is good evidence for a redshift

∼

9 from photometric

data (W13), this has not yet been spectroscopically con-

firmed. Section 3.2 showed that our

500

constraint has

a relatively mild dependence on the assumed redshift.

In contrast, the rest-frame

value inferred from the

measured X-ray flux straightforwardly depends on red-

shift 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

7 and 2

1, the limits of the likely redshift range iden-

tified by W13; the differences from

= 1

91 are small

compared to the measurement errors and intrinsic scat-

ter, and do not change our conclusions above.

Also shown in the figure (the triangular symbol) is the

result assuming

= 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

∼

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

= 1

9 over

= 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 spectroscopic red-

shift confirmation) should be used to better constrain

the slope and evolution of the

–

500

scaling relation,

allowing this technique to be applied to new clusters dis-

covered 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

= 1

91) when adopt-

ing instead the template profile of the Planck Collabora-

tion (2013c). See further discussion in Appendix A.

SUMMARY

We have detected the Sunyaev-Zel’dovich effect of XXL

galaxy cluster XLSSU J0217

−

0345, confirming the pres-

ence of a hot ICM. With a photometrically determined

redshift of

= 1

−

(W13), XLSSU J0217

−

0345

is the most distant cluster for which the SZ effect has

been detected. Extrapolating a variety of locally cali-

brated scaling relations, we estimate a mass in the range

500

∼

(1–2)

from the X-ray and SZ data,

with the caveat that such estimates are heavily depen-

dent on the assumed evolution of the scaling relations. In

contrast, our measurement of the spherically integrated

Comptonization,

500

= (3

−

, is relatively

insensitive to the cluster’s redshift over a broad range.

For redshifts consistent with the photometric data, the

measured

500

and X-ray luminosity are in good agree-

ment with the extrapolation of a

500

–

scaling relation

calibrated from higher-mass and lower-redshift SPT clus-

ters (A11). In principle, requiring consistency with such

a scaling relation provides a way to constrain cluster red-

shifts based only on X-ray flux and SZ measurements. At

the moment, uncertainties in the slope and especially in

the evolution of the

500

–

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 sim-

ilar 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 cm-wave receivers recently installed on

all 23 antennas, similar detection signal-to-noise could

be achieved in roughly one tenth of the time, while also

providing sensitivity over a larger range of angular scales.

ACKNOWLEDGMENTS

XXL is an international project based around an XMM

Very Large Programme surveying two 25 sq. deg. extra-

galactic fields at a depth of

∼

−

erg cm

−

in the 0.5–2.0 keV band. The XXL website is

http:

//irfu.cea.fr/xxl

. Multi-band information and spec-

troscopic 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. McDonnell Foundation, the Gordon and Betty Moore

Foundation, the Kenneth T. and Eileen L. Norris Foun-

dation, the University of Chicago, the Associates of the

California Institute of Technology, and the National Sci-

ence Foundation (NSF). Ongoing CARMA development

and operations are supported by the National Science

Foundation under a cooperative agreement, 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. FP acknowledges

support from BMBF/DLR grant 50 OR 1117 and the

DfG Transregio Programme TR33.

Facilities:

CARMA, XMM (EPIC)

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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 arcmin 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 parametrized 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 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 which

assume templates from Arnaud et al. (2010) and the Planck Collaboration (2013c), in order to estimate the impact

of this choice.

Figure A1 shows constraints from the analysis described in Section 3.2, employing each of the pressure templates.

(These are displayed in terms of

500

rather than

because the templates specify different values of

500

; hence, our

X-ray prior on

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 S13 template (see S13). This is reflected straightforwardly in a relatively smaller value of

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

level. The

marginalized constraints on 10

500

are respectively 4

5 (for the Arnaud et al. 2010 template), 4

5 (for

Planck Collaboration 2013c) and 3

4 (for S13). In terms of Figure 3, the values derived using all three templates

lie within the 1

predictive interval of the SPT scaling relation, i.e., XLSSU J0217

−

0345 is within the intrinsic scatter

SZ Effect of a

= 1

9 Galaxy Cluster

0.20

0.25

0.30

0.35

0.40

0.45

0.50

500

(

)

500

Arnaud 2010

Planck 2013

Sayers 2013

Figure A1.

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 (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.

of the extrapolated relation regardless of which template is used. Note that the significance of the cluster detection, in

terms of the improvement in

when a model for the cluster is included in the fit, is similar across all three templates.

We next consider whether the

∼

discrepancy between the constraints in Figure A1 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.

In contrast, both the

Planck Collaboration (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 from the

S13 analysis (J. Sayers, private communication). Marginalizing over this multi-dimensional prior expands the S13-

template constraints to be consistent with the other templates at the 1

level, as would be expected from the

∼

consistency of the templates themselves within these uncertainties (S13). We cannot repeat this exercise for the Planck

Collaboration (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 relatively strong priors by virtue of adopting a parametrized

model (Equation 1). A non-parametric approach such as the Gaussian process model investigated by S13 may provide

a better alternative, 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.

Marrone et al. (2012) showed that varying the shape of the

Arnaud et al. (2010) template at small radii had only a percent

effect on

500

values derived from CARMA data.