Comparison of Sunyaev-Zel'dovich measurements from Planck and from the Arcminute Microkelvin Imager for 99 galaxy clusters

Abstract

We present observations and analysis of a sample of 123 galaxy clusters from
the 2013 Planck catalogue of Sunyaev-Zel'dovich sources with the Arcminute
Microkelvin Imager (AMI), a ground-based radio interferometer. AMI provides an
independent measurement with higher angular resolution, 3 arcmin compared to
the Planck beams of 5-10 arcmin. The AMI observations thus provide validation
of the cluster detections, improved positional estimates, and a consistency
check on the fitted 'size' ($\theta_{s}$) and 'flux' ($Y_{\rm tot}$) parameters
in the Generalised Navarro, Frenk and White (GNFW) model. We detect 99 of the
clusters. We use the AMI positional estimates to check the positional estimates
and error-bars produced by the Planck algorithms PowellSnakes and MMF3. We find
that $Y_{\rm tot}$ values as measured by AMI are biased downwards with respect
to the Planck constraints, especially for high Planck-SNR clusters. We perform
simulations to show that this can be explained by deviation from the
'universal' pressure profile shape used to model the clusters. We show that AMI
data can constrain the $\alpha$ and $\beta$ parameters describing the shape of
the profile in the GNFW model provided careful attention is paid to the
degeneracies between parameters, but one requires information on a wider range
of angular scales than are present in AMI data alone to correctly constrain all
parameters simultaneously.

Full text

arXiv:1405.5013v1 [astro-ph.CO] 20 May 2014
Astronomy & Astrophysics
manuscript no. ms˙2 c
ESO 2014
May 21, 2014
Comparison of Sunyaev-Zel’dovich measurements from
Planck
and from the Arcminute Microkelvin Imager for 99 galaxy clusters
Y. C. Perrott2⋆, M. Olamaie2, C. Rumsey2, M. L. Brown15, F. Feroz2, K. J. B. Grainge2,16,15, M. P. Hobson2, A. N. Lasenby2,16, C. J. MacTavish16,
G. G. Pooley2, R. D. E. Saunders2,16, M. P. Schammel2,10, P. F. Scott2, T. W. Shimwell2,5, D. J. Titterington2, E. M. Waldram2, N. Aghanim11,
M. Arnaud17, M. Ashdown16,2, H. Aussel17, R. Barrena14,8, I. Bikmaev7,1, H. B¨ohringer19, R. Burenin21,20 , P. Carvalho12,16, G. Chon19,
B. Comis18, H. Dahle13, J. Democles17, M. Douspis11, D. Harrison12,16, A. Hempel14,8, G. Hurier11, I. Khamitov22,7, R. Kneissl9,3,
J. F. Mac´ıas-P´erez18, J.-B. Melin6, E. Pointecouteau24,4, G. W. Pratt17, J. A. Rubi˜no-Mart´ın14,8, V. Stolyarov2,16,23, and D. Sutton12,16
(Affiliations can be found after the references)
Received ; Accepted
ABSTRACT
We present observations and analysis of a sample of 123 galaxy clusters from the 2013 Planck catalogue of Sunyaev-Zel’dovich sources with
the Arcminute Microkelvin Imager (AMI), a ground-based radio interferometer. AMI provides an independent measurement with higher angular
resolution, 3arcmin compared to the Planck beams of 5–10arcmin. The AMI observations thus provide validation of the cluster detections,
improved positional estimates, and a consistency check on the fitted ‘size’ (θs) and ‘flux’ (Ytot) parameters in the Generalised Navarro, Frenk and
White (GNFW) model. We detect 99 of the clusters. We use the AMI positional estimates to check the positional estimates and error-bars produced
by the Planck algorithms PowellSnakes and MMF3. We find that Ytot values as measured by AMI are biased downwards with respect to the Planck
constraints, especially for high Planck-SNR clusters. We perform simulations to show that this can be explained by deviation from the ‘universal’
pressure profile shape used to model the clusters. We show that AMI data can constrain the αand βparameters describing the shape of the profile
in the GNFW model provided careful attention is paid to the degeneracies between parameters, but one requires information on a wider range of
angular scales than are present in AMI data alone to correctly constrain all parameters simultaneously.
Key words. Cosmology: observations −Galaxies: clusters: general −Galaxies: clusters: intracluster medium −Cosmic background radiation −
X-rays: galaxies: clusters
1. Introduction
The Planck satellite data-release of 2013 included a catalogue
of 1227 galaxy clusters detected via the Sunyaev-Zel’dovich
(SZ, Sunyaev & Zel’dovich 1972) effect (Planck Collaboration
et al. 2013b). This is the deepest all-sky cluster catalogue in
SZ to date, consisting of clusters spanning redshifts up to ≈1,
and masses of around 1014M⊙to 1015M⊙. SZ-selected sam-
ples have the advantage of a clean, and approximately redshift-
independent (above z≈0.3), selection function in mass (Planck
Collaboration et al. 2013c); in addition, simulations predict that
the SZ ‘flux’ correlates more tightly with mass than, for exam-
ple, X-ray or optical observable quantities (e.g. da Silva et al.
2004,Motl et al. 2005,Nagai 2006,Aghanim et al. 2009,Angulo
et al. 2012,Kay et al. 2012). The Planck SZ catalogue is there-
fore a potentially very powerful tool for investigating the growth
of structure in the Universe; clusters in the catalogue are being
followed up with optical, radio and X-ray telescopes in order to
provide multi-wavelength information to understand fully their
properties.
The Arcminute Microkelvin Imager (AMI; AMI
Consortium: Zwart et al. 2008) is a dual-array interferom-
eter designed for SZ studies, which is situated near Cambridge,
UK. AMI consists of two arrays: the Small Array (SA), opti-
mised for viewing arcminute-scale features, having an angular
resolution of ≈3 arcmin and sensitivity to structures up to
≈10arcmin in scale; and the Large Array (LA), with angular
resolution of ≈30 arcsec, which is insensitive to the arcminute-
⋆Corresponding author: Y. C. Perrott, ycp21@mrao.cam.ac.uk
scale emission due to clusters and is used to characterise and
subtract confusing radio sources. Both arrays operate at a central
frequency of ≈15 GHz with a bandwidth of ≈4.5 GHz, divided
into six channels. For further details of the instrument, see AMI
Consortium: Zwart et al. (2008).
In a previous paper, (Planck Collaboration et al. 2013e, from
here on AP2013) a sample of 11 clusters selected from the
Planck Early Release Catalogue was followed up with AMI in
order to check the consistency of the cluster parameters as mea-
sured by the two telescopes, finding the SZ signals as measured
by AMI to be, on average, fainter and of smaller angular size. We
have used AMI to observe all of the clusters in the Planck 2013
SZ catalogue that are at declinations easily observable with AMI
(excluding those at very low redshift). This serves two purposes:
(a) to investigate the discrepancies found in AP2013 further, and
(b) to provide validation of, improved positional estimates for,
and higher-resolution SZ maps of a large number of Planck clus-
ter detections. We here present these observations and our anal-
ysis of them.
The paper is organised as follows. In Section 2we describe
the selection of the cluster sample. In Section 3we describe the
AMI observations and data reduction, and in Section 4we out-
line the model used to describe the SZ signal. In Section 4.2 we
briefly describe the Planck data analysis and describe in more
detail the analysis of the AMI data in Section 4.3, including
our detection criteria. Section 4.4 contains some representative
examples of the results, and Sections 4.4.6 and 4.4.7 compare
the cluster parameter estimates produced by AMI to those pro-
duced by Planck. In Section 5we use simulations to investigate
1

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
the issue of variation from the ‘universal’ model described in
Section 4, and in Section 5.3 we present results from reanalysing
the real data allowing the shape parameters in the model to vary.
Finally, we conclude in Section 6.
2. Selection of the cluster sample
An initial selection cut of 20◦≤δ < 87◦was applied to sat-
isfy AMI’s ‘easy’ observing limits; although AMI can observe
to lower declinations, increased interference due to geostation-
ary satellites makes observing large samples below δ=20◦
currently difficult. In addition, clusters with known redshifts of
z≤0.100 were excluded since these have large angular sizes
and will be largely resolved out by AMI; although the brightest
of these will still be detectable, it will be difficult to constrain
their properties using AMI data. These initial cuts resulted in an
initial sample size of 337 with Planck SNR values ranging from
4.5 – 20. In this paper, we present results for the subset of the
sample with SNR ≥5; this reduces the sample to 195. Results
for the remaining clusters with 4.5≤SNR <5 will be released
at a later date.
As in the optical, where confusion due to a bright star or a
crowded field can affect the detection likelihood, a benign radio
point source environment is important for AMI, but the requi-
site benignness is difficult to quantify. In practice, the effect of
the source environment on the detection potential of a cluster
depends on many factors including the number, location and ori-
entation of the sources with respect to each other and to the side-
lobes of the primary and synthesised beams. Non-trivial source
environments can create complex and overlappingsidelobe pat-
terns which can create spurious sources or reduce the flux den-
sity of real sources. In turn, the synthesised beam depends on
uv-coverage, which changes for different δand hour-angle cov-
erage of observations of a given cluster. The primary beam is a
function of frequency so the effect of a source at a given offset
from the pointing centre also depends on its spectrum. These ef-
fects are almost impossible to quantify in a systematic way. In
order to apply at least consistent criteria across the whole sam-
ple, the following criteria were applied based on LA observa-
tions: clusters were discarded if there were radio sources of peak
flux density Speak >5mJy within 3 arcmin of the pointing cen-
tre, of Speak >20mJy within 10 arcmin of the pointing centre,
or extended emission with fitted (deconvolved) major-axis size
>2 arcmin and integrated flux density Sint >2 mJy anywhere on
the map; experience suggests that observation of the SZ signal
in such clusters with AMI is unreliable. Clusters were discarded
for source environment based either on existing observations or,
for clusters that had not been previously observed with AMI,
based on a short pre-screening observation carried out with the
LA. It should be noted that some clusters which have been previ-
ously observed and detected by AMI are excluded by these cuts;
some of the new clusters discarded by this process may also be
observable.
In addition, clusters were visually inspected at various stages
of the follow-up and analysis process, and some were rejected at
later stages due to extra source environment problems such as
extended emission not visible on the LA map, or very bright
sources just outside the LA detection radius which affect the SA
map due to the larger primary beam. Here we present results for
the so obtained final sub-sample, which we will refer to as the SZ
sample, consisting of 123 clusters. A breakdown of the numbers
of clusters rejected for various reasons is shown in Table 1.
The full list of clusters within the AMI observational bounds
and their reason for rejection, if not part of the SZ sample, is
Table 1: Numbers of clusters in the 20◦≤δ < 87◦,Planck SNR
≥5 sub-sample in various categories.
Category Number of clusters
Total 229
z≤0.100 34
Automatic radio-source environment rejection 52
Manual radio-source environment rejection 20
Included in sample 123
GREY: A0001 IPOL 15772.689 MHZ A.FLATN.1
Grey scale flux range= 67.0 240.0 MicroJY/BEAM
100 150 200
Declination (J2000)
Right ascension (J2000)
01 10 00 09 30 00 08 30 00 07 30 00 06 30 00 05 30
54 25
20
15
10
05
00
53 55
50
GREY: A0001 IPOL 15734.113 MHZ SA.OHGEO.1
Grey scale flux range= 0.107 1.118 MilliRATIO
200 400 600 800 1000
Declination (J2000)
Right ascension (J2000)
01 10 00 09 30 00 08 30 00 07 30 00 06 30 00 05 30
54 25
20
15
10
05
00
53 55
50
(a) (b)
Fig. 1: Noise maps for a typical cluster observation at δ≈54◦on
the AMI-LA (a) and SA (b). The grey-scales are in µJy beam−1
and on (a) the grey-scale is truncated to show the range of noise
levels. (b) is cut offat the 10% power point of the primary beam.
given in Appendix A. In addition, as a service to the commu-
nity for each cluster we provide information on the 15GHz ra-
dio point source environment (available online at http://www.
mrao.cam.ac.uk/facilities/surveys/ami-planck/).
3. Description of AMI data
Clusters are observed using a single pointing centre on the SA,
which has a primary beam of size ≈20 arcmin FWHM, to noise
levels of /120µJy beam−1. To cover the same area with the LA,
which has a primary beam of size ≈6 arcmin FWHM, the clus-
ter field is observed as a 61-point hexagonal raster. The noise
level of the raster is /100 µJy beam−1in the central 19 point-
ings, and slightly higher in the outer regions. Typical noise maps
and uv-coverages are displayed for both arrays in Figs. 1and 2.
The average observation time for a cluster is ≈30 hours on both
arrays.
Data on both arrays are flagged for interference and cali-
brated using the AMI in-house software package reduce. Flux
calibration is applied using contemporaneous observations of the
primary calibration sources 3C286, 3C48, and 3C147. The as-
sumed flux densities for 3C286 were converted from Very Large
Array total-intensity measurements (Perley & Butler 2013), and
are consistent with the Rudy et al. (1987) model of Mars trans-
ferred on to absolute scale, using results from the Wilkinson
Microwave Anisotropy Probe. The assumed flux densities for
3C48 and 3C147 are based on long-term monitoring with the
SA using 3C286 for flux calibration (see Table 2). Phase calibra-
tion is applied using interleaved observations of a nearby bright
source selected from the VLBA Calibrator survey (Petrov et al.
2008); in the case of the LA, a secondary amplitude calibration is
also applied using contemporaneous observations of the phase-
calibration source on the SA.
2

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
(a) (b)
Fig.2: uv-coverages for a typical cluster observation at δ≈54◦, for the AMI-LA (a) and SA (b). The colours indicate different
channels. Note the different axis scales; the short baselines of the SA are designed for sensitivity to arcminute-scale cluster emission,
while the longer baselines of the LA are insensitive to emission on this scale andare used to characterise and subtract the foreground
radio sources.
Table 2: Assumed I +Q flux densities of 3C286, 3C48 and
3C147.
Channel ¯ν/GHz S3C286/Jy S3C48/Jy S3C147/Jy
3 13.88 3.74 1.89 2.72
4 14.63 3.60 1.78 2.58
5 15.38 3.47 1.68 2.45
6 16.13 3.35 1.60 2.34
7 16.88 3.24 1.52 2.23
8 17.63 3.14 1.45 2.13
Maps of the SA and LA data are made using aips1,cleaning
in an automated manner. Source-finding is carried out at 4σ
on the LA continuum map, as described in AMI Consortium:
Davies et al. (2011) and AMI Consortium: Franzen et al. (2011),
and sources that are detected at ≥3σon at least three channel
maps and are not extended have a spectral index αfitted across
the AMI band. SA data are binned on a grid in uv-space in order
to reduce the memory required for subsequent analysis.
4. Analysing the SZ signal
4.1. Cluster model
For consistency with the Planck catalogue, in this paper we as-
sume the electron pressure profile Pe(r) of each cluster follows
a generalised Navarro-Frenk-White (NFW, Navarro et al. 1997)
model, which is given by (assuming spherical geometry)
Pe(r)=P0 r
rs!−γ"1+ r
rs!α#(γ−β)/α
,(1)
1http://aips.nrao.edu/
where P0is a normalisation coefficient, ris the physical radius,
rsis a characteristic scale radius, and the parameters (γ, α, β) de-
scribe the slopes of the pressure profile at radii r≪rs,r≈rs,
and r≫rsrespectively (Nagai et al. 2007). Following Arnaud
et al. (2010), we fix the slope parameters to their ‘universal’
values, γ=0.3081, α =1.0510, β =5.4905 derived from the
REXCESS sample (B¨ohringer et al. 2007). They are also fixed
to these values in the Planck analysis.
Given this model, the integrated SZ surface brightness, or
integrated Compton-yparameter, for a cluster is given by
Ysph(r)=σT
mec2Zr
0Pe(r′)4πr′2dr′,(2)
where σTis the Thomson scattering cross-section, meis the elec-
tron mass, and cis the speed of light. This has an analytical solu-
tion as r→ ∞, giving the total integrated Compton-yparameter
Ytot,phys as
Ytot,phys =4πσT
mec2P0r3
s
Γ3−γ
αΓβ−3
α
αΓβ−γ
α.(3)
With (γ, α, β) fixed, a cluster’s appearance on the sky
may be described using four (observational) parameters only:
(x0,y0, θs,Ytot), where x0and y0are the positional coordinates
for the cluster, θs=rs/DAis the characteristic angular scale of
the cluster on the sky (DAis the angular diameter distance to
the cluster), and Ytot =Ytot,phys/D2
Ais the SZ surface brightness
integrated over the cluster’s extent on the sky.
This model does not require any redshift information; physi-
cal quantities such as rsand Ytot,phys can be recovered from θsand
Ytot given a redshift. Alternatively, rXand MXfor some overden-
sity radius Xcan be recovered given a redshift, a concentration
parameter cX≡rX/rsand some model or scaling relationship for
3

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
translating Yinto mass (e.g. Planck Collaboration et al. 2013c,
Olamaie et al. 2012). Physical modelling will not be addressed
in this paper.
Note that in the Planck analysis, in order to impose a finite
integration extent, Y5R500 (the SZ surface brightness integrated to
5×R500) is estimated rather than Ytot. For the ‘universal’ GNFW
parameter values, (with c500 =1.177), the two quantities are
equivalent to within 5%.
4.2. Analysis of
Planck
data
The Planck SZ catalogue is the union of the catalogues
produced by three detection algorithms: MMF1 and MMF3,
which are multi-frequency matched-filter detection methods,
and PowellSnakes (PwS), which is a Bayesian detection method.
Full details of these algorithms are provided in Melin et al.
(2006), Carvalho et al. (2009), Carvalho et al. (2012) and Melin
et al. (2012). Since the PwS analysis methodology most closely
matches the Bayesian analysis procedures used to analyse AMI
data, we take cluster parameters produced by PwS as our pre-
ferred ‘Planck’ values, followed by MMF3, and finally MMF1
values where a particular cluster is not detected by all algo-
rithms.
4.3. Analysis of AMI data
The model attempting to describe the AMI data is produced by
a combination of the cluster model described above, the radio
source environment as measured by the LA and a generalised
Gaussian noise component comprising instrumental noise, con-
fusion noise from radio sources below the detection threshold,
and contamination from primordial CMB anisotropies.
Each foreground radio source is modelled by the parameters
(xS,yS,S0, α). Positions (xS,yS) and initial estimates of the flux
density at a central frequency (S0) are produced from the LA
channel-averaged maps; for sources detected at ≥3σon at least
three of the individual channel maps, a spectral index αis also
fitted to the channel flux densities. The flux density and spec-
tral index of sources which are detected at ≥4σon the SA map
are modelled simultaneously with the cluster; this accounts for
possible source variability (although we attempt to observe clus-
ters close in time on the two arrays, this is not always possible
due to different demands on the observing time of the arrays)
and inter-array calibration uncertainty. Flux densities are given
a Gaussian prior with σ=40%; where αhas been fitted from
the LA data, a Gaussian prior with width corresponding to the
fitting uncertainty is applied, otherwise a prior based on the 10C
survey is applied (AMI Consortium: Davies et al. 2011). Sources
detected at <4σon the SA map are subtracted directly based on
the LA values of S0and α(or the median of the 10C prior where
αhas not been fitted) initially. If the cluster position output from
the analysis has directly-subtracted sources within 3 arcmin, the
analysis is repeated with those sources also modelled. The po-
sitions of the sources are always fixed to their LA values as the
LA has higher positional precision.
In the cluster model, x0and y0are the offsets in RA and δ
from the pointing centre of the SA observation; for previously-
known clusters with existing AMI data, the pointing centre is
the X-ray position of the cluster, while for new clusters it is the
Planck position. Gaussian priors are used on x0and y0, centred
on the Planck position (i.e. offset from the pointing/phase ref-
erence centre, if the pointing centre is the X-ray position) and
with width given by the Planck positional uncertainty up to a
maximum of 5 arcmin; larger priors allow the detection algo-
rithm to fix on noise features toward the edges of the SA pri-
mary beam, which has a FWHM of ≈20 arcmin. In practice, no
PwS positional errors in the sample are greater than 5 arcmin.
MMF1 does not give positional error estimates, so clusters de-
tected only by MMF1 are given the maximum 5arcmin error;
some clusters detected by MMF3 (but not PwS) have positional
errors >5 arcmin, but as will be shown in Section 4.4.6, MMF3
positional errors tend to be over-estimated.
Model parameter estimation is performed in a fully Bayesian
manner using the AMI in-house software package McADAM, in
uv-space (see, e.g. Feroz et al. 2009b for more details). Bayes’
theorem states that
Pr(Θ|D,H)=Pr(D|Θ,H) Pr(Θ|H)
Pr(D|H),(4)
where Θis a set of parameters for a model, H, and Dis the data.
Thus, the posterior probability distribution, Pr(Θ|D,H), is pro-
portional to the likelihood, Pr(D|Θ,H), multiplied by the prior,
Pr(Θ|H). The normalising factor is the evidence, Pr(D|H)≡
Z. McADAM uses the nested sampler MultiNEST (Feroz &
Hobson 2008,Feroz et al. 2009a) to obtain the posterior distri-
bution for all parameters, which can be marginalised to provide
two- and one-dimensional parameter constraints.
MultiNEST also calculates the evidence, which can be ig-
nored for parameter estimation but is important for model selec-
tion, since it represents the probability of the data given a model
and a prior, marginalised over the the model’s parameter space:
Z=ZPr(D|Θ,H)Pr(Θ|H)dDΘ,(5)
where Dis the dimensionality of the parameter space. The prob-
ability of two different models given the data can be compared
using their evidence ratio:
Pr(H1|D)
Pr(H0|D)=Pr(D|H1) Pr(H1)
Pr(D|H0)Pr(H0)=Z1
Z0
Pr(H1)
Pr(H0),(6)
where Pr(H1)/Pr(H0) is the a priori probability ratio for the
two models. To assess the detection significance of a cluster, we
therefore perform two parameter estimation runs – one with the
full cluster +radio source environment model (H1), and one with
only the radio source environment model (the ‘null’ run, H0). We
set Pr(H1)/Pr(H0)=1 so that Z1/Z0is a measure of the detec-
tion significance for the cluster. This ratio takes into account the
various sources of noise as well as the goodness of fit of the radio
source and cluster models.
Fig. 3shows the distribution of ∆ln(Z) values in the SZ
sample. It is also useful to define discrete ‘detection’ and ‘non-
detection’ categories based on the continuous evidence ratio val-
ues. We follow Jeffreys (1961) in taking ∆ln(Z)=0 as the
boundary between detections and non-detections. We also de-
fine an additional boundary ∆ln(Z)=3 between ‘moderate’
and ‘clear’ detections, where ‘moderate’ detections are cases
where the data are more consistent with the presence of a cluster
than not, but there is not enough information in the data to con-
strain the model parameters well. For symmetry, we also define
a boundary at ∆ln(Z)=−3 to indicate cases where the cluster
model is strongly rejected by the data. These boundaries were
chosen empirically, by inspecting final maps and posterior dis-
tributions. The four categories are listed in Table 3.
4

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
∆ln(Z)
Number of clusters
0 20 40 60 80 100 120
0
5
10
15
20
Fig.3: The distribution of evidence ratio values in the SZ sam-
ple, with the division into detection categories given in Table 3
indicated by red vertical lines.
Table 3: The evidence difference (∆ln(Z)) boundaries used for
categorising clusters as clear detections, moderate detections,
non-detections and clear non-detections, and the number of clus-
ters in each category in the SZ sample.
Category ∆ln(Z) boundaries Number
Clear detection (Y) ∆ln(Z)≥3 79
Moderate detection (M) 0 ≤∆ln(Z)<3 20
Non-detection (N) −3≤∆ln(Z)<0 21
Clear non-detection (NN) ∆ln(Z)<−3 3
4.3.1. Prior on Ytot and θs
The priors assigned to Ytot and θsin AP2013 and used for the
Planck PwS analysis are based on marginalised distributions of
Ytot and θsin a simulated population of clusters generated ac-
cording to the Jenkins mass function (Jenkins et al. 2001), as
described in Carvalho et al. (2012). The parameterisation func-
tions for these priors are listed in Table 4. These priors ignore,
however, the correlation between Ytot and θs; in addition, they
take into account the Planck selection function only in assuming
minimum and maximum cutoffs in each parameter.
To produce a better approximation to the true distribution of
clusters expected to be detected by Planck, we used the results of
the Planck completeness simulation (Planck Collaboration et al.
2013b, Section 3.1 and 3.2, Fig. 9). This simulation was pro-
duced by drawing a cluster population from the Tinker mass
function (Tinker et al. 2008), and converting the redshifts and
masses to Y500 and θ500 observable quantities using the scaling
relations in Planck Collaboration X (2011). This cluster popu-
lation was injected into the real Planck data assuming GNFW
pressure profiles with the shape parameters varying according
to results from Planck Collaboration et al. (2013d) and a simu-
lated union catalogue was created by running the Planck detec-
tion pipelines on the simulated dataset in the usual manner; see
Planck Collaboration et al. (2013b) for more details.
We noted that the resulting two-dimensional distribution in
θsand Ytot in log-space was elliptical in shape with roughly
Gaussian distribution along the principal axes and performed a
two-dimensional Gaussian fit to the distribution, parameterised
by width and offset in x=log10(θs), width and offset in y=
log10(Ytot), and angle φmeasured clockwise from the y-axis. The
best-fit parameters are listed in Table 4, and the fit and residuals
with respect to the simulated population are shown in Fig. 4. We
use this fit to the simulated population as our prior on θsand Ytot.
θs/arcmin
Ytot /arcmin2
Number of clusters
θs/arcmin
Number of clusters
-20 -10 0 10 20
2510 20 40
0 20 40
2510 20 40
0.001
0.01
0.1
0.001
0.01
0.1
(a) (b)
Fig.4: (a) shows the sampled distribution (red histogram), and
the two-dimensional elliptical Gaussian fit to the Ytot vs θsdis-
tribution in log-space (black lines, enclosing 68% and 95% of
the probability). (b) shows the residuals with respect to the sim-
ulated distribution. Note that the colour-axis scales are different.
4.4. Results
In the SZ sample, 79 are clear detections, 20 are moderate de-
tections, 21 are non-detections and 3 are clear non-detections. A
summary of the results for each cluster in the sample is presented
in Appendix A.
Some representative examples from each category are dis-
cussed in the following. In each case, two foreground-source-
subtracted maps are shown; both are produced using natural
weighting, and the second also has a Gaussian weighting func-
tion with the 30% point at 600 λapplied (the ‘uv-tapered’ map).
This taper downweights the longer baselines, which are only
sensitive to small-angular-scale features, making the extended
cluster more visible. The symbols ×and +show the positions
of subtracted sources, respectively either modelled in McAdam
or directly subtracted based on LA values. shows the AMI
(McAdam-determined) position of the cluster, and the 1×σPlanck
positional error radius is shown as a circle. Contours are plotted
at ±(2,3,4, ..., 10)×the r.m.s. noise level (measured using the
aips task imean), and dashed contours are negative. The synthe-
sised beam is shown in the bottom left-hand corner. We empha-
sise that these maps are only shown for visual inspection and
to assess the residual foreground contamination; all parameter
estimation is done in uv-space.
Posterior distributions for position offset, cluster model pa-
rameters and the flux densities of the closest radio sources to the
cluster centre are also shown; in these plots the units are arc-
sec on the sky for offset in RA (x0) and δ(y0), arcmin2for Ytot,
arcmin for θsand mJy for radio source flux densities. The blue
(pink) areas correspond to regions of higher (lower) probabil-
ity density, and the contours mark the 68% and 95% confidence
boundaries. The Ytot-θsposterior distribution is shown separately
in black overlaid with that obtained by PwS using Planck data
for the cluster in red, as well as the AMI prior (black dashed
line). The joint constraint is shown in yellow where appropri-
ate. Similar maps and posterior distribution plots for the entire
sample are available online at http://www.mrao.cam.ac.uk/
facilities/surveys/ami-planck/.
5

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table 4: Priors used on profile fit parameters
Parameter Prior type Parameters Limits
x0,y0Gaussian, e−x2/2σ2σ=max(5arcmin, σPlanck ) -
Ytot (old) Power-law, x−aa=1.6 0.0005 <x<0.2
θs(old) Exponential, λe−λxλ=0.2 1.3<x<45
Ytot,θs(new) 2D elliptical Gaussian x0=0.6171, σx=0.1153,1.3< θs
in x=log10(θs),y0=−2.743, σy=0.2856,
y=log10(Ytot)φ=40.17◦
4.4.1. Clear detections
Abell 2218 (PSZ1 G097.72+38.13)
Abell 2218 (Abell 1958) is an extremely well-known cluster and
one of the earliest SZ detections (e.g. Birkinshaw et al. 1978,
Birkinshaw et al. 1984,Jones et al. 1993). It lies at redshift
z=0.171 (Kristian et al. 1978). It has been observed by AMI
previously as part of the LoCuSS sample (AMI Consortium:
Rodr´ıguez-Gonz´alvez et al. 2012) and was also in AP2013. It
has the highest Planck SNR in the final subsample and is also
well-detected by AMI with ∆ln(Z)=34. Fig. 5shows that
the cluster is resolved by AMI as the depth of the decrement
increases in the uv-tapered map, and structure can be clearly
seen in the naturally-weighted map. The posterior distributions
(Fig. 6) show good constraints in both position and the cluster
model parameters. The two-dimensional posterior distributions
for the flux densities of the three most significant nearby sources
are included in the plot; it can be seen that there is some cor-
relation between the flux densities of the sources and Ytot, i.e.
lower values of the flux densities allow lower values of Ytot,
but this does not affect the parameter constraints significantly.
There is also some correlation between the flux densities of the
sources and the cluster position. The remaining two sources near
the cluster centre are fainter and were not modelled in the initial
analysis since they appear at <4σon the SA map; there is no ev-
idence for degeneracy between the flux densities of these sources
and the cluster parameters. As in AP2013 (see their Fig. 5), the
PwSYtot-θsposterior overlaps with the AMI posterior, but AMI
finds the cluster to be smaller and fainter than Planck (at low
significance for this particular cluster).
Ytot is the total SZ signal of the cluster and corresponds to
the zero-spacing flux, which is not measured by an interferome-
ter; the constraints produced by AMI on Ytot therefore rely on
extrapolating the signal on the angular scales that AMI does
measure (≈200 to 1200λ, corresponding to ≈15 to 3 arcmin)
to 0λassuming a fixed profile. Since this is a relatively nearby,
large-angular-size cluster (i.e. θ500 inferred from the X-ray lu-
minosity is 6.4 arcmin (B¨ohringer et al. 2000,Piffaretti et al.
2011) corresponding to θs=5.4 arcmin for the ‘universal’ value
of c500 =1.177, in agreement with the AMI constraint and
slightly smaller than the preferred Planck value), much of the
flux of the cluster exists on scales that are not measured by
AMI. Ytot is therefore not well constrained and the Ytot-θsdegen-
eracy is large compared to that produced by Planck, which mea-
sures Ytot directly. Nonetheless, the different degeneracy direc-
tion means that combining the two posteriors results in a tighter
constraint (assuming no systematic difference between the two
instruments, which will be discussed in Section 4.4.7).
PSZ1 G060.12+11.42
This is a new, previously unconfirmed (at the time the catalogue
CONT: A0001 IPOL 15801.167 MHZ Aca.ICL001.1
Cont peak flux = -1.2804E-03 JY/BEAM
Declination (J2000)
Right ascension (J2000)
16 38 00 37 30 00 36 30 00 35 30 00 34 30 00
66 25
20
15
10
05
00
3
45
CONT: A0001 IPOL 15801.167 MHZ Aca.ICL001.1
Cont peak flux = -1.8656E-03 JY/BEAM
Declination (J2000)
Right ascension (J2000)
16 38 00 37 30 00 36 30 00 35 30 00 34 30 00
66 25
20
15
10
05
00
3
45
(a) (b)
Fig.5: SA source-subtracted map of A2218 with (a) natural
weighting and (b) a uv-taper. The r.m.s. noise levels are 131 and
163µJybeam−1respectively. The numbered sources have pos-
terior distributions for their flux densities plotted in Fig. 6. See
Section 4.4 for more details on the plots.
S5
y0
θs
Ytot
×103
S3
S4
x0
S5
y0θsYtot ×103S3S4
1.5 2
5.5 65 15
4 8 12-30 0 30-20 20 60 2.5 3
2.5
3
1.5
2
5.5
6
5
15
5
10
-30
0
30
Fig. 6: AMI posterior distributions for A2218 and the Ytot-θspos-
terior overlaid with that obtained by Planck in red, and the prior
as a black dotted line (upper right-hand corner). The joint con-
straint is shown in yellow. See Section 4.4 for more details on
the plots.
was published) cluster discovered by Planck at high SNR (7.2)
and clearly detected by AMI with ∆ln(Z)=16. The source-
subtracted maps for the cluster are shown in Fig. 7, and the pos-
terior distributions in Fig. 8. Again, it is clear that AMI resolves
the cluster. The source flux densities of the two nearest sources
are shown in the posterior distributions; there is no apparent de-
6

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
CONT: A0001 IPOL 15730.784 MHZ Aca.ICL001.1
Cont peak flux = -9.7653E-04 JY/BEAM
Declination (J2000)
Right ascension (J2000)
18 59 45 30 15 00 58 45 30 15 00 57 45
29 30
25
20
15
10
05
19
CONT: A0001 IPOL 15730.784 MHZ Aca.ICL001.1
Cont peak flux = -1.3182E-03 JY/BEAM
Declination (J2000)
Right ascension (J2000)
18 59 45 30 15 00 58 45 30 15 00 57 45
29 30
25
20
15
10
05
19
(a) (b)
Fig. 7: SA source-subtracted map of PSZ1 G060.12+11.42 with
(a) natural weighting and (b) a uv-taper. The r.m.s. noise levels
are 96 and 131 µJy beam−1respectively. The numbered sources
have posterior distributions for their flux densities plotted in
Fig. 8. See Section 4.4 for more details on the plots.
S9
y0
θs
Ytot
S1
x0
S9
y0θsYtot S1
44.5 5
0 40 510-100 -50
-100 -50 11.5
1
1.5
4
4.5
5
0
4
0
5
10
-100
-50
0
Fig. 8: AMI posterior distributions for PSZ1 G060.12+11.42and
the Ytot-θsposterior overlaid with that obtained by Planck (upper
right-hand corner). The joint constraint is shown in yellow. See
Section 4.4 for more details on the plots.
generacy between the source flux densities and any of the param-
eters. In this case, the posterior distributions for θsand Ytot are
very consistent with the PwS posteriors. The AMI and PwS de-
generacies are in different directions, meaning that the joint con-
straints produced by combining the two are considerably tighter.
4.4.2. Moderate detections
ZW8503 (PSZ1 G072.78-18.70)
ZW8503 is a well-known cluster at z=0.143 (Allen et al.
1992) with a large angular size (θs≈8 arcmin as measured by
Planck); it is therefore not too surprising that AMI does not de-
tect it well. A decrement at the phase centre is visible in the
source-subtracted maps (Fig. 9), and a model with a cluster is
favoured over one without by ∆ln(Z)=1.8, but Fig. 10 shows
that there is not enough information in the AMI data to constrain
the cluster parameters well, and the Ytot-θsposterior distribution
is strongly influenced by the prior (plotted as a black dotted line
for comparison). There is also significant degeneracy between
CONT: A0001 IPOL 15734.193 MHZ Aca.ICL001.1
Cont peak flux = 5.9762E-04 JY/BEAM
Declination (J2000)
Right ascension (J2000)
21 23 15 00 22 45 30 15 00 21 45 30
23 20
15
10
05
00
1
2
CONT: A0001 IPOL 15734.193 MHZ Aca.ICL001.1
Cont peak flux = 5.9791E-04 JY/BEAM
Declination (J2000)
Right ascension (J2000)
21 23 15 00 22 45 30 15 00 21 45 30
23 20
15
10
05
00
1
2
(a) (b)
Fig.9: SA source-subtracted map of ZW8503 with (a) natural
weighting and (b) a uv-taper. The r.m.s. noise levels are 90 and
122µJybeam−1respectively. The numbered sources have poste-
rior distributions for their flux densities plotted in Fig. 10. See
Section 4.4 for more details on the plots.
S2
y0
θs
Ytot
S1
x0
S2
y0θsYtot S1
4.5 5
2610
10 300 100-100 0 11.5
1
1.5
4.5
5
2
6
10
10
30
0
100
Fig.10: AMI posterior distributions for ZW8503 and the Ytot-θs
posterior overlaid with that obtained by Planck (upper right hand
corner). See Section 4.4 for more details on the plots.
the cluster parameters (x0,y0, θs,Ytot) and the flux densities of
the closest sources. The parameter space indicated by the Planck
posterior is completely ruled out by the AMI posterior distribu-
tion. The AMI map shows a good positional coincidence with
the X-ray emission (Fig. 11) and also shows some substructure
within the cluster; if this is real, the spherical, isothermal cluster
model may not provide a good fit and the extrapolated Ytot result
may be biased.
4.4.3. Non-detections
PSZ1 G074.75-24.59
PSZ1 G074.75-24.59 is associated in the Planck catalogue with
ZwCl 2143.5+2014. Despite having an SNR of 6.1 and being
detected by all three of the Planck detection algorithms, it is not
detected by AMI, with an evidence difference of ∆ln(Z)=−2.6.
2Courtesy of the Chandra X-ray Observatory Center and
the Chandra Data Archive, http://cxc.cfa.harvard.edu/cda/
(ivo://ADS/Sa.CXO#obs/13379)
7

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
CONT: A0001 IPOL 15733.883 MHZ Aca.OHGEO.1
Grey scale flux range= 0.00 31.00
0 10 20 30
Declination (J2000)
Right ascension (J2000)
21 22 45 30 15 00 21 45
23 18
16
14
12
10
08
06
Fig.11: A Chandra X-ray map of ZW85032with AMI-SA con-
tours at ±(2,3,4) ×100 µJy overlaid to show the substructure.
The grey-scale is in units of counts per pixel and is truncated at
the peak value in the centre of the cluster. The AMI synthesised
beam is shown in the top right-hand corner. Note that the axis
scale is different to Fig. 9
CONT: A0001 IPOL 15739.522 MHZ Aca.ICL001.1
Cont peak flux = -4.5910E-04 JY/BEAM
Declination (J2000)
Right ascension (J2000)
21 47 15 00 46 45 30 15 00 45 45 30 15
20 40
35
30
25
20
15
CONT: A0001 IPOL 15739.522 MHZ Aca.ICL001.1
Cont peak flux = 6.4123E-04 JY/BEAM
Declination (J2000)
Right ascension (J2000)
21 47 15 00 46 45 30 15 00 45 45 30 15
20 40
35
30
25
20
15
(a) (b)
Fig. 12: SA source-subtracted map of PSZ1 G074.75-24.59 with
(a) natural weighting and (b) a uv-taper. The r.m.s. noise levels
are 105 and 166 µJybeam−1respectively. The position of ZwCl
2143.5+2014 is shown as a triangle (Zwicky & Kowal 1968).
See Section 4.4 for more details on the plots.
Although there is some negative flux visible on the map, it is
ruled out by the Planck positional prior (Fig. 12).
A simulated cluster using the PwS maximum a-posteriori
values for θsand Ytot, ‘observed’ using the same visibilities and
noise levels as those in the real AMI observation, shows that
this cluster should be detected at a SNR of ≈8 in the naturally-
weighted map, and ≈9 in the uv-tapered map. However, the pos-
terior distributions (Fig. 13) show that the θs/Ytot parameter space
preferred by Planck cannot be ruled out by the AMI observa-
tions, so the cluster could be more extended than the Planck
MAP estimate shows (although the redshift is given as 0.250 so
this seems unlikely) and/or be significantly offset from its given
position.
4.4.4. Clear non-detections
PSZ1 G137.56+53.88 is a clear non-detection with evidence ra-
tio ∆ln(Z)=−4.1. There is no negative flux near the phase cen-
tre and no nearby point sources or positive extended emission
to cause the non-detection of the cluster (Fig. 14). Simulations
show the cluster should have a significance of ≈17 in both the
naturally-weighted and uv-tapered maps. The posterior distribu-
tion (Fig. 15) shows that very large values of θsare required to
provide any kind of consistency with the data, so that nearly all
of the cluster flux would be resolved out, in disagreement with
the small value for θsindicated by PwS. Noting also that al-
though the cluster has an SNR of 5.7, it was detected by PwS
Ytot ×103
y0
θs
x0
Ytot
×103
y0θs
20 40 60-150 0150
-100 0 100 0 510
0
5
10
20
40
60
-150
0
150
Fig.13: AMI posterior distributions for PSZ1 G074.75-24.59
and the Ytot-θsposterior overlaid with that obtained by Planck
(upper right hand corner). See Section 4.4 for more details on
the plots.
CONT: A0001 IPOL 15784.287 MHZ Aca.ICL001.1
Cont peak flux = 2.8105E-03 JY/BEAM
Declination (J2000)
Right ascension (J2000)
11 41 30 00 40 30 00 39 30 00 38 30 00
61 20
15
10
05
00
60 55
CONT: A0001 IPOL 15784.287 MHZ Aca.ICL001.1
Cont peak flux = 3.3666E-03 JY/BEAM
Declination (J2000)
Right ascension (J2000)
11 41 30 00 40 30 00 39 30 00 38 30 00
61 20
15
10
05
00
60 55
(a) (b)
Fig.14: SA source-subtracted map of PSZ1 G137.56+53.88
with (a) natural weighting and (b) a uv-taper. The r.m.s. noise
levels are 109 and 150µJybeam−1respectively. See Section 4.4
for more details on the plots.
only and not the other algorithms, we consider it likely to be a
spurious detection.
4.4.5. Validation
Detection of new clusters
Of our SZ sample, 82 clusters are previously known (the ‘vali-
dation’ flag in the Planck catalogue is 20). 16 of the new clusters
are already confirmed by other followup (‘validation’ =10); of
these, we re-confirm 14.
We detect 14 of the remaining 25 new clusters that have not
been previously confirmed by other methods, at the time of pub-
lishing of the catalogue. All of these are detected by at least two
Planck pipelines, and 8 are detected by all three. For these clus-
ters, the Planck catalogue provides a quality assessment flag be-
tween 1 and 3 (1 being the most reliable); there are 6, 4 and 4
AMI detections in the 1, 2 and 3 categories respectively.
8

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Ytot ×103
y0
θs
x0
Ytot
×103
y0θs
20 40 60
-200 0 200-200 0 200 0 10
0
10
20
40
60
-200
0
200
Fig.15: AMI posterior distributions for PSZ1 G137.56+53.88
and the Ytot-θsposterior overlaid with that obtained by Planck
(upper right hand corner). See Section 4.4 for more details on
the plots.
Discussion of AMI non-detections
Across the whole sample, 75% of the AMI non- and clear non-
detections have less than three Planck pipeline detections, com-
pared to 18% for the AMI clear and moderate detections; of the
previously unconfirmed clusters, none of the AMI non- and clear
non-detections has a quality flag value of 1. Although it is dif-
ficult to rule out the presence of a cluster entirely using AMI
data alone, these correlations indicate that an AMI non-detection
is a useful indicator for a possible spurious Planck detection.
Fig. B.2 shows θs-Ytot posteriors for all of the non-detections; the
Planck parameter space is often ruled out by the AMI posterior.
All of the three clear non-detections have <3Planck
pipeline detections. Two of these (PSZ1 G053.50+09.56 and
PSZ1 G142.17+37.28) are within 5 arcmin of thermal, compact
sources at 545 and/or 857GHz, which are another indicator of
a potentially spurious Planck detection caused by contamination
by dust emission. The third has been addressed in Section 4.4.4;
we consider these three likely to be spurious.
The Planck catalogue produced by the intersection of de-
tections by the three algorithms is expected to be ≈99% pure
at SNR ≥5 (Planck Collaboration et al. 2013b). Our SZ sam-
ple of 123 clusters contains 87 in the ‘intersection’ catalogue, of
which 81 are detected by AMI. This leaves six non-detections.
Of these, three (PSZ1 G099.48+55.62, PSZ1 G107.32-31.51,
and PSZ1 G084.84+35.04) are at known, low redshift and the
posteriors in Fig. B.2 show that the region of θs-Ytot parameter
space preferred by Planck cannot be ruled out by the AMI obser-
vations; i.e. these clusters are likely to be too large in angular size
(and not bright enough) to be seen by AMI. Of the remaining
four, PSZ1 G094.69+26.34 is predicted to have a low SNR of ≈4
in the AMI data based on the Planck maximum a-posteriori val-
ues of θsand Ytot, and could also be resolved out if the true val-
ues are toward the upper edge of the constraint. Also, although
PSZ1 G050.46+67.54 should be well-detected according to its
Planck size estimate of θs≈3 arcmin, it is within 220 arcsec of
an MCXC cluster with size θ500 =6.89 arcmin (Piffaretti et al.
2011), corresponding to θs=5.85 arcmin for c500 =1.177 and
Probability density
(AMI-PwS separation) /σtot (AMI-MMF3 separation) /σtot
0 1 2 3 4 5
0 1 2 3 4 50
0.5
1
1.5
2
2.5
0
0.2
0.4
0.6
0.8
1
1.2
Fig.17: Positional offset from AMI, normalised by total error
σtot =qσ2
AMI +σ2
Planck, for PwS and MMF3. The solid his-
togram shows the clear detections only, and the red outline
shows clear and moderate detections together. A Rayleigh dis-
tribution is plotted in red for comparison.
may therefore also be resolved out if the Planck size is an under-
estimate.
This leaves one cluster only in the ‘intersection’ catalogue,
PSZ1 G074.75-24.59, which simulations based on the Planck
maximum a-posteriori parameter estimates predict should be
well-detected by AMI; the AMI maps (Fig. 12) show no source
environment problems which could explain its non-detection.
More follow-up data will be required to definitively determine
if this is a spurious detection, as the pressure profile of the clus-
ter gas could deviate significantly from the ‘universal’ pressure
profile and/or the Planck position estimates could be offset sig-
nificantly from the true position, so that the simulations do not
accurately predict the AMI detection significances.
4.4.6. Positional comparison
The higher angular resolution of AMI enables a more accurate
positional estimate to be produced for the clusters (although
in practice this depends on a variety of factors such as signal-
to-noise over the angular scales observed by both telescopes,
and how successful the decoupling of the signal from the fore-
grounds is). This allows the accuracy of the Planck positions
and error estimates to be checked. Fig. 16 compares positional
offsets between AMI and the three Planck detection algorithms.
The offsets for MMF1 and MMF3 are very similar. The PwS
offsets are slightly more clustered toward zero, and also show a
greater correlation with the SNR (i.e. the highest SNR points are
closer to zero than the low-SNR points).
The MMF1 algorithm does not currently output positional
errors, so Fig. 17 shows the distribution of positional offsets
normalised by the total error qσ2
AMI +σ2
Planckfor PwS and
MMF3 only. A Rayleigh distribution, (x/σ2) exp(−x2/2σ2) with
σ=1, is plotted for comparison – this is the expected distribu-
tion assuming the errors in RA and δare uncorrelated and nor-
mally distributed. The PwS distribution is a reasonable match,
showing that the error estimates are a good representation of the
true uncertainty in the positions. In contrast, the MMF3 errors
are generally overestimated3.
3The MMF3 positional error overestimation is a known is-
sue; see http://www.sciops.esa.int/wikiSI/planckpla/
index.php?title=Catalogues&instance=Planck_Public_PLA#
The_SZ_catalogues under ‘Caveats’. This is expected to be corrected
in a forthcoming updated version of the catalogue.
9

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
∆δ/arcsec
PwS MMF1
∆RA /arcsec
MMF3
-200 0 200 -200 0 200-200 0 200
-200
0
200
-200
0
200
-200
0
200
Fig. 16: Positional offset from AMI for the three Planck detection algorithms. The size of the points plotted increases with increasing
Planck SNR; clear detections are plotted as filled circles, and moderate detections as empty circles.
(AMI-MMF3 separation) /σtot,rescaled
Probability density
PwS (compatibility) SNR
∆MMF3/∆PwS
4 8 12 16
0 1 2 3 4 5
100
101
0
0.2
0.4
0.6
0.8
1
(a) (b)
Fig.18: (a) shows the MMF3 positional offset from
AMI, normalised by rescaled total error σtot =
qσ2
AMI +(0.28 ×σMMF3)2. The solid histogram shows the
clear detections only, and the red outline shows clear and
moderate detections together. A Rayleigh distribution is plotted
in red for comparison. (b) shows the ratio between the absolute
offsets (∆) between AMI and MMF3 and AMI and PwS as a
function of SNR; as shown in Fig. 16, PwS does better at high
SNR.
We estimate a rescaling factor of 0.28 for the MMF3 errors,
by minimising the Kolmogorov-Smirnov test statistic between
the distribution and the Rayleigh distribution. Fig. 18 shows the
rescaled histogram, which agrees much more closely with the
Rayleigh distribution. In contrast, the same procedure gives a
rescaling factor of 0.51 for the PwS errors. Fig. 18 also shows a
comparison between the absolute offsets between AMI and PwS
and AMI and MMF3; confirming what is seen in Fig. 16, the
PwS offsets are generally smaller, especially at high SNR.
4.4.7. Ytot-θscomparison
A major conclusion of AP2013 was that the clusters were found
overall to be smaller in angular size and fainter (lower Ytot)
by AMI than by Planck. The comparison for the larger sample
shows a similar trend.
To properly compare the quantities, it is necessary to look
at the full, two-dimensional posteriors for Ytot and θssince the
quantities are correlated. Fig. B.1 shows the two-dimensional
posteriors for θsand Ytot as measured by both AMI and Planck,
and the joint constraints where appropriate, in descending
Planck SNR order. It is clear that, especially at the high-SNR
end, there are many cases where the constraints are inconsistent
and in these cases the Planck posteriors usually prefer higher
values of θsand Ytot.
Fig. 19 shows the comparison between the AMI and PwS
mean values for the entire sample of clear and moderate de-
tections. Aside from some outliers, the θsvalues do not seem
to be biased, but only correlate weakly, with a Pearson corre-
lation coefficient of 0.25 (0.18) for all common AMI and PwS
detections (clear AMI detections only). However, the Ytot values
for the high-SNR clusters as measured by AMI are still lower
overall than the Planck values; for lower SNR clusters, the bias
may be obscured by the noise. Following Planck Collaboration
et al. (2013c) for the definition of ‘high-SNR’, we make a cut at
Planck SNR of 7 and fit a linear model to the Planck and AMI
results for Ytot, using the SciPyorthogonal distance regression
function4to take into account errors in both the xand ydirection.
The best fit slope for all clusters (clear AMI detections only)
above SNR of 7 is 4.2±1.5 (2.45±0.72); note that the slope for
all clusters is driven by one very discrepant moderate detection.
The slope for clear AMI detections only is consistent with the
slope found in AP2013 (1.05 ±0.05) at <2σsignificance; note
however that this relationship was obtained by fixing the cluster
size to the θ500 inferred from the X-ray luminosity for improved
consistency.
The comparison between AMI values and the values pro-
duced by the MMF algorithms is very similar.
This inconsistency could be due to the fact that AMI does
not measure Ytot directly, since it is an interferometer and there-
fore resolves out the larger scales; as long as the cluster is re-
solved, the zero-spacing flux, and therefore Ytot, is never mea-
sured directly. In this case the discrepancy should be worse for
larger angular-size clusters since more of an extrapolation is re-
quired to infer the zero-spacing flux. In Fig. 20(a), the ratio of the
Ytot values is plotted as a function of θsas measured by AMI and
Planck; the discrepancy does appear worse for larger values of
θs,Planck, but occurs across all values of θs,AMI. In Fig. 20(b) the
correlation between θsand Ytot is plotted as measured by AMI
and Planck, which also shows that the discrepancy occurs over
the entire sample.
Potential origins of the discrepancy
4http://docs.scipy.org/doc/scipy/reference/odr.html
10

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
θs,AMI /arcmin
θs,PwS /arcmin
Ytot,AMI /arcmin2
Ytot,PwS /arcmin2
10−310−2
510 15
10−3
10−2
5
10
15
Fig.19: Comparison between PwS and AMI mean Ytot and θs
values. The size of the points plotted increases with increas-
ing Planck SNR; clear detections are plotted as filled circles,
and moderate detections as empty circles. The one-to-one rela-
tionship is plotted as a black dashed line. The fitted linear rela-
tionship for all clusters (clear AMI detections only) with SNR
greater than 7 is plotted as a black solid (black dotted) line.
θs/arcmin
Ytot,PwS/Ytot,AMI
θs/arcmin
Ytot ×103/arcmin2
0510 15
0510 15 0
4
8
12
16
10−1
100
101
(a) (b)
Fig.20: (a) shows a comparison between PwS and AMI MAP
Ytot values as a function of AMI (PwS) θsvalues in black (red).
The one-to-one relationship is plotted as a black dashed line.
(b) shows Ytot as a function of θsas measured by AMI (black)
and PwS (red) for all of the moderate and clear detections. In
both plots, the size of the points plotted increases with increasing
Planck SNR, clear detections are plotted as filled circles, and
moderate detections as empty circles.
To first eliminate the possibility that the discrepancy is caused
by absolute calibration problems, we obtained flux densities for
two of our primary calibration sources, 3C286 and 3C147, at 30
and 44 GHz from the Planck Compact Source Catalogue (Planck
Collaboration et al. 2013a). These are shown in Fig. 21 with the
power-law used to calculate the AMI primary calibration flux
densities for comparison. All flux densities are within 3σof the
power-law, and there does not appear to be a systematic bias. We
therefore discard absolute calibration as a potential cause of the
discrepancy.
Several potential origins of the discrepancy were investi-
gated in AP2013, as follows.
1. The possibility that a population of faint sources existed
below the LA detection threshold and acted to ‘fill in’ the
decrement was investigated by obtaining very deep LA ob-
servations toward the central pointing of the raster for each
cluster, obtaining r.m.s. noise levels /30µJybeam−1, and
re-extracting the cluster parameters, subtracting any extra
sources detected. In one case this shifted the Ytot estimate up-
ward by ≈1σ, but the parameters for the remaining 10 cases
were not significantly changed. This is clearly not the source
of the discrepancy.
Frequency /GHz
Flux density /Jy
3C286
3C147
15 30 44
1
2
4
Fig.21: The power-law relationships used to calculate primary
calibration flux densities for AMI for two calibrators, 3C286 and
3C147, are shown with ±5% uncertainty limits as the grey filled
bands. The AMI frequency band is shown in black. Flux den-
sities for both sources at 30 and 44 GHz taken from the Planck
Compact Source Catalogue (Planck Collaboration et al. 2013a)
are shown as points with errorbars.
2. To eliminate any effects from differing centroid positions, the
AMI and Planck data were both analysed with the position
of the cluster fixed to the best-fit position obtained from an
initial AMI analysis where the central position was allowed
to vary. Fixing the position also had a negligible effect on the
derived θsand Ytot posterior distributions.
3. For five clusters with measured X-ray profiles, the cluster
parameters were re-extracted using the appropriate X-ray-
determined γand αparameters rather than the ‘universal’ pa-
rameters. This did not significantly improve the agreement.
Note that the parameter affecting the cluster outskirts, β, was
not varied since the X-ray data do not extend to this region.
See AP2013 for more details.
When a point source very near the cluster centre is fitted si-
multaneously with the cluster model, there is often a correla-
tion between the point source flux and the Ytot value, i.e. the data
can constrain the sum of the point source flux and the cluster
flux well, but not separate the two components. If this effect led
to biases in the fitted Ytot values, it would worsen for smaller
angular-size clusters since it becomes more difficult to distin-
guish between the profiles in uv-space of a marginally-resolved
cluster and an unresolved point source. To test whether this could
cause the discrepancy, we replotted Fig. 20 using only clusters
with no fitted sources within 3 arcmin of the cluster position.
This is shown in Fig. 22; although the number of clusters in
the plot is much smaller, the discrepancy is clearly not resolved.
In addition, we conducted tests on simulations of clusters with
point sources of varying flux densities and at varying distances
from the cluster centres, and found that we were able to recover
Ytot values correctly.
Another potential problem is the mismatch between the
spherical model and the real data; the higher resolution AMI
data will be much more sensitive to this issue than the Planck
data (in some cases, also dependent on other factors as dis-
cussed in Section 4.4.6). Some of the clusters have clearly non-
spherical shapes in the AMI maps, but modelling with an ellip-
soidal GNFW profile does not change the constraints on Ytot and
θssignificantly.
11

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
θs/arcmin
Ytot,PwS/Ytot,AMI
θs/arcmin
Ytot ×103/arcmin2
0510 15
0510 15 0
4
8
12
16
10−1
100
101
(a) (b)
Fig.22: Comparison between PwS and AMI θsand Ytot MAP
values, for clusters selected to have no radio point sources within
3arcmin of the cluster position. In both plots, the black (red)
points show the AMI (PwS) values, larger points have higher
Planck SNR values and filled (empty) circles represent AMI
clear (moderate) detections.
5. Profile investigation
The outstanding issue to be considered is the use of the ‘univer-
sal’ profile shape for all clusters. AMI-SA data are not of high
enough resolution to measure γ; the range of scales measured by
the SA corresponds to 0.3.θ/θs.9 for clusters with angular
sizes θsin the range 2 to 10 arcmin. For the smallest (largest)
clusters in the sample, α(β) will be the parameter most affecting
AMI data; for most clusters, both will be important.
5.1. Analysis of simulations
As a first step to understanding how variation in the shape pa-
rameters affects constraints derived from AMI data, we gen-
erated a set of simulations with realistic thermal, CMB and
source confusion noise levels. We chose three representative val-
ues of θsbased on the follow-up sample, and assigned realistic
Ytot values to each based on clusters in the sample with a simi-
lar angular size and that were well-detected by AMI, giving (θs,
Ytot)=(1.8, 0.0009), (4.5, 0.001) and (7.4, 0.007). For each (θs,
Ytot), we generated simulations with αand γset to the 31 indi-
vidual fitted values from the REXCESS sample (B¨ohringer et al.
2007;Arnaud et al. 2010), and with βdrawn from a uniform
distribution between 4.5 and 6.5. Fig. 23(a) shows the result
of analysing these simulations with the standard AMI analysis
pipeline, assuming the ‘universal’ profile parameters, whereas
Fig. 23(b) shows the results when the simulation is both gener-
ated and analysed with the ‘universal’ profile. In the former case,
for the two smaller clusters, the true value is within the 68%
confidence limit 29 times out of 31, but it is clear that the size
and degeneracy direction of the contours varies wildly for dif-
ferent sets of (γ, α, β); on the whole, the mean and MAP values
of θsand Ytot are biased upward slightly. For the largest cluster,
the true value is within the 68% confidence limit only 2 times
out of 31, and within the 95% confidence limit only 14 out of
31 times. Again, the size and degeneracy directions of the con-
tours vary wildly; note that the very tight contours which are
significantly discrepant from the rest correspond to the profile
in the REXCESS sample that is most discrepant from the ‘uni-
versal’ profile, with shape parameters γ=0.065, α =0.33. On
the whole, the mean and MAP values of θsand Ytot are biased
downward significantly for this cluster.
To assess the potential for constraining αand βusing AMI
data, we next analysed the simulations, allowing the shape pa-
θs/arcmin
log(Pe)
uv-distance /λ
Visibility amplitude /mJy
0 400 800 12000 510 15 20 0
1
2
3
(a) (b)
Fig. 24: A profile generated with β=5.4905, θs=1.8 (the ‘uni-
versal’ profile, black lines) can be mimicked for β=8.9 using
θs=4.1 and adjusting Ytot downward (red lines). The two pro-
files are almost identical over the AMI-SA range of baselines,
while Planck would measure the zero-spacing flux which differs
by ≈7% between the two models. (a) shows the pressure pro-
files in radial coordinates (note that the y-axis scale is log), and
(b) shows the profiles in uv-space for channel 5, with the simu-
lated AMI data shown as dots. Note that this simulation has been
generated with an unrealistically small amount of thermal noise.
rameters to vary one at a time and using wide, uniform priors
on all parameters. We found that, due to the lack of information
on Ytot in the data, there are very strong degeneracies between θs
and αand β, even when data with very small amounts of noise
are analysed. For example, Fig. 24 shows that a profile gener-
ated with the ‘universal’ value of βand a small angular size can
be mimicked almost identically across a given range of angular
scales using a much larger βand θsvalue.
In practice, these strong degeneracies were found to lead
to spurious constraints in αand βin the one-dimensional
marginalised posterior distribution. This is simply due to the
shape of the three-dimensional posterior; more Ytot-θsspace be-
comes available for lower values of αand β. Applying the two-
dimensional prior on Ytot and θsto ensure that physically moti-
vated parts of the Ytot-θsspace are selected reduces, but does not
eliminate, the problem. This is illustrated in Fig. 25 and Fig. 26
where the two- and one-dimensional posterior distributions are
shown for θs,Ytot and α, with the standard two-dimensional prior
on θsand Ytot and a uniform prior between 0.1 and 3.0 on α(with
βfixed to the correct, input value of 5.4905). When there is little
information on αin the data (particularly for the smallest clus-
ter), the shape of the two-dimensional posteriors produces an
apparent (and incorrect) constraint on αin the one-dimensional
posteriors. Similar effects occur in the constraints on β, shown
in Fig. 27 and 28 (in which αis fixed to the correct, input value
of 1.0510).
To attempt to control these biases, we reanalysed the simu-
lations using a Gaussian prior based on the REXCESS sample
on α, namely N(1.0510,0.47) truncated at 0.3, and a tighter uni-
form prior on β,U[4.5,6.5]. Fig. 29 shows the resulting poste-
rior distributions, varying both αand β(but with γfixed to the
‘universal’ value). For the two smaller angular-size clusters, this
results in correct recovery of θsand Ytot, and reduces the biassing
considerably in αand β. For the largest angular-size cluster, the
input values of θsand Ytot are not recovered correctly, because
there is not enough information available in the angular scales
measured by the SA to constrain these parameters simultane-
12

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
0510 15
0510 15 0
3
6
0
3
6
Ytot ×103/arcmin2
0 10 20 300 10 20 30 0
5
10
15
0
5
10
15
θs/arcmin 0 10 200 10 20 0
5
10
15
0
5
10
15
(a) (b)
Fig. 23: The posterior distribution for Ytot and θsfor simulated clusters with realistic CMB and noise levels (see text for details), and
(a) differing GNFW shape parameter values (γ, α, β) based on the REXCESS sample (B¨ohringer et al. 2007;Arnaud et al. 2010),
and (b) simulated with the ‘universal’ values. In all cases the model used for recovering the parameters has the shape parameter
values fixed to the ‘universal’ values, and the joint two-dimensional prior on Ytot and θsis used. Results for three different angular
sizes are shown (from top to bottom, θs=1.8,4.5 and 7.4); the input parameter values are marked with red triangles. The contours
are at the 68% and 95% confidence boundaries.
ously, so the prior on Ytot and θsbiases the recovered posteriors
downwards.
We check for any biases due to γbeing fixed (incorrectly) to
the ‘universal’ value by plotting the error in the recovered val-
ues of θsand Ytot as a function of the true input γvalue. There
is some correlation between the fractional difference in θsand γ,
especially for the two smaller clusters, but mostly any correla-
tion is beneath the level of the noise (Fig. 30).
We also add point sources of varying flux densities and at
varying distances from the phase centre to test for any issues in
decorrelating point source flux from cluster flux when varying
the shape parameters; the parameter estimation is unaffected.
13

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
θs
Ytot ×103
α−αtrue
Probability density
β−βtrue
Probability density
-2 -1 0 1-2 -1 0 10 510 15
0
3
6
Ytot ×103/arcmin2
Probability density
Probability density
-2 -1 0 1-2 -1 0 1 20 10 20 30
0
5
10
15
θs/arcmin α−αtrue β−βtrue
-2 -1 0 1-2 -1 0 10 10 20
0
5
10
15
(a) (b) (c)
Fig. 29: The posterior distributions for simulated clusters with realistic noise levels (see text for details), and varying GNFW shape
parameter values based on the REXCESS sample (B ¨ohringer et al. 2007;Arnaud et al. 2010). (a) shows the two-dimensional θsand
Ytot posterior, and (b) and (c) show the one-dimensional posteriors for αand β, shifted to be centred on the appropriate true value. In
all cases γis fixed to the ‘universal’ value, αhas a truncated Gaussian prior based on the REXCESS sample, βis varied uniformly
between 4.5 and 6.5, and the joint two-dimensional prior on Ytot and θsis used. Results for three different angular sizes are shown
(from top to bottom, θs=1.8,4.5 and 7.4 arcmin); the input parameter values are marked with red triangles and lines.
5.1.1. Adding
Planck
information
Although the immediate issue is to check whether we can
achieve consistency between AMI and Planck results, it is also
interesting to consider whether we can take advantage of the
complementary nature of the two instruments to derive better
constraints on the behaviour of the pressure profile over a range
of radii. To this end, for each of our three simulated cluster
sizes we derived a Planck-like prior on Ytot by marginalising
over the θsdimension of the two-dimensional constraint pro-
duced by Planck for a cluster with similar angular size, and ap-
proximating as a Gaussian. We use this marginalised constraint
as a prior rather than the full two-dimensional constraint since
Planck Ytot estimation is more robust to changes in the profile
shape parameters than θsestimation (see, e.g. Sutton et. al., in
prep.). We then use our standard two-dimensional prior on θs
conditioned on values drawn from the Planck-like Ytot prior; pri-
ors on αand βare as in the previous section. Fig. 31 shows the
resulting posterior distributions. For all three clusters, the con-
straints on θsand Ytot are much tighter, and for the large angular-
size cluster, the true values of θsand Ytot are now recovered cor-
rectly. However, the constraints on the shape parameters are not
very different.
This is a fairly crude way of including Planck information in
the analysis and does not make the best use of the information
available in the Planck data on the cluster shape. A full joint
analysis of AMI and Planck data would fill in the gap in uv-
coverage between the zero-spacing flux and the shortest AMI-
SA baselines, and there would be some overlap with the shortest
baselines since the resolution of Planck is ≈5 arcmin; this should
produce better constraints on the profile shape parameters. This
will be addressed in a future paper.
5.2. Summary of simulation results
We have shown with the simulated bank of clusters based on
the REXCESS sample, that when a cluster has an angular size
θs'5 arcmin, the true input values of θsand Ytot can only be re-
covered correctly using AMI data when the model for the pres-
sure profile used for parameter extraction is a good match to the
14

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
-2 -1 0 1-2 -1 0 10 510 15
0
2
4
Ytot ×103/arcmin2
Probability density
Probability density
-2 -1 0 1-2 -1 0 1 20 10 20
0
2
4
θs/arcmin α−αtrue β−βtrue
-2 -1 0 1-2 -1 0 10 10 20 30
5
7
9
(a) (b) (c)
Fig. 31: The posterior distributions for simulated clusters with realistic noise levels (see text for details), and varying GNFW shape
parameter values based on the REXCESS sample (B ¨ohringer et al. 2007;Arnaud et al. 2010). (a) shows the two-dimensional θsand
Ytot posterior, and (b) and (c) show the one-dimensional posteriors for αand β, shifted to be centred on the appropriate true value. In
all cases γis fixed to the ‘universal’ value, αhas a truncated Gaussian prior based on the REXCESS sample, βis varied uniformly
between 4.5 and 6.5, a Planck-like Gaussian prior is used on Ytot and θshas the conditional prior drawn from the two-dimensional
prior. Results for three different angular sizes are shown (from top to bottom, θs=1.8,4.5 and 7.4); the input parameter values are
marked with red triangles and lines.
actual pressure profile of the cluster. This is not surprising since,
as we have mentioned, an interferometer does not measure zero-
spacing flux directly and so the Ytot value ‘measured’ by AMI is
actually an extrapolation based on the assumed profile. This is
also consistent with what we observe in the real sample; clusters
with high Planck SNR (and therefore large θs) are consistently
measured to be smaller and fainter by AMI.
When attempting to vary the GNFW shape parameters, we
must be careful to avoid over-interpretation of apparent con-
straints on parameters which are actually just caused by the
shape of the two-dimensional degeneracies. Reducing the range
of βand imposing a prior based on the REXCESS sample on α
reduces these problems significantly. However, it is clear from
Fig. 29 that in some cases these spurious constraints still do oc-
cur, particularly in αfor small angular-size clusters, and βfor
medium angular-size clusters. Surprisingly, βis often recovered
correctly for large angular-size clusters – this is due to the inter-
section of the physically motivated prior on θsand Ytot and the
degeneracy direction between θsand β.
It is also clear from Fig. 29 that varying the shape param-
eters does not aid in recovering the correct θsand Ytot values
for large angular-size clusters; joint analysis of Planck and AMI
data is required to achieve this. As a first approximation, using a
Planck-derived prior on Ytot can help, but does not improve the
constraints on αand β.
It is also interesting to note that our parameter constraints
are not very reliant on noise level. Our initial tests were made on
simulated data with unrealistically small noise levels of 100µJy
per visibility; when we moved to simulations with more realistic
noise levels (of ≈120 µJybeam−1across the channel-averaged
map), the constraints changed very little. As long as one has a
good detection, it seems that the limiting factor on our parameter
constraints is very much the range of angular scales present in
the data with respect to the size of the cluster, rather than the
detection significance.
15

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
α
θs
α
Ytot ×103
θs
Ytot ×103
510 15
1 2 3
12 3
1
3
5
1
3
5
5
10
15
α
θs
α
Ytot ×103
θs
Ytot ×103
510 15 201 2 31 2 3 0
4
8
12
0
4
8
12
5
10
15
20
α
θs
α
Ytot ×103
θs
Ytot ×103
5101 2 3
1 2 3 2
6
10
2
6
10
5
10
Fig.25: The posterior distributions for Ytot,θsand αfor simu-
lated low-noise data, for clusters with θs=1.8 (top), 4.5 (cen-
tre) and 7.4 (bottom) arcmin and ‘universal’ (γ, α, β), with the
two-dimensional prior on Ytot and θsand a uniform prior on α
between 0.1 and 3.0 (βfixed to the correct, input value). The in-
put values are indicated by red triangles, and the posterior means
with green crosses. θsis in arcmin and Ytot is in arcmin2.
θs
Probability density
Ytot ×103α
1 2 30 4 8 12
510 15 20
Fig. 26: The one-dimensional marginal constraints on Ytot,θsand
αfor simulated low-noise data, for clusters with θs=1.8 (solid
lines), 4.5 (dashed lines) and 7.4 (dotted lines) arcmin and ‘uni-
versal’ (γ, α, β), with the two-dimensional prior on Ytot and θs
and a uniform prior on αbetween 0.1 and 3.0 (βfixed to the cor-
rect, input value). Input values are shown as red lines. θsis in
arcmin and Ytot is in arcmin2.
5.3. Analysis of real data
For all the clear detections in the sample, we re-extract the
cluster parameters allowing αand βto vary as described in
Section 5.1. The constraints on Ytot and θsare on the whole
broader but the positions of the maxima are unchanged. The
full two-dimensional constraints for the whole sample are avail-
able online at http://www.mrao.cam.ac.uk/facilities/
surveys/ami-planck/; here we present a few examples.
5.3.1. Abell 1413 (PSZ1 G226.19+76.78)
Abell 1413 is well-detected by AMI, with an evidence ratio of
∆ln(Z)=26, and Planck, with a PwS SNR of 9.8 and detections
by all three algorithms. It is at redshift z=0.143 (e.g. Struble
β
θs
β
Ytot ×103
θs
Ytot ×103
05104 684 680
1
2
3
0
1
2
3
0
5
10
β
θs
β
Ytot ×103
θs
Ytot ×103
510 15
468 4 680
4
8
5
10
15
0
4
8
β
θs
β
Ytot ×103
θs
Ytot ×103
510 15
4684 682
6
10
2
6
10
5
10
15
Fig.27: The posterior distributions for Ytot,θsand βfor simu-
lated low-noise data, for clusters with θs=1.8 (top), 4.5 (cen-
tre) and 7.4 (bottom) arcmin and ‘universal’ (γ, α, β), with the
two-dimensional prior on Ytot and θsand a uniform prior on β
between 3.5 and 9.0 (αfixed to the correct, input value). The in-
put values are indicated by red triangles, and the posterior means
with green crosses. θsis in arcmin and Ytot is in arcmin2.
θs
Probability density
Ytot ×103β
4680 4 80 510 15
Fig. 28: The one-dimensional marginal constraints on Ytot,θsand
βfor simulated low-noise data, for clusters with θs=1.8 (solid
lines), 4.5 (dashed lines) and 7.4 (dotted lines) arcmin and ‘uni-
versal’ (γ, α, β), with the two-dimensional prior on Ytot and θs
and a uniform prior on βbetween 3.5 and 9.0 (αfixed to the cor-
rect, input value). Input values are shown as red lines. θsis in
arcmin and Ytot is in arcmin2.
γ
∆θs
γ
∆Ytot
0 0.3 0.6 0.90 0.3 0.6 0.9 -1
0
1
-0.5
0
0.5
1
(a) (b)
Fig. 30: The fractional difference [(MAP value - true value)/(true
value)] in θs(a) and Ytot (b) as a function of the input value of
γ. Clusters with θs=1.8 are plotted as dots, θs=4.5 as crosses
and θs=7.4 as open circles.
16

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
β
Ytot
×103
α
θs
β
Ytot ×103α
1 22 4
510 45 6
4
5
6
1
2
2
4
Fig.32: AMI posterior distributions for A1413, allowing αand
βto vary. Posterior means are indicated with green lines and
crosses, and the Planck +XMM-Newton estimates of αand β
from Planck Collaboration et al. (2013d) are shown with red
lines and crosses. The priors on the parameters in the AMI anal-
ysis are shown as black dashed lines. θsis in arcmin and Ytot is
in arcmin2.
& Rood 1987) so could be expected to have a large angular size;
the θ500 value inferred from the X-ray luminosity is ≈7.9 arcmin
(B¨ohringer et al. 2000,Piffaretti et al. 2011), corresponding to
θs≈6.7 arcmin for c500 =1.177. The AMI constraints on θsand
Ytot could therefore be expected to be biased downward if the
profile differs from the ‘universal’ profile. Indeed, the Planck
constraints indicate much higher values of both (see Fig. B.1 un-
der the Planck name of PSZ1 G226.19+76.78). From the simula-
tion results we can therefore expect to produce some constraints
on αand βfrom the AMI data, although not to recover the cor-
rect values of θsand Ytot; the posterior distributions for the real
data are shown in Fig. 32.
In Planck Collaboration et al. (2013d), Planck and XMM-
Newton data were used to produce fitted values for αand βfor a
sample of high-SNR Planck clusters. The sample includes seven
of the clear detections in our SZ sample (however we note that
for three of these, Planck Collaboration et al. (2013d) report
non-physical values for (γ, α, β) producing negative values of
Ytot because of the Γfunctions in Equation 4.1). Their reported
values for Abell 1413 are α=0.83 and β=4.31 (γfixed at
0.31), which are plotted for comparison in Fig. 32. The AMI
analysis produces a somewhat higher (but consistent) value for
α; although the Planck βestimate is outside our prior range for β,
our analysis shows no tendency to push toward the lower limit,
toward the Planck value. However, assuming the shape of the
Planck α-βdegeneracy for the individual clusters is similar to
that for their stacked profile (reproduced in Fig. 33), the AMI
and Planck constraints on βcould be consistent.
5.3.2. RXC J2228.6+2036 (PSZ1 G083.30-31.01)
Similarly to Abell 1413, RXC J2228.6+2036 is well-detected
by AMI (∆ln(Z)=28) and Planck (SNR =7.3, detected by
all algorithms). It is at higher redshift, z=0.412 (B¨ohringer
012345
α
0.0
0.2
0.4
0.6
0.8
1.0
L
012345
α
2
3
4
5
6
7
8
β
2 3 4 5 6 7 8
β
0.0
0.2
0.4
0.6
0.8
1.0
L
Fig.33: Marginalised posterior likelihood distribution for αand
βbased on stacked Planck and XMM-Newton data for a sample
of high-SNR Planck clusters (from Planck Collaboration et al.
2013d). The white cross marks the position of the best-fit value,
and the white triangle marks the ‘universal’ values.
et al. 2000) so the large value for θsof ≈4.5 arcmin preferred
by Planck is slightly surprising. Fig. 34 shows the posteriors
on θsand Ytot produced by AMI and Planck, as well as the re-
gion of the space predicted by the physical model described in
Olamaie et al. (2012) assuming the ‘universal’ pressure profile
for the gas, and the Tinker mass function (Tinker et al. 2008).
The AMI posterior is much more consistent with the predic-
tion than the Planck posterior; also our simulations have shown
that if the correct value were θs≈4.5, we should recover it
even if the profile deviates from the ‘universal’ profile. In ad-
dition, θ500 determined from the X-ray luminosity is 3.9 arcmin
(B¨ohringer et al. 2000,Piffaretti et al. 2011), corresponding to
θs=3.3arcmin for c500 =1.177 is consistent with the AMI
mean value of 2.3 arcmin. We therefore conclude that in this case
the Planck θsestimate is likely to be an over-estimate.
Fig. 34 also shows the posteriors on αand βresulting from
the AMI analysis. Assuming the AMI value of θsis correct, we
should be able to produce some constraint on β; indeed, there
is a weak preference for higher values of β, while the posterior
distribution for αmostly recovers the prior. The fitted αand β
values from Planck Collaboration et al. (2013d) are also shown
and in this case are very consistent with the AMI constraints.
5.4. PSZ1 G134.31-06.57
PSZ1 G134.31-06.57 is a new Planck cluster at unknown red-
shift, with Planck SNR =5.4 and AMI ∆ln(Z)=31. The Planck
and AMI constraints for this cluster overlap, and the different
degeneracy directions result in a considerably tighter joint con-
straint, giving θs≈4.5 arcmin (see Fig. B.1). At this angular size,
AMI data should produce constraints on α. Fig. 35 shows the pa-
rameter constraints – αmoves away from the prior to a higher
value of ≈1.5, while βalso shows a weak constraint to values
higher than the ‘universal’ value.
17

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
β
Ytot
×103
α
θs
β
Ytot ×103α
1 21 2 32 4 64.5 5.5 6.5
4.5
5.5
6.5
1
2
1
2
3
Fig.34: AMI posterior distributions for RXC J2228.6+2036,
allowing αand βto vary. Posterior means are indicated with
green lines and crosses, and the Planck values for αand βfrom
Planck Collaboration et al. (2013d) are shown with red lines
and crosses. The priors on the parameters in the AMI analy-
sis are shown as black dashed lines. θsis in arcmin and Ytot
is in arcmin2. Also shown in the upper right hand corner are
the posteriors produced by AMI (black) and Planck (red) using
the ‘universal’ profile, and a prediction produced by the physical
model described in Olamaie et al. (2012) based on a redshift of
z=0.412 (yellow).
5.4.1. Properties of αand βin the sample
Fig. 36 shows a histogram of the recovered mean αand βvalues
for all the clear detections in the sample.
β
Ytot
×103
α
θs
β
Ytot ×103α
1 22 6104 8 12 4.5 5.5 6.5
4.5
5.5
6.5
1
2
2
6
10
Fig.35: AMI posterior distributions for PSZ1 G134.31-06.57,
allowing αand βto vary. Posterior means are indicated with
green lines and crosses. The priors on the parameters in the AMI
analysis are shown as black dashed lines. θsis in arcmin and Ytot
is in arcmin2.
Mean α
Number of clusters
Mean β
4.5 5.5 6.50.5 11.5 0
5
10
15
20
0
5
10
15
20
(a) (b)
Fig. 36: The distribution of mean values of αand βobtained for
all the clear detections in the SZ sample. For comparison, the
REXCESS-based prior on α(scaled arbitrarily) is also plotted
in red, and the ‘universal’ value of βpredicted from numerical
simulations is indicated with a red line.
Planck Collaboration et al. (2013d) and Sayers et al. (2013)
both derive average pressure profiles for smaller samples of clus-
ters using SZ data from Planck and BOLOCAM respectively.
In both analyses, the radial profiles derived from the SZ maps
are scaled by X-ray-determined r500 values and then stacked; a
GNFW model is fitted to the stacked profiles (+X-ray points for
the inner part of the profile in Planck Collaboration et al. 2013d).
Their final best fit parameters are given by (c500, γ, α, β)=(1.81,
0.31, 1.33, 4.1) and (1.18, 0.67, 0.86, 3.67) respectively. In con-
trast, the AMI analysis does not rely on X-ray estimates of r500,
being based purely on the AMI SZ data. The AMI preferred val-
ues for βare on the whole centred around the ‘universal’ value
predicted by simulations, and do not show a trend towards the
lower values derived from the Planck and BOLOCAM analyses.
The AMI mean αestimates show a slight trend toward higher
values, in agreement with the Planck value and in disagreement
with the BOLOCAM value. However, since there are large (and
different) degeneracies between the GNFW model parameters in
the three analyses it is difficult to judge whether the analyses
truly disagree (see Fig. 33, where it is clear that higher βvalues
are not ruled out by the Planck likelihood).
6. Conclusions
We have followed up the 195 clusters from the Planck union
catalogue that are visible to AMI, lie at z>0.100 and have
Planck SNR ≥5. Of these, we reject 72 due to difficult radio
source environment, leaving a total SZ sample of 123. We find
that:
1. We detect 99 of the clusters, including 79 very good detec-
tions.
2. We re-confirm 14 of 16 new clusters already confirmed by
other observations, and validate 14 of 25 new clusters which
were not confirmed at the time the Planck catalogue was
published.
3. We do not detect 24 of the clusters, which may be too ex-
tended for AMI to detect, be significantly offset from the
phase centre, have a gas pressure profile deviating signifi-
cantly from the ‘universal’ profile, or be spurious detections
by Planck. 75% of the AMI non-detections are detected by
<3Planck algorithms, as opposed to 18% of the AMI de-
tections; none of the AMI non-detections have quality flag
values of 1. These correlations indicate that an AMI non-
detection is a good indicator for a spurious Planck detection.
18

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
4. Comparing the AMI positional estimates to those produced
by PwS and the MMF algorithms shows that PwS positional
estimates are generally more accurate, a more reliable func-
tion of SNR, and have a positional error estimate consis-
tent with the true uncertainty in the positions; in contrast,
the MMF3 positional errors are over-estimatedby a factor of
≈3.
5. The trend seen in AP2013 where Planck consistently char-
acterises clusters to be of larger angular size and brighter is
continued in the larger sample, particularly for high Planck
SNR clusters; our simulation results suggest that this may
be caused by deviation from the ‘universal’ profile used for
parameter recovery.
6. We can generalise the model used for parameter extraction
from AMI data to consider variation in αand β, however
the priors on the shape parameters must be considered care-
fully since degeneracies with θsand Ytot can produce spuri-
ous one-dimensional constraints on the shape parameters.
7. AMI data alone cannot reliably constrain θsand Ytot for clus-
ters of angular size θs'5 arcmin when there is uncertainty
in the pressure profile of the cluster; it can however be used
to constrain αand β.
8. AMI data can be used to constrain θs,Ytot and β(α) simulta-
neously for clusters of angular size ≈3 arcmin (≈5arcmin),
given a careful choice of priors on αand β.
9. While deviation from the ‘universal’ profile has been shown
to be important for analysing AMI data on a cluster-by-
cluster basis, overall the βvalues obtained by re-analysing
all of the clear detections from the Planck sample with vary-
ing αand βdo not show support for deviation from the ‘uni-
versal’ βvalue derived from numerical simulations.
Acknowledgements. The AMI telescope is supported by Cambridge University.
YCP and CR acknowledge support from CCT/Cavendish Laboratory and STFC
studentships, respectively. YCP and MO acknowledge support from Research
Fellowships from Trinity College and Sidney Sussex College, Cambridge, re-
spectively. This work was partially undertaken on the COSMOS Shared Memory
system at DAMTP, University of Cambridge operated on behalf of the STFC
DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure
capital grant ST/J005673/1 and STFC grants ST/H008586/1, ST/K00333X/1.
CM acknowledges her KICC Fellowship grant funding for the procurement of
the cluster used for computational work. In addition, we would like to thank the
IOA computing support team for maintaining the cluster.
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19

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Appendix A: Results table
Table A.1. Summary of results for all clusters between 20◦≤δ < 87◦with Planck SNR >5. The rejection reason (LZ =low redshift, R =rejected
by automated point-source criteria, SE =rejected manually for difficult source environment) or detection category (Y =clear detection, M =
moderate detection, N =non-detection, NN =clear non-detection) is given in each case. Also given is the Planck SNR and the pipelines detecting
the cluster (e.g. 110 indicates that the cluster was detected by MMF3, MMF1 but not PwS). Redshifts are taken from the Planck 2013 SZ catalogue.
Reference numbers refer to previously published AMI analyses, (1) AMI Collaboration et al. (2006), (2) AMI Consortium: Hurley-Walker et al.
(2011), (3) AMI Consortium: Zwart et al. (2011), (4) AMI Consortium: Hurley-Walker et al. (2012), (5) AMI Consortium: Rodr´ıguez-Gonz´alvez
et al. (2012), (6) AP2013, (7) AMI Consortium: Shimwell et al. (2013). ∆ln(Z) is the Bayesian evidence difference. For non-detections, predicted
signal-to-noise ratios in the naturally-weighted (σNW) and uv-tapered (σtap) maps are also given based on the Planck mean posterior parameter
values.
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G075.71+13.51 25.96 111 LZ RXC J1921.1+4357,
A2319 0.0557
PSZ1 G110.99+31.74 22.70 111 LZ RXC J1703.8+7838,
A2256 0.0581
PSZ1 G044.24+48.66 19.56 111 LZ RXC J1558.3+2713,
A2142 0.0894
PSZ1 G072.61+41.47 19.42 111 R RXC J1640.3+4642,
A2219 0.228
PSZ1 G093.93+34.92 18.07 111 LZ RXC J1712.7+6403,
A2255 0.0809
PSZ1 G097.72+38.13 17.21 111 Y 33.77 RXC J1635.8+6612,
A2218 2,5,6 0.1709
PSZ1 G186.37+37.26 15.51 111 R RXC J0842.9+3621,
A0697, A697 0.282
PSZ1 G057.84+87.98 15.25 111 LZ RXC J1259.7+2756,
Coma, A1656 0.0231
PSZ1 G086.47+15.31 14.97 111 Y 14.58 RXC J1938.3+5409,
CL1938+54 0.26
PSZ1 G033.84+77.17 14.20 111 LZ RXC J1348.8+2635,
A1795 0.0622
PSZ1 G170.22+09.74 14.12 111 R 1RXS J060313.4+421231
PSZ1 G149.21+54.17 13.60 111 R RXC J1058.4+5647,
A1132 0.1369
PSZ1 G092.67+73.44 13.41 111 R RXC J1335.3+4059,
A1763 0.2279
PSZ1 G072.78-18.70 13.09 111 M 1.78 ZwCl 2120.1+2256,
ZW8503 0.143
PSZ1 G149.75+34.68 12.97 111 Y 46.38 RXC J0830.9+6551,
A0665, A665 0.1818
PSZ1 G191.00+06.65 12.44 111 LZ RXC J0635.0+2231 0.068
PSZ1 G058.29+18.57 11.78 111 LZ RXC J1825.3+3026,
CZJ1825+3026 0.065
PSZ1 G067.19+67.44 11.76 111 Y 28.83 RXC J1426.0+3749,
A1914 1,2,4,6 0.1712
PSZ1 G107.14+65.29 11.20 111 R RXC J1332.7+5032,
A1758 5 0.2799
PSZ1 G055.58+31.87 10.83 111 R RXC J1722.4+3208,
A2261 0.224
PSZ1 G062.94+43.69 10.78 111 LZ RXC J1628.6+3932,
A2199 0.0299
PSZ1 G042.85+56.63 10.67 111 LZ RXC J1522.4+2742,
A2065 0.0723
PSZ1 G094.00+27.41 10.56 111 R H1821+643 0.3315
PSZ1 G180.25+21.03 10.54 111 R RXC J0717.5+3745,
MAJ0717+3745,
MACS6-0717
2 0.546
Continued on next page
20

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G053.52+59.52 10.46 111 Y 31.24 RXC J1510.1+3330,
A2034 6 0.113
PSZ1 G125.34-08.65 10.22 111 Y 12.26 RXC J0107.7+5408,
ZwCl0104.9+5350 0.1066
PSZ1 G124.20-36.47 10.13 111 R RXC J0055.9+2622,
A115 4 0.1971
PSZ1 G112.48+57.02 9.97 111 LZ RXC J1336.1+5912,
A1767 0.0701
PSZ1 G049.22+30.84 9.90 111 M 1.61 RXC J1720.1+2637 5 0.1644
PSZ1 G226.19+76.78 9.79 111 Y 25.52 RXC J1155.3+2324,
A1413 5,6 0.1427
PSZ1 G067.36+10.74 9.61 111 Y 10.47 RXC J1916.1+3525 0.209
PSZ1 G056.79+36.30 9.58 111 LZ RXC J1702.7+3403,
A2244 0.0953
PSZ1 G084.47+12.63 9.54 111 Y 4.75 RXC J1948.3+5113 0.185
PSZ1 G166.11+43.40 9.53 111 Y 27.21 RXC J0917.8+5143,
A0773, A773 2,5,6 0.2172
PSZ1 G139.17+56.37 9.48 111 R RXC J1142.5+5832,
A1351,
MAJ1142+5831
0.322
PSZ1 G167.64+17.63 9.43 111 Y 4.74 RXC J0638.1+4747,
ZwCl0634.1+4750,
ZW1133
0.174
PSZ1 G057.63+34.92 9.03 111 LZ RXC J1709.8+3426,
A2249 0.0802
PSZ1 G113.84+44.33 8.98 111 Y 3.10 RXC J1414.2+7115,
A1895 0.225
PSZ1 G046.90+56.48 8.96 111 M 0.88 RXC J1524.1+2955,
A2069 0.1145
PSZ1 G077.89-26.62 8.74 111 Y 35.33 RXC J2200.8+2058,
A2409 5,6 0.147
PSZ1 G139.61+24.20 8.66 111 Y 27.08 6 0.2671
PSZ1 G118.58+28.57 8.57 111 Y 4.83 RXC J1723.7+8553,
A2294 0.178
PSZ1 G071.21+28.86 8.46 011 Y 12.60 RXC J1752.0+4440,
MAJ1752+4440 0.366
PSZ1 G125.72+53.87 8.45 111 R RXC J1236.9+6311,
A1576,
MAJ1236+6311
0.3019
PSZ1 G098.12+30.30 8.45 111 LZ RXC J1754.6+6803,
Zw1754.5+680 0.077
PSZ1 G165.06+54.13 8.44 111 Y 16.86 RXC J1023.6+4907,
A0990, A990 5,6 0.144
PSZ1 G180.56+76.66 8.43 111 Y 7.13 RXC J1157.3+3336,
A1423 5 0.2138
PSZ1 G048.08+57.17 8.36 101 LZ RXC J1521.2+3038,
A2061 0.0777
PSZ1 G157.32-26.77 8.35 111 Y 25.87 RXC J0308.9+2645,
MAJ0308+2645,
MACSD-0308
2 0.356
PSZ1 G163.69+53.52 8.26 111 Y 5.10 RXC J1022.5+5006,
A980 0.158
PSZ1 G157.44+30.34 8.19 011 Y 32.51 [ATZ98] B100,
RXJ0748+5941 6
PSZ1 G143.28+65.22 8.19 111 Y 5.85 RXC J1159.2+4947,
A1430 0.211
Continued on next page
21

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G046.09+27.16 8.19 111 R RXC J1731.6+2251,
MAJ1731+2252 0.389
PSZ1 G229.70+77.97 8.18 111 R RXC J1201.3+2306,
A1443 0.269
PSZ1 G132.49-17.29 8.09 111 Y 33.24 RXC J0142.9+4438 0.341
PSZ1 G114.78-33.72 7.92 111 LZ RXC J0020.6+2840,
A0021, A21 0.094
PSZ1 G088.83-12.99 7.70 111 R ClG 2153.8+3746 0.292
PSZ1 G150.56+58.32 7.61 111 Y 8.63 RXC J1115.2+5320,
XMJ1115+5319 7 0.47
PSZ1 G114.29+64.91 7.48 111 Y 6.48 RXC J1315.1+5149,
A1703 0.2836
PSZ1 G182.55+55.83 7.46 111 R RXC J1017.0+3902,
A963 0.206
PSZ1 G134.73+48.89 7.41 111 SE RXC J1133.2+6622,
A1302 0.116 63 mJy source at 17
arcmin causes
artifacts in the SA
map
PSZ1 G080.38+14.65 7.41 111 LZ RXC J1926.1+4832 0.098
PSZ1 G114.99+70.36 7.40 111 R RXC J1306.9+4633,
A1682 0.2259
PSZ1 G091.82+26.11 7.26 111 SE 0.24
PSZ1 G083.30-31.01 7.26 111 Y 28.09 RXC J2228.6+2036 0.412
PSZ1 G161.39+26.24 7.24 111 LZ RXC J0721.3+5547,
A0576, A576 0.0381
PSZ1 G060.12+11.42 7.22 111 Y 16.07
PSZ1 G207.87+81.31 7.19 111 Y 19.99 RXC J1212.3+2733,
A1489 0.353
PSZ1 G085.98+26.69 7.13 111 M 2.89 RXC J1819.9+5710,
A2302 0.179 Positional error
increased to 5 arcmin
to encompass visible
decrement in map
PSZ1 G228.21+75.20 7.12 111 Y 112.81 RXC J1149.5+2224,
MAJ1149+2223,
MACS9-1149
6 0.545
PSZ1 G099.48+55.62 7.06 111 N -0.01 RXC J1428.4+5652,
A1925 0.1051 Predicted σNW =
4.4;σtap =6.9
PSZ1 G071.63+29.78 7.01 111 Y 3.01 RXC J1747.2+4512,
ZW8284,
ZW1745+4513
0.1565
PSZ1 G115.70+17.51 7.00 111 M 0.76
PSZ1 G133.56+69.05 6.97 111 Y 5.05 RXC J1229.0+4737,
A1550 0.254
PSZ1 G359.99+78.04 6.96 111 R RXC J1334.1+2013,
A1759 0.171
PSZ1 G140.67+29.44 6.94 111 Y 5.93 RXC J0741.7+7414,
ZW1370,
ZW0735+7421
0.2149
PSZ1 G318.61+83.80 6.93 001 SE 33mJy source
(extended to LA) at
10 arcmin leaves
significant residuals
in the SA map
Continued on next page
22

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G067.52+34.75 6.92 111 R RXC J1717.3+4226,
ZW8193,
ZwCl1715.5+4
0.1754
PSZ1 G113.26-29.69 6.91 111 R RXC J0011.7+3225,
A0007, A7 0.1073
PSZ1 G098.85-07.27 6.89 011 SE
PSZ1 G096.89+24.17 6.89 111 Y 3.54 ZwCl 1856.8+6616,
PLCKESZ G096.87 0.3
PSZ1 G138.60-10.85 6.86 111 Y 6.15
PSZ1 G153.41+36.58 6.85 010 N -2.70 Predicted σNW =
3.0;σtap =3.7
PSZ1 G146.37-15.57 6.83 111 LZ RXC J0254.4+4134,
AWM7 0.0172
PSZ1 G148.20+23.49 6.77 111 Y 3.19
PSZ1 G121.09+57.02 6.72 111 Y 10.37 3,6 0.3436
PSZ1 G118.46+39.31 6.67 111 Y 4.73 RXC J1354.6+7715 0.3967
PSZ1 G094.69+26.34 6.66 111 N -0.26 RXC J1832.5+6449 0.1623 Predicted σNW =
4.1;σtap =5.3
PSZ1 G084.41-12.43 6.59 011 Y 15.82
PSZ1 G102.97-04.77 6.56 011 Y 4.27
PSZ1 G162.30-26.92 6.56 100 R
PSZ1 G109.14-28.02 6.56 111 SE WHL J358.303+33.2696 0.4709
PSZ1 G127.55+20.84 6.55 011 R
PSZ1 G100.18-29.68 6.54 111 R 0.485
PSZ1 G049.35+44.36 6.53 111 LZ RXC J1620.5+2953,
A2175 0.0972
PSZ1 G063.80+11.42 6.53 111 Y 3.78
PSZ1 G098.96+24.87 6.52 111 LZ RXC J1853.9+6822 0.0928
PSZ1 G108.18-11.53 6.49 111 Y 16.62
PSZ1 G066.41+27.03 6.48 111 Y 16.80 WHL J269.219+40.1353 0.5699
PSZ1 G100.16+41.66 6.43 111 R RXC J1556.1+6621,
A2146 5 0.2339
PSZ1 G068.23+15.20 6.42 011 LZ RXC J1857.6+3800 0.0567
PSZ1 G166.61+42.12 6.38 111 Y 3.79 RXC J0909.3+5133,
A746 0.23225
PSZ1 G099.84+58.45 6.35 111 Y 29.56 WHL J213.697+54.7844 0.6305
PSZ1 G054.99+53.42 6.31 111 Y 16.98 RXC J1539.7+3424,
A2111 4,5 0.229
PSZ1 G136.94+59.46 6.31 111 LZ RXC J1200.3+5613,
A1436 0.065
PSZ1 G057.91+27.62 6.30 111 LZ RXC J1744.2+3259,
ZW8276 0.0757
PSZ1 G105.25-17.96 6.29 111 R RXC J2320.2+4146 0.14
PSZ1 G195.60+44.03 6.27 111 R RXC J0920.4+3030,
A0781, A781 5 0.2952
PSZ1 G068.32+81.81 6.27 111 SE RXC J1322.8+3138 0.3083 Extended source to
south-east
PSZ1 G118.88+52.40 6.25 111 Y 21.80 RXC J1314.4+6434,
A1704 5 0.22
Continued on next page
23

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G186.98+38.66 6.22 111 Y 4.68 RXC J0850.2+3603,
ZW1953 0.378
PSZ1 G083.62+85.08 6.17 111 R RXC J1305.9+3054,
A1677 0.1832
PSZ1 G143.67+42.63 6.16 111 R RXC J1003.1+6709,
A910 0.206
PSZ1 G192.19+56.12 6.14 111 M 0.22 RXC J1016.3+3338,
A961 0.124
PSZ1 G135.03+36.03 6.12 111 Y 6.11 RXC J0947.2+7623,
MAJ0947+7623 0.345
PSZ1 G074.75-24.59 6.10 111 N -2.58 ZwCl 2143.5+2014 0.25 Predicted σNW =
7.7;σtap =9.2
PSZ1 G152.68+25.43 6.10 111 LZ RXC J0704.4+6318,
A0566, A566 0.098
PSZ1 G223.97+69.31 6.09 111 M 1.34 RXC J1123.9+2129,
A1246 0.1904
PSZ1 G184.70+28.92 6.06 101 Y 20.64 RXC J0800.9+3602,
A0611, A611 2,4,5 0.288
PSZ1 G040.63+77.13 6.05 111 LZ RXC J1349.3+2806,
A1800 0.0748
PSZ1 G131.02+29.98 6.02 111 M 2.98 RXC J0825.7+8218,
A0625 0.2
PSZ1 G171.01+39.44 6.01 111 Y 27.90 0.5131
PSZ1 G050.41+31.18 5.98 111 Y 10.30 RXC J1720.1+2740,
A2259 4 0.164
PSZ1 G153.56+36.23 5.96 110 M 0.64
PSZ1 G205.85+73.77 5.96 111 Y 17.84 WHL J174.518+27.9773 0.4474
PSZ1 G031.94+78.71 5.95 111 LZ RXC J1341.8+2622 0.0724
PSZ1 G187.53+21.92 5.88 111 Y 12.52 RXC J0732.3+3137,
A0586, A586 5 0.171
PSZ1 G201.50+30.63 5.87 111 Y 15.32 ZwCl 0824.5+2244 0.287
PSZ1 G096.87+52.48 5.85 111 M 1.25 RXC J1452.9+5802,
A1995 0.3179
PSZ1 G078.67+20.06 5.84 011 R 0.45
PSZ1 G040.06+74.94 5.84 111 LZ RXC J1359.2+2758,
A1831 0.0612
PSZ1 G142.38+22.82 5.81 110 Y 7.22
PSZ1 G142.17+37.28 5.79 100 NN -5.05 Predicted σNW =
6.5;σtap =8.6
PSZ1 G186.81+07.31 5.79 001 R WHL J97.3409+26.5054 0.2577
PSZ1 G105.91-38.39 5.77 111 Y 13.03 Positional
uncertainty increased
to 5 arcmin to
encompass large
decrement visible in
map
PSZ1 G099.31+20.89 5.75 111 Y 7.41 RXC J1935.3+6734 0.1706
PSZ1 G137.56+53.88 5.73 001 NN -4.14 Predicted σNW =
17.3;σtap =17.6
PSZ1 G189.27+59.24 5.73 111 R RXC J1031.7+3502,
A1033 0.1259
PSZ1 G095.37+14.42 5.72 011 R 0.1188
Continued on next page
24

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G183.27+34.97 5.69 111 Y 9.64 WHLJ127.437+38.4651 0.3919
PSZ1 G069.92-18.89 5.68 111 R 0.3076
PSZ1 G156.88+13.48 5.67 111 Y 7.57
PSZ1 G109.99+52.87 5.64 111 Y 17.90 RXC J1359.8+6231,
ZW6429,
ZW1358+6245
0.3259
PSZ1 G179.13+60.14 5.61 111 R RXC J1040.7+3956,
A1068 0.1372
PSZ1 G107.32-31.51 5.60 111 N -2.03 RXC J2350.5+2929 0.1498 Predicted σNW =
7.0;σtap =9.8
PSZ1 G084.62-15.86 5.59 111 M 1.47
PSZ1 G145.19+32.14 5.58 001 R RXC J0811.1+7002,
A0621, A621 5 0.223
PSZ1 G127.36-10.69 5.58 100 R
PSZ1 G097.93+19.46 5.54 111 M 1.30 4C 65.28 0.25
PSZ1 G136.62-25.05 5.52 111 LZ RXC J0152.7+3609,
A0262, A262 0.0163
PSZ1 G094.54+51.01 5.52 011 Y 24.04 WHL J227.050+57.9005 0.5392
PSZ1 G123.55-10.34 5.51 111 SE 0.1 Lots of extended
emission across the
centre of the map
PSZ1 G100.82+24.61 5.50 011 LZ RXC J1900.4+6958,
A2315 0.0877
PSZ1 G103.58+24.78 5.48 011 SE 0.33 30mJy source at 11
arcmin leaves
substantial residuals
at map centre
PSZ1 G092.46-35.25 5.47 100 SE Large amounts of
extended emission
present on the map
after point source
subtraction
PSZ1 G151.19+48.29 5.45 111 R RXC J1017.5+5934,
A0959, A959 0.353
PSZ1 G109.88+27.94 5.44 111 Y 3.41 0.4
PSZ1 G134.31-06.57 5.44 011 Y 30.68
PSZ1 G172.64+65.29 5.43 111 LZ RXC J1111.6+4050 0.0794
PSZ1 G101.52-29.96 5.43 111 R 0.227
PSZ1 G168.34+69.73 5.42 011 SE ACO 1319 0.288 Many radio sources
close together and
unresolved on the
SA map, plus some
extended emission,
make source
subtraction too
difficult
PSZ1 G134.59+53.41 5.42 011 N -2.05 WHLJ177.705+62.3301 0.3452 Predicted σNW =
19.3;σtap =20.8
PSZ1 G135.03+54.38 5.40 001 SE WHL J178.058+61.3331 0.3169 Lots of extended
emission across the
centre of the map
PSZ1 G106.49-10.43 5.40 110 R
Continued on next page
25

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G188.41+07.04 5.39 001 LZ RXC J0631.3+2500,
ZwCl0628.1+2502 0.081
PSZ1 G108.13-09.21 5.39 110 Y 29.88
PSZ1 G090.82+44.13 5.37 110 N -0.97 ZwCl 1602.3+5917 0.2544 Predicted σNW =
2.4;σtap =2.2
PSZ1 G127.02+26.21 5.37 111 M 1.98
PSZ1 G164.63+46.37 5.36 111 M 0.93 ZwCl 0934.8+5216,
PLCKESZ G164.61 0.3605
PSZ1 G085.71+10.67 5.35 001 R
PSZ1 G050.46+67.54 5.35 111 N -2.30 RXC J1432.4+3137,
A1930 0.1313 Predicted σNW =
11.1;σtap =15.1
PSZ1 G137.51-10.01 5.33 010 R
PSZ1 G098.64+23.20 5.33 011 Y 5.57 RXC J1910.4+6741 0.2471
PSZ1 G060.50+26.94 5.33 110 R RXC J1750.2+3504 0.1712
PSZ1 G169.80+26.10 5.32 010 N -1.46 Predicted σNW =
14.4;σtap =16.1
PSZ1 G135.12+57.90 5.29 010 SE RXC J1201.9+5802,
A1446 0.1031 Only observed on
SA, 64 mJy source
on pointing centre
PSZ1 G157.67+77.99 5.28 111 R WHL J184.380+36.6865 0.3732
PSZ1 G101.36+32.39 5.27 011 N -1.60 RXC J1727.4+7035 0.3059 Predicted σNW =
4.6;σtap =5.8
PSZ1 G121.75+51.81 5.26 111 Y 119.16 ZwCl 1256.1+6537 0.23765 Lots of unsubtracted
extended emission
on the maps; the
cluster is clearly
detected, but
parameter estimation
may be unreliable
PSZ1 G130.26-26.53 5.25 010 SE ZwCl 0120.8+3538 0.2159
PSZ1 G084.85+20.63 5.25 111 Y 8.75 0.29
PSZ1 G149.38-36.86 5.25 111 Y 11.63 ACO 344 0.1696
PSZ1 G138.11+42.03 5.24 011 R 0.4961
PSZ1 G198.50+46.01 5.24 111 M 1.01 ZwCl 0928.0+2904 0.222
PSZ1 G091.81-26.97 5.23 011 R RXC J2245.4+2808,
MAJ2245+2808 0.3551
PSZ1 G031.91+67.94 5.23 100 N -0.29 Predicted σNW =
5.8;σtap =6.5
PSZ1 G213.37+80.60 5.23 111 Y 22.50 WHL J182.349+26.6796 0.5586
PSZ1 G100.03+23.73 5.22 001 Y 8.84 RXC J1908.3+6903,
A2317 0.2103
PSZ1 G135.92+76.21 5.22 010 N -2.91 Predicted σNW =
2.6;σtap =4.0
PSZ1 G071.44+59.57 5.21 111 R RXC J1501.3+4220,
ZW7215,
ZwCl1459.4+4
0.2917
PSZ1 G164.26+08.91 5.21 111 Y 14.38 WHL J85.8665+46.9358 0.2505
PSZ1 G084.84+35.04 5.21 111 N -0.66 RXC J1718.1+5639,
ZW8197 0.1138 Predicted σNW =
5.0;σtap =5.3
Continued on next page
26

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G119.37+46.84 5.21 111 SE RXC J1320.0+7003,
A1722,
MAJ1319+7003
0.3275 Extended structure to
the west not detected
in LA map
PSZ1 G076.44+23.53 5.21 111 SE 0.1685
PSZ1 G077.71+26.72 5.20 011 LZ RXC J1811.0+4954,
ZW8338 0.0501
PSZ1 G183.26+12.25 5.20 011 N -1.52 Predicted σNW =
17.1;σtap =18.2
PSZ1 G085.85+35.45 5.20 011 LZ RXC J1715.3+5724 0.0276
PSZ1 G114.98+19.10 5.19 010 N -0.75 Predicted σNW =
14.6;σtap =17.0
PSZ1 G059.51+33.06 5.18 011 SE RXC J1720.2+3536,
MAJ1720+3536 0.387 280 mJy source at 13
arcmin produces
artifacts on SA map
PSZ1 G172.93+21.31 5.18 011 Y 4.86 0.3309
PSZ1 G091.93+35.48 5.18 100 N -2.80 Predicted σNW =
14.1;σtap =12.4
PSZ1 G075.29+26.66 5.17 100 N -2.85 Predicted σNW =
17.3;σtap =17.1
PSZ1 G175.89+24.24 5.16 010 N -0.65 ZwCl 0723.4+4239 0.19175 Predicted σNW =
2.7;σtap =2.5
PSZ1 G144.86+25.09 5.15 111 Y 44.36 RXC J0647.8+7014,
MAJ0647+7015,
MACS5-0647
0.584
PSZ1 G123.72+34.65 5.14 100 R RXC J1231.3+8225 0.2053
PSZ1 G197.13+33.46 5.13 110 R WHL J128.694+26.9757 0.4561
PSZ1 G122.98-35.52 5.11 001 Y 11.74 RXC J0051.6+2720,
MAJ0051+2720 0.3615
PSZ1 G053.50+09.56 5.11 101 NN -4.20 Predicted σNW =
15.9;σtap =19.3
PSZ1 G045.07+67.80 5.11 100 N -2.05 ACO 1929 0.2191 Predicted σNW =
13.8;σtap =13.4
PSZ1 G116.79-09.82 5.11 011 R ZwCl 0008.8+5215 0.104
PSZ1 G189.29+07.44 5.10 001 R
PSZ1 G103.16-14.95 5.08 110 SE
PSZ1 G157.84+21.23 5.08 111 M 2.15
PSZ1 G048.09+27.18 5.07 111 M 1.04 0.73608
PSZ1 G087.47+37.65 5.07 010 R 0.1132
PSZ1 G111.74+70.35 5.07 111 M 1.06 RXC J1313.1+4616,
A1697 0.183
PSZ1 G066.20+12.87 5.06 001 N -0.95 0.23 Predicted σNW =
9.3;σtap =11.2
PSZ1 G045.85+57.71 5.06 111 Y 10.15 0.611
PSZ1 G079.33+28.33 5.06 011 SE ZwCl 1801.2+5136 0.2036 Too many radio
sources near the
cluster centre to be
sure of a
non-detection
Continued on next page
27

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Table A.1 – continued from previous page
Cluster name Planck
SNR Planck
det. Category ∆ln(Z) Aliases Previous
AMI Redshift Notes
PSZ1 G097.52-14.92 5.06 010 Y 35.39 Bright, extended
radio galaxy at about
10 arcmin removed
from the SA data
manually using
CLEAN components
leaving significant
residuals in the
source-subtracted
map; cluster is
clearly detected but
parameter estimation
is suspect
PSZ1 G118.06+31.10 5.05 011 SE Extended emission
near the cluster
centre
PSZ1 G056.13+28.06 5.05 011 Y 4.13 WHLJ265.066+31.6026 0.426
PSZ1 G083.35+76.41 5.03 011 R
PSZ1 G073.64+36.49 5.03 001 N -0.05 0.56 Predicted σNW =
21.1;σtap =22.2
PSZ1 G129.81+16.85 5.03 100 Y 3.91 0.41159
PSZ1 G134.64-11.77 5.02 111 Y 31.69 66mJy source at 10
arcmin leaves
residuals in the
source-subtracted
map; cluster is
clearly detected but
parameter estimation
is suspect
PSZ1 G178.10+18.58 5.01 101 SE
PSZ1 G165.41+66.17 5.00 111 M 1.96 WHL J170.907+43.0578 0.1957
PSZ1 G099.48+37.72 5.00 101 M 0.79 RXC J1634.6+6738,
A2216 0.1668
28

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Appendix B: Ytot-θsposterior comparison
Fig.B.1: Ytot-θsposterior distributions for AMI and Planck, in descending Planck SNR order (note that this is the ‘compatibility’
SNR for PwS), for all AMI detections (∆ln(Z)≥0).
29

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
30

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
31

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
32

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
33

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
34

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
35

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
36

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.1: Continued.
37

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig.B.2: Ytot-θsposterior distributions for AMI and Planck, in descending Planck SNR order (note that this is the ‘compatibility’
SNR for PwS), for all AMI non-detections (∆ln(Z)<0).
38

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
Fig. B.2: Continued.
39

Y. C. Perrott et al.: Planck and AMI SZ measurements for 99 galaxy clusters
1Academy of Sciences of Tatarstan, Bauman Str.,20, Kazan,
420111, Republic of Tatarstan, Russia
2Astrophysics Group, Cavendish Laboratory, University of
Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, U.K.
3Atacama Large Millimeter/submillimeter Array, ALMA Santiago
Central Offices, Alonso de Cordova 3107, Vitacura, Casilla 763
0355, Santiago, Chile
4CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulouse
cedex 4, France
5CSIRO Astronomy & Space Science, Australia Telescope National
Facility, PO Box 76, Epping, NSW 1710, Australia
6DSM/Irfu/SPP, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France
7Department of Astronomy and Geodesy, Kazan Federal University,
Kremlevskaya Str., 18, Kazan, 420008, Russia
8Dpto. Astrof´ısica, Universidad de La Laguna (ULL), E-38206 La
Laguna, Tenerife, Spain
9European Southern Observatory, ESO Vitacura, Alonso de Cordova
3107, Vitacura, Casilla 19001, Santiago, Chile
10 INAF - Osservatorio Astronomico di Roma, via di Frascati 33,
Monte Porzio Catone, Italy
11 Institut d’Astrophysique Spatiale, CNRS (UMR8617) Universit´e
Paris-Sud 11, Bˆatiment 121, Orsay, France
12 Institute of Astronomy, University of Cambridge, Madingley Road,
Cambridge CB3 0HA, U.K.
13 Institute of Theoretical Astrophysics, University of Oslo, Blindern,
Oslo, Norway
14 Instituto de Astrof´ısica de Canarias, C/V´ıa L´actea s/n, La
Laguna,Tenerife, Spain
15 Jodrell Bank Centre for Astrophysics, Alan Turing Building,
School of Physics and Astronomy, The University of Manchester,
Oxford Road, Manchester, M13 9PL, U.K.
16 Kavli Institute for Cosmology Cambridge, Madingley Road,
Cambridge, CB3 0HA, U.K.
17 Laboratoire AIM, IRFU/Service d’Astrophysique - CEA/DSM -
CNRS - Universit´e Paris Diderot, Bˆat. 709, CEA-Saclay, F-91191
Gif-sur-Yvette Cedex, France
18 Laboratoire de Physique Subatomique et de Cosmologie, Universit´e
Joseph Fourier Grenoble I, CNRS/IN2P3, Institut National
Polytechnique de Grenoble, 53 rue desMartyrs, 38026 Grenoble
cedex, France
19 Max-Planck-Institut f¨ur Extraterrestrische Physik,
Giessenbachstraße, 85748 Garching, Germany
20 Moscow Institute of Physics and Technology, Dolgoprudny,
Institutsky per., 9, 141700, Russia
21 Space Research Institute (IKI), Russian Academy of Sciences,
Profsoyuznaya Str, 84/32, Moscow, 117997, Russia
22 T¨
UB˙
ITAK National Observatory, Akdeniz University Campus,
07058, Antalya, Turkey
23 Space Research Institute (IKI), Russian Academy of Sciences,
Profsoyuznaya Str, 84/32, Moscow, 117997, Russia
24 Universit´e de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex
4, France
40