Blind and Pointed
Sunyaev-Zel’dovich Observations
with the Arcminute Microkelvin
Imager
Timothy William Shimwell
Cavendish Astrophysics and Churchill College
University of Cambridge
A dissertation submitted to the University of Cambridge for the degree of
Doctor of Philosophy
September, 2011
To my family.
i
Declaration
This dissertation is the result of work carried out in the Astrophysics
Group of the Cavendish Laboratory, Cambridge, between October
2007 and September 2011. Except where explicit reference is made
to the work of others, the work contained in this dissertation is my
own and is not the outcome of work done in collaboration. No part
of this dissertation has been submitted for a degree, diploma or other
qualification at this or any other university. The total length of this
dissertation does not exceed 60,000 words.
Timothy William Shimwell
September 2011
ii
Acknowledgements
I have thoroughly enjoyed the four years that I have spent living in
Cambridge and working at the Cavendish. There are many people
that I need to thank for this.
My supervisors Keith Grainge and Richard Saunders have been excep-
tionally supportive throughout my PhD, they have offered me endless
encouragement and countless helpful suggestions. I would have found
many of the problems I have faced, far more difficult, had not been
for the excellent help that I received from Dave Green, Mike Hobson,
Guy Pooley, Paul Scott, Dave Titterington and Liz Waldram. Ad-
ditionally, I was lucky enough to receie advice from other students
working with AMI, including Matthew Davies, Farhan Feroz, Tom
Franzen, Natasha Hurley-Walker, Malak Olamaie, Yvette Perrott,
Carmen Rodr´ıguez Gonza´lvez, Michel Schammel and John Zwart. I
also would like to thank all other members of the AMI Consortium
and the Astrophysics group. I feel privileged to have been welcomed
by such a kind, enthusiastic and encouraging community.
I started my PhD along with Luke Butcher, Douglas O’Rourke, John
Pober, Carmen Rodr´ıguez Gonza´lvez and Chris Thomas – all of whom
have become good friends. Carmen Rodr´ıguez Gonza´lvez has pa-
tiently tried to teach me Spanish and has been a fantastic office
mate. With Luke Butcher and Douglas O’Rourke I have enjoyed many
evenings out and about in Cambridge. Chris Thomas has taught me
all about military history and John Pober has been missed since he
left for America after the first year. I am grateful to have met all the
other PhD (and postdoc) students from the Cavendish (and Kavli).
I will miss you all. I also would like to thank all of my friends who
iii
are not based at the Cavendish or Kavli, including those I met whilst
living in Wilbarston, Rutland, Sheffield and at Churchill College. I
am especially indebted to my friends from Sheffield who supported
my application and undergraduate studies, without your help I would
never have been here.
My family have provided me with so much help over the years and I
am sure that without their tireless encouragement my life would have
been very different. Without all of this support I would never have
achieved this PhD. The help that each of you has provided is far too
much to even begin describing here but I hope that you all know just
how much I appreciate everything that you have done for me over the
years.
I am grateful for the financial support provided by STFC, the com-
puter services and expertise provided by Stuart Rankin and Andrey
Kaliazin, who respectively ran the Darwin and COSMOS supercom-
puters. I would also like to extend my thanks to my examiners Michael
Brown and Richard Davis. Finally, I would like to thank Cambridge
University and Churchill College for the opportunity to study in such
a wonderful environment.
iv
Abstract
In this thesis I discuss my work on the Arcminute Microkelvin Imager
(AMI). I focus on the detection of Sunyaev-Zel’dovich (SZ) signatures
at 14-18GHz.
Once the background science and operation of the instrument are de-
scribed I proceed to present my contribution to the calibration of AMI,
including: primary beam measurements; refinements to the known an-
tenna geometry and flagging geostationary satellite interference. This
is followed by an outline of the software that I have developed to
subtract sources from visibilities, concatenate data from multiple ob-
servations, simulate data, and perform jack-knife tests to evaluate the
magnitude of systematic errors.
The Bayesian analysis that I use to obtain parameter estimates and
to quantify the significance of putative SZ detections is described. I
perform realistic simulations of clusters and use these to characterise
the analysis. I then, for the first time, apply the analysis to data from
the AMI blind cluster survey. I identify several previously unknown
SZ decrements.
Finally, I conduct pointed observations towards a high luminosity sub-
sample of eight clusters from the Local Cluster Substructure Survey
(LoCuSS). For each of these I provide probability distributions of
parameters such as mass, radius, β and temperature. I compare my
results to those in the literature and find an overall agreement.
v
Contents
1 Introduction 1
1.1 Cosmological Background . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 The Cosmic Microwave Background . . . . . . . . . . . . . 8
1.1.2 Structure Formation . . . . . . . . . . . . . . . . . . . . . 11
1.1.3 The Thermal Sunyaev-Zel’dovich Effect . . . . . . . . . . . 13
1.2 The Arcminute Microkelvin Imager . . . . . . . . . . . . . . . . . 18
1.2.1 Radio Interferometry with AMI . . . . . . . . . . . . . . . 21
1.3 Blind SZ Effect Surveys . . . . . . . . . . . . . . . . . . . . . . . 31
1.3.1 AMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.3.2 South Pole Telescope . . . . . . . . . . . . . . . . . . . . . 31
1.3.3 Atacama Cosmology Telescope . . . . . . . . . . . . . . . . 32
1.3.4 Planck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.3.5 Sunyaev-Zel’dovich Array . . . . . . . . . . . . . . . . . . 33
1.3.6 The Latest Results from Blind SZ Surveys . . . . . . . . . 34
1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Calibration 37
2.1 Correlator Lag Calibration . . . . . . . . . . . . . . . . . . . . . . 37
2.1.1 Calibrating a PC Drift Observation . . . . . . . . . . . . . 40
2.2 Geometry of the Large Array . . . . . . . . . . . . . . . . . . . . 44
2.3 Smoothing Amplitude Corrections . . . . . . . . . . . . . . . . . . 47
2.4 Flagging Interference . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 Interference Spikes . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Geostationary Satellites . . . . . . . . . . . . . . . . . . . 48
2.5 Power Primary Beam Measurements . . . . . . . . . . . . . . . . 50
vi
CONTENTS
2.5.1 Raster Offset Observations . . . . . . . . . . . . . . . . . . 51
2.5.2 Hour Angle and Declination Offset Observations . . . . . . 53
2.5.3 Drift Scan Observations . . . . . . . . . . . . . . . . . . . 55
2.5.4 Small Array Primary Beam . . . . . . . . . . . . . . . . . 56
2.5.5 Large Array Primary Beam . . . . . . . . . . . . . . . . . 59
2.6 Standard Reduction for AMI Observations . . . . . . . . . . . . . 61
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3 Post-Reduction Data Manipulation Tools 65
3.1 Concatenating AMI data . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.1 FUSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.1.2 Secondary Functionalities of FUSE . . . . . . . . . . . . . 67
3.1.2.1 Mapping AMI Data in AIPS . . . . . . . . . . . 67
3.1.2.2 Flagging Interference . . . . . . . . . . . . . . . . 68
3.1.2.3 Reweighting the Data . . . . . . . . . . . . . . . 68
3.2 Separating Multi-source Data . . . . . . . . . . . . . . . . . . . . 69
3.3 Source Subtraction and Data Simulation . . . . . . . . . . . . . . 69
3.3.1 MUESLI Source Subtraction . . . . . . . . . . . . . . . . . 70
3.3.1.1 MUESLI Simulation . . . . . . . . . . . . . . . . 71
3.4 Jack-knife Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Preparing to analyse the AMI blind survey fields 76
4.1 McAdam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.1.1 Physical Cluster Model . . . . . . . . . . . . . . . . . . . . 81
4.1.1.1 Priors . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1.2 Phenomenological Model . . . . . . . . . . . . . . . . . . . 83
4.1.2.1 Priors . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 SZ Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.1 Simulation Properties . . . . . . . . . . . . . . . . . . . . . 85
4.2.2 The Mass Limit of the AMI Survey . . . . . . . . . . . . . 87
4.2.3 Probability of Cluster Detection . . . . . . . . . . . . . . . 94
4.2.4 A Comparison Between Simulated and Derived Mass . . . 98
vii
CONTENTS
4.2.5 Testing the Influence of the Mass Limit on the Probability
of Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.6 Testing the Influence of the Cluster Search Area on the
Probability of Cluster Detection . . . . . . . . . . . . . . . 107
4.3 Computational Challenges . . . . . . . . . . . . . . . . . . . . . . 108
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.5 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5 The AMI blind survey 112
5.1 Survey Observations . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2 Source Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.3 McAdam Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.4 Cluster Identification . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.5 The Analysis of Survey Fields . . . . . . . . . . . . . . . . . . . . 120
5.6 AMI002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.6.1 Candidate 1: 12-15-16 and 15-16-20 . . . . . . . . . . . . . 127
5.6.1.1 Pointed Follow-up Observation . . . . . . . . . . 128
5.6.2 Candidate 2: 11-12-15, 11-14-15, 15-19-20 and 14-15-19 . . 131
5.6.2.1 Pointed observation . . . . . . . . . . . . . . . . 132
5.6.3 Candidate 3: 18-19-22 . . . . . . . . . . . . . . . . . . . . 137
5.6.3.1 Pointed Follow-up Observations . . . . . . . . . . 138
5.6.4 Candidate 4: 6-7-11, 3-6-7 and 6-10-11 . . . . . . . . . . . 141
5.6.4.1 Pointed Follow-up Observations . . . . . . . . . . 142
5.6.5 Candidate 5: 7-11-12 and 7-8-12 . . . . . . . . . . . . . . . 145
5.6.5.1 Pointed Follow-up Observations . . . . . . . . . . 146
5.6.6 Candidate 6: 2-3-6 . . . . . . . . . . . . . . . . . . . . . . 149
5.6.6.1 Pointed Follow-up Observations . . . . . . . . . . 150
5.6.7 Candidate 7: 5-9-10 and 1-2-5 . . . . . . . . . . . . . . . . 153
5.6.7.1 Pointed Follow-up Observations . . . . . . . . . . 154
5.6.8 Candidate 8: 6-10-11 . . . . . . . . . . . . . . . . . . . . . 157
5.6.8.1 Pointed Follow-up Observations . . . . . . . . . . 158
5.6.9 Candidate 9: 13-14-18 and 13-17-18 . . . . . . . . . . . . . 162
5.6.9.1 Pointed Follow-up Observations . . . . . . . . . . 162
viii
CONTENTS
5.7 AMI005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.7.1 Candidate 1: 3-4-7 and 4-7-8 . . . . . . . . . . . . . . . . . 167
5.7.1.1 Pointed Follow-up Observations . . . . . . . . . . 168
5.7.2 Candidate 2: 13-14-18 and 14-18-19 . . . . . . . . . . . . . 171
5.7.2.1 Pointed Follow-up Observations . . . . . . . . . . 172
5.7.3 Candidate 3: 9-10-13 . . . . . . . . . . . . . . . . . . . . . 174
5.7.3.1 Pointed Follow-up Observations . . . . . . . . . . 175
5.8 Survey Source Properties . . . . . . . . . . . . . . . . . . . . . . . 177
5.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.10 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6 SZ Observations of LoCuSS clusters with AMI: High X-ray Lu-
minosity Sample 182
6.1 X-ray emission and the SZ Effect . . . . . . . . . . . . . . . . . . 183
6.2 The LoCuSS Cluster sample . . . . . . . . . . . . . . . . . . . . . 183
6.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.4 Bayesian Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.5 Maps and Derived Cluster Parameters . . . . . . . . . . . . . . . 186
6.5.1 Abell 586 . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.5.2 Abell 611 . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.5.3 Abell 773 . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.5.4 Abell 781 . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.5.5 Abell 1413 . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.5.6 Abell 1758 . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.5.7 Zw1454.8+2233 . . . . . . . . . . . . . . . . . . . . . . . . 197
6.5.8 RXJ1720.1+2638 . . . . . . . . . . . . . . . . . . . . . . . 202
6.6 Cluster Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7 Conclusions 209
7.1 Commissioning and Calibration . . . . . . . . . . . . . . . . . . . 209
7.2 AMI blind survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.3 Pointed SZ observations . . . . . . . . . . . . . . . . . . . . . . . 210
ix
CONTENTS
A The Friedmann Equation 211
B AMI002 LA Source Properties 215
B.1 AMI005 LA Source Properties . . . . . . . . . . . . . . . . . . . . 221
References 243
x
Chapter 1
Introduction
An unbiased study of the evolution of clusters of galaxies can be used to tie-down
the growth of large-scale structure and measure the rms mass fluctuation ampli-
tude as a function of redshift. This chapter is largely introductory; much of the
material presented here can be found, in one form or other, in e.g. Peebles (1993),
Carlstrom et al. (1996), Longair (1996), Birkinshaw (1999), Peacock (1999) and
Thompson et al. (2001).
The largest cluster catalogues currently available are built up from clusters
discovered either in the X-ray or optical wavebands. These catalogues are unfor-
tunately strongly biased because the radiation that X-ray and optical telescopes
detect from clusters falls off rapidly with redshift, is particularly sensitive to mass
concentrations and suffers from confusion from foreground and background ob-
jects. The surface brightness of the Sunyaev-Zel’dovich (SZ; Sunyaev & Zeldovich
1970) effect of a particular cluster is wholly independent of the redshift at which
it lies: this redshift-independence is unique in cosmology and is of fundamental
importance. The SZ signal is also much less affected by confusion and is a direct
measure of cluster thermal energy and hence a clear proxy of the key quantity,
mass. Several blind surveys for galaxy clusters via SZ are underway but none is
yet finished.
The Arcminute Microkelvin Imager (AMI) is a radio interferometer optimised
to observe the SZ effect from galaxy clusters. AMI has been conducting a blind
cluster survey over a 12 deg2 region, searching for galaxy clusters with total
masses greater than ≈ 3 × 1014M⊙h−170 (with h70 = 1 if H0 = 70kms−1Mpc−1).
1
1.1 Cosmological Background
AMI has also accumulated a large collection of high quality, low noise, pointed
observations towards galaxy clusters that appear in X-ray, optical, or other SZ
catalogues. In this thesis I present results from survey and pointed observations
and I explain the reduction, commissioning, observing and analysis tasks that I
have been involved with.
This first chapter provides a brief introduction to basic cosmology, the SZ
effect and the operation of AMI.
1.1 Cosmological Background
The Einstein field equation is vital to our understanding of how the evolution of
the Universe is affected by its energy and matter content. It is a cornerstone of
modern cosmological theories. The Einstein field equation is
Guv =
8piG
c4
Tuv, (1.1)
where the Einstein tensor (Guv) relates the geometry of space-time to the energy-
momentum tensor (Tuv).
The curvature of space can be described by a metric. The Euclidean metric
is used to define a classical, flat and static space with three dimensions (x, y, z),
and takes the form
guv =

1 0 00 1 0
0 0 1

 . (1.2)
It is used to determine the separation (ds) between two points in Euclidean space:
ds2 = gαβdx
αdxβ = dx2 + dy2 + dz2. (1.3)
This line element describes the distance between points on a three dimensional
static gird that has no time dimension.
To account for four-dimensional space-time the Euclidean metric is modified
to the Minkowski metric – this also describes a flat and static space.
guv =


−1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

 . (1.4)
2
1.1 Cosmological Background
The separation between two points in Minkowski space-time is
ds2 = dx2 + dy2 + dz2 − c2dt2, (1.5)
However, the Universe is expanding and a modification to the static Minkowski
metric is required. The Universe expands at a rate that can be described by a
comoving coordinate system, such as that depicted in Figure 1.1.
Figure 1.1: Comoving coordinate system. The scale factor, a(t), of the coordinate
system is defined to be proportional to the distance between coordinates.
In a comoving coordinate system objects retain the same coordinates through-
out the expansion of the space, even though the separation between the objects
is changing. Consider two objects of separation r¯(t) which are not moving with
respect to the Hubble flow; their comoving separation is
x¯ = r¯(t)/a(t), (1.6)
where a is the scale factor.
In a four-dimensional expanding Universe the three spatial dimensions evolve
according to Equation 1.6, but the time dimension is not affected by the ex-
pansion. This alteration, together with the addition of curvature to the static
Minkowski metric gives the Friedmann-Robertson-Walker (FRW) metric:
guv =


−1 0 0 0
0 a2(t) 0 0
0 0 a2(t) 0
0 0 0 a2(t)

 . (1.7)
This metric is an accurate description of the geometry of an expanding (or con-
tracting) Universe. The separation between two points in the FRW metric is
3
1.1 Cosmological Background
given, in spherical coordinates, by
ds2 = c2dt2 − a(t)2
(
dr2
1 + kr2
+ r2(dθ2 + sin2θdφ2)
)
. (1.8)
Here, t is the cosmic time, r, θ and φ are comoving spherical coordinates and k
is a constant that describes the geometry of the Universe. k-values of +1, 0, and
-1 correspond to a closed, flat and an open Universe respectively (see Figure 1.2).
The geodesics described by the FRW metric follow the curvature of space.
Figure 1.2: A two-dimensional analogy of the three-dimensional curvature in the
Universe, with white lines showing geodesics and red lines showing the shortest
distance between two points. At the top is a closed Universe (k = −1), in the
middle is a open Universe (k = −1) and at the bottom is a flat Universe (k = 0).
The FRW metric is used to derive the Einstein tensor in the Einstein field
equation (Equation A.1). This describes how energy density affects the curvature
of the Universe:
Guv = Ruv − 1
2
guvR, (1.9)
where Ruv is known as the Ricci tensor, R the Ricci scalar and guv is the FRW
metric.
The stress energy tensor Tuv for an observer in an homogeneous and isotropic
Universe is
Tuv =


ρ 0 0 0
0 p 0 0
0 0 p 0
0 0 0 p

 , (1.10)
4
1.1 Cosmological Background
where p is the mean pressure and ρ is the mean energy density (ρ = ρR + ρM).
Using the FRW metric and the stress energy tensor we can find a solution to
the Einstein field equation, the Friedmann equation (see Appendix A for deriva-
tion):
H2 =
(
a˙
a
)2
=
8piGρ
3
− const, (1.11)
where H is the Hubble parameter and the constant arises from integration and
represents the curvature of the Universe. The constant is given by kc
2
a2
.
The original field equations were revised by Einstein in 1917 to include the
cosmological constant (ρΛ).
Guv =
8piG
c4
Tuv + ρΛguv (1.12)
This in turn has an effect on the Friedmann equation, which now has the form
H2 =
(
a˙
a
)2
=
8piGρ
3
− kc
2
a2
+
Λc2
3
. (1.13)
By defining ρΛ
c2
= Λ
8piG
and −ρk
3c3
= k
8piGa2
the Friedmann equation is frequently
written as (
a˙
a
)2
= H20
(
ΩMa
−3 + ΩRa
−4 + ΩΛ + Ωka
−2
)
, (1.14)
where ρtot =
∑
i ρi = ρM + ρR + ρλ + ρk and Ωtot =
∑
iΩi = ΩM +ΩR +Ωλ +Ωk
Ωi =
ρi
ρc
=
8piGρi
3H20
(1.15)
and ΩM is the density parameter of non relativistic matter, ΩR is the density
parameter of relativistic matter, ΩΛ the density parameter of the cosmological
constant, Ωk is the curvature of the Universe and ρc is the critical energy density
of the Universe. For a flat Universe
ρc =
3H20
8piG
. (1.16)
The orders of the scale-factor terms in Equation 1.14 are explained later in this
section.
5
1.1 Cosmological Background
By taking the trace of the Einstein field equation one can derive another
important equation called the acceleration equation:
a¨
a
=
−4piG
3
(
ρtot +
3ptot
c2
)
. (1.17)
This equation shows how the expansion of the Universe depends upon the mean
energy density ρtot and the mean pressure density ptot. If the Universe is matter
or radiation dominated where (ρtot+3ptot) > 0 then the expansion of the Universe
will decelerate. It is also possible for the expansion of the Universe to accelerate
if (ρtot + 3ptot) < 0, however, this requires a substance that has negative energy
density or negative pressure density.
By relating the time derivative of Equation 1.13 to Equation 1.17 and assum-
ing a flat Universe one can derive
ρ˙ = −3H(ρtot + ptot
c2
), (1.18)
for which a solution is
ρtot ∝ a−3(1+ω), (1.19)
where ω is the equation of state parameter (ω = ptot
ρtot
). Note that this equation
can also be derived by assuming an adiabatic and homogeneous expanding Uni-
verse and applying the first law of thermodynamics. From Equation 1.19 the a
dependencies of the density parameters in Equation 1.14 can be obtained. For
radiation ω=1/3, for matter ω=0, for Λ ω = −1 and for k ω = −1/3. Therefore
the density components vary with the scale factor as:
radiation :ρR ∝ a−4, (1.20)
matter :ρM ∝ a−3, (1.21)
dark energy :ρΛ ∝ a0, (1.22)
curvature :ρk ∝ a−2. (1.23)
The cosmological constant was originally introduced to explain a static Uni-
verse, although it is unable to do so. It is now used to explain the observed
acceleration in the expansion of the Universe. This acceleration was originally
discovered by comparing the measured redshifts of type Ia supernovae to their
6
1.1 Cosmological Background
measured luminosity distances. The supernovae have a consistent peak luminos-
ity and such observations reveal the variation in the scale factor as a function of
redshift. The redshift is determined from supernovae emission/absorption lines
from
1 + z =
λobs
λem
=
a(tobs)
a(tem)
, (1.24)
where λem is the wavelength of emitted light, λobs is the wavelength of observed
light, a(tem) and a(tobs) are the scale factors at the redshift of the emitting object
and the observer respectively. For a flat Universe luminosity distance, dL, is given
by
dL =
c(1 + z)
H0
∫ z
0
dz√
ΩM (1 + z)3 + ΩΛ
, (1.25)
and plotted in Figure 1.8. Because the type Ia supernovae are standard candles
their dL can also be determined from their apparent magnitude. If both dL
and z are known then the values of ΩM and ΩΛ can be constrained. The first
measurements of ΩΛ were presented in Riess et al. (1998).
The latest Cosmic Microwave Background (CMB) observations have shown
that the Universe is flat (k = 0) to within 1% (Larson et al. 2011) with con-
tributions from ΩM , ΩR and ΩΛ. The ΩM component can be split into weakly
interacting cold dark matter (Ωc) of which the exact form is presently unknown,
and baryonic matter (Ωb). Estimated density parameters for the current epoch
are given in Table 1.1 and an image showing the evolution of these density pa-
rameters is presented in Figure 1.3. This description of the Universe is known as
the flat ΛCDM Universe.
Table 1.1: Cosmological density parameters taken from Larson et al. (2011).
Parameter Value
Ωb 0.0449±0.0028
Ωc 0.222±0.026
ΩM 0.266±0.029 (Ωb + Ωc)
ΩΛ 0.734±0.029
ΩR 6×10−5
7
1.1 Cosmological Background
Figure 1.3: The evolution of the density parameters with scale factor for a flat
Universe. The present values
(
a
a0
= 1
)
are given in Table 1.1.
1.1.1 The Cosmic Microwave Background
An almost uniform background of radiation in all directions was discovered by
Penzias & Wilson (1965). This background is now known as the CMB and is well
explained in the Big Bang theory of the Universe.
As the Universe expanded after the Big Bang, its content cooled sufficiently
so that the formation of hydrogen and helium atoms was no longer prohibited.
At this point the Universe became transparent rather than opaque because the
Thomson scattering of the huge excess of photons by ions ceased. This phase
transition, known as recombination or the surface of last scattering, occurred at
z = 1, 100 with a thickness of ∆z ≈ 80 and at a temperature of ≈ 3, 000K.
Before recombination the baryon-photon coupling kept the plasma in thermal
equilibrium and as a result the CMB photons have a characteristic blackbody
spectrum. Once recombination was complete the photons have since travelled
through the Universe almost undisturbed. As they have travelled they have cooled
and redshifted as a result of the expansion of the Universe; the temperature of
the CMB is now TCMB = 2.71K and the CMB spectrum peaks at 160GHz.
8
1.1 Cosmological Background
We know from the existence of planets, stars, galaxies and clusters that the
Universe cannot have been completely uniform at the time of recombination (or
indeed far earlier). Hence, after the discovery of the CMB many experiments
have focused on detecting and characterising the predicted anisotropies. Tem-
perature fluctuations in the CMB were first discovered by the Cosmic Back-
ground Explorer (COBE) satellite (Smoot et al. 1992); the maximum ampli-
tude of these spatial fluctuations is ∆T/T ≈ 10−5. Since COBE, many ground-
based and balloon-borne instruments have studied the temperature fluctuations
in greater detail. Notably, a second generation satellite, the Wilkinson Microwave
Anisotropy Probe (WMAP), was launched in 2001 and a third generation satel-
lite, Planck, was launched in 2009.
Presently the most detailed all-sky CMB map has been produced from the
WMAP 7-year data (Larson et al. 2011). However, the Planck satellite is currently
performing an all-sky scan with improved resolution and 10× higher sensitivity;
Planck will continue to gather data until at least the end of 2011. The WMAP
resolution is low and the satellite only obtains excellent constraints on the large
angular features in the CMB. The ground-based South Pole Telescope (SPT) has
made measurements of the anisotropies with a much higher angular resolution
(Keisler et al. 2011). The WMAP image of the CMB and the combined WMAP
and SPT power spectrum are shown in Figure 1.4.
9
1.1 Cosmological Background
Figure 1.4: Left: The WMAP 7-year data release q-band (41GHz) all-sky map
before galaxy subtraction. The colour scale is from blue (-200µK) to red (200µK)
(WMAP Science Team). Right: The corresponding WMAP 7-year power spec-
trum (Larson et al. 2011) together with the higher resolution SPT power spectrum
(Keisler et al. 2011). l of 1000 corresponds to an angular scale of ≈ 0.2 deg. The
best fit ΛCDM model is shown with the dashed line; the solid line shows the best
fit ΛCDM+foregrounds.
The anisotropies that are observed in the CMB can be split into two types: pri-
mary anisotropies that occur either before or at the surface of last scattering, and
secondary anisotropies that have developed since the surface of last scattering.
Main causes of primary anisotropies are: gravitational redshifting of the pho-
tons as they climb out of potential wells (the non-integrated Sachs-Wolfe effect);
temperature fluctuations caused by the interplay between pressure and gravity
in the photon-baryon plasma (acoustic perturbations), and the Doppler shift of
photons due to the photons’ peculiar bulk velocities. Secondary anisotropies can
be induced by: gravitational redshifting of the photons as they climb out of
evolving potential wells after the surface of last scattering (the integrated Sachs-
Wolfe effect and the Rees-Sciama effect); gravitational lensing of the CMB and
the scattering of CMB photons off hot plasma in galaxy clusters (the kinetic
Sunyaev-Zel’dovich effect and the thermal Sunyaev-Zel’dovich effect).
The peaks in the CMB power spectrum (Figure 1.4) are due to acoustic pertur-
bations. The amplitude of the CMB begins to fall off at about l of 1000 due to a
combination of silk dampening and incoherent addition. Silk damping (Silk 1968)
is caused by photon diffusion during recombination and dramatically reduces the
10
1.1 Cosmological Background
amplitude of small scale photon perturbations. Incoherent addition arises due to
the finite thickness (∆z ≈ 80) of recombination; for small scale peaks we would
expect cancellation effects due the existence of many such oscillations along the
line of sight.
1.1.2 Structure Formation
The full relativistic derivation for the evolution of structure formation is pre-
sented in detail in e.g. Liddle (2003). A perturbation is added to the FRW
metric and to the energy-momentum tensor, and the evolution of this pertur-
bation is calculated. The evolution of the density perturbations with conformal
time η (where adη = dt) produces simple solutions when the Universe is matter-
dominated, radiation-dominated or Λ-dominated (see Figure 1.3). The solutions
are found to depend upon the size of the perturbation – in the radiation era the
sub-horizon perturbations evolve differently to super-horizon perturbations. The
sound horizon is the speed of sound multiplied by the age of the Universe, the
sound horizon is used here because the sound speed is the rate at which pressure
can be transmitted. Sub-horizon perturbations are entirely enclosed within a hori-
zon, super-horizon fluctuations are not. The equations describing the evolution
of the density perturbations are given in Table 1.2.
Table 1.2: Evolution of density perturbations with conformal time in the matter,
radiation and Λ dominated eras.
Super-horizon Sub-horizon
Radiation era δm ∝ η2 δm ∝ 1
Matter era δm ∝ η2 δm ∝ η2
Λ era 1 1
As the Universe evolves the size of the horizon increases and larger length-
scale perturbations enter the horizon. In Figure 1.5 the evolution of two different
sized perturbations through the matter, radiation and Λ dominated eras is shown.
11
1.1 Cosmological Background
Figure 1.5: The evolution of density perturbations A and B. Perturbation B is
smaller in length-scale and enters the horizon at ηBH . Perturbation A is larger in
length-scale and enters the horizon at ηAH . ηeq is the η of matter and radiation
equality and ηΛ is the η when the Λ density begins to dominate.
Although the general evolution of a perturbation is described in Figure 1.5
it must also be considered that before the surface of last scattering the photons
and baryons were tightly coupled. After perturbations enter the horizon the
opposing gravitational and pressure forces cause an oscillation with a frequency
that depends upon their length-scale size. At the time of recombination (when
oscillation ceases) the phase of the perturbation depends upon the time since that
perturbation entered the horizon (this is the cause of the acoustic peaks in Figure
1.4). It should be noted that even before the surface of last scattering the dark
matter was not tightly coupled to photons. As a consequence the dark matter
density perturbations did not oscillate but evolved as would be expected from
matter (Figure 1.5).
The gravitational potentials of the overdense regions continue to grow until Λ
domination. This hierarchical growth implies that the largest structures (clusters
of galaxies) form last.
12
1.1 Cosmological Background
1.1.3 The Thermal Sunyaev-Zel’dovich Effect
The Sunyaev-Zel’dovich (SZ; Sunyaev & Zeldovich 1970, Sunyaev & Zeldovich
1972) effect is a secondary CMB anisotropy and occurs when CMB radiation
interacts with the plasma in the potential well of clusters of galaxies (see Birkin-
shaw (1999) and Carlstrom et al. (2002) for reviews). There are two types of SZ
effect, these are: the thermal SZ effect which is caused by the scattering of CMB
photons in the hot plasma contained by the cluster’s gravitational well, and the
kinetic SZ effect caused by the bulk motion of the cluster plasma with respect to
the Hubble flow. Here I focus on the thermal SZ effect which for typical clusters
causes significantly larger secondary anisotropies in the CMB than the kinetic SZ
effect (for ν not close to 220GHz).
Observations of clusters indicate that they typically have a virial radius of
1-2Mpc (within which the average density is greater than ≈200 times the critical
density at the cluster redshift) and within this radius the total mass can occa-
sionally exceed 1015M⊙. The intracluster “gas” is a plasma with temperature
typically 4-8 keV. The SZ effect is caused when a CMB photon passing through a
cluster of galaxies interacts with an energetic intracluster electron and undergoes
inverse Compton scattering. The isotropic CMB photons that scatter off intr-
acluster electrons have altered directions and on average an increase in energy.
Although the net direction change cancel out, the increase in energy is observ-
able. Kompaneets (1957) demonstrated that first order scattering effects cancels,
but to second order the energy gain of an electron is ∝ v2
c2
∝ kBTe
mec2
, where v is the
electron velocity, kB is the Boltzmann constant, Te is the electron temperature
and mec
2 is the electron rest mass energy. The fractional temperature change of
the CMB due to the thermal SZ effect is
∆TSZ
TCMB
= f(x)y = f(x)
∫
nekBTe
mec2
σTdl, (1.26)
where y is the Compton y-parameter, ne is the electron number density, σT is
the Thomson cross section and the integral is over the line of sight through the
cluster. The frequency dependence is contained within the f(x) term:
f(x) =
(
x
ex + 1
ex − 1 − 4
)
(1 + δ(x, Te)) . (1.27)
13
1.1 Cosmological Background
Here x = hν
KBTCMB
and δ(x, Te) is a relativistic correction (see e.g. Challinor et al.
1997 and Itoh et al. 1998). In the Rayleigh-Jeans regime f(x) = −2 and Equation
1.26 reduces to
∆TSZ
TCMB
≈ −2
∫
nekBTe
mec2
σTdl. (1.28)
This temperature change in the CMB blackbody radiation causes a shift in the
CMB frequency spectrum. At frequencies less than 218GHz an intensity drop is
observed while for higher frequencies an increment is observed. Figure 1.6 shows
an exaggerated shift in the CMB intensity.
Figure 1.6: The dashed line shows the CMB thermal spectrum before any sec-
ondary distortions and the solid line shows the CMB spectrum after thermal SZ
distortion, note the effect is exaggerated by a factor of 1000 for clarity. At fre-
quencies less than 218 GHz the SZ effect decreases the CMB intensity. Figure
taken from Carlstrom et al., (2002).
To determine the total SZ flux density from a cluster we integrate over its
solid angle, Ω, on the sky:
∆SSZ ≈ −2TCMB
d2A
∫
nekBTe
mec2
σTdldΩ. (1.29)
The integrated SZ signal is thus dependent upon the integral along the line of
sight of the density of electrons multiplied by their temperature,
∆SSZ ∝ − 1
d2A
∫
neTedV, (1.30)
14
1.1 Cosmological Background
i.e. the plasma thermal energy (e.g. Bartlett & Silk 1994). With the assumption
that the cluster is virialized, isothermal, spherical and that all its kinetic energy
is in plasma microscopic internal energy, Te ∝M2/3, whereM is the cluster mass,
and the integrated SZ effect is
∆SSZ ∝ −M
5/3
d2A
. (1.31)
Equation 1.31 implies that the SZ signal is an excellent measure of cluster mass.
This relationship has support from galaxy cluster observations: in Figure 1.7 I
show the Planck observed relationship between d2AYSZ and Mgas,500, where YSZ is
the y-parameter integrated out to r500.
Figure 1.7: The d2AYSZ (within r500) and Mg,500 relationship from Planck observa-
tions of 62 clusters that have been observed with XMM-Newton. The d2AYSZ was
derived from Planck data andMg,500 was derived from XMMmeasurements. Cool
core systems are in blue and all other clusters are in black. The best fit relation is
E(z)−2/3d2AYSZ = 10
C
(
Mg,500
1×1014
)B
, where C = 4.044± 0.010 and B = 1.36± 0.07.
The logarithmic intrinsic scatter is σlog,i = 0.092± 0.011. These results are taken
from Planck Collaboration et al. (2011c)
Another important property of the SZ effect is the independence of its surface
brightness on redshift. It may be expected that the SZ signal surface brightness
15
1.1 Cosmological Background
be dimmed with redshift like the CMB surface brightness ((1 + z)4), in fact,
this dimming is exactly cancelled by the increasing temperature of the CMB
with redshift, i.e. the ratio of the magnitude of the SZ to the CMB is redshift
independent. However, the integrated SZ flux from a cluster does depend upon
the angular size of the clusters via d2A. Although at high redshifts the angular
diameter distance is relatively redshift independent (Figure 1.8).
A further property is that the SZ effect is not significantly affected by the
dynamical history of clusters, this is demonstrated by Arnaud et al. (2010), whose
results are presented in Figure 1.9.
 0
 200
 400
 600
 800
 1000
 1200
 1400
 1600
 1800
 0  0.5  1  1.5  2  2.5  3
A
n
g
u
la
r 
d
ia
m
e
te
r 
d
is
ta
n
ce
 (M
pc
)
Redshift
Angular diameter distance
 0
 5000
 10000
 15000
 20000
 25000
 30000
 0  0.5  1  1.5  2  2.5  3
L
u
m
in
o
si
tiy
 d
is
ta
n
ce
 (M
pc
)
Redshift
Luminosity distance
L
u
m
in
o
si
tiy
 d
is
ta
n
ce
 (M
pc
)
Figure 1.8: On the left is the angular diameter distance (dA) as a function of
redshift, on the right is a corresponding plot for the luminosity distance (dL). dA
is given by c
H0(1+z)
∫ z
0
dz√
ΩM (1+z)3+ΩΛ
and for these plots I have used ΩM = 0.3,
ΩΛ = 0.7 and h70 = 1. The luminosity distance is a factor of (1 + z)
2 larger
than the angular diameter distance. The angular diameter distance is the ratio
of an objects physical size to its angular size, it does not increase indefinitely with
redshift due to the expansion of the Universe.
16
1.1 Cosmological Background
Figure 1.9: XMM Newton cluster profiles of electron density, temperature and
pressure from 33 low-redshift (z < 0.2) clusters in the Representative XMM-
Newton Cluster Structure Survey (REXCESS). The top left shows the ne varia-
tion with radius and the top right shows T as a function of radius. There is an
anti-correlation between ne and T . On the bottom left plot the scaled pressure
as a function of radius is shown (the SZ effect is the integrated pressure). The
thick black line gives the average scaled profile and the grey area shows the 1σ
dispersion. The bottom right plot shows the unscaled pressure profiles with error
bars. Because of the anti-correlation between ne and T the pressure profile is
quite consistent between all the observed clusters. Plots are taken from Arnaud
et al. (2010).
17
1.2 The Arcminute Microkelvin Imager
1.2 The Arcminute Microkelvin Imager
Sited at the Mullard Radio Astronomy Observatory, Cambridge, AMI consists of
a pair of aperture synthesis interferometric arrays optimised for SZ-effect imaging
over 14-18GHz.
The Small Array (SA) has been operating since 2005, with a resolution to
match the typical size of a galaxy cluster (∼ 3′) and is used to observe the SZ
effect. The Large Array (LA) has been operating since 2008 with a high resolution
(∼ 30′′) and a sensitivity aimed at detecting radio sources that can contaminate
our SZ observations.
The specifications of the arrays are summarised in Table 1.3, and AMI Con-
sortium: Zwart et al. (2008) thoroughly describes the telescope. A schematic of
the AMI LA hardware, which is almost identical for the two arrays, is shown in
Figure 1.10. The geometric configurations of the arrays is shown in Figure 1.11.
Table 1.3: AMI technical summary. In practice on six of the eight frequency
channels are used. This is due to severe interference in the two lowest frequency
channels.
SA LA
Antenna diameter 3.7m 12.8m
Number of antennas 10 8
Number of baselines 45 28
Baseline length 5–20m 18–110m
16-GHz power primary beam FWHM 19.6′ 5.6′
Synthesized beam FWHM ≈ 3′ ≈ 30′′
Flux-density sensitivity 30mJy s−1/2 3mJy s−1/2
Observing frequency 13.9–18.2GHz
Bandwidth 6.0GHz
Number of channels 8
Channel bandwidth 0.72GHz
Polarization measured I + Q
18
1.2 The Arcminute Microkelvin Imager
Figure 1.10: The Large Array RF-IF system. Thanks to Tak Kaneko, Brian
Wood and Jonathan Zwart.
19
1.2 The Arcminute Microkelvin Imager
Figure 1.11: Top: The configuration of the SA antennas. Bottom: The configu-
ration of the LA antennas.
20
1.2 The Arcminute Microkelvin Imager
1.2.1 Radio Interferometry with AMI
Imagine two aerials (Ae1 and Ae2), separated by a distance D and pointing
towards an astronomical point source in the far field (Figure 1.12). Each aerial
receives electromagnetic waves from the point source, and brings the wave front
to a focus at which
Figure 1.12: Two antennas separated by a distance D pointing towards a source
in the far field; their separation in the x (east-west) direction.
(
∇2 − 1
c2
δ2
δt2
)
E = 0, (1.32)
where ∇2 is the Laplace operator in space, c is the speed of light, t is time and
E is electric field and so the received wave can be described by
E(x, t) = E0e
i(kRF x−ωRF t), (1.33)
where RF denotes radio (incident) frequency, kRF =
2pi
λRF
is the wave number of
the incoming radiation, E0 is the amplitude and ωRF is the angular frequency.
The wave from Ae2 travels a distance Dsinθ further. The signals received by
Ae1 and Ae2 are given at time t by
E1(x1, t) = E1e
−i(ωRF t)ei(kRF x1), (1.34)
21
1.2 The Arcminute Microkelvin Imager
Figure 1.13: Two antennas separated by a distance Dλ both pointing towards a
source in the far field.
E2(x2, t) = E2e
−i(ωRF t)ei(kRF (x1+Dsinθ)). (1.35)
An interferometer measures the correlation between the two signals received by
the antennas using a correlator. The response, r(x,t), of the correlator is
r(x, t) =< E1(x1, t)E
∗
2(x2, t) > . (1.36)
This response is independent of the distance from the source to the antennas and
instead depends upon the separation of the antennas (D) and the position of the
source in the sky (θ), i.e. as
r(D, θ) = E1E
∗
2e
−i(kRFDsinθ). (1.37)
By defining s0 as a vector that connects the baseline to the source and Dλ as the
separation of the antennas in λ (Figure 1.13), we can derive
r(Dλ, s0) = E1E
∗
2e
−i(2pi(Dλ·s0)). (1.38)
This can be generalised for sources offset from s0 by σ to
r(Dλ, s0) = E1E
∗
2e
−i(2pi(Dλ)·(s0+σ))). (1.39)
E1 and E
∗
2 are the amplitudes of the electromagnetic waves and are dependent
upon both the brightness of the source, B(σ), and the antenna response attenua-
tion, which is also known as the power primary beam, AP (σ). To obtain the total
22
1.2 The Arcminute Microkelvin Imager
instantaneous response of the interferometer to a single frequency we integrate
Equation 1.39 over the whole sky, giving
r(Dλ, s) =
∫
4pi
B(σ)AP (σ)e
−i(2pi(Dλ)·(s0+σ)))dσ. (1.40)
Equation 1.40 describes the basic response of a single frequency interferometer.
But AMI has a 6GHz passband and its response is integrated over frequency. If
we assume that AMI has a perfectly rectangular passband centred on νRF with
a bandwidth ∆ν, then the response of AMI is
r(Dλ, s) =
∫
4pi
∫ νRF+∆ν/2
νRF−∆ν/2
B(σ)AP (σ)e
−i(2pi(Dλ)·(s0+σ)))dνdσ. (1.41)
Defining the geometric delay τg as τg =
D·(s0+σ)
c
and recalling that λRF =
c
νRF
,
the AMI response simplifies to
r(Dλ, s0) =
∫
4pi
∫ νRF+∆ν/2
νRF−∆ν/2
B(σ)AP (σ)e
−i(2piτgν)dνdσ. (1.42)
When integrated over frequency, this gives
r(Dλ, s0) =
∫
4pi
B(σ)AP (σ)
2piτg
e−i(2piνRF τg)(e−i(2pi
∆ν
2
τg) − ei(2pi∆ν2 τg))dσ. (1.43)
Using eiθ = cosθ + isinθ gives
r(Dλ, s0) =
∫
4pi
B(σ)AP (σ)
sinpi∆ντg
pi∆ντg
e−i(2piνRF τg)dσ. (1.44)
The sinc function in Equation 1.44 has the characteristic that when pi∆ντg is
large the response is small. However, it is desirable that ∆ν is large so that
the telescope’s sensitivity is maximised. To solve this apparent contradiction and
ensure that the response does not become too small when τg is non zero, we insert
an artificial delay, the path compensation, τi, into the path of the antenna with
the shorter path. This delay is inserted into the telescope at an intermediate
frequency νIF , which is related to the radio frequency by νRF = νLO+ νIF , where
νLO = 24GHz is the frequency of the local oscillator (Figure 1.10). Note that νRF
and νIF have a bandwidth whereas νLO is a single value and that νIF is negative
(implying that the wave travels in the opposite direction). The delay is inserted
23
1.2 The Arcminute Microkelvin Imager
at an intermediate frequency because the electronics are cheaper and work better
at lower frequencies. Also, if the path compensation were to be inserted into
the RF then the astronomical fringe rate would be removed, this would make it
harder to apply fringe rate filtering to reject interference from e.g. geostationary
satellites. It is appropriate to insert this extra delay into Equation 1.42, hence
the response of the telescope is
r(Dλ, s0) =
∫
4pi
∫ νRF+∆ν/2
νRF−∆ν/2
B(σ)AP (σ)e
−i2pi(τgν−τiνIF )dνdσ, (1.45)
which is equal to
r(Dλ, s0) =
∫
4pi
∫ νRF+∆ν/2
νRF−∆ν/2
B(σ)AP (σ)e
−i2piν(τg−τi)e−i2pi(τiνLO)dνdσ (1.46)
and integrates to
r(Dλ, s0) =
∫
4pi
B(σ)AP (σ)
sinpi∆ν(τg − τi)
pi∆ν(τg − τi) e
−i(2pi(νRF (τg−τi)+τiνLO)dσ. (1.47)
The AMI correlator does not measure all of this signal. It uses a “real” correlator,
implying that it only measures the real part of r(Dλ, s0); the imaginary parts are
measured later by a process that is described later in this section. Hence the
actual response from the AMI correlator is
r(Dλ, s0) =
∫
4pi
B(σ)AP (σ)
sinpi∆ν(τg − τi)
pi∆ν(τg − τi) cos(2pi(νRF (τg − τi) + τiνLO))dσ.
(1.48)
As the Earth rotates, θ changes, as does τg; to compensate for the changes in τg
we switch cables of different electronic lengths in and out of the system to alter
τi. By altering τi (our smallest path compensation is 25mm) we can try to keep
τg = τi for sources at the phase centre; this ensures that the telescope’s response
to these sources is maximum.
AMI has a non-zero beam size and it is also important to consider the response
to sources away from the pointing centre. If τg = τi at the pointing centre, then
for a source offset from the phase centre by τg − τi = ∆τg, the larger the value of
∆ν∆τg the lower the response, and to keep the response for these sources high
it is essential that ∆ν∆τg << 1. The maximum extra geometric delay from the
source at the edge of the field is
24
1.2 The Arcminute Microkelvin Imager
Figure 1.14: Two antennas separated by a distance Dλ pointing towards a source
in the far field. There is a another source an angle ∆θ from the pointing centre,
this is at the edge of the field of view and introduces an extra geometric time
delay ∆τg.
∆τg = (D/c)cosθsin∆θ < D∆θ/c, (1.49)
where we have used the approximation sin∆θ ≈ ∆θ. The field of view of the
antennas in radians is ∆θ ≈ λRF/d, where d is the antenna diameter. Hence, for
a source at the edge of the field ∆τg =
λRFD
cd
= D
νRF d
. Both arrays operate at
νRF ≈ 15GHz and we can calculate that for the LA (d = 13m and D = 110m)
∆τg << 7.2× 10−10s which corresponds to 216mm; we obtain a similar result for
the SA (d = 3.7m and D = 20m). It must be borne in mind that this calculation
has been performed for the longest baseline and it should be noted that for most
AMI SA and LA baselines this value will be significantly less. However, this does
indicate that for a source right at the edge of our field of view, τg 6= τi.
Recalling that we require ∆ν∆τg << 1, we find that
∆ν <<
νRF d
D
. (1.50)
This implies that for the LA, ∆ν << 1.8GHz, whilst for the SA, ∆ν << 2.8GHz.
Unless you have an bandwidth smaller than these limits the data will suffer from
chromatic aberration. In order to have a bandwidth greater than this, whilst
25
1.2 The Arcminute Microkelvin Imager
also making the most of our field of view, a lag correlator measuring the response
at different time delays, or lags, is used to correlate the signals on AMI. The
correlator on both the AMI SA and LA has 16 lags from -200mm to +175mm
with a nominal step of 25mm – this additional path will be referred to as τic.
A lag correlator can be used to calculate the frequency spectrum (S(ν)) from a
response recorded at lags (R(τic)) by
S(ν) =
∫ ∞
−∞
R(τic)e
−i2piντdτ. (1.51)
If we consider the simple case of a bright source in the phase centre of the telescope
with τg = 0 or τg − τi = 0, then τic varies as the signal is correlated with different
instrumental lags in the correlator. If the bright point source is the only significant
signal in the telescope’s field of view then we can disregard the integral over the
whole sky and substitute Equation 1.48 into Equation 1.51 to find
S(ν) =
∫ ∞
−∞
B(σ)AP (σ)
sinpi∆ντic
pi∆ντic
cos(2piτicνIF )e
−i2piντicdτic. (1.52)
This Fourier transform can be solved using the modulation theorem (see e.g.
Bracewell 2000). This states that if f(τ) has the Fourier transform F (ν), then
f(τ)cos(ωτ) has the Fourier transform 1
2
F (ν − ω
2pi
) + 1
2
F (ν + ω
2pi
). The function
that we have in Equation 1.52 is a cosine modulated by a sinc. Therefore, as the
Fourier transform of a sinc is a top-hat function, the resulting Fourier transform
of Equation 1.52 has a real component of two top-hat functions and the imaginary
component is zero. Hence, all the spectral information is contained within the
sinc and not the cosine. It is important that the sinc function is Nyquist-sampled,
so the minimum lag spacing is given by δτic =
1
2∆ν
. AMI has ∆ν = 6GHz and
a corresponding δτic = 25mm. In Figure 1.15 the AMI response is plotted along
with its Fourier transform.
26
1.2 The Arcminute Microkelvin Imager
Figure 1.15: The response of a lag correlator to a point source at the phase
centre (where τg = 0) is a cosine modulated by a sinc function. This response is
sampled by the 16 lags of the AMI correlator; lag 8 is the central lag and samples
at delay space 0, lags are separated by 25mm, and so the outer lags sample at
200mm. The top Figure shows the response across the lags, whilst the bottom
Figure illustrates the Fourier transform of this response in the frequency domain.
Figure taken from Holler et al. (2007b).
Numerical integration of Equation 1.52 is in practice challenging because AMI
has non-equally spaced lags and we have to deal with unknown lag errors. Note
that the Discreet Fourier Transform (DFT) allows for non equally spaced lags,
although, in the present version of our data reduction software, reduce, we
assume all lags are equally spaced and apply a Fast Fourier Transform (FFT)
which we find produces the same result as a DFT but is faster. For a DFT the
frequency response of channel S(νk) (for channels k=0, ..., N-1) is
S(νk) =
1
N
N−1∑
τic=0
R(τic)e
−
i2piνkτic
N , (1.53)
where
R(τic) =
1
T
∫ T
0
A(t)B(t + τic)dt. (1.54)
A(t) and B(t) are the signals received by the antennas at a time t, T is the
integration time and N is the number of lags. Defining τ0 as the time taken for
27
1.2 The Arcminute Microkelvin Imager
light to travel 25mm ( 1
12∗109
seconds). The DFT can be expanded to give
S(νk) =
1
16
(R(τ0) +R(τ1)e
−
i2piνkτ0
16 +R(τ2)e
−
i4piνkτ0
16 + ...
+R(τ14)e
−
i28piνkτ0
16 +R(τ15)e
−
i30piνkτ0
16 )
Because R(τic) is real, this DFT is symmetric according to S(νk) = S(νN−k)
∗.
From the 16 independent measurements of the cross-correlation function we there-
fore obtain 8 complex frequency channels.
When the signals A(t) and B(t) enter Ae1 and Ae2, we obtain A(t)B(t) by
multiplying the signal from Ae1 and Ae2 with the Walsh functions f(t) and g(t)
respectively. Walsh functions have the following properties: they are either +1
or -1; over some period they integrate to zero; the multiple of two different Walsh
functions is a new Walsh function and the square of a Walsh function is equal to
1. The output from the AMI add and square correlator is multiplied by fg and
integrated to give
∫
fg(fA+ gB)2dt =
∫
fg(fA)2 + 2(fg)2AB + fg(gB)2dt ∝ AB. (1.55)
In the AMI system we have + and - correlator boards for each baseline. Whilst
one of these correlators is measuring the (A+B)2 signal the other measures the
(A − B)2 signal. Having two independent measures of the signal increases the
sensitivity by
√
2. Walsh functions are also very useful as they allow us to reject
signals which occur within the phase-switch loop but on just a single antenna,
such as cross talk (see e.g. Kaneko 2005).
A final essential component of interferometry is the spatial frequency to which
the interferometric arrays are sensitive to. The coordinate transform between
(u, v, w) and the fixed position of the AMI antennas (X, Y, Z) is
28
1.2 The Arcminute Microkelvin Imager
Figure 1.16: The relationship between different coordinate systems of AMI, cour-
tesy of John Zwart.


u
v
w

 =


− cosH sinH sinL sinH cosL
− sin δ sinH − sin δ cosH sinL− cos δ cosL − sin δ cosH cosL+ cos δ sinL
cos δ sinH cos δ cosH sinL− sin δ cosL cos δ cosH cosL+ sin δ sinL




Xλ
Yλ
Zλ


(1.56)
where L is the latitude of the telescope, H is the hour angle of the source and
δ is the source declination. A visual representation the (u, v, w) and (X, Y, Z)
coordinate systems is shown in Figure 1.16.
When we observe an object we only sample specific angular spatial frequencies;
these are set by the u and v coordinates of our antennas which describe the
projected baseline vector perpendicular to the source. An example of the SA and
LA u, v coverage is shown in Figure 1.17.
29
1.2 The Arcminute Microkelvin Imager
Ants * - *    Stokes YY  IF# 1  Chan# 3 - 8
K
ilo
 W
av
ln
gt
h
Kilo Wavlngth
1.0 0.5 0.0 -0.5 -1.0
1.0
0.5
0.0
-0.5
-1.0
Ants * - *    Stokes I  IF# 1  Chan# 3 - 8
K
ilo
 W
av
ln
gt
h
Kilo Wavlngth6 4 2 0 -2 -4 -6
5
4
3
2
1
0
-1
-2
-3
-4
-5
Figure 1.17: On the left is the typical SA uv coverage whilst on the right is the
typical LA uv coverage. Both observations are at declination +34, the duration
of the SA observation is 40 hours and the LA observation consists of 17 hours of
data.
To form an image of the sky we first consider the frequency response of AMI.
Given that the time sample function is described by C(u, v) (the LA samples
every 1/2 second and the SA samples every second) then the frequency response
of a uv baseline is derived from Equation 1.52 to give:
S(u, v) =
∫
4pi
∫ ∞
−∞
B(σ)AP (σ)C(u, v)
sinpi∆ν∆τg
pi∆ν∆τg
cos(2pi(ν0∆τg+(τi+τic)νLO))e
−i2piντicdσdτic,
(1.57)
where ∆τg = τg − (τi + τic). This can be inverse Fourier transformed to find the
sky brightness:
B(σ)AP (σ) =
∫
4pi
∫ ∞
−∞
S(u, v)C(u, v)
sinpi∆ν∆τg
pi∆ν∆τg
cos(2pi(ν0∆τg+(τi+τic)νLO))e
i2piντicdσdτic.
(1.58)
Note that this sky brightness is known as the dirty image. To find the true image
we must remove the sampling function, C(u, v, ); this operation can be done with
deconvolution because 1.58 is the convolution of the true sky brightness with∫ ∞
−∞
C(u, v)ei2piντicdσdτic. (1.59)
30
1.3 Blind SZ Effect Surveys
This Fourier transform of the sampling function is known as the synthesized
beam.
1.3 Blind SZ Effect Surveys
1.3.1 AMI
AMI is conducting a blind cluster survey at 16GHz in 12 regions, each typically a
deg2. The AMI cluster survey focuses on depth, aiming to detect weak SZ effect
signals from clusters of galaxies with a mass above M200 = 3×1014M⊙h−170 , where
M200h
−1
70 corresponds to the cluster mass within a spherical volume such that
the mean interior density is 200 times the mean density of the Universe at the
cluster epoch, the radius of this volume is r200. The first blind cluster detected
in the AMI survey is presented in AMI Consortium: Shimwell et al. (2010) and
discussed further in Section 5.
The AMI SA is designed to have a typical uv coverage to maximise the arrays
sensitivity to arc minute angular scales, as this matches the angular size of typical
galaxy clusters. With this resolution the SA resolves out the majority of the larger
scale primordial CMB signal and atmospheric effects. The main contaminant of
the SZ-effect at the range of frequencies which AMI operates within is the signal
from radio point sources. To remove this contamination we make use of the higher
resolution and flux-density sensitivity of the AMI LA. The LA resolution is high
enough to resolve out almost all of the SZ signal but is of course just as suitable
for observing radio point sources whose signal is independent of the angular scale
sampled. By observing the same area with both arrays we use our knowledge
of radio sources from the LA observations to help model the contamination they
cause to our SA data. Once we have modelled the radio source contamination
we can statistically account for the CMB and thermal noise contributions to our
data and search for any SZ contribution.
1.3.2 South Pole Telescope
The South Pole Telescope (SPT) is a 10-metre telescope operating with a deg2
field of view at an altitude of 2800m in the South Pole (Carlstrom et al. 2009).
31
1.3 Blind SZ Effect Surveys
The array operates at 95GHz, 150GHz and 220GHz with beam full-widths at
half-maxima (FWHM) of 1.6′, 1.1′ and 1.0′ respectively. The SZ signal is a
decrement at 95GHz and 150GHz and close to the null at 220GHz.
The SPT blind SZ survey plans to cover an area of 2500 deg2 to a depth of
18µK-arcmin2 at 150 GHz. The first 4 galaxy clusters detected (3 previously
unknown) in the survey are detailed in Staniszewski et al. (2009) who report
results from a preliminary study of 40 deg2; these detections represented the
first clusters discovered by an SZ survey. In Vanderlinde et al. (2010) 178 deg2
were analysed and within this region 21 clusters were detected, 12 of which were
new discoveries. In the latest results, Williamson et al. (2011) have analysed the
entire 2500 deg2, 1500 deg2 of which have been surveyed to the final depth and the
remaining 1000 deg2 to a depth of 54µK-arcmin2 at 150 GHz. The high signal-
to-noise (> 7) SZ detections within this area consists of 26 clusters with masses
in the range 9.8 × 1014M⊙h−170 ≤ M200 ≤ 3.1 × 1015M⊙h−170 . In Williamson et al.
(2011) they emphasise that the upcoming publications will significantly expand
the SPT catalog and include lower signal-to-noise detections. By extrapolating
from their current yields they expect to detect ≈ 750 clusters with S/N > 4.5.
1.3.3 Atacama Cosmology Telescope
The Atacama Cosmology Telescope (ACT) is a 6-metre telescope operating with
a deg2 field of view at an altitude of 5200m in the Atacama Desert (Fowler 2004).
The telescope operates at 148GHz, 218GHz and 277GHz with beam FWHM of
1.37′, 1.01′ and 0.91′. The SZ signal will be a decrement at 148GHz, at its null
at 218GHz and an increment at 277GHz.
In Hincks et al. (2010), the first SZ maps of 8 previously known clusters
that have been detected in the ACT survey were presented. In Marriage et al.
(2010) 23 clusters were blindly detected in the 148GHz, 455 deg2 2008 survey
data, 10 of these were new discoveries. The ACT cluster sample is 80% complete
at M500 > 6.0 × 1014M⊙h−170 , where M500 is the mass of the cluster within a
radius corresponding to an average density of 500 times the critical density of
the Universe at the cluster redshift. The ACT SZ survey is not finished – there
32
1.3 Blind SZ Effect Surveys
is data from other observing seasons and a new survey area has been chosen, for
future publications all three frequency bands will be used.
1.3.4 Planck
The Planck satellite (Planck Collaboration et al. 2011a) is in the unique position
of being sensitive to the SZ effect and having full sky coverage. The satellite will
produce the first all-sky cluster survey since the ROSAT all-sky survey which was
conducted at X-ray frequencies. The capabilities of Planck are demonstrated by
the 189 clusters which have been detected with high signal-to-noise ratios (> 6σ)
in data obtained from only 10 months of observations (Planck Collaboration
et al. 2011b). Included in this 189 clusters are 20 previously unknown cluster
candidates, many of which have now been confirmed (Planck Collaboration et al.
2011e and AMI Consortium et al. 2011). Planck was launched in May 2009 and
will continue collecting data until at least the end of 2011. Once complete the
Planck SZ catalogue will contain substantially more than the 189 clusters already
detected.
The Planck High Frequency Instrument (HFI) that is used to search for galaxy
clusters has a beam size of 4-10 arcmin depending on frequency (Planck HFI Core
Team et al. 2011). This is sufficient resolution to find typical clusters of galaxies
anywhere from nearby to redshifts of 0.3-0.7, these limits are highly dependent on
the cluster mass and size. At larger redshifts beam dilution becomes significant
and cluster detection is hindered. However, recently Planck discovered a massive
cluster at redshift 1.0 (Planck Collaboration et al. 2011d).
1.3.5 Sunyaev-Zel’dovich Array
The Sunyaev-Zel’dovich Array (SZA) is a radio interferometer situated in Owens
Valley Radio Observatory. It consists of eight 3.5m antennas and operates from
27-35GHz. Six of the antennas are in a close-packed configuration with spacings
from 4.5-11.5m, the other two antennas provide longer baselines of up to 65m.
The close-packed array is sensitive to arcminute scales and the longer baselines
provide higher-resolution data that is suitable for point source detection. The
33
1.3 Blind SZ Effect Surveys
detected sources are subtracted from the short baseline data to remove the point
source contamination from SZ observations.
The SZA has completed a blind SZ survey covering an area of 6.1 square de-
grees. Simulations have shown that the survey is 50% complete at 6×1014M⊙h−170 .
The final results from the survey are described in Muchovej et al. (2011): within
the survey area no SZ decrements were detected.
1.3.6 The Latest Results from Blind SZ Surveys
As described in the previous sections the AMI, SPT, ACT and Planck have all
blindly discovered galaxy clusters. Most of the clusters that have been discovered
in these surveys are shown in Figure 1.18 which is taken from Planck Collabora-
tion et al. (2011b).
Figure 1.18 highlights the very different selection functions of the SZ surveys.
To understand these selection functions is challenging, not only because of the
telescope properties (i.e. the beam size) and contamination but also because the
detection of clusters is sensitive to the temperature and electron number, both
of these are highly dependent upon the clusters dynamical state. However, to
extract cosmology from a SZ survey it is essential that the selection function is
thoroughly understood. Otherwise, accurate knowledge of the number of clusters
as a function of mass and redshift cannot be obtained.
34
1.4 Thesis Outline
Figure 1.18: The mass versus redshift for a selection of galaxy clusters. Included
on this plot are: the Planck all-sky early SZ cluster sample Planck Collaboration
et al. (2011b); the SPT blindly detected clusters in Menanteau (2010); the ACT
blindly detected clusters in Vanderlinde et al. (2010) and a selection of SZ effects
observed prior to 2010. Each SZ experiment has a different selection function,
the SPT is able to detect higher redshift and less massive clusters than Planck.
A prediction of the AMI selection function is shown in Figure 4.2.
1.4 Thesis Outline
• Chapter 2 describes my contribution to the commissioning and calibration
of AMI. I also outline the current AMI data reduction pipeline.
• Chapter 3 provides details of the software that I have developed to ma-
nipulate AMI data and perform tasks such as source subtraction and data
concatenation.
• Chapter 4 presents the Bayesian analysis that is used to analyse our AMI
observations and describes simulations that I have performed to characterise
this analysis.
35
1.4 Thesis Outline
• Chapter 5, an analysis of the AMI SA and LA survey data. Including the
identification of several previously unknown SZ decrements.
• Chapter 6 describes AMI observations of eight clusters from the Local Clus-
ter Substructure Survey (LoCuSS).
• Chapter 7 summarises the results from preceding Chapters.
36
Chapter 2
Calibration
On my arrival in Cambridge much of the software required for the AMI data
reduction was complete and the commissioning of the arrays was moving towards
the final stages. However, several tools still needed to be developed in order
to improve the telescope’s performance and to streamline the data reduction
pipeline.
In this chapter I discuss several of the main calibration and reduction tasks
that I have undertaken, including: correlator lag calibration; time average smooth-
ing corrections; identifying and flagging interference and measuring the primary
beam. After this discussion I present the current standard AMI data reduction
pipeline.
2.1 Correlator Lag Calibration
An AMI correlator board is shown in Figure 2.1; the theory behind this correlation
was discussed in Section 1.2.1.
IF signals from two antennas enter the correlator board and are propagated
along thin microstrip lines. Each signal is split into two at four separate occasions
and are correlated at 16 different lags. The electrical path difference between the
signals from the two antennas is 175mm at lag 1 and -200mm at lag 16; the design
spacing between lags is 25mm. The design and testing of the AMI correlator is
described in detail in Kaneko (2005), Holler (2003) and Holler et al. (2007a).
37
2.1 Correlator Lag Calibration
Figure 2.1: An AMI correlator board, showing the signal inputs, microstrip and
the detectors.
The AMI correlator boards require careful calibration for two reasons. Firstly,
the gain of the detectors (Schotty barrier diodes) varies by a factor of up to 4.
Secondly, the separation in lag lengths is not exactly 25mm but are typically
between 24mm and 26mm.
The correlator lag spacings and the lag gains can be extracted from the data
of a pc drift observation. This type of observation is carried out by tracking a
point source with the path compensators fixed. As the source moves in the sky
the apparent path difference between the antennas changes and the signal from
the source drifts through the AMI correlator lags. The time the signal takes to
shift from one lag to the next depends upon the rate of change of the path length
of the source and also on the distance between lags on the correlator board. The
shape of the interference fringe is a cosine function modulated by a sinc curve,
as is described by Equation 1.48 and the amplitude of the signal is indicative of
the detector gains. If the correlator were perfect, the fringes would all have the
same amplitude and the lag spacings would be equal to 25mm (Figure 2.2(a)),
although as previously explained this is not the case (Figure 2.2(b)).
38
2.1 Correlator Lag Calibration
(a) Simulated pc drift lag data; the lag spacings and the
lag amplitudes are all equal. The passband is a top hat and
the shape of the lag response is clearly a cosine modulated
by a sinc curve.
(b) Real pc drift data, demonstrating the variation in lag
gains and spacings. The lag gains vary by a factor of 2 and
none of the lag lengths are exactly 25mm. The passband is
not a perfect top hat and as a consequence the lag data is
not perfectly sinc-like.
Figure 2.2: A comparison between the lag data from a simulated pc drift
observation and a real observation. Amplitude is plotted on the y-axis and delay
(mm) is plotted on the x-axis.
39
2.1 Correlator Lag Calibration
2.1.1 Calibrating a PC Drift Observation
The reduce routine cal pcdrift is used to analyse pc drift observations after
the data has been flagged for pointing errors, shadowing, path compensator errors
and slow fringes. This routine uses the rms of the pc drift data within a fringe
as a measure of the lag gain. For the lag spacings we align the lag fringes using the
correlation between the response of each lag and a reference lag. I have made the
lag calibration routine significantly more robust by implementing the following:
• Variations in atmospheric absorption affect the amplitude of the lag gains
(Figure 2.3(a)). The AMI data are not amplitude corrected for system
temperature variations until after they have been Fourier transformed to
frequency space. Hence observations with significant variation in the system
temperature must be flagged.
• Interference can cause spikes in a pc drift observation (Figure 2.3(b)). If
the lag gains are determined by the maximum amplitude of the sinc curve
then this can result in a spurious value. Instead, the rms value around the
sinc curve is used because it is less susceptible to interference.
• Visibilities that have been flagged, because of e.g. pointing errors, can
occur during the observation of the fringes (Figure 2.4(a)). If there are
incomplete fringes then neither the cross correlation nor the amplitude of
the fringe can be accurately determined. A check is now in place to ensure
that data within the fringe used are not flagged.
• If the projected baseline is close to the line of sight then the path difference
between the antennas varies slowly (Figure 2.4(b)). This slow fringe rate
would require a long observation to observe the fringe drift between all 16
lags. Often a pc drift observation is an hour long and we found that
unless the projected baseline is more than 30 degrees from the line of sight
it is not possible for all the fringes on all the lags to be observed. Baselines
with slow fringe rates are now flagged for pc drift analysis.
40
2.1 Correlator Lag Calibration
• A pc drift observation that is contaminated with a large amount of in-
terference must be identified. Often such observations are recognisable be-
cause an error occurs in the cross correlation and the distance between lags
is grossly overestimated.
41
2.1 Correlator Lag Calibration
(a) The bottom two traces show the rain gauge. Rain causes the
system temperature to vary dramatically during the observation.
The lag gains are affected.
(b) A spike in the data has produced a spike in the fitted sinc curve
which has provided a false maximum gain.
Figure 2.3: Pc drift calibration errors. Amplitude is plotted on the y-axis and
delay (mm) is plotted on the x-axis.
42
2.1 Correlator Lag Calibration
(a) Some of the fringes are partially flagged, leading to lag gain and
lag spacing errors.
(b) The projected baseline is close to the line of sight, this leads to
a low fringe rate and fringes are not observed in all lags .
Figure 2.4: Pc drift calibration errors. Amplitude is plotted on the y-axis and
delay (mm) is plotted on the x-axis.
43
2.2 Geometry of the Large Array
2.2 Geometry of the Large Array
The positions of the AMI antennas are specified by a right handed Cartesian
coordinate system (X, Y, Z). However, in radio interferometry it is common to
use the (u, v, w ) orthogonal coordinate system. The relationship between these
coordinate systems depends upon the latitude of the telescope (L), the hour angle
of the source being observed (H) and the source declination (δ) see Figure 1.16
and Equation 1.56. When observing a point source at the phase reference position
(the field centre) the geometric phase contribution is 2piω (see e.g Thompson et al.
(2001)). From Equation 1.56 we can calculate that
φ = 2piω = 2pi((Xλ cos δ) sinH + (Yλ cos δ sinL+ Zλ cos δ cosL) cosH
+ (−Yλ sin δ cosL+ Zλ sin δ sinL)). (2.1)
In the AMI reduce program the fringe rotation routine subtracts the
calculated phase (Equation 2.1) from the observed phase. For an observation
which has a point source at the pointing centre and no other bright sources within
the field of view, we expect that after fringe rotation the residual phase is
approximately zero. However, if there are errors in the positions of the antennas
then the phase is incorrectly calculated, the phase error is
∆φ = 2pi
15
24
((∆Xλ cos δ) sinH + (∆Yλ cos δ sinL+∆Zλ cos δ cosL) cosH
+ (−∆Yλ sin δ cosL+∆Zλ sin δ sinL)), (2.2)
where the ∆X , ∆Y and ∆Z are the geometry errors that must be added
to the currently applied values to obtain the true geometry. The 15
24
factor is
9
24
less than unity and arises because the path compensators have been applied
at the IF frequency (-9GHz) and the LO operates at 24GHz. By observing a
bright source with an interleaved calibrator that is offset in declination but at
a very similar hour angle, the geometry errors can be determined. This fitting
task is performed by the reduce routine fit geometry. Figure 2.5(a) shows
an example of a geometry error and Figure 2.5(b) shows the phase of the same
observation once the fitted geometry has been applied. It should be noted that
phase errors are not always associated with incorrect geometry and can occur due
to a combination of: path compensation artifacts; drifts in e.g. cable lengths and
even temperature fluctuations in the correlator room. In practice it took many
44
2.2 Geometry of the Large Array
observations to correct the geometry and we still perform monthly observations
to ensure that the geometry errors in both arrays are minimised.
45
2.2 Geometry of the Large Array
(a) The source J1332+4722 is offset by 17 degrees in declination
from the interleaved calibrator (3C286); the phases do not track
each other particularly well implying that the phase varies with dec-
lination, hence a geometry error.
(b) Once geometry corrections are applied the phases track each
other well, implying that the phase no longer varies with declination.
Figure 2.5: Manual X-Y-Z geometry corrections. Amplitude and phase are plot-
ted on the y-axis and time is plotted on the x-axis.
46
2.3 Smoothing Amplitude Corrections
2.3 Smoothing Amplitude Corrections
The AMI correlators integrate the signal for a finite period of time before the time
average of the integrated signal is passed to the readout board. The minimum
possible integration time is 1/8s but with this value the AMI data files will be
large. Instead, we sample at 0.5s for LA data and at 1s for SA data. By sampling
the signal at these lower rates the quantity of data will be significantly decreased
but we must account for the effects of the averaging.
Given that a complex signal with a fringe rate ω can be described by
V (t) = V0e
iωt, (2.3)
where V0 is the initial amplitude, ω is the angular frequency and t is time. When
this complex signal is integrated over the time period ∆T , the mean amplitude
of the signal is
V¯ =
1
∆T
∫ ∆T
2
−∆T
2
V (t)dt = V0sinc(ω∆T/2). (2.4)
As the integration time is increased the amplitude of the signal drops but because
ω is known (Equation 2.1) the drop in amplitude can be correctly calibrated out.
Note that the signal-to-noise decrease can not be corrected. I have added a
routine to reduce that automatically performs this correction which is less than
3% for all observations.
2.4 Flagging Interference
Although there are many procedures in place to flag interference in AMI data I
have helped implement an additional two procedures into the reduce package
to further improve the AMI data quality.
2.4.1 Interference Spikes
In the AMI lag data there is often significant interference. The routine flag interference
(see Hurley-Walker 2009) scans the lag data for interference. It focuses on find-
ing and flagging interference with a duration of at least several samples. How-
47
2.4 Flagging Interference
ever, individual spikes in the data and low level interference can be missed by
flag interference.
The new routine flag data allows the user to flag the data either with a hard
cut or a cut at a multiple of the rms of the data. This routine can be applied to
both lag data and frequency data. In the lag data the amplitude has not been
calibrated and due to different settings of AGC units the number of correlator
units varies dramatically for different baselines. Hence a hard cut should not be
used to flag lag data.
2.4.2 Geostationary Satellites
The emission from geostationary satellites contaminates the AMI observations,
especially at low declinations. When AMI is tracking an astronomical object the
observed phase of the object changes with time because the object moves with
respect to the observing baseline (this is corrected for by the fringe rotation
command). However, for a geostationary satellite the phase will remain constant
because the satellite is always above the same point on earth and therefore its
position with respect to the observing baseline is constant.
To distinguish between astronomical signals and geostationary satellites the
signal from the telescope can be Fourier transformed to frequency space, phase
corrected for the effects of path compensation on the phase, but not phase cor-
rected for the path of the astronomical source (Equation 2.1). If the data are then
smoothed over several samples, the amplitude of the signal from geostationary
satellites will be enhanced compared to the amplitude from astronomical sources.
An example of a satellite signal in the frequency domain is shown in Figure 2.6(a),
here the data has been smoothed by 20 seconds.
48
2.4 Flagging Interference
(a) Before flag amplitude is applied.
(b) After flag amplitude is applied.
Figure 2.6: Plot of the channel 3-8 amplitudes and phases (y-axis) versus time
(x-axis) of a faint object at declination ≈ +25◦. There is significant interference
towards the end of the observation. The data has been smoothed by 20 and phase
corrected for path compensators but not for the astronomical path of the object
being observed. Note that the amplitude scales for plots a) and b) are different.
49
2.5 Power Primary Beam Measurements
The satellite interference can be identified by its amplitude and non random
phase, as is very clear in Figure 2.6(a). However, this interference was not de-
tected in the lag space at greater than three times the rms of the data (using the
routine flag data) or by the routine flag interference. After applying the
above procedure, using a smoothing of 20 and an amplitude cut of three times
the rms, the interference from Figure 2.6(a) was flagged and the remaining data
are shown in Figure 2.6(b). Dave Titterington has adapted the reduce routine
flag amplitude so that it can adaptively smooth the data and implement the
procedure outlined.
2.5 Power Primary Beam Measurements
Each AMI antenna has a voltage primary beam pattern (AV (σ+φ)) that describes
its response as a function of angle (φ) from the pointing centre (σ). When the
signals from two dishes are correlated the combined beam pattern (AV,1(σ +
φ)A∗V,2(σ + φ)) is known as the power primary beam (AP (σ + φ)).
To measure the beam I have used three types of observation: the raster offset,
the ha offset or declination dec offset, and the drift scan. raster offset
observations are useful to determine the 2D primary beam. Both ha offset
and dec offset observations determine a 1D slice through the primary beam.
drift scan observations are useful because they eliminate any pointing errors
that may contaminate the other observations.
Ideally each baseline on an array will have an identical AP (σ + φ) to all
other baselines on that array. Although this is not exactly the case due to slight
dish distortions and slight feed positioning errors, we have used the observations
mentioned above to determine an accurate mean power primary beam model
for both the SA and the LA. I have calculated the best fit Gaussian models
and derived the nth order polynomial parameters (these are used in the imaging
software aips)1 which describe the beam according to
PB(x) = 1.0 + x
PB3
103
+ x2
PB4
107
+ x3
PB5
1010
, (2.5)
1http://www.aips.nrao.edu
50
2.5 Power Primary Beam Measurements
where x is the distance from the pointing centre in arc minutes. To derive the
polynomial equations I have used Dave Green’s program pbparms.
2.5.1 Raster Offset Observations
For a raster offset observation we observe a bright point source at the phase
centre; the source is selected to have no significantly bright sources nearby. The
frequency response of AMI to such an observation is given in Equation 1.52, and
plotted in Figure 1.15. We then offset one of the antennae in the baseline by an
angle ∆φ(∆H,∆δ), where ∆H is the hour angle offset and ∆δ is the declination
offset. The offset antenna is moved around a grid of different ∆H and ∆δ. At each
position in the grid the baseline response is recorded. Hence we are measuring
AV,1(σ + ∆φ) × AV,2(σ), and because AV,2(σ) is not offset we know its value is
unity and by shifting one antennas pointing around a grid we map out AV,1(σ+φ).
An example of a SA raster offset observation is shown in Figure 2.7, for this
example the grid size is 25× 25 and the spacing between grid points is 3.25′.
51
2.5 Power Primary Beam Measurements
Figure 2.7: The variation of amplitude as a function of ∆H and ∆δ from the
data of a single baseline, lighter colours are higher amplitude. In this 6 hour
observation taken on the 30th January 2009 the grid size is 25×25 (625 pointings),
the separation between grid pointings is 3.25′ and the integration time at each
grid position is 15 seconds. The 6 hour observation contains two complete cycles
through the 625 pointings; here I have plotted cycle 1 for antenna 8 channel 4.
The lighter colour indicates higher amplitude and the amplitude ranges from 2600
to 80 correlator units. Contour levels start at 80; thereafter contours are spaced
by a factor of
√
(2).
To analyse a raster offset observation the reduce routine plot raster
is used after the data have been flagged for pointing errors, shadowing, path
compensator errors and slow fringes, Fourier transfered to the frequency domain,
fringe rotated to the position of the source, phase corrected for the path compen-
sation and amplitude corrected for system temperature variations (Section 2.6
describes these reduce procedures). plot raster outputs a file containing the
identity of the offset antenna, the grid spacing and the mean amplitude at each
position in the grid. plot raster was used to output a separate file for each of
the AMI channels. In a typical observation half the antennas will be offset, so
for the SA there will be 25 baselines each with “plus” and “minus” correlations
52
2.5 Power Primary Beam Measurements
with one offset antenna and one on source, and for LA observations there will be
16 such baselines.
For each grid in the output files the amplitudes are fitted with a two dimen-
sional Gaussian. The fitted Gaussian which is not centred on 0,0 is shifted and
centred on 0,0 using bilinear interpolation. We centre each Gaussian because
this corrects for pointing errors, assuming the pointing errors are equal for each
point on the grid. After this procedure is performed for each grid, the standard
deviation and mean are calculated at each grid position. The grid amplitudes are
then averaged together, discarding any data that contains significantly discrepant
amplitudes. Discarding such data helps to eliminate the effects of interference.
We assume that the AV,1(σ + φ) = AV,2(σ + φ) and square our resulting data to
obtain AP (σ + φ). The power primary beam was calculated for each of the six
AMI channels and for the “continuum”. The “continuum” is the average over
channels 3-8.
2.5.2 Hour Angle and Declination Offset Observations
ha offset and dec offset offset observations are similar to a raster offset
observation, but instead of the offset antenna moving in both hour angle and
declination it moves on only one axis. This is therefore simply a 1 dimensional
slice of a raster offset observation. An example of the frequency data from a
LA dec offset observation is shown in Figure 2.8.
The reduce routine offset scan is used to analyse the data after the data
has been reduced following the procedure outlined for raster offset obser-
vations. The offset scan routine identifies all baselines containing one offset
antenna and one on source, it proceeds to calculate the average amplitude and
its error for each offset. Pointing errors are included by calculating the average
pointing error for each offset; the position of the offset is then set as the average
pointing position rather than the desired pointing position. Figure 2.9 shows
typical LA pointing errors during a dec offset observation; the pointing errors
are largest for the first few data samples and are around 1′ throughout the rest
of the observation. Each offset cycle (Figure 2.8 contains 6 offset cycles) is fitted
with a Gaussian. The fitted Gaussian which is not centred on 0′ is normalised
53
2.5 Power Primary Beam Measurements
Figure 2.8: A LA dec offset primary beam measurement. One antenna is offset
by 11 steps of 1′. At each declination offset 120 data samples (60 seconds) are
obtained, the total observation length for this run is around 2 hours. Amplitude
and phase are plotted on the y-axis and time is plotted on the x-axis.
54
2.5 Power Primary Beam Measurements
Figure 2.9: Declination pointing errors on LA antenna 1 during a dec offset
observation. The x axis indicates time and the y axis shows the pointing error
in degrees. At the beginning of the run antenna 1 is supposed to be offset by 5′
and 12 samples later by 4′ (moving by 1′ or 0.017 degrees). However, for the first
pointing there is a -0.01 degree pointing error and when supposedly pointing at
offset 2 there is a -0.01 degree pointing error in the opposite direction. Hence the
antenna is pointing half way between offsets 1 and 2 instead of moving between
the two offsets. Also it is apparent that at the start of the run the offset antenna
is pointing at the source and hence there is a large error in its pointing as the
antenna slews to the desired position (5′ offset).
to have an amplitude of 1.0 and then shifted to be centred on 0′ offset. After all
Gaussians within a data set are aligned those with significantly different widths
from the mean are discarded. This helps to eliminate the effects of interference.
The mean fitted Gaussian is squared to give AP (σ + φ) as a function of either
∆H or ∆δ. This procedure was followed for each channel and the continuum.
2.5.3 Drift Scan Observations
A drift scan observation can be used to determine the primary beam. In this
observing mode we keep the antennas stationary while keeping the path com-
pensators tracking a bright source. As the bright source passes through the
telescope’s field of view we are able to trace out the beam because we know the
rate of change of the position of the source. If both antennas are offset we mea-
55
2.5 Power Primary Beam Measurements
sure AP (σ + φ) directly and if one antenna is offset we measure AV,1(σ + φ) or
AV,2(σ + φ).
The frequency response of the drift scan observations are analysed by fitting
a Gaussian to the response of each baseline, rejecting outliers and taking an
average of the fit for each channel and the continuum.
2.5.4 Small Array Primary Beam
Using the SA I have conducted both raster offset and drift scan observa-
tions and in Hurley-Walker (2009) the SA primary beam was measured using
a ha offset observation in which a single antenna was offset. The drift scan
measurements were used only as a confirmation of the results from the raster offset
observations, to ensure that they were not contaminated with pointing errors.
The raster offset results that I obtained for SA power primary beam mea-
surements were calculated from two 4 hour observations made between 3rd De-
cember 2008 and 30th January 2009. The derived beams for channels 3-8 and the
continuum are plotted in Figure 2.10.
The fitted parameters for SA power primary beams are shown in Table 2.1,
and these values agree well with the values quoted in Hurley-Walker (2009) and
those that I derived from drift scan observations. In Figure 2.11 I plot the σ
of the best fitted Gaussians (σδ and σH) as a function of frequency (ν) and find
that σ ∝ 1
ν
. The best fit values from Figure 2.11 are presented in Table 2.1.
56
2.5 Power Primary Beam Measurements
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch3.list’ matrix
(a) SA channel 3.
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch4.list’ matrix
(b) SA channel 4.
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch5.list’ matrix
(c) SA channel 5.
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch6.list’ matrix
(d) SA channel 6.
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch7.list’ matrix
(e) SA channel 7.
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch8.list’ matrix
(f) SA channel 8.
 0
 5
 10
 15
 20
 25 0
 5
 10
 15
 20
 25
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
’average_SA_beam_ch9.list’ matrix
(g) SA continuum.
Figure 2.10: SA power primary beam measurements. Amplitude is plotted on
the z-axis against pixel offset in RA and Dec on the x-axis and y-axis (the pixel
size is 3.25’).
57
2.5 Power Primary Beam Measurements
Table 2.1: The parameters for the SA power primary beam. These have been
determined from 25×25 raster offset observations with a spacing of 3.25′. The
σfit value is derived from Figure 2.11. The polynomial parameters are derived
from σfit using Dave Green’s program pbparms.
Chan Freq σδ σH σfit PB3,fit PB4,fit PB5,fit
GHz ′ ′ ′ 10−02 10−03 10−05
3 13.87 9.39 9.22 9.18 -3.02 3.95 -2.11
4 14.62 8.57 8.53 8.80 -2.95 3.78 -1.98
5 15.37 8.44 8.47 8.46 -2.89 3.62 -1.85
6 16.12 8.32 8.28 8.15 -2.82 3.47 -1.74
7 16.87 8.01 7.94 7.88 -2.76 3.32 -1.63
8 17.62 7.53 7.52 7.62 -2.71 3.18 -1.53
Cont 15.75 8.31 -2.85 3.53 -1.79
 7
 7.5
 8
 8.5
 9
 9.5
 0.056  0.058  0.06  0.062  0.064  0.066  0.068  0.07  0.072  0.074
Si
gm
a 
(ar
cm
in)
1/freq(GHz)
SA power primary beam
RA
DEC
Figure 2.11: The SA power primary beam sigma vs the frequency. I have included
both the σδ and σH derived parameters to give an indication of the errors. The
line of best fit is σ = m
ν
+ c, where ν is in GHz, m was found to be 101 and c was
1.89.
58
2.5 Power Primary Beam Measurements
2.5.5 Large Array Primary Beam
The ha offset results that I obtained for LA power primary beam measurements
were calculated from the 2 hour ha offset observation on the 4th June 2009 and
the 1 hour dec offset observation also on the 4th June 2009. I found that the
three 2 hour raster offset observations made between 11th March 2009 and 3rd
April 2009 were significantly contaminated with pointing errors and therefore I did
not extract primary beam parameters from these observations. I used drift scan
measurements to check the results obtained from the ha offset and dec offset
offset observations.
The ha offset and dec offset observations I have used have a 1′ step size,
11 steps and an integration of 60 seconds at each step. Each step is revisited
several times (Figure 2.8). The primary beam from each offset cycle is plotted
in Figure 2.12 together with the best-fit Gaussian. The best-fit parameters are
presented in Table 2.2 and the best fit Gaussians (σδ and σH) as a function
of frequency (ν) are plotted in Figure 2.13. The noise on these measurements
was lower than that obtained in the drift scan observations and the agreement
between the derived parameters was good.
59
2.5 Power Primary Beam Measurements
 0
 20
 40
 60
 80
 100
 120
-6 -4 -2  0  2  4  6
Am
pl
itu
de
Offset (arc minutes)
LA Channel 3 Primary Beam
HA beam
HA beam fit
DEC beam
DEC beam fit
 0
 20
 40
 60
 80
 100
 120
-6 -4 -2  0  2  4  6
Am
pl
itu
de
Offset (arc minutes)
LA Channel 4 Primary Beam
HA beam
HA beam fit
DEC beam
DEC beam fit
Left: channel 3. Right: channel 4.
 0
 20
 40
 60
 80
 100
 120
-6 -4 -2  0  2  4  6
Am
pl
itu
de
Offset (arc minutes)
LA Channel 5 Primary Beam
HA beam
HA beam fit
DEC beam
DEC beam fit
 0
 10
 20
 30
 40
 50
 60
 70
 80
 90
 100
 110
-6 -4 -2  0  2  4  6
Am
pl
itu
de
Offset (arc minutes)
LA Channel 6 Primary Beam
HA beam
HA beam fit
DEC beam
DEC beam fit
Left: channel 5. Right: channel 6.
 0
 10
 20
 30
 40
 50
 60
 70
 80
 90
 100
-6 -4 -2  0  2  4  6
Am
pl
itu
de
Offset (arc minutes)
LA Channel 7 Primary Beam
HA beam
HA beam fit
DEC beam
DEC beam fit
 0
 20
 40
 60
 80
 100
 120
-6 -4 -2  0  2  4  6
Am
pl
itu
de
Offset (arc minutes)
LA Channel 8 Primary Beam
HA beam
HA beam fit
DEC beam
DEC beam fit
Left: channel 7. Right: channel 8.
Figure 2.12: LA power primary beam measurements.
60
2.6 Standard Reduction for AMI Observations
Table 2.2: The derived parameters for the LA power primary beam. These have
been determined from ha offset and dec offset observations with a spacing
of 1.0′. The σfit value is derived from Figure 2.13. The polynomial parameters
are derived from σfit using Dave Green’s program pbparms.
Chan Freq σδ σH σfit PB3,fit PB4,fit PB5,fit
GHz ′ ′ ′ 10−01 10−01 10−02
3 13.87 2.58 2.65 2.60 -3.79 6.23 -4.19
4 14.62 2.50 2.46 2.50 -3.66 5.83 -3.79
5 15.37 2.41 2.40 2.41 -3.55 5.47 -3.44
6 16.12 2.34 2.35 2.34 -3.44 5.13 -3.13
7 16.87 2.27 2.32 2.27 -3.33 4.82 -2.85
8 17.62 2.07 2.22 2.07 -3.23 4.53 -2.60
all 15.75 2.38 -3.48 5.25 -3.24
2.6 Standard Reduction for AMI Observations
The data from the LA and SA are reduced using the same pipeline.
The raw data from all 16 lags of the correlator are loaded into reduce. It is
then the responsibility of the user to manually check for dead or faulty antennas,
large system temperature fluctuations (referred to as “rain gauge” fluctuations)
and AGC errors. After the user has flagged out any obvious errors then if the
field contains no bright point sources the user runs the following procedures:
• Flag all– Visibilities (samples from a single channel of a baseline) affected
by pointing errors, correlator errors, path compensator errors, shadowing
or slow fringe rates are flagged.
• Flag interference – The data is scanned for interference spikes which
persist over several samples.
• Flag data – The data is scanned for 3×σlag features which are flagged,
where σlag is the rms of the data in each lag.
61
2.6 Standard Reduction for AMI Observations
 2.2
 2.25
 2.3
 2.35
 2.4
 2.45
 2.5
 2.55
 2.6
 2.65
 0.056  0.058  0.06  0.062  0.064  0.066  0.068  0.07  0.072  0.074
Si
gm
a 
(ar
cm
in)
1/freq(GHz)
LA sigma vs 1/freq
RA sigma
DEC sigma
y(x)
Figure 2.13: The LA power primary beam σδ and σH versus ν. The difference
between the derived σδ and σH gives an indication of the errors. The line of best
fit has been added as σ = m
ν
+ c, where ν is in GHz, m was found to be 24.905
and c was 0.79
• Update pcals– A primary calibrator is used to update the baseline gains
and nominal rain gauge values for each baseline.
• Update lcals – The lag amplitudes are corrected for known correlator
board detector gain variations.
• Subtract zeros – Subtract a residual zero level from the data.
• Subtract means – Subtract a mean level from the data.
• FFT – Fast Fourier transform the data to convert from the time domain to
the frequency domain. The 16 lags provide a phase and amplitude for eight
frequency channels each with a bandwidth of 0.75GHz.
• Frotate – Correct the phase of the data for the path compensation. The
primary calibrator gains (that were updated with the routine update pcals)
are also applied, these convert the amplitude from correlator units to Jy.
62
2.6 Standard Reduction for AMI Observations
• Flag amplitude – Perform an adaptive smoothing and flag features with
an amplitude > 3σsm20,chan from the mean, where σsm20,chan is the rms of
the channel data that have been averaged over 20 samples.
• Frotate – Fringe rotate the data to the phase centre by subtracting the
calculated astronomical phase at the field centre from the observed phase.
• Flag amplitude – Flag data where the amplitude is more than 3 σchan
from the mean amplitude, where σchan is the rms of the channel data on a
specific baseline and channel.
• Apply rain – Apply an amplitude correction to the data and their weights
to account for atmospheric absorption and increases in system temperature.
• Cal inter – Apply a phase correction and shift the phase of the data to
ensure that the phase of the interleaved calibrator is 0. The phase of the
field being observed is corrected by extrapolating between the interleaved
calibrator observations.
• Reweight – Weight each visibility according to σchan. Noisier baselines are
downweighted.
• Smooth 200 – Apply a time smoothing of 200 samples by taking the mean
of the real and the imaginary parts. This significantly reduces the size of the
output files without causing significant time average smearing and enables
deeper flagging.
• Flag bad – Compare the mean amplitude for the channel data on all base-
lines. Baselines that have channels with high or low means have those
channels flagged.
• Flag amplitude – Flag the smoothed 200 data at an amplitude of 3σsm200,chan
from the mean, where 3σsm200,chan is the rms of the smoothed 200 data.
• Write fits/multifits – Write the observation out as a uvfits or a multi-
source uvfits file.
After applying the above pipeline typically 25% of the data is flagged.
63
2.7 Conclusions
2.7 Conclusions
I have contributed to the overall pipeline used to reduce the AMI data, in par-
ticular I have achieved the following:
• Added functionality to the lag calibration routine – this has created a sig-
nificantly more robust algorithm.
• Improved the accuracy with which the geometry of the AMI antennas is
known.
• Corrected the amplitude of AMI observations to compensate for the finite
integration time of the correlator readout boards.
• Implemented several routines to remove interference from the AMI data; in
particular reducing the interference from geostationary satellites.
• Primary beams of the SA and the LA are now well characterised.
64
Chapter 3
Post-Reduction Data
Manipulation Tools
The AMI data are output from reduce in uvfits format after they have been
Fourier transformed to the frequency domain, flagged for interference and phase
and amplitude calibrated. I have developed several useful tools that can be used
to manipulate these uvfits files. In this chapter I focus on the routines that have
been developed to concatenate the data, separate multi-source uvfits files, sub-
tract sources from our maps, simulate sources on maps and to perform jackknife
tests on our data. I also include details of additional secondary functionalities of
the programs that I have developed.
3.1 Concatenating AMI data
Often there are many separate AMI observations of a specific object or area; each
of these observations is run through reduce using the standard data reduction
pipeline (see Section 2.6) to produce a uvfits or multi-source uvfits file and
it is useful to have the ability to concatenate uvfits files. The tool that I have
developed for this purpose is the python program fuse.
65
3.1 Concatenating AMI data
Table 3.1: uvfits file data table; each multi-channel visibility from each baseline
has one entry in this table.
Row name Information
uu The u coordinate
vv The v coordinate
ww The w coordinate
date The Julian date of the observation
baseline The baseline identity
source The pointing identity (if multi-source
uvfits)
data The real, imaginary and weight for each fre-
quency channel
3.1.1 FUSE
All uvfits files output by reduce have the same format. Each file begins with
a header, this contains the basic information about the observation, such as its
frequency, name, date, position and the history of the reduce routines that have
been applied. The main body of the uvfits file is split into either 2 or 3 sections:
the data table, the AIPS AN table, and for multi-source uvfits files the AIPS
SU table.
The data table contains one row for each multi-channel visibility, the details
stored for each of these visibilities is shown in Table 3.1. The AIPS AN table
contains one entry for each antenna in the array and describes the antenna in-
formation such as its position and name. The AIPS SU table is only required in
multi-source uvfits files, this table is linked to the “source” row in the visibility
data table (see Table 3.1) and it specifies the “source” identity, right ascension
and declination. For more information on the structure of the AIPS AN and
AIPS SU tables the reader is referred to the programmers guide to the AIPS
system.
Given a list containing a combination of uvfits and multi-source uvfits files,
fuse is able to concatenate the data. This function is performed by copying the
data, AIPS AN and AIPS SU tables from the first file in the list and appending or
66
3.1 Concatenating AMI data
altering each table accordingly. First, fuse sorts the data into separate sources
(pointings), sources with a J2000 right ascension and declination within 10′′ are
assumed to be at the same position. We must use this tolerance because AMI
observations are observed at the targets current epoch position, i.e. J2011. Hence,
an observation of the same object but on different dates will have slightly different
J2000 coordinates. The data table from the first file in the list is then appended
with the data from all subsequent data tables. If the first file is a single-source
uvfits file then a “source” row is added to the table and all data are relabelled
according to which “source” it belongs to. The AIPS SU is appended to contain
enough rows to describe all the “source” positions. The AIPS AN table is the
same for each observation, so the table from the first file does not require any
alterations.
3.1.2 Secondary Functionalities of FUSE
The main purpose of fuse is to concatenate the uvfits data, but several other
functionalities have been added to the program. fuse can create aips scripts for
mapping, flag interference and perform a data reweight.
3.1.2.1 Mapping AMI Data in AIPS
The aips script output by fuse, images either raster or pointed observations
from the LA or the SA using the following pipeline:
• Fitld – Load the uvfits data.
• Imagr – Fourier transform the uvfits data to create an image for each
channel and pointing. clean the image to three times the thermal noise on
the map.
• Flatn – Combine the images from different positions and perform a primary
beam correction, neglecting any data outside the 0.1 power circle. The
optype command is used to create an appropriately weighted noise map
from the thermal noise levels on the individual pointings. If the uvfits file
contains only a single pointing then the task comb (rather than flatn) is
used to perform the primary beam correction.
67
3.1 Concatenating AMI data
• Lwpla and Fittp – Export the images in postscript and fits formats.
3.1.2.2 Flagging Interference
During the data concatenation process fuse runs through all visibilities and
ensures that they are linked to the correct “source” in the AIPS SU table. At
the same time fuse calculates the amplitude of each visibility and provides the
user with the opportunity to flag any visibilities with an excessive amplitude.
Such flagging is useful because in reduce only a single observation is flagged
and calibrated at one time. Hence, if there is a problem with the array and this
causes consistently high amplitudes for the entirety of a single observation, the
flagging routines contained within reduce will not identify this bad data. For
this reason it is important to combine data from different observations together
and scan for interference.
3.1.2.3 Reweighting the Data
When interference is flagged in either fuse or reduce it is not necessarily flagged
equally in all channels, resulting in an uneven distribution of weights between
channels and pointings. This implies that each observation and each pointing
has a slightly different frequency.
For the 10C survey (Davies et al. 2010 and ?) it was important that the
central frequency of each pointing was the same. Matthew Davies analysed the
10C data and found that the mean central frequency over the entire survey was
15.7GHz. In fuse an option was inserted to make the mean frequency for all
pointings equal to 15.7GHz. This applies the weights in Table 3.2 to reweight the
data according to
rchan =
wtotwdes
100 ∗ wchan , (3.1)
where rchan is the reweighting factor, which is multiplied by the weight of each
visibility, wtot is the total weight for all channels in the pointing, wdes is the
reweighting percentage in Table 3.2 and wchan is the total weight in a channel for
the pointing. Although this reweighting ensures that every pointing has a central
frequency of 15.7GHz it does cause a slight loss of sensitivity.
68
3.2 Separating Multi-source Data
Table 3.2: The percentage weights that can be applied in fuse to ensure that
the mean frequency is 15.7GHz.
Channel Weights (%) Frequency(GHz)
1 0.0 12.37
2 0.0 13.12
3 7.31 13.87
4 23.03 14.62
5 23.39 15.37
6 20.98 16.12
7 15.26 16.87
8 10.03 17.62
3.2 Separating Multi-source Data
uvsep is a tool that has been developed to separate multi-source uvfits files into
single-source uvfits files. This routine is useful to extract individual pointings
from an AMI multi-source uvfits file, allowing the user to thoroughly analyse
the data from a given pointing.
As each visibility in a multi-source uvfits file is linked to a specific pointing
(see Table 3.1), the individual pointings can easily be extracted. Once the desired
visibilities have been identified they can be copied to a new uvfits file. The
header of the input file is copied to the new file and updated with the correct
right ascension and declination from the AIPS SU table of the input file. The
AIPS AN table is also copied from the input file to the new file. The AIPS SU
table is not required for single-source uvfits files.
3.3 Source Subtraction and Data Simulation
Sources can significantly contaminate the SZ effect in AMI SA maps. The
python program muesli was created to subtract these contaminating sources
from AMI uvfits data. muesli is also able to simulate AMI data. mueslisim
was developed to test the completeness of the 10C survey (Davies et al. 2010 and
69
3.3 Source Subtraction and Data Simulation
Franzen et al. 2010).
3.3.1 MUESLI Source Subtraction
To subtract sources from a uvfits file we must determine the contribution of
each source to each visibility. For this calculation we need to know the phase
of the source (φ) and its amplitude as a function of frequency (S(ν)). With
this knowledge the real and imaginary components of the source signal can be
calculated as a function of the baseline u, v and w position. The phase of a source
offset from the pointing centre by ∆δ and ∆H is:
φ(u, v, w) = 2pi

uv
w

 .

sin(∆H)cos(∆δ)sin(∆δ)
cos(∆δ)cos(∆H)

 . (3.2)
In the reduce fringe rotation routine the phase associated with the w coordi-
nate is removed (see Equation 2.1), implying that the data output from reduce
is the same as those obtained from tracking a source with a baseline perpendicular
to the line of sight. Hence, the above equation is simplified to
φ(u, v) = 2pi(usin(∆H)cos(∆δ) + (vsin(∆δ))). (3.3)
The Re and Im components of a source with flux S(ν) are:
Re(u, v) = Spb(ν) ∗ cos(φ(u, v)) (3.4)
Im(u, v) = Spb(ν) ∗ sin(φ(u, v)), (3.5)
where Spb(ν) is the power primary beam attenuated source flux as a function of
frequency.
Given a uvfits file and a source list that contains the spectral index and
flux of a source, muesli calculates the contribution of each source to the Re and
Im components of each visibility. These calculated values are subtracted from
the Re and Im values in the input uvfits file. Assuming that the input source
70
3.3 Source Subtraction and Data Simulation
parameters accurately describe the source, the output uvfits file will have the
contributions of these sources removed.
muesli contains models for both the SA and LA primary beams (see Section
2.5) and can therefore subtract sources from uvfits data that has been obtained
from either array. muesli is able to subtract from both uvfits and multi-source
uvfits files. To increase efficiency when operating on multi-source uvfits files
muesli only subtracts sources from pointings within 20′ on the SA or 5′ on the
LA. At these distances the primary beam attenuation is large enough to ensure
that only very bright unsubtracted sources will influence the map.
3.3.1.1 MUESLI Simulation
The muesli simulation routinemueslisim reads in uvfits (or multi-source uvfits)
data and a source list. The user is given the option to overwrite the Re and
Im components of the visibilities and construct a data set that consists only of
Gaussian random noise, the level of which is specified by the user. The noise is
simulated according to
σchan =
√
σ2Re + σ
2
Im√
2nvis × nchan
, (3.6)
where σchan is the channel thermal noise, nchan is the number of channels and
nvis is the total number of visibilities. If the user chooses to set the noise at
σchan, mueslisim draws points from a Gaussian distribution centred on 0 with a
standard deviation equal to
σRe = σIm = σchan
√
nvis × nchan. (3.7)
These generated values overwrite the Re and Im components of the input vis-
ibility. mueslisim resets all visibility weighting, hence the noise on the output
continuum map (6 channels) is σchan/
√
6.
To add or subtract sources to the simulated Gaussian random noise data we
follow the procedure described in Section 3.3.1.
71
3.4 Jack-knife Tests
3.4 Jack-knife Tests
Systematic uncertainties can be a problem in astronomical observations; given
that the AMI correlator does not operate perfectly (see Section 2.1) such errors
must be searched for.
I have written the routine Jack-Knife, this performs several different tests
on the AMI single-source or multi-source uvfits data. These tests are:
1. Reverse the Re and Im measurements for all the plus correlator boards.
Each baseline has a plus and minus correlator board shifted 180 degrees in
phase from each other (see Section 1.2.1).
2. Reverse the Re and Im measurement for the first half of the data.
After Jack-Knife has operated on the uvfits data, the data can then be
mapped. The features seen on the maps reveal systematic errors in the observa-
tion. The first test checks to see if the lag length errors on the correlator boards
result in significant artifacts on the maps. The second check shows the effects of
source variability and also longer term instrumental drifts. It should be noted
that for the second Jack-Knife test the weights in the first half of the data
must be kept the same as the weights in the second half. Also, if the weighted uv
coverages in each half of the data are not equal then residuals will be expected
in regions close to bright sources.
When these two Jack-Knife tests are performed on simulated data the re-
sulting image consists of thermal noise. The thermal noise level on the Jack-
knifed image is as expected equal to the thermal noise of the data before the
Jack-knife test. An example of a Jack-Knife test on the simulated data is
shown in Figure 3.1.
72
3.4 Jack-knife Tests
Cont peak flux = -3.8720E-04 JY/BEAM 
Levs = 7.658E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Cont peak flux = -4.0588E-04 JY/BEAM 
Levs = 8.116E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Figure 3.1: jack-knife tests on the simulated data that is presented in Figure
4.3 on the right. Left: the results from plus correlator boards against minus
correlator boards (or odd versus even visibilities). Right: the image from the
first half of the data minus the second half.
When jack-knife tests are performed on real data they highlight the con-
taminated regions of the map, for example, regions around bright sources are
often associated with significant residuals on maps of the jack-knifed data. In
Figure 3.2 I present images of the jack-knifed data from a region of the AMI002
survey data (Figure 5.5). From these tests it is apparent that significant residuals
are associated with the bright point sources which have fluxes > 10mJy/beam.
These errors are larger when the data are split according to date. Both the
Jack-Knife tests indicate that neither the flux stability nor the phase stability
of AMI are good enough to accurately model the contribution of bright sources
to our data. However, for the dimmer sources in the field the Jack-Knife tests
indicate no significant errors associated with these regions. Also, when the Jack-
Knife test of plus versus minus baselines is performed the thermal noise level
on the resulting map is 40% lower than the thermal noise level on the original
map. However, when the data is split according to date the thermal noise level is
73
3.5 Conclusions
the same as on the original map. This effect was not seen in Jack-Knife tests
of simulated data, but can be explained if both the plus and minus baselines
are measuring a noise-like signal that is correlated, a possibility could be faint
satellite interference.
Cont peak flux = -9.2827E-04 JY/BEAM 
Levs = 1.130E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 30 00 01 30 00 00 30 00 02 59 30
26 10
05
00
25 55
50
45
40
35
30
25
Cont peak flux = -2.5337E-03 JY/BEAM 
Levs = 1.839E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 30 00 01 30 00 00 30 00 02 59 30
26 10
05
00
25 55
50
45
40
35
30
25
Figure 3.2: Jack-Knife tests on the real data presented in a portion of Figure
5.5. The portion was chosen to show the contamination that can be caused by
a bright source. Left: the data is split according to baseline. Right: the data is
split according the median date.
3.5 Conclusions
I have developed several routines to manipulate AMI data outside of the reduce
software package. The requirements and achievements of these routines are as
follows.
• A routine to concatenate AMI data was needed to simplify our mapping
procedure and data storage. The fuse routine reliably concatenates AMI
uvfits data from either array and produces a standard mapping script for
aips.
74
3.6 Further Work
• For detailed analysis of a small area it is often useful to extract single source
uvfits files from multi-source uvfits files. The script uvsep performs this
task.
• At 15GHz radio sources are a major contamination for SZ observations.
Given source positions, flux-densities and spectral indices the muesli soft-
ware reliably subtracts sources from either the SA or the LA data.
• To understand the completeness of the 10C survey it was necessary to sim-
ulate sources in real and simulated AMI survey data. mueslisim allows the
user to perform these simulations.
• Recognising contaminated data in all AMI observations is important and
especially important for the AMI blind cluster survey. The jack-knife
routine provides two tests for identifying contaminated data.
3.6 Further Work
• Presently muesli can only subtract point sources from data, it would
be useful to add the functionality so that muesli can subtract extended
sources. A simple elliptical Gaussian could be used to describe extended
sources.
75
Chapter 4
Preparing to analyse the AMI
blind survey fields
In this chapter I first describe the Bayesian inference package, McAdam, that
is used to analyse AMI observations. I include an introduction to the physical
cluster model and a description of a phenomenological model. I describe how
these two methods can be used to quantify the significance of cluster detection.
Even thoughMcAdam has been used to analyse many SA observations of known
clusters (e.g Zwart et al. 2010, AMI Consortium: Rodriguez-Gonzalvez et al.
2010, AMI Consortium: Rodriguez-Gonzalvez et al. 2011 and AMI Consortium:
Shimwell et al. 2011), only in the work of this thesis has it been applied to search
for blind clusters in the SA survey data. Using simulated cluster observations
I have investigated the performance of our analyses and the effects of several
fundamental priors then address the computational challenges of analysing the
entire AMI blind cluster survey.
Hereafter we assume a concordance ΛCDM cosmology, with Ωm = 0.3, ΩΛ =
0.7 and H0 = 70kms
−1Mpc−1. The dimensionless Hubble parameter hX is defined
as hX = H0/(X kms
−1Mpc−1) and σ8 = 0.8.
4.1 McAdam
The McAdam package has been developed by Hobson & Maisinger (2002), Mar-
shall et al. (2003) and Feroz et al. (2009a). I focus on using it to: search the AMI
76
4.1 McAdam
survey data for clusters; confirm AMI detections of known clusters; derive cluster
parameters; and model the properties of contaminating sources. The operation
of McAdam requires the user to input prior knowledge of the parameters that
are used to model both sources and clusters. For the analysis of the SA survey
data,McAdam is used to calculate the probability that a detected cluster is real
without prior knowledge of its existence.
Given a set of AMI data, McAdam can calculate the Bayesian evidence of
a model that consists of the parameters (Θ) which describe a galaxy cluster and
nearby radio sources. As by-products, the posterior probability distributions
for the entire set of parameters are also calculated. In the analysis McAdam
can take into account receiver noise, the background flux from undetected radio
sources (confusion noise) and the statistics of the primary CMB structures. Bayes’
theorem states that
Pr(Θ|D,H) = Pr(D|Θ,H)Pr(Θ|H)
Pr(D|H) , (4.1)
where Pr(Θ|D,H) is the posterior probability distribution of the parameters given
the dataD and the hypothesisH , Pr(D|Θ,H) ≡ L(Θ) is the likelihood, Pr(Θ|H) ≡
pi(Θ) is the prior probability distribution, and Pr(D|H) ≡ Z is the Bayesian
evidence.
To perform parameter estimation it is not necessary to calculate Z as the
value of this is independent of the parameters Θ. The probability distributions
for the parameters are found by sampling from the posterior Pr(Θ|D,H). To
determine individual parameter probability distributions,McAdam marginalises
the posterior over the desired parameter.
It is Z that is important for model selection. The higher the value of Z,
the better the data support the hypothesis. This implies that for observations
towards known clusters we can determine whether AMI has detected the cluster
by simply taking the evidence ratio between a run containing a cluster with the
position of the cluster (xc, yc) and the cluster redshift (if known) set as priors and
another run on the same data but without a cluster – this ‘null’ run is achieved
by placing a delta-function prior of value zero on the cluster gas fraction.
For the AMI blind cluster survey, we can also use the Bayesian evidence to
determine the probability of cluster detection. However, we are faced with the
77
4.1 McAdam
additional problem that our fields have been chosen to contain no known clusters
and therefore we do not have a priori evidence for a cluster at a particular position
(or redshift). In analysing a survey field, the marginalised posterior distribution in
the (xc, yc)-plane will typically contain a number of local peaks; some of these may
correspond to the presence of a real cluster, whereas others may result from chance
statistical fluctuations in the primordial CMB, instrument noise and/or source
artifacts. I stress that local peaks may also arise from systematics, but I note that,
given that the blind survey fields have been chosen to exclude very bright sources
and that we are wary of apparent peaks near bright sources (the AMI synthesized
beam is shown in Figure 5.2), we have not come up with significant ways that
AMI can ‘invent’ clusters, although of course a real cluster can be hidden by
radio emission which obscures its SZ effect. Each local peak in the posterior
is automatically identified by the MultiNest sampler (Feroz & Hobson 2008
and Feroz et al. 2009b) that is used in our Bayesian analysis. To determine the
significance of each such putative cluster detection, we perform a Bayesian model
selection, which makes use of the expected number of clusters per unit sky area:
µ =
∫ zmax
zmin
∫ MT,max
MT,lim
d2n
dMdz
dMdz, (4.2)
where zmax is the maximum cluster redshift, zmax is the minimum cluster redshift,
MT,lim is the limiting cluster mass that can be detected, MT,max is the maximum
mass of a cluster and n(z,M) is the comoving number density of clusters as
a function of redshift and mass. We use cluster number counts from analytical
theory (e.g. the Evrard et al. 2002 approximation to Press & Schechter 1974 which
is tied to cluster counts at redshift zero) or numerical modelling (e.g. Jenkins
et al. 2001) together with measurements of the rms mass fluctuation amplitude
on scales of size 8 h−1100Mpc at the current epoch, σ8 (see e.g. Lahav et al. 2002,
Seljak et al. 2005 and Vikhlinin & et al 2009). Although there are many more
recent attempts to estimate the cluster number counts (e.g. Sheth & Tormen
2002, White 2002, Reed et al. 2003, Heitmann et al. 2006, Warren et al. 2006,
Reed et al. 2007, Lukic´ et al. 2007, Tinker et al. 2008, Boylan-Kolchin et al. 2009,
Crocce et al. 2010 and Bhattacharya et al. 2011), the n(z,M) predicted by these
more recent estimates is similar to that which I have used. It must be borne in
78
4.1 McAdam
mind that the actual values of the number density of clusters, particularly at high
redshift, are uncertain and hence the degree of applicability of these as priors is
unclear.
We calculate the probability of two hypotheses: the first, Pr(H≥1|D), assumes
at least one cluster with MT,lim < MT < MT,max is associated with the local peak
in the posterior distribution under consideration; the second, Pr(H0|D), assumes
no such cluster is present. Throughout these calculations we define MT,lim, MT
and MT,max to be total masses within r200, which is defined as the radius inside
which the mean total density is 200 times the critical density ρcrit at the cluster
redshift. In particular, we consider the ratio R of these two probabilities
R ≡ Pr(H≥1|D)
Pr(H0|D) . (4.3)
To evaluate this ratio, let us first denote by S the area in the (xc, yc)-plane of
the ‘footprint’ of the local posterior peak under consideration (we will see below
that a precise value for S is not required). This footprint represents the angular
extent of the cluster. Also, we denote by Hn the hypothesis that there are n
clusters with MT,lim < MT < MT,max with centres lying in the footprint S, so
that
Pr(H≥1) =
∞∑
n=1
Pr(Hn). (4.4)
Thus equation (4.3) can be written as
R =
∑∞
n=1Pr(Hn|D)
Pr(H0|D) =
∑∞
n=1 Pr(D|Hn) Pr(Hn)
Pr(D|H0) Pr(H0) , (4.5)
where we have used Bayes’ theorem in the second equality. Assuming that objects
are randomly distributed over the sky, then
Pr(Hn) =
e−µSµnS
n!
, (4.6)
where µS is the expected number of clusters with MT,lim < MT < MT,max in the
footprint S and is given by µS = Sµ. A typical footprint is small (S < 60
′′×60′′)
and there is a very low probability of two or more clusters having their centres
79
4.1 McAdam
within this region (µS ≪ 1). Hence, we neglect µ2S and larger powers of µS, so
that equation (4.5) can be approximated simply by
R ≈ Z1(S)µS
Z0
, (4.7)
where the Z1(S) = Pr(D|H1) is the ‘local evidence’ (see Feroz et al. 2009)
associated with the posterior peak under consideration in the single-cluster model,
and Z0 = Pr(D|H0) is the ‘null’ evidence (which does not depend on S).
Our Bayesian analysis uses MultiNest to calculate the Bayesian evidence
for the different hypotheses. When searching for clusters in some survey area A,
a uniform prior pi(xc, yc) = 1/A is assumed on the position of any cluster, rather
than assuming a uniform prior over the footprint S. Thus, MultiNest returns
a local evidence associated with the posterior peak that is given by
Z˜1(S) =
S
A
Z1(S), (4.8)
and the ‘null’ evidence Z˜0 = Z0 remains unchanged. Thus, if we denote the
expected number of clusters in the survey area by µA = (A/S)µS, then Equation
4.7 becomes
R ≈ Z˜1(S)µA
Z˜0
(4.9)
Here Z˜1(S) and Z˜0 are outputs of MultiNest and µA is easily calculated from
Equation 4.2 (using a Fortran algorithm written by Carmen Rodriguez-Gonzalvez)
given some assumed cluster mass function, and so R may then be calculated with-
out exact knowledge of S. Moreover, the R value in Equation 4.9 can be turned
into a probability p that the putative detection is indeed due to a cluster with
mass MT,lim < MT < MT,max and centre lying in S, which is given by
p =
R
1 +R
. (4.10)
We run McAdam with two models: the first, a physical model, fits a pa-
rameterisation based on physical variables such as cluster mass and temperature;
the second, a phenomenological model, fits a parameterisation based on observ-
able quantities such as angular size and temperature decrement. For both cluster
models we use the same source model, which is discussed in Section 5.8.
80
4.1 McAdam
4.1.1 Physical Cluster Model
The SA observations of our survey data are analysed using a model characterised
by the sampling parameters Θ = (Θc,Ψ), where Θc = (xc, yc, φ, f, β, rc, fg,MT,200, z)
are physical cluster parameters and Ψ = (xs, ys, S0, α) are source parameters.
Here xc and yc give the cluster position, φ is the orientation angle measured from
N through E, f is the ratio of the lengths of the semi-minor (a) to semi-major (b)
axes of the best fitting ellipse, β describes the shape of the cluster gas density ρg
according to Cavaliere & Fusco-Femiano (1976) and Cavaliere & Fusco-Femiano
(1978), where the gas density decreases with radius r
ρg(r) =
ρg(0)
[1 + (r/rc)2]
3β
2
, (4.11)
rc is the core radius, fg is the baryonic mass fraction, MT,200 is the cluster total
mass within a radius r200 and z is the cluster redshift.
From the sampling parameters we are able to derive other cluster parameters
such as the cluster gas mass (Mg,200), radius (r200) and the cluster electron tem-
perature (T ). It should be noted that the physical β model that I have described
is not the only cluster profile that McAdam can fit; for example, we are also
able use the Navarro et al. (1995) (NFW) profile and Generalised NFW (GNFW)
models (see e.g. AMI Consortium: Olamaie et al. 2010).
4.1.1.1 Priors
It is essential that we understand the effects of our priors in the calculation of
Bayesian evidence values (Equation 4.9 and 4.10). Several of the priors, namely
those on β, rc, φ and f have been used extensively on simulations and observations
of known clusters (see Feroz et al. 2009a, Zwart et al. 2010, AMI Consortium:
Rodriguez-Gonzalvez et al. 2010 and AMI Consortium: Olamaie et al. 2010). For
the fg prior we have chosen to use a delta function on 0.154h
−1
70 ; this value is
derived from the results of Komatsu et al. (2010), who found that the universal
baryonic mass fraction fb = 0.169 ± 0.029h−172 , taking into account our value for
h and that the baryonic fraction in galaxy clusters is ∼0.9 (see e.g. McCarthy
et al. 2007)of the universal baryonic mass fraction. For the analysis of known
81
4.1 McAdam
clusters we (e.g. AMI Consortium: Rodriguez-Gonzalvez et al. 2011 and AMI
Consortium: Shimwell et al. 2011) have used a Gaussian prior on fg but for blind
observations we have decided not to do this. This is because SZ data alone can
not constrain fg and there is a large degeneracy between MT,200 and fg. Such a
degeneracy will produce a difficulty in determining whether the cluster mass is
above a specified MT,lim and hence will complicate our R and p calculations. The
effects of xc, yc,MT,200 and z on R are less clear. To understand the effects of such
priors I simulated AMI SA data according to Grainge et al. (2002). The search
area prior must be uniform as we have not prior knowledge of cluster positions
and I test the effects of varying the search area in Section 4.2.6. The options for
MT,200 and z priors are limited because our analysis technique requires that we
use a prior on the cluster number counts as a function of redshift (Evrard et al.
(2002) or Jenkins et al. (2001)), but we are able to alter the mass range of the
prior – this is explored in Section 4.2.5. The standard priors for the physical
cluster model are presented in Table 4.1. The Evrard et al. (2002) and Jenkins
et al. (2001) joint MT,200 and z prior is plotted in Figure 4.1 for several cluster
masses.
Table 4.1: Priors used for the Bayesian analysis assuming a physical cluster model.
Parameter Prior
Redshift (z) 0.2-2.0
(Jenkins et al. 2001 or Evrard et al. 2002)
Core radius (rc/h
−1
70 kpc) Uniform between 10 and 1000
Beta (β) Uniform between 0.3 and 2.5
Mass (MT,200/h
−1
70M⊙) MT,lim – 5 ×1015
(Jenkins et al. 2001 or Evrard et al. 2002)
Gas fraction (fg/h
−1
70 ) Set to 0.154
Cluster Position (xc) Uniform search box
Orientation angle (φ/ deg) Uniform between 0 and 180
Ratio of the length of Uniform between 0.5 and 1.0
semi-minor to semi-major axes (f)
82
4.1 McAdam
 1
 10
 100
 1000
 10000
 100000
 1e+06
 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
Lo
g 
N
z
Jenkins M=2.0e14
Press-Shechter M=2.0e14
Jenkins M=5.0e14
Press-Shechter M=5.0e14
Jenkins M=7.0e14
Press-Shechter M=7.0e14
Figure 4.1: The (log) number of clusters (N) as a function of cluster redshift
(z) predicted by Evrard et al. (2002) and Jenkins et al. (2001). I have included
clusters of mass MT,200 = 2.0× 1014, 5.0× 1014 and 7.0× 1014.
4.1.2 Phenomenological Model
In this case, at the location of each putative cluster detection identified using the
physical cluster model, we simply fit a β profile to the SZ temperature decrement
using the parameters θc, β and ∆T0 to characterise shape and magnitude of the
decrement according to
∆TSZ = ∆T0
(
1 +
θ2
θ2c
)(1− 3β
2
)
. (4.12)
83
4.2 SZ Simulations
4.1.2.1 Priors
We use non informative priors – the priors are wide enough to comfortably fit the
probability distributions of the parameters derived from expected cluster observa-
tions. The derived temperature posterior distribution allows for the significance
of an SZ temperature decrement to be assessed whilst taking into account the
CMB anisotropies, radio sources and thermal noise.
The assumed priors on the phenomenological model parameters are sum-
marised in Table 4.2.
Table 4.2: Priors used for the Bayesian analysis of the observational properties
of the temperature decrement (equation 4.12).
Parameter Prior
Cluster Position (xc) Gaussian prior centred on candidate (σ = 60
′′)
∆T0 Uniform between −3000µK and −10µK
θc Uniform between 20
′′ and 500′′
β Uniform between 0.3 and 2.5
Orientation angle (φ/ deg) Uniform between 0 and 180
Ratio of the length of Uniform between 0.5 and 1.0
semi-minor to semi-major axes (f)
4.2 SZ Simulations
Simulations of SA observations were created in the Profile package (see Grainge
et al. (2002)). In this package a two-dimensional image of a β profile cluster was
created together with Gaussian random noise and primordial CMB (Lewis et al.
2000). The SA baselines and typical uv coverage were stated and the maps were
convolved with the synthesized beam before being Fourier transformed to create
simulated visibilities for the six SA channels. These realistic AMI simulations
have been used to: estimate the mass limit (MT,lim) of the AMI blind survey;
demonstrate the robustness of the probability of detection calculation (Equation
84
4.2 SZ Simulations
4.9 and 4.10); and determine whether we can retrieve the simulated cluster pa-
rameters in our analysis of the data. In addition, I have used the simulations to
understand the effects of changing MT,lim and the search area prior.
4.2.1 Simulation Properties
To perform simulations in Profile we input the cluster parameters z, T , β, rc
and the central electron number density ne0. The simulations are performed with
values xc, yc, φ, f, β, rc, fg and z that lie comfortably within our priors in Table
4.1. However, the lower end of the range of MT,200 values in the simulations
falls below the lower end of the range of the prior on this parameter – this is to
understand how McAdam interprets the signals from clusters whose true mass
lies below MT,lim.
To simulate clusters of different masses we note that if we assume that cluster
gas is ideal and virialized, and that clusters are singular isothermal spheres whose
kinetic energy is all in gas internal energy then the total cluster mass, MT,200, can
be calculated using
kBT =
GµMT,200
2r200
, (4.13)
where kB is the Boltzmann constant, G is the gravitational constant and µ is the
mass per particle. Assuming spherical symmetry we also have
MT,200 =
4pi
3
r3200200ρcrit(z). (4.14)
By combining Equations 4.13 and 4.14 and using ρcrit(z) =
3H(z)2
8piG
we find that
MT,200
1015h−1M⊙
=
(
kBT
8.2keV
)3/2(
H0
H(z)
)
. (4.15)
Here H is the Hubble parameter and H(z) is given by
H2(z) = H20 (ΩM (1 + z)
3 + ΩΛ), (4.16)
where ΩM is the matter density (ΩM =
ρm0
ρcrit(0)
= 8piG
3H2
0
ρm0, where ρm0 is the present
matter density) and ΩΛ is the energy density of the vacuum (ΩΛ =
Λc2
3H2
0
where Λ
is the cosmological constant). Here we have assumed that the universe has zero
85
4.2 SZ Simulations
curvature. Thus, Equation 4.15 implies thatMT,200 is dependent only on T, z,ΩM
and ΩΛ. The cluster gas mass (Mg,200) is given by
Mg,200 = 4pi
∫ r200
0
r2ρg(r)dr, (4.17)
where ρg(r) is described by the β profile (Equation 4.11).
I have simulated two types of cluster:
• Group A – ρcrit(0.2) = 3H(0.2)28piG .
• Group B – ρcrit(z) = 3H(z)28piG
For all the simulations I set fg,200 =
Mg,200
MT,200
= 0.154h−170 to match the McAdam
prior (Table 4.1) but the mass and redshift of the simulated cluster are varied.
For simulations in group A, ρcrit(z) is calculated at z = 0.2 for all simulations.
Hence, group A simulations take the same physical object (i.e. of particular fixed
temperature and radius) and move it to a different z. For group A simulations I
vary MT,200 by altering T and to obtain the desired fg,200 I tweak Mg,200 via its
dependence on rc. For the simulations in group B the ρcrit(z) value varies with z,
so to take a cluster of a specificMT,200 to a different z (keeping fg,200 = 0.154h
−1
70 ),
both T and rc must be altered. For group B simulations physical properties of
the cluster change with z. Hence, group A and group B simulations are effectively
non-evolving and evolving cluster models.
I have simulated clusters with masses in the range 1 − 10 × 1014M⊙h−170 and
redshifts in the range 0.2-2.0. The iteration in total mass between simulations is
0.2×1014M⊙h−170 and the redshift iteration is 0.1. Each simulation of a particular
MT,200 and z is simulated with 10 random realisations of the primary CMB.
Therefore, in total we have 8740 unique simulations in each group A and B. For
all simulations the CMB contribution is calculated using a power spectrum of
primary anisotropy that has been generated for l < 8000 using CAMB (Lewis
et al. 2000) with a ΛCDM cosmology (Ωm = 0.3, ΩΛ = 0.7, σ8 = 0.8 and h = 0.7)
assumed. Each simulation consisted of four observations each lasting a duration
of eight hours. A rms noise of 0.6Jy per baseline in one second was included to
provide to a total Gaussian random noise level with an rms of 110µJy/beam (no
uv taper) on each set of four concatenated observations – this is a good match
86
4.2 SZ Simulations
to the thermal noise level in our concatenated SA survey field observations. The
simulated data were smoothed by 200. The parameters used for both groups of
simulated clusters are summarised in Table 4.3.
Table 4.3: Parameters of simulated clusters.
Parameter
Cluster position (J2000) 03 00 08.66 +26 15 16.1
Mass (MT,200/h
−1
70M⊙) 1 ×1014 - 10 ×1014
Redshift (z) 0.2-2.0
Gas fraction (fg/h
−1
70 ) 0.154
Beta (β) 0.8
Core radius (rc/h
−1
70 kpc) 100 – 220 (A) 100 – 310 (B)
Temperature (T/keV) 1.49 - 6.90 (A) 1.49 - 13.35 (B)
Central electron number density (ne0/m
−3h−170 ) 0.01 ×10−6
Orientation angle (φ/ deg) 0
Ratio of the length of
semi-minor to semi-major axes (f) 1.0
4.2.2 The Mass Limit of the AMI Survey
The AMI blind cluster survey has a well defined MT,lim only if for a specific value
ofMT,200 the magnitude of the SZ decrement is independent of the cluster redshift.
Previously there have been several attempts to find the mass limit of the AMI
survey. In Culverhouse (2006), the AMI selection was explored and 25,000 clusters
were simulated with masses in the range 4×1012h−170M⊙ < MT,200 < 1×1015h−170M⊙
at redshifts 0 < z < 4 according to Evrard et al. (2002) and Jenkins et al. (2001).
The simulated clusters were inserted into simulated AMI observations with a
realistic thermal noise (100µJy/beam), CMB and point source contamination.
The signal to noise for each simulated cluster was calculated and a plot of the
limiting mass function verses redshift was presented – this is shown in Figure 4.2.
In Culverhouse (2006) the selection function has a significant redshift dependence
and shows that AMI is expected to be able to detect less massive clusters at
87
4.2 SZ Simulations
higher z; the selection function is steepest at z < 0.6. For z > 0.6 AMI is
expected to detect clusters with MT,200 ≥ 3.0 × 1014M⊙h−170 . In Culverhouse
(2006) the effects of varying the thermal noise level, cluster density profile and
cosmology on the selection function are explored. In Hurley-Walker (2009) the
mass limit of the survey was estimated using SA observations of the relaxed,
small, low-temperature cluster Abell 2259. Hurley-Walker (2009) derived MT,lim
by assuming S ∝M5/3, where S is the SZ flux from a cluster. Using an estimate
of the mass of Abell 2259 together with the noise on the Abell 2259 observations
and an estimate of the survey noise (σsur) Hurley-Walker (2009) derived that at
4σsur it should be possible to detect Abell 2259 like clusters with a mass higher
than MT,lim = 2.0× 1014M⊙h−1100 (MT,lim = 2.9× 1014M⊙h−170 ).
Figure 4.2: A simulated AMI blind survey selection function from Culverhouse
(2006) for a thermal noise of 100µJy/beam with realistic CMB and radio source
contamination. Here the lowest detectable (limiting) mass is plotted against
redshift. The limiting mass decreases with redshift due to the electron density
and temperature increasing with redshift and also because the angular size of the
clusters is better match to the AMI synthesized beam at higher redshift. The
results are presented for Mtot, Mvir, M200 and Mgas. Here h = h70.
I have calculated MT,lim by evaluating how the flux of the SZ decrement
88
4.2 SZ Simulations
varies as a function of simulated MT,200 and z. Each simulation (in both groups
A and B) was mapped using Aips (example maps are presented in Figure 4.3)
and the resulting map was searched for decrements within 60′′ of the simulated
cluster position and of a peak flux greater than three times the thermal noise
of the simulation (σsim). Figure 4.4 shows the magnitude of these decrements
as a function of the simulated MT,200 and z for both groups A and B. Figure
4.5 shows the variation of decrement with z and CMB realisation for the most
massive cluster simulated (MT,200 = 1.0× 1015M⊙h−170 ).
Cont peak flux =  6.1861E-04 JY/BEAM 
Levs = 8.682E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Cont peak flux = -1.9974E-03 JY/BEAM 
Levs = 7.047E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Figure 4.3: Simulated group B cluster maps. The cluster on the left is simulated
with MT,200 = 1 ×1014M⊙h−170 and the simulation on the right is of a cluster
withMT,200 = 1 ×1015M⊙h−170 . Both simulations are at redshift 1.0. Each map uses
a different CMB realisation and there are no simulated point sources. Therefore,
all features on these maps arise from a cluster signal, CMB and thermal noise.
The boxes represent the positions of the modes detected by McAdam, note that
theMT,200 = 1 ×1014M⊙h−170 is not a significant detection. These maps have not
been primary beam corrected.
89
4.2 SZ Simulations
 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2 1e+14
 2e+14
 3e+14
 4e+14
 5e+14
 6e+14
 7e+14
 8e+14
 9e+14
 1e+15
 0
 0.5
 1
 1.5
 2
 2.5
Peak decrement (mJy)
Redshift
Simulated Mass (Msun)
 0
 0.5
 1
 1.5
 2
 2.5
 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2 1e+14
 2e+14
 3e+14
 4e+14
 5e+14
 6e+14
 7e+14
 8e+14
 9e+14
 1e+15
 0
 0.5
 1
 1.5
 2
 2.5
 3
 3.5
 4
Peak decrement (mJy)
Redshift
Simulated Mass (Msun)
 0
 0.5
 1
 1.5
 2
 2.5
 3
 3.5
 4
Figure 4.4: The magnitude of the peak decrement of the simulated SZ effect
against the simulated cluster mass and redshift. On the left ρcrit(z) is fixed at
redshift 0.2 for all simulations (group A) whereas on the right ρcrit(z) is redshift
dependent (group B).
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2
 2.2
 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
P
e
a
k 
d
e
cr
e
m
e
n
t 
(m
Jy
)
Redshift
 1
 1.5
 2
 2.5
 3
 3.5
 4
 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
P
e
a
k 
d
e
cr
e
m
e
n
t 
(m
Jy
)
Redshift
Figure 4.5: A slice taken through the above plots at a simulated cluster mass of
MT,200 = 1.0 × 1015M⊙. Group A results are on the left and group B results are
on the right. The 10 different peak decrements at each z correspond to the 10
random CMB realisations.
90
4.2 SZ Simulations
All group A simulations of a specific mass have an equal central y-parameter
(Equation 1.26); however, due to synthesized beam dilution we find that the
recorded peak decrement of a group A cluster of specific mass (Figures 4.4 and 4.5)
is redshift dependent – the steepest dependence occurs at z < 0.6. The magnitude
of the effects of beam dilution is related to both the cluster y-parameter profile
and the angular diameter distance to the cluster (Figure 1.8). For example,
consider a group A simulated cluster of mass MT,200 = 1.0×1015M⊙h−170 at either
z = 0.2 or z = 1.0. For the cluster simulated at z = 0.2 the y-parameter drops
significantly slower with angular distance from the cluster centre than for the
same cluster simulated at z = 1.0 (see Figure 4.6). Hence, even though group A
clusters of the same mass all have equal central y-parameters, the y-parameter
within the AMI synthesized beam (3′) is substantially different, and we expect
the peak decrement on the map to vary with z. However, the peak decrement
would not vary with z for an instrument with infinite resolution.
Figure 4.6: The y-parameter for a MT,200 = 1 × 1015M⊙h−170 mass cluster (group
A) as a function of angular distance from the cluster centre. On the left the
redshift of the cluster is 0.2 and on the right it is 1.0.
For roup B simulations the central y-parameter for a specific mass cluster
91
4.2 SZ Simulations
is dependent on redshift because the temperature as well as the core radius is
redshift dependent (see Equation 4.15). For example, a simulated cluster of mass
MT,200 = 1×1015M⊙h−170 at z = 0.2 has T = 6.90keV, whereas a cluster at z = 2.0
has T = 13.35keV. Hence, a cluster of MT,200 = 1 × 1015M⊙h−170 at z = 2.0 has
a significantly larger y-parameter than a cluster of the same mass at z = 0.2.
The curvature of the peak signal with redshift (Figures 4.4 and 4.5) is due to a
combination of the y-parameter changing and beam dilution. Figure 4.7 shows
the y-parameter as a function of angular distance for a group B simulated cluster
of mass MT,200 = 1.0× 1015M⊙h−170 at z = 0.2 and z = 1.0.
Figure 4.7: The y-parameter for a MT,200 = 1 × 1015M⊙h−170 mass cluster (group
B) as a function of angular distance from the cluster centre. On the left the
redshift of the cluster is 0.2 and on the right it is 1.0. Note that the Figure on the
left is identical to the group A simulated cluster of this mass and redshift (Figure
4.6), this is because group A simulations use ρcrit(0.2). However, the Figure on
the right is for a group B cluster simulated z = 1.0, this has a slightly smaller
angular extent and significantly higher central y-parameter than the equivalent
group A simulation, the reason for this is that both T and rc are different.
To determine the probability that a cluster of a certain MT,200 will produce
92
4.2 SZ Simulations
a signal greater than 3 times the thermal noise, I have chosen to calculate the
weighted (over z) proportion of clusters that are detected at each value of MT,200.
I use the Evrard et al. (2002) approximation to Press & Schechter (1974) or
Jenkins et al. (2001) cluster number counts to weight each simulation. Given
the model number count, C(MT,200, z) at a specific MT,200 and z, I weight each
simulation according to
W (MT,200, z) =
C(MT,200, z)∑2.0
z=0.2C(MT,200, z)
. (4.18)
The weighted probability of the decrement being >3σsim versus MT,200 is shown
for both simulation groups A and B in Figure 4.8.
 0
 0.2
 0.4
 0.6
 0.8
 1
 1e+14  2e+14  3e+14  4e+14  5e+14  6e+14  7e+14  8e+14  9e+14  1e+15
P
ro
b
a
b
ili
ty
 o
f 
d
e
te
ct
io
n
Simulated Mass (Msun)
Jenkins (Integrated)
Jenkins (Peak)
Press (Integrated)
Press (Peak)
 0
 0.2
 0.4
 0.6
 0.8
 1
 1e+14  2e+14  3e+14  4e+14  5e+14  6e+14  7e+14  8e+14  9e+14  1e+15
P
ro
b
a
b
ili
ty
 o
f 
d
e
te
ct
io
n
Simulated Mass (Msun)
Jenkins (Integrated)
Jenkins (Peak)
Press (Integrated)
Press (Peak)
Figure 4.8: The proportion of clusters detected at S > 3σsim as a function of mass.
The Evrard et al. (2002) approximation to Press & Schechter (1974) and the
Jenkins et al. (2001) cluster number counts were used for the weighted averaging
over the simulated z range. The results are shown for both peak and integrated
fluxes. On the left ρcrit(z) is fixed at redshift 0.2 for all simulations (group A)
whereas on the right ρcrit(z) is redshift dependent (group B). The value MT,lim =
2.9 × 1014M⊙h−170 is marked with a vertical line and corresponds to the MT,lim
value that was derived in Hurley-Walker (2009).
93
4.2 SZ Simulations
The simulations have revealed the magnitude with which the signal from a
cluster of specific mass (either group A or B) is redshift dependent. There are
also other effects that make deciding upon a value for MT,lim difficult, such as:
the true CMB contamination at a specific position rather than a statistical CMB
contribution; accounting for different cluster morphologies and density profiles;
point source contamination; the variation of fg with redshift and systematics in
the SA data. However, group A simulations have a much better defined MT,lim
than those from group B. Unfortunately, our prior on n(z,M) is obtained from
simulations that have used a redshift-dependent ρcrit. Hence, until n(z,M) is
derived for a redshift independent ρcrit our analysis is restricted to group B type
simulations only.
TheMT,lim = 2.9×1014M⊙h−170 value that was derived in Hurley-Walker (2009)
is similar to the results presented in Culverhouse (2006) for clusters at z > 0.6
and agrees well with my simulations. In Figure 4.8 I find that 80% of the group
B simulated clusters are detected above this mass.
4.2.3 Probability of Cluster Detection
The group B simulations described in the previous section were run through
McAdam using the priors shown in Table 4.1, MT,lim = 2.9 × 1014 h−170M⊙ and
a uniform search box centred on the pointing centre with sides of 1000′′. The
Bayesian evidences Z˜1 and Z˜0 were calculated and used together with the cluster
number counts (µA) to calculate the p and R values, which are related simply by
Equation 4.10, of all putative cluster detections.
In most simulations, McAdam detected multiple modes – in the 8740 simu-
lations a total of 27233 modes were detected, many of which do not correspond
to the simulated cluster (I deal with these later in this Section). In Figures 4.9
and 4.10 I plot the mean p and R values for each mode that corresponds to
a simulated cluster. These modes are identified as those with a mean position
within 2.5′ of the simulation cluster position. The lowest probability of detection
occurs for the MT,200 = 1 ×1014M⊙h−170 simulations and the largest for the MT,200
= 1 ×1015M⊙h−170 simulations; however, for a cluster of given mass there is a
significant redshift dependence in the p and R values.
94
4.2 SZ Simulations
 1e+14
 2e+14
 3e+14
 4e+14
 5e+14
 6e+14
 7e+14
 8e+14
 9e+14
 1e+15 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
Mean Probability
Mass
Redshift
 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
 1e+14
 2e+14
 3e+14
 4e+14
 5e+14
 6e+14
 7e+14
 8e+14
 9e+14
 1e+15 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2
 1e-20
 1
 1e+20
 1e+40
 1e+60
 1e+80
 1e+100
 1e+120
 1e+140
 1e+160
 1e+180
Mean R value
Mass
Redshift
Figure 4.9: The p and R values for clusters of different simulated masses. On the
left I present the p values and on the right are the corresponding R values. For
these calculations I have used the priors listed in Table 4.1, MT,lim = 2.9 × 1014
h−170 M⊙ and a uniform search box of size 1000
′′ × 1000′′.
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
 1.1
 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
P
ro
b
a
b
ili
ty
Redshift
Realisations
Mean
 1e-05
 1
 100000
 1e+10
 1e+15
 1e+20
 1e+25
 1e+30
 1e+35
 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
R
 v
a
lu
e
Redshift
Realizations
Mean
Figure 4.10: The p and R values of the MT,200 = 5 ×1014M⊙h−170 simulations,
taken from the above plots. I show the derived values for each of the 10 CMB
realisations at each redshift, I also plot the mean value with error bars that
correspond to the rms of the values obtained from the 10 CMB realisations.
95
4.2 SZ Simulations
The p and R value curves in Figure 4.9 indicate that in a manner reminis-
cent to the peak decrement probability of detection graph (Figure 4.4 right), the
McAdam derived probability of detection is not just function ofMT,200 but has a
significant z dependence. Figure 4.10 shows that for theMT,200 = 5 ×1014M⊙h−170
simulation the R value varies from as low 1 at z = 0.3 up to 1× 1030 at z = 2.0,
the corresponding p values are ≈ 0.4 to 1.0 respectively. The redshift that has a
dramatic effect on the derived R value. However, the CMB realisation also has a
significant impact, unfavourable CMB realisations may have an R value ∼ ×105
lower than favourable CMB realisations. All but 9 of the 190 simulations at
MT,200 = 5 ×1014M⊙h−170 are detected with probability of detection, p, of greater
than 0.8.
In Figure 4.11 I present the weighted mean for the p and R values as a function
of mass. Jenkins et al. 2001 and Evrard et al. 2002 number counts have been
used for the weighting. The weighting seems to have an insignificant effect on
our results.
96
4.2 SZ Simulations
 0
 0.2
 0.4
 0.6
 0.8
 1
 1e+14  2e+14  3e+14  4e+14  5e+14  6e+14  7e+14  8e+14  9e+14  1e+15
P
ro
b
a
b
ili
ty
Mass
Jenkins
Press
 1e-20
 1
 1e+20
 1e+40
 1e+60
 1e+80
 1e+100
 1e+120
 1e+140
 1e+160
 1e+180
 1e+14  2e+14  3e+14  4e+14  5e+14  6e+14  7e+14  8e+14  9e+14  1e+15
R
 v
a
lu
e
Mass
Jenkins
Press
Figure 4.11: The weighted mean p and R values as a function of mass. The
weighting used either the Jenkins et al. 2001 and Evrard et al. 2002 number
counts. The error bars on the p values are large because for a cluster of a particular
mass there is a significant redshift dependence on the derived p value (see Figure
4.9).
The weighted mean of the p value versus redshift bears a significant resem-
blance to the probability of detection curves calculated from the measured decre-
ments on the maps (Figure 4.8 right). The shape of the curve is the same, al-
though in theMcAdam derived probabilities the entire curve is shifted to higher
MT,200. Rather than 2.9 × 1014M⊙h−170 corresponding to ≈80% of clusters being
detected (above 3σsim), we find that this mass corresponds to a weighted mean
probability of detection of ≈30%. It is not until the clusters are simulated with a
mass > 4× 1014M⊙h−170 that we obtain a mean probability of detection of ≈80%.
This shift is expected because McAdam uses estimated cluster number counts
to account for the probability that the decrement is caused by a noise feature.
In Figure 4.12 I present a plot showing all the false detections as a function
of the simulated mass and redshift. These false detections are defined as being
those which are more than 2.5′ away from the simulated cluster position.
97
4.2 SZ Simulations
 1e+14
 2e+14
 3e+14
 4e+14
 5e+14
 6e+14
 7e+14
 8e+14
 9e+14
 1e+15 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2
 0
 0.05
 0.1
 0.15
 0.2
 0.25
 0.3
 0.35
Probability
Mass
Redshift
Figure 4.12: A plot showing the derived p values for false-positive detections that
McAdam has identified; these do not correspond to significant decrements in
the map plane. For these low p values the R value of a mode is almost equal
to its P value. For these calculations I have used the priors given in Table 4.1
and MT,lim = 2.9 × 1014 h−170M⊙. The highest probability of detection for an
false-positive identifications is 0.3.
The highest probability of a false detection is 0.3. On Figure 4.11 this value
would correspond to MT,200 = 3.0× 1014M⊙h−170 , but the error bars indicate that
we would also be likely to find many higher and lower mass clusters that produce a
feature from whichMcAdam derives this probability. For the vast majority of the
false detections we obtain probability of detection values at < 5%. For candidates
detected with 30 < p < 90% I would recommend that further independent AMI
observations be used to confirm the cluster candidates existence or non existence.
4.2.4 A Comparison Between Simulated and Derived Mass
For simulated clusters that are detected by McAdam, it is important to deter-
mine whether the simulated cluster parameters are recovered accurately and of
primary importance is the mass parameter. Clusters from simulation group B
98
4.2 SZ Simulations
have been run through McAdam twice: firstly, with a log uniform prior on the
mass (1−10×1014 h−170M⊙) and a delta prior on the redshift (B1), secondly, with
the Jenkins et al. (2001) number count as a joint prior on mass and redshift (B2).
For the other priors both runs use those given in Table 4.1 and a uniform search
box of 1000′′ × 1000′′.
In Figure 4.13 I present the mean derived McAdam mass (averaged over 10
CMB realisations) as a function of simulated mass and redshift for both runs
B1 and B2. Figure 4.14 shows the mean mass and the mass derived from each
realisation for the clusters simulated with MT,200 = 1.0× 1015 h−170M⊙.
99
4.2 SZ Simulations
 1e+14
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McAdam Mass (Msun)
Simulated Mass (Msun)
Redshift
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McAdam Mass (Msun)
Simulated Mass (Msun)
Redshift
 2e+14
 4e+14
 6e+14
 8e+14
 1e+15
 1.2e+15
 1.4e+15
 1.6e+15
 1.8e+15
Figure 4.13: The variation in the McAdam derived mass as a function of sim-
ulated cluster mass and redshift. The plot on the left shows the results when
McAdam is run with a log uniform prior on the mass and a delta prior on the
redshift (B1) and on the right McAdam has been run with the Jenkins et al.
(2001) number count as a joint prior on mass and redshift (B2). The lower limit
on the mass prior is 1 × 1014 h−170M⊙ for B1 runs; for B2 runs the lower limit is
2.9× 1014 h−170M⊙. Every McAdam derived mass value must be above the lower
limit and this introduces the curvature at low masses that we see in both plots.
 2e+14
 4e+14
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M
cA
d
a
m
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a
ss
 (M
su
n)
Redshift
Realisations
Mean
 4e+14
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M
cA
d
a
m
 M
a
ss
 (M
su
n)
Redshift
Realisations
Mean
Figure 4.14: A slice taken from the above plots along simulated mass MT,200 =
1.0 × 1015 h−170 M⊙, including the independent results from all the different CMB
realisations. Left – B1 runs. Right – B2 runs.
100
4.2 SZ Simulations
Figures 4.13 and 4.14 demonstrate that McAdam is able to derive the cor-
rect cluster mass when it is given the cluster redshift (B1). For blind clusters
McAdam is run with only prior knowledge of the cluster number counts as a
function of mass and redshift (Jenkins et al. (2001) prior, run B2) we are unable
to accurately recover the simulated mass of the cluster. Instead, the apparent
curve in the derived mass for a cluster of a specific mass has a significant redshift
dependence, this behaviour is similar to the peak decrement on the map as a
function of redshift (group B in Figures 4.4 and 4.5).
In Figure 4.15 I present the weighted mean derived McAdam mass as a
function of input simulated mass. Here I have used the Jenkins et al. (2001)
number counts for the weighting.
 0
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M
cA
d
a
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a
ss
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su
n)
Simulated Mass (Msun)
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M
cA
d
a
m
 M
a
ss
 (M
su
n)
Simulated Mass (Msun)
Figure 4.15: The McAdam derived mass as a function of simulated mass, av-
eraged over redshift and different CMB realisations. The plot on the left is for
runs B1 (log uniform prior on the mass and a delta prior on the redshift) and
on the right are the B2 results from runs with the Jenkins et al. (2001) joint
prior on mass and redshift. For both B1 and B2 McAdam always outputs a
mean mass higher than the lower limiting prior (1 ×1014M⊙h−170 for B1 and 2.8
×1014M⊙h−170 for B2). This explains the McAdam overestimates for the mass of
low-mass clusters.
101
4.2 SZ Simulations
It is very important that the results presented in Figure 4.15 are clarified.
When McAdam is run with B1 priors we obtain a good mass estimate, but
when run with the B2 priors the mass estimate is significantly discrepant from
the real cluster mass. Initially, this seemed like a problem with the analysis, but it
can be explained by the degeneracy between redshift and mass (see Figure 4.16).
The Jenkins et al. (2001) prior follows hierarchical structure formation and as
such predicts that there are fewer high mass clusters than low mass clusters and
that these high mass clusters lie at low redshift. However, for our simulations we
have sampled uniformly in both z and MT,200. As a consequence of our n(z,M)
priors it may be expected thatMcAdam typically underpredicts the cluster mass.
Additionally because of the degeneracy between mass and redshift we have a large
degree of uncertainty in the derived parameters (Figure 4.16 shows the parameters
derived from B2 runs of a cluster simulated with MT,200 = 1 ×1014M⊙h−170 and
from a cluster simulated with MT,200 = 1 ×1015M⊙h−170 – corresponding maps for
these simulations are shown in Figure 4.3).
Figure 4.15 should not be interpreted as evidence that analyses with a Jenkins
et al. (2001) prior overestimate the mass of the low mass clusters. This is not
the case as long as one looks at the corresponding detection probability. The
reason for this apparent overestimation is that the mass prior range begins at
MT,lim = 2.9 × 1014 h−170 M⊙, hence any object that McAdam detects must be
given a mass greater than this. This behaviour also occurs in B1 simulations,
but in that case the lower mass limit is MT,200 = 1 ×1014M⊙h−170 . It is clear from
the probability of detection calculation that McAdam does not conclude that
these low mass cluster exists. It is also apparent from the MT,200 probability
distribution of theMT,200 = 1 ×1014M⊙h−170 presented in Figure 4.16 which shows
that the probability distribution is pressed towards the lower limit of the prior.
102
4.2 SZ Simulations
4 6 8
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
4
6
8
x 1014
y0/arcsec
−500 0 500
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 5 10
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−20
−10
0
10
z
0.5
1
1.5
2
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−20 0 20
4
6
8
10
12
x 1014
y0/arcsec
−20−10 0 10
z
1 2
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
Figure 4.16: McAdam derived parameters from cluster simulations. On the left
are the derived parameters from a cluster simulated MT,200 = 1 ×1014M⊙h−170
(p = 0.0) and on the right is the parameters for a cluster simulated with MT,200
= 1 ×1015M⊙h−170 . The lower mass cluster is a non-detection (p = 0.0) whereas
the higher mass cluster is detected with p = 1.0. Both simulations are at redshift
1.0.
In conclusion to this subsection I emphasise that although the Jenkins et al.
(2001) prior can be used to calculate the probability of detection it does not
produce a mass estimate that is necessarily indicative of the real cluster mass.
However, if we obtain redshift information we are able to accurately recover the
true mass.
4.2.5 Testing the Influence of the Mass Limit on the Prob-
ability of Detection
The concept of a limiting cluster mass (MT,lim) is fundamental to the extraction
of probabilities from the Bayesian evidences. Without an MT,lim value neither
the numerator or the denominator in Equation 4.9 can be determined nor can
103
4.2 SZ Simulations
we estimate the expected number of clusters within a region. In this subsection
I demonstrate how the value of µS, the evidences and the probability of cluster
detection vary as a function MT,lim.
A group B cluster simulated with a mass ofMT = 5×1014h−170 M⊙ at a redshift
of 1.0 was run throughMcAdam with 1×1014 h−170M⊙ < MT,lim < 9×1014 h−170M⊙.
In total the data were passed through McAdam 40 times – each time MT,lim is
increased by 0.2 × 1014 h−170 M⊙. The rest of the priors given to these runs are
those listed in Table 4.1.
In Figure 4.17 I show the variation of the p and R values with MT,lim. In
Figure 4.18 I present the Z˜1
Z˜0
and µ dependence on MT,lim, which are of interest
because R ≈ Z˜1(S)µA
Z˜0
and p = R
1+R
.
104
4.2 SZ Simulations
 0
 0.1
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 0.3
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P
 v
a
lu
e
Mass Limit (Msun)
 0.001
 0.01
 0.1
 1
 10
 100
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 10000
 100000
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R
 v
a
lu
e
Mass Limit (Msun)
Figure 4.17: The p (left) and R (right) values for a simulation with mass MT =
5 × 1014h−170 M⊙ at redshift 1.0 as the limiting mass is varied between MT,lim =
1− 9× 1014h−170M⊙
 0
 10000
 20000
 30000
 40000
 50000
 60000
 70000
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Z
1
0
/Z
0
0
Mass Limit (Msun)
 0.001
 0.01
 0.1
 1
 10
 1e+14  2e+14  3e+14  4e+14  5e+14  6e+14  7e+14  8e+14  9e+14
m
u
s
Mass Limit (Msun)
Figure 4.18: The Z˜1
Z˜0
(left) and µjenkins (right) values which are multiplied to give
the R value for a simulation of a cluster with mass MT = 5 × 1014h−1M⊙ at
redshift 1.0 as the limiting mass is varied between MT,lim = 1− 9× 1014h−1M⊙
105
4.2 SZ Simulations
Figure 4.17 demonstrates that until MT,lim ≈ 7.5 × 1014h−1M⊙ we derive
a probability of detection of greater than 80% for a simulation with mass of
MT,200 = 5.0 × 1014h−1M⊙. Additionally the R values presented in Figure 4.17
indicate that as MT,lim changes from MT,lim = 1 − 4 × 1014h−1M⊙ the R value
decreases gently; however, for MT,lim > 4 × 1014h−1M⊙ the variation in R value
is much greater. This gradient change is associated with the turnover in the Z˜1
Z˜0
ratio (Figure 4.18). The curvature in Figure 4.18 occurs because Z˜0 is constant
(regardless of MT,lim), whereas when MT,lim is increased in the region MT,lim <
4× 1014h−1M⊙ the corresponding parameter space of the priors decreases, which
therefore results in a better model and hence Z˜1 increases. However, at a certain
MT,lim (≈ 4.0 × 1014h−1M⊙) the model will stop improving because the derived
mass probability distribution will be driven too much by the MT,lim prior and at
this point the model becomes worse as MT,lim increases and Z˜1 decreases. This
effect is shown in Figure 4.19 which shows that for MT,lim ' 4 × 1014h−1M⊙
the derived mass increases at the same rate as MT,lim, indicating that the prior
is driving the mass estimate. For lower values of MT,lim the derived mass does
not rise so rapidly indicating that the effect of raising MT,lim in this region is
excluding an area in the parameter space with a low likelihood.
For a simulation of a different mass (e.g. MT,lim = 6× 1014h−1M⊙) we would
expect a similar shape to the plots, although there would be a shift on the mass
axis. As MT,lim is increased but remains in the mass range below the simulated
cluster mass we expect that Z˜1 will increase but p and R will slowly decrease;
however, as soon as the prior starts to drive our results then Z˜1 will begin to
decrease and p and R will begin to decrease more rapidly.
Overall, the effect of MT,lim on the p and R values for this cluster is very
dramatic. But MT,lim is not a completely unknown quantity. If for example, the
limit MT,lim = 3 × 1014h−1M⊙ was used to analyse a survey that was sensitive
to MT,lim = 2 × 1014h−1M⊙, the derived R values would be a factor five lower
than if the correct MT,lim were used. The corresponding p value will remain
substantial until MT,lim is larger than the derived mass of the cluster. In previous
sections it was concluded that MT,lim cannot be exactly defined but a value of
MT,lim = 2.9×1014h−1M⊙ was thought to be suitable. Although the work of this
106
4.2 SZ Simulations
section highlights the importance of MT,lim there is no indication that MT,lim =
2.9× 1014h−1M⊙ is inappropriate.
 2e+14
 3e+14
 4e+14
 5e+14
 6e+14
 7e+14
 8e+14
 9e+14
 1e+15
 1e+14  2e+14  3e+14  4e+14  5e+14  6e+14  7e+14  8e+14  9e+14
M
cA
d
a
m
 m
a
ss
Mass Limit (Msun)
Figure 4.19: The variation in the mean derived MT,200 as a function of MT,lim.
4.2.6 Testing the Influence of the Cluster Search Area on
the Probability of Cluster Detection
The search area is another potentially important parameter in the calculation of
the R value (Equation 4.9), since both the evidence and the µS parameter are
dependent on the area.
For the group B simulation of a cluster with mass MT,200 = 5 × 1014h−1M⊙,
the R value has been calculated for McAdam runs with search boxes of various
sizes. The length of the box sides are changed from 5′′ to 500′′ in iterations of 5′′.
In Figure 4.20 I present the R values calculated from these runs. These results
demonstrate that the area is not particularly important as the evidence change
and the change in the value of µ cancel each other out. However, the R value
drops dramatically as the cluster comes to the edge of the search box and it is
therefore important that the search boxes of adjacent areas in the blind survey
overlap so that no cluster candidates are consistently at the edge of a search box.
107
4.3 Computational Challenges
 0
 1000
 2000
 3000
 4000
 5000
 6000
 7000
 0  5e-06  1e-05  1.5e-05  2e-05  2.5e-05
R
 v
a
lu
e
Search area (steradians)
Figure 4.20: The dependence of the R value of cluster detection for the cluster
simulated with mass MT,200 = 5× 1014h−1M⊙ with search area.
4.3 Computational Challenges
The reduced AMI blind visibilities have been analysed on both the COSMOS and
HPC supercomputers in Cambridge. The specifications of these two machines are
summarised in Table 4.4.
Table 4.4: Specification of the COSMOS and HPC supercomputers.
Component COSMOS HPC
CPU Intel NehalemEX 2.67GHz Intel Westmere 2.67 GHz
Cores 768 (6 per CPU) 1536 (6 per CPU)
RAM 2048GB (16GB per CPU) 4608GB (18GB per CPU)
To reduce the size and hence the computational requirements of the analyses
we bin the data from each pointing into three files, each containing all the data
from two frequency channels. Note that binning channels together reduces the
information content of the data because it decreases our spectral resolution, but
108
4.3 Computational Challenges
the effect of such binning is small and I have tested that when data are run with
two frequency channel binning the derived cluster parameter values, the proba-
bility of cluster detection and source parameters are very similar to those derived
from the same analysis but with individual channels rather than the two channel
bin. We then bin the visibilities from each of these files according to their position
on the uv-plane, with a bin size of 40λ – this typically leaves 1000 visibilities per
pointing for each two channel file. A value of 40λ is used because the dish diame-
ter is 180λ so a 40λ binning should not result in a significant smearing on the uv
plane. Our SA survey fields contain between 24 and 48 different pointing centres.
A single Bayesian analysis of the entire field is prohibitively computationally ex-
pensive because of the large volume of data and the high dimensionality of the
parameter space. Instead, three pointings are analysed at a time. Each set of
three pointing centres form a triangle, an example of which is shown in Figure
4.21.
Figure 4.21: Noise map for a SA triangle of observations out to the 0.1 contour of
the power primary beam. The inner triangle is between the pointing centres; the
outer triangle is the area that is searched for clusters with our Bayesian analysis.
109
4.4 Conclusions
4.4 Conclusions
I have performed a large number of realistic simulations of clusters with various
masses and redshifts. All simulations were analysed in the map plane and in
McAdam. From these simulations I found that:
• Simulating clusters with a ρcrit that does not vary with redshift have much
less variation of SZ signal with redshift than those simulated with ρcrit that
is redshift dependent.
• The AMI cluster survey should be able to detect clusters with MT,200 >
2.9× 1014h−1M⊙.
• The Bayesian probability of detection values derived from simulated ob-
servations do accurately represent the significance with which an object is
detected. The highest false positive detection that is obtained from 8740
McAdam analyses is p = 0.3.
• Our analysis will typically underestimate the mass of the cluster, because of
the redshift dependence in the observed SZ signal; the problem disappears
if the redshift is included.
• The derived p values are sensitive to the MT,lim data that we use to analyse
our data.
• The derived p value is insensitive to the search area but due to the computa-
tional challenge we are limited to analysing SA survey data three pointings
are a time.
• Important to overlap AMI search triangles because the results from candi-
dates at the edge of the search area are unreliable.
• The final priors that are to be used for the analysis of SA survey are sum-
marised in Table 4.1. We have chosen to set MT,lim = 2.9×1014h−1M⊙ and
the search area as an uniform triangle encompassing the pointing centres
between the three triangles.
110
4.5 Further Work
4.5 Further Work
The simulations that were created for these tests contained realistic CMB and
thermal noise contributions. However, it is known that AMI observations are sig-
nificantly contaminated with point sources. A good understanding of the number
of point sources as a function of area and flux density was gained from the 10C
survey (Davies et al. 2010). An analysis of simulations that contain contributions
from a realistic distribution of sources would be insightful.
111
Chapter 5
The AMI blind survey
In this chapter I describe the two AMI blind deg2 survey fields that I have anal-
ysed, AMI002 and AMI005, as well as the source finding procedure and the
McAdam priors. I note the existence of known clusters within the AMI fields
before identifying the candidates that have been discovered in my analysis. For
each cluster candidate I perform a follow-up investigation with pointed SA ob-
servations. The follow-up pointed SA observations have been carefully manually
flagged in addition to applying the automatic flagging routines described in Sec-
tion 2.6. For the survey data such manual flagging was not possible due to the
large quantity of data.
As a by-product of the McAdam analysis of these two AMI fields, I have
compared the SA and LA source fluxes and investigated the accuracy of the
SA-LA calibration.
5.1 Survey Observations
Each survey field has been observed by the LA and the SA. The key points are
summarised in Table 5.1.
112
5.1 Survey Observations
Table 5.1: Observations of the AMI survey fields.
Field SA AMI002 LA AMI002 SA AMI005 LA AMI005
Right ascension 02:59:30 09:39:20
Declination +26:16:30 +31:17:30
Start date 2008 Jul 19 2008 Aug 8 2008 Sep 1 2008 Aug 24
End date 2010 Mar 3 2011 Jan 20 2009 Sep 23 2011 Jan 1
Total observing 1100 710 760 490
time (hours)
Number of 255 65 106 58
observations
Noise level 100 50 (inner) 110 50 (inner)
(µJy/beam) 100 (outer) 100 (outer)
Number of pointings 24 600 24 600
Phase calibrator J0237+2848 +J1018+357 or +J0940+2603
A rastering technique was used for both the LA and the SA survey observa-
tions, where the pointing centres lie on a 2-D hexagonally-gridded lattice. The
LA observations form a part of the 10C survey data, which are described in de-
tail in Franzen et al. (2010). Additional dedicated pointings towards the cluster
candidates are included to ensure that maximum sensitivity was obtained in the
LA maps. For the 10C survey observations, the pointing centres are separated
by 4′ , which allows us to obtain close to uniform sensitivity over the field while
minimising the observing time lost to slewing. In order to detect all important
sources within the SA field, the LA field is slightly larger and the thermal noise is
typically a factor of two lower than the SA thermal noise. To account for the SA
map noise (σSA,SUR) increasing towards the edge of the field, the LA map consists
of two distinct regions, the inner and the outer. The inner area of the LA field
was observed to an noise level of ≈ 50µJy/beam, whereas the noise in the outer
area was approximately twice as high. The outer region of the LA map is also
used to detect bright sources lying just outside the SA field. An example LA noise
map is shown in Figure 5.1. For the SA survey observations the pointing centres
are separated by 13′ giving a close-to-uniform noise level of ≈ 100µJy/beam over
the map. The SA noise map is shown in Figure 5.1.
113
5.1 Survey Observations
The phase calibrator was observed for two minutes every hour with the SA
and for two minutes every ten minutes with the LA. The amplitude calibration for
the SA uses 3C286 and 3C48; the assumed flux densities are shown in Table 5.2
and are consistent with the Rudy et al. (1987) model of Mars. The LA was flux-
density-calibrated from the SA measurements of the LA interleaved calibrator;
we adopted this approach to minimise inter-array flux density calibration errors.
Typically our individual observations were 8 hours; this often comprised two
separate observations each of 4 hours, interleaved with an observation of a flux
density calibrator. Observations were started at different positions in the field to
improve the uv coverage.
Figure 5.1: On the left is the noise map for the LA AMI002 survey field. The
inner region noise is ≈ 50µJy/beam, while the noise on the outer region is ≈
100µJy/beam. The hexagonal region around 03:00:10 +26:15:00 is next to a
cluster candidate and was observed to ≈ 30µJy/beam. The inner region of the LA
noise map consists of three subregions; these have slightly different sensitivities
due to varying weather conditions and slight differences in observing time. On
the right is the noise map for the SA AMI002 field. The noise at the edge of the
map increases due to the primary beam of the SA. In the central region the map
noise is ≈ 100µJy/beam.
114
5.2 Source Finding
Table 5.2: Assumed flux densities for the SA flux density calibrators.
Channel ν¯/GHz SI+Q/Jy
3C286 3C48
1 14.2 3.663 1.850
2 15.0 3.535 1.749
3 15.7 3.414 1.658
4 16.4 3.308 1.575
5 17.1 3.206 1.500
6 17.9 3.111 1.431
Each observation is passed through reduce using the standard data reduction
pipeline which is detailed in Section 2.6. All imaging is done using aips by
applying the procedure summarised in Section 3.1.2.1.
5.2 Source Finding
Source finding is carried out on the LA continuum map using the AMI sourcefind
software. In this software all pixels on the map with a flux density greater than
0.6 × 4 × σLA,SUR, where σLA,SUR is the LA noise map value for that pixel, are
identified as peaks i.e. candidate sources. The flux densities and positions of
the peaks are determined using a tabulated Gaussian sinc degridding function to
interpolate between the pixels. Only peaks where the interpolated flux density is
greater than 4× σLA,SUR are identified as sources.
For each source we use sourcefind to find the flux densities in the individual
AMI-LA channel maps at the positions of the detected sources. Assuming a
power-law relationship between flux density and frequency (S ∝ ν−α), we use
the channel flux densities to determine the spectral index α for each source. The
spectral index is calculated using an MCMC method based on that of Hobson &
Baldwin (2004) – the prior on the spectral index has a Gaussian distribution with
a mean of 0.5 and σ of 2.0, truncated at ±5.0. The map noise in each channel
map in the vicinity of the sources was used to calculate the weighted mean of the
channel frequencies and determine the effective central frequency ν0 of the source
115
5.3 McAdam Priors
flux measurement. The effective central frequency varies between pointings due
to flagging applied in reduce. Unlike the work for the 10C survey, the data
are not reweighted to the same frequency because this leads to a small loss of
sensitivity.
The aips routine jmfit fits a two-dimensional Gaussian to each source iden-
tified by sourcefind and gives the angular size and the integrated flux density
for the source. These fitted values are compared to the point-source response
function of the observation to determine whether the source is extended on the
LA map. We find that ∼5% of sources are extended on our LA observations; this
is in agreement with the 10C survey. However, as the SA synthesized beam is
significantly larger we expect far fewer extended sources in the SA maps. It is
important that we recognise when a source is extended since currently we have
no mechanism for dealing with extended sources inMcAdam. If many SZ candi-
dates are discovered close to extended sources then we must add this functionality
to McAdam.
For each source we catalogue the right-ascension xs, declination ys, flux density
at the central frequency S0, spectral index and the central frequency. If a source
is extended on the LA maps we use the centroid of the fitted Gaussian for the
position and the integrated flux density instead of the peak flux density.
5.3 McAdam Priors
McAdam was run with both the physical cluster model and the phenomeno-
logical model, the priors for these models are given in Table 4.1 and Table
4.2 respectively. This analysis of the survey data has been performed with
MT,lim = 3 × 1014M⊙h−170 . I have used a triangular search area which is an
enlarged version of the triangle formed between the pointing centres – the radius
of the inscribed circle is 3′ larger to give overlap between adjacent search trian-
gles (see Figure 4.21). For a typical survey field the minimum rms noise within a
search triangle is ≈ 100µJy and the maximum is ≈ 140µJy.
Given the large number of sources detected by the LA in each of the AMI
survey fields the source priors in McAdam are very important. For each source
there are four possible priors: xs, ys, S0 and α. Modelling all four for all sources in
116
5.3 McAdam Priors
the McAdam analysis of each survey triangle would be far too computationally
expensive. Instead, we only model sources that have a LA measured flux density
which exceeds 4σSA,SUR. For the rest of the sources we use the LA values as
delta-function priors – this will not increase the parameter space but will inform
McAdam of their presence. Sources that are modelled in the survey data are
given Gaussian priors on spectral indices and flux densities but delta-function
priors on their positions. For the standard deviation of the Gaussian prior on
spectral index we use the LA estimated error, whereas on the flux density we use
40% of the measured LA flux density. A wide prior on flux density is used because
if the SA flux density is discrepant from the LA value and McAdam is pushed
towards the edge of its given prior, then the McAdam run time is significantly
increased. A wider prior on the source flux often prevents this from happening
so frequently. The SA-measured flux density may be different from that of the
LA because of source variability, calibration errors and thermal noise levels. For
sources that are not modelled, we use delta-function priors on source positions,
spectral indices and flux densities.
All of the cluster candidates have been followed up with SA pointed obser-
vations. For the analysis of these follow-up observations the prior on position
is a box of 1000′′ × 1000′′ centred on the cluster position. The priors on the
cluster are the same as those used to analyse the survey observations and again
sources with flux densities exceeding 4σSA,POI (where 4σSA,POI is the thermal
noise on the pointed observation) are modelled. Sources that are modelled in a
pointed observation are different to those modelled in the survey observation of
that candidate because σSA,POI 6= σSA,SUR. Often there are fewer sources mod-
elled in a pointed observation than in a survey triangle and as a consequence
the dimensionality of the pointed McAdam run is lower. We can thus increase
the number of source parameters that are modelled in pointed observations. For
pointed observations we have chosen to allow McAdam to fit for the positions
of the sources by using a Gaussian prior centred on the LA derived position of
the source with a 5′′ standard deviation. By fitting for the source positions we
obtain a cleaner source subtraction and as a result there are fewer residuals on
the source-subtracted pointed SA maps.
117
5.4 Cluster Identification
We are cautious about cluster candidates located at the position of a faint
source that has been assigned delta-function priors. For candidates with faint
sources that may affect the decrement, I ensure that these sources are modelled in
McAdam regardless of their flux density. This approach is particularly cautious,
because for a source situated on top of a cluster you may expect the source flux
to be underestimated by McAdam, especially if the cluster is at high redshift
and not well resolved. Due to the limited dynamic range of the SA, I have been
cautious of candidates close to bright sources: all candidates lying < 5′ from a
source ≥ 5mJy/beam are discarded.
We only set priors on sources that have been detected by the LA butMcAdam
is given knowledge of the statistics of sources that are below our LA detection
threshold. This background of sources is referred to as confusion noise and was
originally calculated by Scheuer (1957);
σ2conf = Ωsynth
∫ Slim
0
dN
dS
S2dS, (5.1)
where dN
dS
is the differential source count, Ωsynth is the synthesized beam and
Slim is the limiting flux density. As a standard we set Slim to four times the LA
thermal noise of the source that is closest to the pointing centre of the SA data.
For confusion noise we are currently using the combined 10C and 9C 15GHz
source counts that were derived in Davies et al. (2010):
dN
dS
=


48
(
S
Jy
)−2.13
(Jy−1sr−1) for 2.2mJy ≤ S ≤ 1Jy,
340
(
S
Jy
)−1.81
(Jy−1sr−1) for 0.50mJy ≤ S ≤ 2.2mJy.
The 10C source counts were obtained from the LA data that are used in the AMI
blind cluster survey, although as previously described the reduction was slightly
different. The 9C counts were taken from Waldram et al. (2003).
5.4 Cluster Identification
The AMI survey fields were chosen to avoid:
• Objects in the nearby galaxies atlas (Tully et al. 1989).
118
5.4 Cluster Identification
• Nearby superclusters.
• Abell et al. (1994) – this all-sky catalogue contains 4073 rich galaxy clusters
at redshifts ≤ 0.2
• Abell (1995) catalogue which contains 9134 Zwicky galaxy clusters (as well
as 2712 Abell clusters)
• ROSAT All Sky Survey (NORAS, REFLEX, BCS, SGP, NEP, MACS and
CIZA) catalogues.
These searches were performed by Richard Saunders before the blind cluster
survey began. The fields were also carefully selected so that they did not contain
objects bright than magnitude 14 (AB system) in the R or z′ bands.
I have checked the literature again to ensure that there are no known clusters
additionally I have searched the Sloan Digital Sky Survey (SDSS) cluster cata-
logues compiled by Koester et al. 2007 and Wen et al. 2010, which contain 13823
and 39716 clusters respectively.
The search revealed that the AMI002 field contains no known clusters but
that the AMI005 field contains 11 known galaxy clusters. These known clusters
were all found in the SDSS optical cluster catalogues. For each of these clusters I
have used the mass-richness scaling relationship from Rozo et al. (2009) to obtain
mean mass estimates. The mass-richness scaling relationship which relates the
richness at r200 to the mass at that radius is
< M |N >
1014M⊙
= eBM|N
(
N
40
)αM|N
. (5.2)
The constants BM |N and αM |N are 0.95 and 1.06 respectively. The maximum
derived mass of the 11 known clusters is 1.07×1014M⊙ which is significantly lower
than the MT,lim of the AMI survey.
In Table 5.3 I present the coordinates, redshift, richness and estimated mass
for these known clusters.
119
5.5 The Analysis of Survey Fields
Table 5.3: The known galaxy clusters in the AMI005 survey field. For entries that
exist in both Koester et al. (2007) and Wen et al. (2010) I have quoted the values
given in the later publication. The stated redshift is the cluster photometric
redshift. The masses were obtained from the mass-richness relation presented
in Rozo et al. (2009). All the derived cluster masses are well below the AMI
detection limit.
Right ascension Declination Redshift Richness Mass Source
×1014M⊙
09:40:03.2 +30:39:53 0.29 9.2 0.54 Wen et al. (2010)
09:37:21.7 +30:42.13 0.34 11.4 0.68 Wen et al. (2010)
09:42:09.5 +30:57:17 0.31 12.1 0.73 Wen et al. (2010)
09:37:38.3 +30:59:36 0.23 12.0 0.72 Koester et al. (2007)
and Wen et al. (2010)
09:38:39.1 +31:03:59 0.12 12.0 0.72 Koester et al. (2007)
09:40:00.7 +31:27:57 0.52 12.8 0.77 Wen et al. (2010)
09:37:38.5 +31:23:57 0.37 14.2 0.86 Wen et al. (2010)
09:37:41.8 +31:31:18 0.38 9.1 0.54 Wen et al. (2010)
09:38:12.6 +31:33:53 0.35 17.4 1.07 Wen et al. (2010)
09:40:38.2 +31:52:33 0.38 12.7 0.77 Wen et al. (2010)
09:38:22.7 +31:53:38 0.36 10.4 0.62 Wen et al. (2010)
5.5 The Analysis of Survey Fields
For the analysis of each field I present maps of the entire field, individual can-
didates in the field and pointed follow-up observations towards these candidates.
For each candidate I present McAdam derived p values and the parameter prob-
ability distributions for both the physical cluster model and the SZ cluster model.
As previously described, the McAdam analysis of the survey data properly
accounts for the contribution of sources (LA and confusion), the statistics of
the CMB primary anisotropies and the thermal noise level; hence the derived
probability distributions accurately depict the errors as long as no other random
120
5.5 The Analysis of Survey Fields
or systematic error is present. I have presented maps because in these it is easy
to spot contamination and also to judge the apparent significance of candidate
decrements. However, the interpretation of these maps is non-trivial:
• The clean algorithm is used to deconvolve the synthesized beam (see Fig-
ure 5.2 for an example synthesized beam) from the maps because it reduces
the sidelobes from objects. However, the clean procedure is not entirely
robust: differently cleaned data, for example to different depths or with
different clean boxes, can produce significantly different maps.
• The primordial CMB anisotropies contribute to the maps (see Figure 5.3).
• The weighted uv coverage and therefore the synthesized beam of each data-
set is different (see Figure 5.2 for an example beam).
121
5.5 The Analysis of Survey Fields
Cont peak flux =  1.0000E+00 JY/BEAM 
Levs = 3.000E-02 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 30 15 0002 59 45 30 15 00 58 45
26 45
40
35
30
25
Figure 5.2: A typical AMI synthesized beam for an AMI002 observation. Con-
tours are at ±2σ, ±3σ, ±4σ etc ., where σ is 3%; negative contours are dashed
and positive contours are solid. This beam is for a total of 23 hours of pointed SA
observation towards AMI002 candidate 3 at a declination of +25 (Figure 5.16).
Cont peak flux =  1.0059E-04 JY/BEAM 
Levs = 3.000E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
04 01 00 00 45 30 15 00 30 15 00
40 10
05
00
39 55
50
Cont peak flux =  2.5565E-04 JY/BEAM 
Levs = 3.000E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
04 01 00 00 45 30 15 00 30 15 00
40 10
05
00
39 55
50
Figure 5.3: The simulated CMB contribution to SA maps assuming the Lewis
et al. 2000 power spectrum. The contours are at ±2σ, ±3σ, ±4σ etc ., where
σ is 30µJy; negative contours are dashed and positive contours are solid. 20
simulations were run – the map on the left shows the lowest peak CMB flux
density obtained and the map on the right shows the highest peak flux density
obtained. The mean peak flux density due to the CMB was 150µJy/beam.
122
5.6 AMI002
Throughout this chapter I refer to survey search triangles via the identities
of the pointings that constitute that specific triangle. Note that pointings are
numbered from right to left and bottom to top; for example, in Figure 5.5 and
5.1(right) the bottom right pointing centre has ID 1 and on the same row but at
the far left the pointing has ID 4. In the maps the pointings can be distinguished
by the circular edge effects which are caused by the primary beam corrections.
Maps from the LA and SA survey data (triangles and complete fields) have
been primary beam corrected and the noise varies across the image. For these
maps I present signal divided by noise maps with contour levels at ±2σ, ±3σ,
±4σ etc ., where σ is stated in the Figure caption. σ is calculated by measuring
the rms on the map outside the primary beam, this is a measure of the thermal
noise and is not contaminated by sources. All the SA maps from pointed follow-
up observations that are presented here have not been primary beam corrected,
i.e. the SA thermal noise is constant across the map. Again the contour levels are
±2σ, ±3σ, ±4σ etc ., where σ is stated in the caption that is output with the aips
image and within the text. For all maps negative contours are dashed and positive
contours are solid. Unless otherwise stated, all maps are naturally weighted, i.e.
have no taper on uv distance. The synthesized-beam FWHM is shown in the
bottom left corner of the maps. For all parameter posterior distribution plots the
lower limit on the MT (r200)/h
−1MSun axis is MT,lim.
Throughout the text I refer to modes that are identified by McAdam. Only
modes that have a derived p ≥ 0.3 in the survey data are referred to as candidates.
5.6 AMI002
The LA and SA AMI002 images of this field are shown in Figures 5.4 and 5.5
respectively. In Figure 5.6 I show maps of the AMI002 SA data subjected to
jack-knife tests (Section 3.4); these highlight contaminated regions of the SA
maps.
In the LA data a total of 210 sources were detected at ≥ 4σLA,SUR; 13 of
these are extended on the LA maps. The flux densities of the sources range
between 0.15mJy/beam and 22mJy/beam. The AMI002 LA source details such
as coordinates, flux density and spectral index are given in Appendix Table B.2.
123
5.6 AMI002
The search for clusters in the 30 data triangles formed within the AMI002
field has produced several cluster candidates. In total 42 modes were detected
but many of these have low p values. In Table 5.4 I present the positions and
p values for each of the nine putative cluster detections which are detected with
p > 0.3. I use this limit because in Section 4.2.3 the highest p value for a false
positive was 0.3.
Cont peak flux =  2.5669E+02 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 03 02 01 00 02 59 58 57
27 00
26 50
40
30
20
10
00
25 50
40
30
20
Figure 5.4: The signal-to-noise map for the AMI002 LA field. In the central region
the noise is ≈ 50µJy/beam and in the outer region the noise is ≈ 100µJy/beam
(see Figure 5.1 for the complete noise map). A total of 210 sources were detected
with flux densities greater than 4σLA,SUR, 13 of these are extended.
124
5.6 AMI002
Cont peak flux =  1.2713E+02 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 01 00 02 59 58 57
27 00
26 50
40
30
20
10
00
25 50
40
30
Cont peak flux =  1.5807E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 01 00 02 59 58 57
27 00
26 50
40
30
20
10
00
25 50
40
30
Figure 5.5: The AMI002 SA signal-to-noise map. On the left, sources have not
been subtracted; on the right, sources have been subtracted. For sources with
flux densities > 4σSA,SUR the McAdam derived values for their flux density and
spectral index were used for the subtraction, whereas for fainter sources the LA
values were used. The thermal noise is σSA,SUR ≈ 100µJy/beam.
.
Cont peak flux = -9.7678E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 01 00 02 59 58 57
27 00
26 50
40
30
20
10
00
25 50
40
30
Cont peak flux = -6.2711E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 01 00 02 59 58 57
27 00
26 50
40
30
20
10
00
25 50
40
30
Figure 5.6: The signal-to-noise map of the AMI002 jack-knifed SA data set. On
the left the data has been split according to the median date and on the right the
data has been split into plus and minus baselines. The noise on the map on the
left is ≈ 100µJy/beam and the noise on the map on the right is ≈ 70µJy/beam.
The noise level on the map on the right is lower than 100µJy/beam as expected
(see Section 3.4). 125
5.6 AMI002
Table 5.4: The derived p values for the nine candidates detected in the AMI002
SA data that have p > 0.3. Often candidates are detected in multiple triangles,
for these I provide the maximum and minimum p and R values. The stated right
ascension and declination are obtained from the triangle in which the candidate
is detected with highest p value.
Candidate Pointings Highest p Lowest p Right Declination
(R) (R) Ascension
1 12-15-16, 1.0 1.0 03:01:14.7 +26:16:41
15-16-20 (4.4×104) (3.2×102)
2 11-12-15, 1.0 0.5 03:00:15.5 +26:14:02
11-14-15, (9.5×102) (1.0)
14-15-19,
15-19-20
3 18-19-22 1.0 1.0 02:59:34.7 +26:35:48
(2.1×102) (2.1×102)
4 6-7-11, 0.99 0.28 02:59:48.1 +25:55:31
3-6-7, (68) (0.4)
6-10-11
5 7-11-12, 0.97 0.90 03:00:33.5 +25:57:47
7-8-12 (34) (9.5)
6 2-3-6 0.80 0.80 02:59:08.2 +25:48:09
(4.1) (4.1)
7 5-9-10, 0.80 0.68 02:58:14.8 +25:57:34
1-2-5 (4.0) (2.1)
8 6-10-11 0.78 0.78 02:59:07.2 +25:59:22
(2.5) (2.5)
9 13-14-18, 0.37 0.07 02:58:50.7 +26:22:23
13-17-18 (0.6) (0.0)
In the AMI002 field I have eliminated four cluster candidates at positions
03:00:58.5 +25:46:13, 02:59:57.5 +26:28:12, 03:00:41.8 +26:27:25 and 02:59:03.9
+25:55:08, even though the derived p values are 1.0, 1.0, 0.79 and 0.50 respec-
tively. These candidates are eliminated because they lay close to the brightest
126
5.6 AMI002
sources in the field; these sources have caused severe contamination that is visible
in the jack-knifed SA data set (Figure 5.6).
5.6.1 Candidate 1: 12-15-16 and 15-16-20
This candidate is detected in the search triangles 12-15-16 and 15-16-19, both
detections have p = 1.0. Given the position of this candidate we would not expect
to detect it in any of the other search triangles. The noise in the region of the
candidate is lowest in the 15-16-20 triangle and the image of these data is shown
in Figure 5.7. We see no bright radio sources in the vicinity of the candidate
and after source subtraction most of the source signal is removed. However, a
0.65mJy/beam decrement is clearly visible at the candidate position even before
source subtraction. There is also a significant decrement to the west; this is
candidate 2 as is described in the Section 5.6.2. In the AMI002 jack-knifed data
set (Figure 5.6) there is no significant or unusual contamination in the region of
this candidate.
There are two sources subtracted close to the candidate at positions 03:01:06.5
+25:48:53 and 03:01:28.1 +26:16:46. The first lies within the decrement and is
not extended on the LA maps and a peak LA flux density of 0.28mJy/beam. The
other is slightly west of the candidate, is extended on the LA maps, has a peak
flux density of 0.45mJy/beam and an integrated flux density of 0.70mJy/beam.
However, even though this source is extended on the LA map it is unlikely to
have a significant impact upon the decrement because it is weak and ≈ 3′ away.
127
5.6 AMI002
Cont peak flux =  3.4412E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 30 00 01 30 00 00 30 00 02 59 30
26 45
40
35
30
25
20
15
10
05
00
Cont peak flux = -6.4674E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 30 00 01 30 00 00 30 00 02 59 30
26 45
40
35
30
25
20
15
10
05
00
Figure 5.7: Signal-to-noise map for the AMI002 search triangle 15-16-20. On the
left is the map before source subtraction and on the right the sources have been
subtracted using muesli. The thermal noise in the region of the candidate is
σA2,SUR,CL1 = 100µJy/beam. The box symbol represents the cluster candidate,
× symbols show sources with a measured LA flux greater than 4σSA,SUR, and +
symbols show fainter sources.
5.6.1.1 Pointed Follow-up Observation
A total of 22 hours of SA pointed observations towards 03:01:15.4 +26:17:26 were
taken between May 2010 and June 2011. The thermal noise on this pointed
follow-up observation, σA2,POI,CL1, is 100µJy/beam; this is similar to the noise
obtained in the survey field observations of this region (σA2,SUR,CL1). The data
were passed through McAdam and the sources were modelled according to the
criteria outlined for pointed observations in Section 5.3; this involves modelling
a total of nine sources including the 0.28mJy/beam source (LA flux) within the
decrement. The images from the pointed observation are shown in Figure 5.8.
The LA measured 0.28mJy/beam (flux density measurement obtained in an
area where σLA,SUR = 0.051mJy) source that is modelled and subtracted from
close to the centre of the candidate decrement has aMcAdam derived mean flux
density of 0.18mJy/beam. It is this derived flux density that is subtracted from
128
5.6 AMI002
the map. Hence, it appears that even though we underestimate the flux density
of this source on the SA map compared with the LA values, we still obtain a
0.60mJy/beam (5σA2,POI,CL1) decrement at the position of this candidate. The
0.70mJy/beam extended LA source appears to be correctly subtracted, leaving
no artifacts. An incorrect subtraction of this source would mainly affect the
morphology of the decrement and not its magnitude.
The follow-up pointed observation has been passed through McAdam using
both the physical cluster model and the phenomenological model, the derived
parameter probability distribution from each model is shown in Figure 5.9. Tables
5.5 and 5.6 give the mean parameter values. For this pointed observation we use
the McAdam evidences to derive a p value of 0.98 (R=44).
129
5.6 AMI002
Cont peak flux =  8.8497E-04 JY/BEAM 
Levs = 9.933E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 15 00 01 45 30 15 00 00 45 30 15
26 30
25
20
15
10
05
Cont peak flux = -5.2065E-04 JY/BEAM 
Levs = 1.001E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 15 00 01 45 30 15 00 00 45 30 15
26 30
25
20
15
10
05
Figure 5.8: Images of the SA follow-up pointed observations towards the AMI002
cluster candidate 1 (03:01:15.4 +26:17:26). These are shown before source sub-
traction on the left and after sources have been subtracted on the right. The trian-
gle symbols represent sources that have flux densities greater than 4σA2,SUR,CL1.
The position, flux and spectral index of these sources have been modelled and the
mean McAdam derived values have been used for the subtraction. The crosses
show sources with flux densities below 4σA2,SUR,CL1; these are subtracted using
the LA measured flux densities.
4 6 8
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−50
0
50
100
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−50 0 50
4
6
8
x 1014
y0/arcsec
−50 0 50 100
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −400 −300 −200 −100∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 200 300 400
−400
−300
−200
−100
β
0.5 1.5 2.5
Figure 5.9: The derived parameters for AMI002 cluster candidate 1 at position
03:01:15.4 +26:17:26. On the left are the physical parameters and on the right
are the phenomenological model parameters.
130
5.6 AMI002
Table 5.5: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 1.
Parameter
z 0.96+0.31−0.30
MT (r200)/h
−1MSun 4.2
+1.0
−1.0 × 1014
rc/h
−1kpc 660+340−85
β 1.0+0.1−0.7
Table 5.6: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 1.
Parameter
∆T0/µK −230+37−37
θc/arcsec 250
+73
−75
β 1.7+0.5−0.5
5.6.2 Candidate 2: 11-12-15, 11-14-15, 15-19-20 and 14-
15-19
A highly-extended, non-circular negative feature is detected in the McAdam
analysis of the search triangles 11-12-15, 11-14-15, 15-19-20 (two modes) and 14-
15-19; the derived p values are 1.0, 1.0, 0.5, 0.78 and 0.95 respectively. The noise
in the locality of the candidate is lowest for the search triangle 11-12-15 and the
map from this triangle is shown in Figure 5.10.
131
5.6 AMI002
Cont peak flux =  2.7075E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 00 01 30 00 00 30 00 02 59 30 00
26 35
30
25
20
15
10
05
00
25 55
50
Cont peak flux = -5.5659E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 00 01 30 00 00 30 00 02 59 30 00
26 35
30
25
20
15
10
05
00
25 55
50
Figure 5.10: Same as for Figure 5.7 but for candidate 2 (found in 11-12-15). The
thermal noise in the region of the candidate is σA2,SUR,CL2 ≈ 100µJy/beam.
There are several sources just north of this candidate, the ones most likely
to influence the decrement are the sources at 03:00:01.3 +26:21:00, 03:00:29.5
+26:18:40, 03:00:24.6 +26:19:41 and 03:00:15.2 +26:19:25, none of these sources is
extended and their LA measured flux densities are 1.8mJy/beam, 1.4mJy/beam,
1.2mJy/beam and 1.1mJy/beam respectively.
The source subtraction leaves little residual flux density on the map. The
positive features to the east and west of the candidate may be associated with
the sidelobes of the candidate, alternatively they may influence the candidate
with their sidelobes. The negative feature at 03:01:14.7 +26:16:41 is candidate 1
and was described in Section 5.6.1. The jack-knife tests (Figure 5.6) reveal only
noise-like features in the vicinity of the candidate. After the source subtraction
we note that the peak flux density of the cluster decrement is ≈ 0.60mJy/beam
(5σA2,SUR,CL2).
5.6.2.1 Pointed observation
This cluster candidate was followed up with 49 hours of pointed observations,
taken in March 2010. The image produced from the pointed-observation data
132
5.6 AMI002
has a thermal noise level of 65µJy/beam and is shown before and after source
subtraction in Figure 5.11. Again we see a highly-extended, non-circular negative
feature with a peak flux density decrement of ≈ 0.60mJy/beam (8σA2,POI,CL2).
The integrated flux density of the decrement is ≈ 1.2mJy/beam.
The source subtracted map has similar flux density residuals to those seen in
the survey data. The positive residuals to the north and west of the candidate
may be associated with badly subtracted sources but the majority of the sources
subtract well.
Cont peak flux =  2.6811E-03 JY/BEAM 
Levs = 6.650E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Cont peak flux = -5.1764E-04 JY/BEAM 
Levs = 6.650E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Figure 5.11: Same as Figure 5.8 but for AMI002 candidate 2. We have detected
two modes, one at 03:00:14.8 +26:10:02 and another at 03:00:08.9 +26:16:29.
When imaging the source subtracted map, clean boxes have been placed around
each candidate.
Our Bayesian analysis of the pointed-observation data, which have a higher
signal-to-noise ratio than the survey data, finds two local peaks in the marginalised
posterior distribution in the (xc, yc)-plane. These cluster candidates are: candi-
date 2a at 03:00:14.8 +26:10:02 and candidate 2b at 03:00:08.9 +26:16:29. The
significances of the two cluster detections are pa = 1.0 and pb = 1.0 (Ra = 6.0×105
and Rb = 7000). I also made a direct comparison of the Bayesian evidence for
a model containing two clusters and a model containing just a single cluster and
133
5.6 AMI002
find that the Bayesian evidence is 7.6 × 105 higher for the model containing two
clusters.
The 1D and 2D marginal posterior distributions for a selection of the physical
parameters of each cluster are shown in Figure 5.12 and the mean values are given
in Table 5.7.
Table 5.7: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 2 modes a and b.
Parameter Mode a Mode b
z 0.59+0.07−0.39 0.71
+0.09
−0.15
MT (r200)/h
−1
70MSun 5.5
+1.2
−1.3 × 1014 3.5+0.9−1.0 × 1014
rc/h
−1
70 kpc 640
+360
−84 340
+73
−330
β 1.8+0.7−0.2 1.7
+0.8
−0.2
5 10
MT(r200)/h70
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
2
r c
/h
70−1
kp
c
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h 7
0
−
1 M
Su
n
−500 0 500
4
6
8
10
y0/arcsec
−500 0 500
z
0.5 1 1.5 2
r
c
/h70
−1kpc
500 1000
β
0.5 1.5 2.5 2 4 6 8
MT(r200)/h70
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
2
r c
/h
70−1
kp
c
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h 7
0
−
1 M
Su
n
−500 0 500
2
4
6
8
y0/arcsec
−500 0 500
z
0.5 1 1.5 2
r
c
/h70
−1kpc
500 1000
β
0.5 1.5 2.5
Figure 5.12: 1D and 2D marginal posterior distributions for a selection of the
parameters in physical cluster model for candidate 2a (left) and candidate 2b
(right). The MT,200 values have been divided by 10
14.
The 1D and 2D marginal posterior distributions for the phenomenological
model parameters θc, β and ∆T0 are shown in Figure 5.13. The mean values and
134
5.6 AMI002
68% confidence limits for each parameter are given in Table 5.8.
Table 5.8: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 2a and candidate 2b.
Parameter Pointed (candidate 2a) Pointed (candidate 2b)
∆T0/µK −295+36−15 −302+70−27
θc/arcsec 156
+27
−25 121
+19
−100
β 1.69+0.81−0.24 1.46
+1.03
−1.06
−600 −400 −200
∆ T0/µ K
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/µ
 
K
100 200 300 400 500
−600
−500
−400
−300
−200
β
0.5 1.5 2.5 −600 −400 −200∆ T0/µ K
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/µ
 
K
100 200 300 400 500
−600
−400
−200
β
0.5 1.5 2.5
Figure 5.13: 1D and 2D marginal posterior distributions for the parameters in
the phenomenological model for candidate 2a (left) and candidate 2b (right).
The jack-knife tests of the pointed observation towards this candidate reveal
that when the data are split according to median date, there is a 4σA2,POI,CL2
decrement centred on the source structure north-east of the cluster candidate
(Figure 5.14). This result implies that the flux of this structure is higher in the
first half of the data than in the second half. An investigation revealed that
the flux of this structure was dependent upon the orientation of the synthesized
beam. When the beam was extended in the south-east – north-west axis we found
135
5.6 AMI002
that the flux density was slightly higher than when the beam was extended in the
south-west – north-east axis. The majority of the data taken before the median
date had synthesized beams that extended along the south-east – north-west axis.
After the median date the majority of the data had a beam extended along the
south-west – north-east axis. Hence the decrement that we see after performing
a jack-knife test and splitting the data according to median date produces results
that we would expect. However, neither jack-knife test reveals any unexpected
contamination.
Cont peak flux =  3.2366E-04 JY/BEAM 
Levs = 6.650E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Cont peak flux = -2.7326E-04 JY/BEAM 
Levs = 6.650E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 45 30 15 0002 59 45 30 15
26 25
20
15
10
05
Figure 5.14: The jack-knifed data from Figure 5.11 (left). On the left, data are
split according to median date, one the right, data are split into plus and minus
baselines. The σ level for contours is 65µJy/beam.
Due to the high p values, high signal-to-noise and the interesting morphology
of this decrement I have submitted the results of this detection for publication
(AMI Consortium: Shimwell et al. 2010) and I have applied for follow-up SZ ob-
servations with the Combined Array for Research in Millimetre-wave Astronomy
(CARMA; Bock et al. 2006).
136
5.6 AMI002
5.6.3 Candidate 3: 18-19-22
An extended negative structure is detected with p = 1.0 in triangle 18-19-20 and
p = 0.52 in triangle 18-21-22. The candidate was not detected in the search
triangle 19-22-23; however, a decrement is clearly visible in that map and the
data from that triangle are significantly contaminated by a bright source (see
Figure 5.6). The lowest noise in the region of this candidate was obtained in
triangle 18-19-22, the image of which is shown in Figure 5.15.
Cont peak flux =  8.5408E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 30 00 02 59 30 00 58 30 00
26 55
50
45
40
35
30
25
20
15
10
Cont peak flux =  7.0691E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 30 00 02 59 30 00 58 30 00
26 55
50
45
40
35
30
25
20
15
10
Figure 5.15: Same as for Figure 5.7 but for candidate 3 (found in 18-19-22). The
thermal noise in the region of the candidate is σA2,SUR,CL3 = 110µJy/beam.
Quite large residuals remain on the map after source subtraction, especially
in the region of the 8.4mJy/beam (LA measurement) source with coordinates
02:59:55.1 +26:27:26. This contamination is apparent in both the source sub-
tracted pointed observations (Figure 5.15) and the SA survey jack-knifed data
set (Figure 5.6). The contamination is not solely confined to the exact position
of the source but it is concentrated within a radius of ≈5′. The cluster candidate
is separated by 9.5′ from this source and the apparent contamination at that
distance is minimal.
On the map there is positive extended structures to the north and to the east
of the candidate – these are not noticeable on the LA maps. There is a possibility
137
5.6 AMI002
that the extended sources at 02:59:55.9 +26:39:23 (peak flux 0.35mJy/beam, in-
tegrated flux 0.50mJy/beam) and 03:00:35.3 +26:35:21 (peak flux 1.3mJy/beam,
integrated flux 1.7mJy/beam) are responsible for this structure. To further in-
vestigate this I have applied a uv cut to the LA data and rejected all data from
baselines longer than 2000λ. This cut significantly reduces the resolution of the
LA images (the typical uv range of the LA is ≈ 1000− 7000λ), and makes them
more comparable to SA images (the SA uv range is ≈ 200 − 1200λ). However,
even in this uv range limited data set the extension that we see on the SA maps
is not visible. The NRAO VLA SkySurvey (radio 21cm, NVSS) was searched for
extended objects in this region but no evidence of extended emission was found.
5.6.3.1 Pointed Follow-up Observations
The map of 23 hours of follow-up observations (σA2,POI,CL3 = 113µJy/beam) is
shown before and after the sources have been modelled and subtracted in Figure
5.16 – a total of nine sources were modelled.
In the pre-source subtracted map we observe a 4σA2,POI,CL3 decrement but
there are several sources whose sidelobes may artificially influence this decrement.
The most likely sources to cause this contamination are the 8.4mJy/beam source
and the 2.4mJy/beam source (2:59:32.3 +26:39:51).
After sources are subtracted the shape of the decrement stays the same but
the magnitude decreases to 3σA2,POI,CL3. After subtraction the 8.4mJy/beam
source leaves an 8σA2,POI,CL3 residual, 10
′ from the candidate – the sidelobes of
this residual are unlikely to cause contamination at > 5% of the residual flux
density (the synthesized beam for this observation is shown in Figure 5.2). Other
sources subtract leaving few residuals.
The data quality of this observation has been carefully checked and the jack-
knife tests do not reveal contamination. Several unexplained positive and nega-
tive features as significant as the candidate are present on the source subtracted
map. Some are associated with sources, whilst the 3σA2,POI,CL3 positive struc-
tures to the north and the east of the candidate were also observed in the survey
observations. However, the cause the other structures is unclear.
138
5.6 AMI002
The derived parameters from the McAdam runs are shown in Figures 5.16
and 5.17; the mean parameters are shown in Tables 5.9 and 5.10. Note that the
derived position parameters clearly show that two distinct modes were detected.
One is the candidate and the second mode corresponds to the 2σA2,POI,CL3 decre-
ment west of candidate 3. The Bayesian evidence of the second mode is 3.9 lower
than that for candidate 3.
For candidate 3 we derive a p value of 0.7 (R=2.3). I find candidate 3 not
wholly convincing given that there are unexplained positive and negative residuals
with higher or comparable flux densities.
139
5.6 AMI002
Cont peak flux =  4.3137E-03 JY/BEAM 
Levs = 1.121E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 30 15 0002 59 45 30 15 00 58 45
26 45
40
35
30
25
Cont peak flux =  6.9434E-04 JY/BEAM 
Levs = 1.129E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 30 15 0002 59 45 30 15 00 58 45
26 45
40
35
30
25
Figure 5.16: Same as Figure 5.8 but for AMI002 candidate 3.
4 6 8
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
4
6
8
x 1014
y0/arcsec
−500 0 500
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −400 −300 −200 −100∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 200 300 400
−400
−300
−200
−100
β
0.5 1.5 2.5
Figure 5.17: The derived parameters for AMI002 cluster candidate 3 . On the
left are the physical parameters and on the right are the phenomenological model
parameters.
140
5.6 AMI002
Table 5.9: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 3.
Parameter
z 0.83+0.30−0.30
MT (r200)/h
−1MSun 3.6
+0.5
−0.6 × 1014 rc/h−1kpc 560+440−550
β 1.4+1.1−1.1
Table 5.10: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 3.
Parameter
∆T0/µK −210+52−53
θc/arcsec 130
+43
−47
β 1.7+0.5−0.5
5.6.4 Candidate 4: 6-7-11, 3-6-7 and 6-10-11
A 4σA2,SUR,CL4 decrement with a similar extent to the synthesized beam that may
be associated with an extended 2σA2,SUR,CL4 structure to the north is detected
by McAdam in 6-7-11, 3-6-7 and 6-10-11 , with p values of 0.99, 0.55 and 0.28
respectively. This candidate lies outside the search area for all other triangles.
The noise is lowest for observation 6-7-11 and an image of these data is shown in
Figure 5.18.
141
5.6 AMI002
Cont peak flux =  4.2475E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 30 00 00 30 00 02 59 30 00 58 30
26 20
15
10
05
00
25 55
50
45
40
35
Cont peak flux =  5.5463E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 30 00 00 30 00 02 59 30 00 58 30
26 20
15
10
05
00
25 55
50
45
40
35
Figure 5.18: Same as for Figure 5.7 but for the candidate 4 (found in 6-7-11).
The thermal noise in the region of the candidate is σA2,SUR,CL4 = 100µJy/beam.
Just to the south of the candidate are two sources that may influence the
magnitude of the decrement. These sources lay at positions 02:59:57.2 +25:53:56
(peak flux 1.6mJy/beam) and 02:59:39.7 +25:53:23 (peak flux 0.78mJy/beam);
neither of these sources is extended on our LA maps. To the north-east of the
candidate there is extended positive structure that is not associated with any LA
sources. To search for this structure a map was made from the LA data from
baselines shorter than 2000λ but nothing was found. NVSS images of this area
also reveal no visible extended structure.
In the 6-7-11 triangle I note that the jack-knifed data (Figure 5.6) does
show residuals that are associated with the 3.5mJy/beam source at 02:59:10.7
+25:54:31. These residuals do extend towards this cluster candidate.
5.6.4.1 Pointed Follow-up Observations
A total of 40 hours of SA pointed observations towards this candidate were con-
ducted in June 2011 and a noise level of σA2,POI,CL4 = 130µJy/beam was reached.
The images before and after source subtraction are shown in Figure 5.19. For the
analysis of this pointed observation a total of four sources were modelled.
142
5.6 AMI002
Candidate 4 was identified in the survey data as a peak decrement (02:59:48.1
+25:55:31) which was possibly associated with the 2σA2,SUR,CL4 negative structure
to north. In these follow-up observations the peak decrement of candidate 4 was
not detected, but the negative structure to the north was.
The source environment around candidate 4 is not severe. The main contam-
inating sources are a 1.7mJy/beam source (02:59:41.1 +26:02:20) north of the
candidate and the 1.6mJy/beam and 0.78mJy/beam sources that lay south of
the candidate. All sources are subtracted from the follow-up data leaving min-
imal residuals. Before source subtraction the decrement just north of candidate
4 was 5σSA,A2CL4, but the source sidelobes contribute to the magnitude of the
decrement. After source subtraction the decrement is decreased to 3σSA,A2CL4.
Neither of the jack-knife tests reveal any contamination of the follow-up obser-
vations. The derived parameters are shown in Figures 5.19 and 5.20 and Tables
5.11 and 5.12. From theMcAdam Bayesian evidences we derive a p value of 0.97
(R=32) for the decrement just north of candidate 4.
143
5.6 AMI002
Cont peak flux =  2.2569E-03 JY/BEAM 
Levs = 1.334E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 45 30 15 0002 59 45 30 15 00 58 45
26 05
00
25 55
50
45
Cont peak flux =  6.2623E-04 JY/BEAM 
Levs = 1.362E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 45 30 15 0002 59 45 30 15 00 58 45
26 05
00
25 55
50
45
Figure 5.19: Images of the SA pointed observations towards the AMI002 cluster
candidate 4.
4 8 12
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
0
200
400
z
0.5
1
1.5
2
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−100 0 100
4
6
8
10
12
14
x 1014
y0/arcsec
0 200 400
z
1 2
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −1500 −1000 −500∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 200 300 400 500
−1500
−1000
−500
β
0.5 1.5 2.5
Figure 5.20: The derived parameters for AMI002 cluster candidate 4. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
144
5.6 AMI002
Table 5.11: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 4.
Parameter Value
z 1.2+0.3−0.3
MT (r200)/h
−1MSun 4.4
+1.3
−1.5 × 1014
rc/h
−1kpc 660+340−84
β 0.6+0.0−0.3
Table 5.12: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 4.
Parameter Value
∆T0/µK −450+140−140
θc/arcsec 340
+97
−96
β 1.2+0.4−0.4
5.6.5 Candidate 5: 7-11-12 and 7-8-12
An extended 4σA2,SUR,CL5 decrement is detected in both 7-11-12 and 7-8-12 tri-
angles; the McAdam derived probabilities are 0.97 and 0.90 respectively. This
candidate can also be seen in the data from 4-7-8 and 3-4-7 but it is outside those
cluster search regions. The map from 7-11-12 is shown in Figure 5.21 – this map
is chosen because it has the lowest noise in the vicinity of the candidate.
After source subtraction we find that sources are generally removed well,
leaving few residuals (excluding the 14mJy/beam source at 03:01:05.5 +25:47:16
which does leave large residuals but is > 15′ from candidate 5). However, there
are several > 4σA2,SUR,CL5 positive features on the SA map which are not de-
tected by the LA. The most significant of which lies just to the north-west of
the candidate and the sidelobes of this structure may have an impact upon the
magnitude of the decrement. Another concerning aspect is the existence of a
0.33mJy/beam (03:00:29.4 +25:57:35) extended LA source within the candidate
145
5.6 AMI002
5 decrement. If this source is extended on the SA then there could be a degener-
acy between its flux density and the magnitude of the candidate decrement. In
the analysis of the 7-11-12 triangle, McAdam models this source to have a flux
density of 0.15mJy/beam. This conservative flux density estimation leads to a
lower SZ decrement.
Cont peak flux =  4.2372E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 00 01 30 00 00 30 00 02 59 30 00
26 20
15
10
05
00
25 55
50
45
40
35
Cont peak flux =  6.1083E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 02 00 01 30 00 00 30 00 02 59 30 00
26 20
15
10
05
00
25 55
50
45
40
35
Figure 5.21: Same as for Figure 5.7 but for the candidate 5 (found in 7-11-12).
The thermal noise in the region of the candidate is σA2,SUR,CL5 = 105µJy/beam.
5.6.5.1 Pointed Follow-up Observations
A follow-up program consisting of 31 hours of SA pointed observations was un-
dertaken in June 2011. The thermal noise level achieved was σA2,POI,CL5 =
110µJy/beam and as a result five sources were modelled in the analysis. The
images of these data before and after source subtraction are shown in Figure
5.22. On the source subtracted map there is a > 3σA2,POI,CL5 negative feature
close to the location of candidate 5, but this is not the brightest negative (or
positive) feature on the map.
Excluding the extended 0.33mJy/beam source which is located very close to
candidate 5, the main contaminating sources are the 1.4mJy/beam point source at
03:00:59.3 +25:56:49 and the 14mJy/beam source. Before source subtraction the
146
5.6 AMI002
sidelobes of these sources may contribute significantly to the decrement. However,
the 1.4mJy/beam source subtracts leaving no residuals and the 14mJy/beam
source leaves only 1.0mJy/beam residuals. The sidelobes of these residuals are
unlikely to have more that a 50µJy/beam effect at the location of candidate 5.
The 0.33mJy/beam extended source was modelled to have a flux density of
0.27mJy/beam in the follow-up data (in the survey the derived flux density is
0.15mJy/beam). McAdam can be forced to use the higher flux density LA mea-
surement for this source by putting a delta-function prior of 0.33mJy/beam on
its flux. If this is done, then a slightly higher magnitude decrement is obtained
at the location of candidate 5. However, the Bayesian evidence drops by 0.2 indi-
cating that McAdam has little preference between the models but does slightly
prefer a lower flux density for this source.
McAdam has been able to detect a mode at the position of candidate 5
but the derived parameters are badly constrained and other negative features of
higher magnitude are visible. The derived parameters obtained from the follow-
up observations of candidate 5 are shown in Figure 5.23 and Tables 5.13 and 5.14.
The p value obtained from the analysis of these follow-up observations was 0.33
(R=0.5).
147
5.6 AMI002
Cont peak flux =  4.1440E-03 JY/BEAM 
Levs = 1.097E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 30 15 00 00 45 30 15 0002 59 45
26 10
05
00
25 55
50
45
Cont peak flux =  1.0358E-03 JY/BEAM 
Levs = 1.080E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 30 15 00 00 45 30 15 0002 59 45
26 10
05
00
25 55
50
45
Figure 5.22: Images of the SA pointed observations towards the AMI002 cluster
candidate 5.
4 6 8
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−400
−200
0
200
400
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
4
6
8
x 1014
y0/arcsec
−400 0 400
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −400 −300 −200 −100∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−400
−300
−200
−100
β
0.5 1.5 2.5
Figure 5.23: The derived parameters for AMI002 cluster candidate 5. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
148
5.6 AMI002
Table 5.13: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 5.
z 0.7+0.2−0.2
MT (r200)/h
−1MSun 3.6
+0.5
−0.7 × 1014
rc/h
−1kpc 620+380−610
β 1.0+1.5−0.7
Table 5.14: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 5.
∆T0/µK −160+53−51
θc/arcsec 290
+110
−100
β 1.5+0.6−0.6
5.6.6 Candidate 6: 2-3-6
A rather peculiar arrangement of 3 > 3σA2,SUR,CL6 negative features lying along
a north-west diagonal are observed in the 2-3-6 triangle. One of these features I
identify as candidate 6; its derived p value is 0.8. Another of these decrements
corresponds to candidate 4 (see Section 5.6.4). The image of 2-3-6 before and
after source subtraction is shown in Figure 5.24. These three decrements were
seen in the 2-5-6 triangle map but for that data McAdam was unable to isolate
candidate 6 from the surrounding negative flux.
The most significant residual after source subtraction is associated with the
3.4mJy/beam source (02:59:10.7 +25:54:31). South-west of candidate 6 at 02:59:41.1
+26:02:20 lies a resolved LA source, its peak flux is 1.2mJy/beam and its in-
tegrated flux is 1.7mJy/beam. This extended source leaves no residuals after
subtraction. Other sources also subtract well, and therefore on the source sub-
tracted map I expect little contamination from source residuals at the location
of candidate 6.
The jack-knife tests reveal no contamination close to this candidate. However
on the SA map, there is a positive feature south of the candidate, which was not
149
5.6 AMI002
detected on the LA maps. The sidelobes of this positive structure may affect the
candidate.
Note that the 4σA2,SUR,CL6 decrement at 02:59:44.3 +25:39:22 lies outside all
the survey search triangles and hence is not detected at all.
Cont peak flux =  3.6501E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 30 00 02 59 30 00 58 30 00
26 10
05
00
25 55
50
45
40
35
30
25
Cont peak flux = -5.2391E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 30 00 02 59 30 00 58 30 00
26 10
05
00
25 55
50
45
40
35
30
25
Figure 5.24: Same as for Figure 5.7 but for the candidate 6 (found in 2-3-6). The
thermal noise in the region of the candidate is σA2,SUR,CL6 = 100µJy/beam.
5.6.6.1 Pointed Follow-up Observations
The follow-up of candidate 6 consisted of 28 hours of pointed SA observations.
From these data a thermal noise level of σA2,POI,CL6 = 110µJy/beam was ob-
tained. Above 4σA2,POI,CL6 there were five LA sources, although another source
of LA flux density 0.18mJy/beam (02:59:10.1 +25:44:39) was modelled because
it lay at the edge of the candidate decrement. The maps before and after source
subtraction are shown in Figure 5.25.
One striking difference between the survey observation and the pointed obser-
vation is the absence of candidate 4 but this was discussed in Section 5.6.4. On the
pre-source-subtracted map the 3.4mJy/beam point source and 1.7mJy/beam ex-
tended source both influence the decrement. Even though the jack-knife tests re-
veal no contamination in this map I find that both these sources leave 3σA2,POI,CL6
150
5.6 AMI002
residuals after subtraction. However, the sidelobes of these residuals will have
a negligible impact at the location of candidate 6. The source of flux density
0.18mJy/beam is modelled to have a mean flux density of 0.13mJy/beam and
also has negligible impact on the candidate decrement.
Positive residuals are observed to the south and although these are not associ-
ated with LA sources they were also present in the SA survey data. These positive
structures are unlikely to cause severe contamination to candidate 6 because they
have a peak flux density of only 4σA2,POI,CL6 and are 5
′ from the candidate.
The candidate is the brightest negative feature on the source subtracted map,
although there are several positive features of higher magnitude. The McAdam
derived parameters from this pointed observation are presented in Figure 5.26
and Tables 5.15 and 5.16 give the mean values of these parameters. For this
candidate 6 follow-up observation I use the Bayesian evidences to calculate p =
0.82 (R=4.5), which matches the value obtained from the survey field.
151
5.6 AMI002
Cont peak flux =  3.2864E-03 JY/BEAM 
Levs = 1.096E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 45 30 15 00 58 45 30 15
26 00
25 55
50
45
40
35
Cont peak flux =  5.0846E-04 JY/BEAM 
Levs = 1.108E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 45 30 15 00 58 45 30 15
26 00
25 55
50
45
40
35
Figure 5.25: Images of the SA pointed observations towards the AMI002 cluster
candidate 6.
4 8 12
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−200
0
200
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−200 0 200
4
6
8
10
12
x 1014
y0/arcsec
−200 0 200
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −800 −600 −400 −200∆ T0/muK
β
0.5
1
1.5
2
θ
c
/arcsec
∆ 
T 0
/m
uK
200 300 400 500
−800
−600
−400
−200
β
0.5 1 1.5 2
Figure 5.26: The derived parameters for AMI002 cluster candidate 6. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
152
5.6 AMI002
Table 5.15: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 6.
Parameter Value
z 0.9+0.3−0.3
MT (r200)/h
−1MSun 4.1
+1.0
−1.2 × 1014
rc/h
−1kpc 700+300−73
β 0.6+0.1−0.3
Table 5.16: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 6.
Parameter Value
∆T0/µK −440+140−130
θc/arcsec 410
+58
−58
β 1.0+0.3−0.3
5.6.7 Candidate 7: 5-9-10 and 1-2-5
A non-circular, double-peaked-decrement is detected between point sources in the
5-9-10 and 1-2-5 search triangles. The derived p values for this candidate are 0.8
and 0.68 from each of these fields respectively. The noise in the region of the
candidate is lowest in 5-9-10, the map of which is shown in Figure 5.27. We do
not expect to detect this candidate in any other triangles.
153
5.6 AMI002
Cont peak flux =  2.1892E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 30 00 58 30 00 57 30 00
26 20
15
10
05
00
25 55
50
45
40
35
Cont peak flux =  5.1658E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 30 00 58 30 00 57 30 00
26 20
15
10
05
00
25 55
50
45
40
35
Figure 5.27: Same as for Figure 5.7 but for the candidate 7 (found in 5-9-10).
The thermal noise in the region of the candidate is σA2,SUR,CL7 = 110µJy/beam.
Judging by the unusual morphology of the candidate and the position of the
surrounding sources it is apparent that the sources to the east and the west
significantly affect the magnitude of the decrement and its shape. The sources
to the east that are most likely to influence the decrement lay at 02:58:28.5
+25:55:59 and 02:58:29.2 +25:57:20 and have flux densities of 1.2mJy/beam and
0.96mJy/beam respectively. To the west of the candidate the 1.34mJy/beam
source at 02:57:58.1 +25:59:47 is the most likely to influence the decrement. None
of these three sources is extended on the LA maps or NVSS images. After source
subtraction the only significant residual is the 4σA2,SUR,CL7 extended positive
structure to the west of the candidate.
The jack-knife tests in Figure 5.6 reveal that there is some contamination
associated with the 1.34mJy/beam source to the west of the cluster candidate.
5.6.7.1 Pointed Follow-up Observations
A total of 23 hours of SA pointed observations towards candidate 7 were ob-
tained in July 2011. A thermal noise level of σA2,POI,CL7 = 110µ Jy/beam
was reached. In McAdam only four sources had a flux density greater than
154
5.6 AMI002
4σA2,POI,CL7 and these were modelled. These were the three sources with flux
densities of 1.2mJy/beam, 0.96mJy/beam and 1.34mJy/beam that were previ-
ously discussed and one other source at 02:59:10.7 +25:54:31 with a flux density
of 3.4mJy/beam. Maps of the data before and after source subtraction are shown
in Figure 5.28.
On the source subtracted map we observe a 4σA2,POI,CL7 decrement at the
location of the candidate. We see positive flux density to the east of the candi-
date, which was also observed in the survey observations. This residual extended
structure is likely to be influenced by sidelobes from the decrement and will itself
give some influence to the decrement. However, the synthesized beam indicates
that this is likely to be less than a 10% effect. Otherwise, the source subtraction
of modelled sources shows few residuals.
The largest decrement on the map is a 4σA2,POI,CL7 decrement at the position
of the candidate 7. However, several other 3 and 4σA2,POI,CL7 decrements are also
observed on the map. Often these other decrements are associated with sources
being subtracted with delta-function priors. The jack-knife tests of this follow-up
data shows no contamination.
The derived parameters for this candidate are given in Figure 5.29 and Tables
5.17 and 5.18. The position parameter has a bimodal distribution but McAdam
is able to separate these modes. From the evidences of the mode corresponding to
candidate 7 we find that p = 0.64 (R=1.8) (for the other mode we find p = 0.22
(R=0.28).
155
5.6 AMI002
Cont peak flux =  1.8003E-03 JY/BEAM 
Levs = 1.059E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
02 59 15 00 58 45 30 15 00 57 45 30 15
26 10
05
00
25 55
50
45
Cont peak flux =  5.6280E-04 JY/BEAM 
Levs = 1.085E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
02 59 15 00 58 45 30 15 00 57 45 30 15
26 10
05
00
25 55
50
45
DE
CL
IN
AT
IO
N 
(J2
00
0)
Figure 5.28: Images of the SA pointed observations towards the AMI002 cluster
candidate 7.
5 10
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−400
−200
0
200
400
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−400−200 0 200
4
6
8
10
x 1014
y0/arcsec
−400 0 400
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −600 −400 −200∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−600
−500
−400
−300
−200
−100
β
0.5 1.5 2.5
Figure 5.29: The derived parameters for AMI002 cluster candidate 7. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
156
5.6 AMI002
Table 5.17: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 7.
Parameter Value
z 0.8+0.3−0.3
MT (r200)/h
−1MSun 3.9
+0.8
−1.0 × 1014
rc/h
−1kpc 620+380−610
β 1.1+1.4−0.8
Table 5.18: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 7.
Parameter Value
∆T0/µK −210+53−51
θc/arcsec 220
+100
−100
β 1.6+0.6−0.6
5.6.8 Candidate 8: 6-10-11
In the 6-10-11 data candidate 8 was detected with p = 0.71 and it shows up as a
3σA2,SUR,CL8 decrement on the map. The image of this search triangle is shown
in Figure 5.30. Given the position of the candidate we would expect it to be
detected in the 5-6-10 triangle but it is not (even though a small decrement is
visible on that map). At the position of candidate 8 there is no contamination
on the image of the jack-knifed SA data.
On the source subtracted map we observe several significant positive and
negative features, including candidate 4 (Figure 5.19) and candidate 6 (Figure
5.25). To the south of candidate 8, the positive and negative residuals appear
to be associated with the 3.4mJy/beam source at 02:59:10.7 +25:54:31 – this is
the only source that is likely to have a significant effect on the candidate. The
positive residuals north and east of the candidate do not have LA counterparts.
157
5.6 AMI002
Cont peak flux =  3.5932E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 30 00 02 59 30 00 58 30 00
26 20
15
10
05
00
25 55
50
45
40
35
Cont peak flux = -5.0227E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 01 00 00 30 00 02 59 30 00 58 30 00
26 20
15
10
05
00
25 55
50
45
40
35
Figure 5.30: Same as for Figure 5.7 but for the candidate 8 (found in 6-10-11).
The thermal noise in the region of the candidate is σA2,SUR,CL8 = 110µJy/beam.
5.6.8.1 Pointed Follow-up Observations
I have obtained 21 hours of SA pointed observations towards this candidate; for
this the thermal noise level is σA2,POI,CL8 = 120µJy/beam. All three sources that
are brighter than 4σA2,POI,CL8 are modelled.
In Figure 5.31 I show images of the data before and after sources have been
subtracted. The source subtracted map has few residuals associated with sources,
the 3.4mJy/beam source that was previously mentioned subtracts leaving no
residual flux density.
At the position of candidate 8 a 4σA2,POI,CL8 decrement is observed. The
candidate is the most significant decrement on the map but there are several
other 3σA2,POI,CL8 decrements. There is also a 4σA2,POI,CL8 increment to the
south east of the map. The 3σA2,POI,CL8 negative residuals to the west of the
map lie close to the positions of candidates 4 and 6.
If a uv taper is applied to the SA data to downweight baselines longer than
600kλ then the decrement is again observed a 4σA2,POI,CL7, however, many of the
other features on the map decrease in significance. This uv tapered image is shown
in Figure 5.33. The brightest feature on the uv tapered map is a 5σA2,POI,CL7
158
5.6 AMI002
positive residual to the south-east of the map. This positive features also can be
seen in the survey data (Figure 5.5) and the data for candidate 7.
The data has been carefully checked for interference and neither of the jack-
knife tests reveal contamination. The derived parameters are shown in Figure
5.32 and Tables 5.20 and 5.20. The derived parameters show that McAdam is
unable to completely isolate this decrement from surrounding residuals, however,
this will have negligible influence on the derived evidences. The p value for this
candidate is 0.56 (R=1.3).
159
5.6 AMI002
Cont peak flux =  4.0820E-03 JY/BEAM 
Levs = 1.237E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 45 30 15 00 58 45 30 15
26 10
05
00
25 55
50
45
Cont peak flux =  5.5522E-04 JY/BEAM 
Levs = 1.223E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 45 30 15 00 58 45 30 15
26 10
05
00
25 55
50
45
DE
CL
IN
AT
IO
N 
(J2
00
0)
Figure 5.31: Images of the SA pointed observations towards the AMI002 cluster
candidate 8.
5 10
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
4
6
8
10
x 1014
y0/arcsec
−500 0 500
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −800 −400 0∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−800
−600
−400
−200
0
β
0.5 1.5 2.5
Figure 5.32: The derived parameters for AMI002 cluster candidate 8. On the left
are the physical parameters and on the right are the phenomenological parame-
ters.
160
5.6 AMI002
Cont peak flux =  7.9081E-04 JY/BEAM 
Levs = 1.547E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 00 02 59 45 30 15 00 58 45 30 15
26 10
05
00
25 55
50
45
DE
CL
IN
AT
IO
N 
(J2
00
0)
Figure 5.33: A uv tapered image of the SA pointed observations towards the
AMI002 cluster candidate 8.
Table 5.19: Mean values and 68% confidence limits for the parameters in the
physical cluster model for candidate 7.
Parameter Value
z 0.8+0.3−0.3
MT (r200)/h
−1MSun 3.7
+0.6
−0.6 × 10−14
rc/h
−1kpc 550+450−540
β 1.3+1.2−1.0e
Table 5.20: Mean values and 68% confidence limits for the parameters in the
phenomenological model for candidate 7.
Parameter Value
∆ −260+110−100
θc/arcsec 170
+110
−100
β 1.5+0.6−0.7
161
5.6 AMI002
5.6.9 Candidate 9: 13-14-18 and 13-17-18
This candidate is detected in 13-14-18 with p = 0.37 and in 13-17-18 at p = 0.07.
Due to the position of this candidate we would not expect to detect it in any of
the other survey runs. The data from 13-14-18 is shown in Figure 5.34 before
and after the sources have been modelled and subtracted.
The only source likely to significantly influence this decrement is the 0.91mJy/beam
point source at 02:58:57.3 +26:24:49. After the sources have been modelled and
subtracted there is little residual flux density and jack-knife tests reveal no con-
tamination. The decrement at the position of candidate 9 is the most significant
feature on the map. The peak decrement has a flux density of 470µJy/beam, this
corresponds to 5σA2,SUR,CL9.
Cont peak flux =  3.1242E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 30 00 02 59 30 00 58 30 00 57 30
26 45
40
35
30
25
20
15
10
05
00
Cont peak flux = -4.9062E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
03 00 30 00 02 59 30 00 58 30 00 57 30
26 45
40
35
30
25
20
15
10
05
00
Figure 5.34: Same as for Figure 5.7 but for the candidate 9 (found in 13-14-18).
The thermal noise in the region of the candidate is σA2,SUR,CL9 = 100µJy/beam.
5.6.9.1 Pointed Follow-up Observations
A total of 25 hours of pointed observations towards this candidate were obtained
between May 2010 and June 2011. The resulting noise level was σA2,POI,CL9 =
120µJy/beam. At this noise level there are seven sources with flux densities above
σA2,POI,CL9. These were modelled by McAdam.
162
5.6 AMI002
The maps of the pointed follow-up observation before and after source sub-
traction are shown in Figure 5.35. In our follow-up observation we observe no
decrement. I have thoroughly checked the data quality in reduce, in total there
were five separate observations and each of these was manually flagged for in-
terference. Also the jack-knife tests have revealed no contamination. It seems
unlikely that point sources are contributing to this non-detection, the main source
that could contribute is the 0.91mJy/beam source that was previously mentioned,
but this subtracts leaving no residuals.
I show the McAdam derived parameters for this non detection in Figure
5.36. These show very little constraint on the position, indicating that no strong
candidate was found within the search area. Note that some parameters appear
constrained, however, this is an effect of our priors. The derived p value is p = 0.23
(R=0.31), this reflects the fact that McAdam was unable to find any strong
candidates.
163
5.6 AMI002
Cont peak flux =  1.7993E-03 JY/BEAM 
Levs = 1.255E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
02 59 45 30 15 00 58 45 30 15 00 57 45
26 35
30
25
20
15
10
Cont peak flux =  7.1161E-04 JY/BEAM 
Levs = 1.244E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
02 59 45 30 15 00 58 45 30 15 00 57 45
26 35
30
25
20
15
10
Figure 5.35: Images of the SA pointed observations towards the AMI002 cluster
candidate 9.
4 6 8
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
4
6
8
x 1014
y0/arcsec
−500 0 500
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −600 −400 −200 0∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−600
−400
−200
0
β
0.5 1.5 2.5
Figure 5.36: The derived parameters for AMI002 cluster candidate 10. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
164
5.7 AMI005
5.7 AMI005
The LA and SA images of the AMI005 field are shown in Figures 5.37 and 5.38
accordingly. In Figure 5.39 I show the AMI005 SA maps after jack-knife tests
have been performed.
Cont peak flux =  2.4661E+02 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 41 40 39 38 37 36
32 00
31 30
00
30 30
Figure 5.37: The map for the LA AMI005 field. In the central region the map
noise is ≈ 50µJy/beam and in the outer region the noise is ≈ 100µJy/beam.
165
5.7 AMI005
Cont peak flux =  1.5011E+02 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 41 40 39 38 37
32 00
31 50
40
30
20
10
00
30 50
40
30
Cont peak flux =  1.0790E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 41 40 39 38 37
32 00
31 50
40
30
20
10
00
30 50
40
30
Figure 5.38: The AMI005 SA signal-to-noise map. On the left sources have not
been subtracted, on the right sources have been subtracted using the McAdam
derived values for their flux and spectral index. The noise level is≈ 110µJy/beam.
Cont peak flux =  9.5101E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 41 40 39 38 37
32 00
31 50
40
30
20
10
00
30 50
40
30
Cont peak flux =  4.4922E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
D
EC
LI
NA
TI
O
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 41 40 39 38 37
32 00
31 50
40
30
20
10
00
30 50
40
30
Figure 5.39: The signal-to-noise map of the AMI005 jack-knifed data set. On the
left the data has been split according to the median data and on the right the
data has been split into plus versus minus baselines. The noise on the map on the
left is ≈ 110µJy/beam and the noise on the map on the right is ≈ 70µJy/beam.
166
5.7 AMI005
In the 30 AMI005 search regions a total 43 modes were detected byMcAdam.
The majority of these modes have a low p value and in this study they are not
investigated further. We detect four distinct modes with p > 0.3, although one
of these modes (15-16-20, p = 1.0 at position 09:40:48.1 +31:26:33) is not in-
vestigated any further due to the severe contamination in this region (see the
jack-knifed SA dataset, Figure 5.39). For the other three candidates I have ob-
tained SA follow-up observations to further investigate the decrements. The
search triangles, derived p values and positions of the three AMI005 candidates
are given in Table 5.21.
Table 5.21: The derived p values for the three modes detected in the AMI002 SA
data that have a highest p > 0.3. Often modes are detected in multiple triangles
(which contain some of the same data), for these I provide the maximum and
minimum derived p and R values. Note that the right ascension and declination
are stated for the candidate detected with the highest p value.
Candidate Fields Highest p Lowest p Right Ascension Declination
(R) (R)
1 3-4-7, 4-7-8 0.93 0.77 09:40:16.5 +30:53:01
(13) (3.4)
2 13-14-18, 14-18-19 0.82 0.01 09:38:48.5 +31:29:54
13-17-18, 18-19-22 (4.7) (0.01)
18-21-22
17-18-21
3 9-10-13 0.42 0.42 09:37:51.6 +31:18:15
(0.80) (0.80)
5.7.1 Candidate 1: 3-4-7 and 4-7-8
A circular decrement of a magnitude of 4σA5,SUR,CL1 and a similar extent to the
SA synthesized beam is detected in the 3-4-7 and 3-4-8 triangles. The derived p
values are p = 0.95 and p = 0.77 respectively. Given the position of the candidate
we would not expect to detect it in any other survey fields. The noise in the region
167
5.7 AMI005
of the candidate is lowest in the 3-4-7 field, the image of these data is shown in
Figure 5.7.1.
There are no sources within 3′ of this candidate. The most likely source to
influence this decrement is the 6.2mJy/beam point source at 09:40:53.1 +30:43:52.
However, this is separated by 12′ from the candidate position and its influence on
the pre source subtracted map is likely to be less than 2% of its peak flux. After
sources have been subtracted the residual source flux is minimal and hence it is
expected that there is negligible contamination from sources at the position of
the candidate. Also the jack-knifed data set does not reveal any contamination
(Figure 5.39).
Cont peak flux =  3.9628E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 00 41 30 00 40 30 00 39 30 00 38 30
31 15
10
05
00
30 55
50
45
40
35
30
Cont peak flux =  5.5330E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 42 00 41 30 00 40 30 00 39 30 00 38 30
31 15
10
05
00
30 55
50
45
40
35
30
Figure 5.40: AMI005 cluster candidate 1 in the data from 3-4-7. In these data
the cluster candidate is detected with p = 0.95. The thermal noise in the region
of the candidate is σA5,SUR,CL1 = 110µJy/beam.
5.7.1.1 Pointed Follow-up Observations
We obtained 29 hours of pointed observations towards this candidate between 4th
June and 7th June 2011. The resulting map before and after sources have been
subtracted is shown in Figure 5.41. For these data we obtained a thermal noise
168
5.7 AMI005
level of σA5,POI,CL1 = 120µJy/beam. Five LA sources have flux densities higher
than 4σA5,POI,CL1 and these were modelled by McAdam.
In our follow-up observation we have not detected this candidate. We do not
observe a decrement greater than 2σA5,POI,CL1 in the data before or after source
subtraction. We do observe a decrement to the north-west of the pointing centre
and this is theMcAdam favoured mode, however, it did not appear in the survey
data. This mode is made slightly larger by the direct subtraction of the LA source
at 09:39:59.0 +30:55:14 with flux density 0.21mJy/beam.
The mild source environment around this candidate means that it is very
unlikely that the data are contaminated by sources. Also, due to the discrepancy
between the survey observation and this pointed follow-up I have taken special
care when manually flagging the data. All interference and bad data that I
noticed was removed and neither of the jack-knife tests that were performed on
the pointed follow-up observation reveal any contamination.
The McAdam derived parameters for this observation are shown in Figure
5.42. These show that the derived position is not consistent with our survey
observation derived position.
169
5.7 AMI005
Cont peak flux =  4.1751E-03 JY/BEAM 
Levs = 1.244E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 41 15 00 40 45 30 15 00 39 45 30 15
31 05
00
30 55
50
45
40
Cont peak flux =  1.0420E-03 JY/BEAM 
Levs = 1.255E-04 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 41 15 00 40 45 30 15 00 39 45 30 15
31 05
00
30 55
50
45
40
Figure 5.41: Images of the SA pointed observations towards the AMI005 cluster
candidate 1.
4 6 8
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
4
6
8
x 1014
y0/arcsec
−500 0 500
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −800 −400 0∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−800
−600
−400
−200
0
β
0.5 1.5 2.5
Figure 5.42: The derived parameters for AMI005 cluster candidate 1. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
170
5.7 AMI005
5.7.2 Candidate 2: 13-14-18 and 14-18-19
A 5σA5,SUR,CL2 elliptical cluster candidate is detected in both 13-14-18 and 14-
18-19 at values of p = 0.82 and p = 0.5 respectively. The noise level in this region
is lowest in 13-14-18 and I present the maps from that search triangle in Figure
5.7.2.
Before the sources are subtracted those that are closest to the candidate and
most likely to influence the decrement have LA measured fluxes of 2.7mJy/beam,
1.0mJy/beam, 1.0mJy/beam and 0.46mJy/beam and lay at 09:38:13.9 +31:31:48,
09:38:20.3 +31:31:28, 09:38:38.6 +31:25:35 and 09:38:26.0 +31:28:40 respectively.
None of these sources are extended on the LA maps.
All sources subtract well and the largest residual flux density is 3σA5,SUR,CL2.
The sidelobes of this residual will cause minimal contamination to the observed
decrement. The negative feature observed at 09:37:51.6 +31:18:15 is AMI005
candidate 3 and is discussed further in Section 5.7.3.
On the jack-knifed SA map (Figure 5.39) we see no significant contamination
with the region of the candidate.
Cont peak flux =  3.4483E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 40 30 00 39 30 00 38 30 00 37 30 00
31 50
45
40
35
30
25
20
15
10
05
Cont peak flux = -5.0868E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 40 30 00 39 30 00 38 30 00 37 30 00
31 50
45
40
35
30
25
20
15
10
05
Figure 5.43: The AMI005 search triangle 13-14-18 in which the AMI005 cluster
candidate 2 is detected with p = 0.82. The thermal noise in the region of the
candidate is σA5,SUR,CL2 = 110µJy/beam.
171
5.7 AMI005
5.7.2.1 Pointed Follow-up Observations
We gathered 27 hours of pointed observations towards this candidate in June 2011
and obtained a thermal noise of σA5,POI,CL2 = 95µJy/beam. The resulting map
before and after sources have been subtracted is shown in Figure 5.44. A total of
10 LA sources have flux densities greater than 4σA5,POI,CL2 and were modelled .
Our image of the follow-up data shows that although the sources are sub-
tracted very well there is only a 3σA5,POI,CL2 decrement at position of candidate
2, but there are several other decrements of similar magnitude. McAdam is
unable to constrain the position of the cluster and this is represented in the
multi-model distribution of the McAdam derived parameters (Figure 5.45). Be-
cause the McAdam derived position is not constrained we are unable to extract
any meaningful p value from this observation.
The data has been carefully checked for interference and neither of the jack-
knife tests that were performed on these observations revealed any contamination
in the data.
It should be noted that the synthesized beam for this follow-up observation
is highly elliptical. Ideally more observations will be gathered in order to obtain
a more circular beam.
172
5.7 AMI005
Cont peak flux =  2.2692E-03 JY/BEAM 
Levs = 9.835E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 39 45 30 15 00 38 45 30 15 00 37 45
31 40
35
30
25
20
Cont peak flux =  5.1975E-04 JY/BEAM 
Levs = 9.757E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 39 45 30 15 00 38 45 30 15 00 37 45
31 40
35
30
25
20
Figure 5.44: Images of the SA pointed observations towards the AMI005 cluster
candidate 2.
4 6
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−500
0
500
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
3
4
5
6
7
x 1014
y0/arcsec
−500 0 500
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −600 −400 −200 0∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−600
−400
−200
0
β
0.5 1.5 2.5
Figure 5.45: The derived parameters for AMI002 cluster candidate 10. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
173
5.7 AMI005
5.7.3 Candidate 3: 9-10-13
An elliptical decrement is observed in the 9-10-13 triangle with a significance of
4σA5,SUR,CL3. This is also detected by McAdam and the Bayesian evidences are
used to calculate p = 0.41. The image of these data is shown in Figure 5.46.
The source environment around this candidate is complex and there are many
sources that are likely to influence the magnitude and shape of the decrement.
The two brightest sources that are close to the candidate are the 4.9mJy/beam
source at 09:37:37.9 +31:22:41 and the 4.5mJy/beam source at 09:38:17.4 +31:18:54.
There are a further eight fainter LA sources within ≈ 10′ of the cluster candi-
date, these have fluxes between 2.4mJy/beam and 0.27mJy/beam, none of these
are extended. McAdam proficiently models these sources and after subtraction
there a few residuals, the largest of which appears to be associated with the
4.9mJy/beam source.
Cont peak flux =  3.8178E+01 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 40 00 39 30 00 38 30 00 37 30 00 36 30
31 40
35
30
25
20
15
10
05
00
30 55
Cont peak flux =  5.2585E+00 RATIO   
Levs = 1.000E+00 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 40 00 39 30 00 38 30 00 37 30 00 36 30
31 40
35
30
25
20
15
10
05
00
30 55
Figure 5.46: AMI005 search triangle 9-10-13. AMI005 candidate 3 is detected
with p = 0.41. The thermal noise in the region of the candidate is σA5,SUR,CL3 =
120µJy/beam.
174
5.7 AMI005
5.7.3.1 Pointed Follow-up Observations
A total of 28 hours SA pointed follow-up observations were conducted between
June 13th 2011 and June 16th 2011. From these observations a thermal noise level
of σA5,POI,CL3 = 90µJy/beam was obtained. A map of the data before and after
source subtraction is shown in Figure 5.47. With flux densities above 4σA5,POI,CL3
there are 14 sources. The 0.25mJy/beam source at 09:37:47.1 +31:20:02 is also
modelled because it is very close to the candidate.
Unlike all other pointed follow-up observations I have not used Gaussian priors
on the source positions and instead I use delta-function priors. The reason for
this is that 15 sources are modelled and the dimensionality of the problem would
be too large if McAdam was allowed to model four parameters for each source.
McAdam has modelled the sources well and on the source subtracted maps
the largest flux density residuals are 3σA5,POI,CL3. We do observe a 3σA5,POI,CL3
decrement close to the pointing centre. However, it can be seen from theMcAdam
derived parameters (Figure 5.48) that the decrement west of the pointing centre is
preferred. Neither of these decrements are well constrained byMcAdam and it is
a possibility that both of these decrements are associated with the 4.9mJy/beam
source.
175
5.7 AMI005
Cont peak flux =  3.6089E-03 JY/BEAM 
Levs = 9.201E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 38 45 30 15 00 37 45 30 15 00 36 45
31 30
25
20
15
10
05
Cont peak flux =  4.8005E-04 JY/BEAM 
Levs = 9.105E-05 * (-10, -9, -8, -7, -6, -5, -4,
-3, -2, 2, 3, 4, 5, 6, 7, 8, 9, 10)
DE
CL
IN
AT
IO
N 
(J2
00
0)
RIGHT ASCENSION (J2000)
09 38 45 30 15 00 37 45 30 15 00 36 45
31 30
25
20
15
10
05
Figure 5.47: Images of the SA pointed observations towards the AMI005 cluster
candidate 3.
4 6
x 1014MT(r200)/h
−1MSun
y 0
/a
rc
se
c
−400
−200
0
200
400
z
0.5
1
1.5
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
x0/arcsec
M
T(r
20
0)/
h−
1 M
Su
n
−500 0 500
3
4
5
6
7
x 1014
y0/arcsec
−400 0 400
z
0.5 1 1.5
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5 −300 −200 −100∆ T0/muK
β
0.5
1
1.5
2
2.5
θ
c
/arcsec
∆ 
T 0
/m
uK
100 300 500
−300
−250
−200
−150
−100
−50
β
0.5 1.5 2.5
Figure 5.48: The derived parameters for AMI005 cluster candidate 3. On the
left are the physical parameters and on the right are the phenomenological model
parameters.
176
5.8 Survey Source Properties
5.8 Survey Source Properties
In the AMI002 field we detect a total of 210 sources on the LA maps with flux
densities in the range 22mJy/beam to 0.20mJy/beam; 13 of these sources are ex-
tended. In the AMI005 field we detect a total of 239 sources on the LA maps with
flux densities in the range 41mJy/beam to 0.20mJy/beam, 11 of these sources
are extended.
All sources have LA measured flux densities and the majority of the sources
have their SA flux density modelled in McAdam. I compare the McAdam flux
density to the LA measured flux density. A systematic discrepancy between these
two flux values would reveal a systematic difference between the flux estimates of
the two arrays. Some sources will be modelled in several search triangles, hence
for a single LA measured flux density there are often several McAdam derived
flux densities. When several modes have been detected within a search triangle I
use the derived source parameters from the mode with the highest evidence.
Figure 5.49 is a histogram of the ratio of the McAdam flux density to the
LA flux density for all sources from both AMI002 and AMI005 sources. I find
that the best-fit Gaussians have a peak at ≈ 1.0 and a σ ≈ 0.2.
In Figure 5.50 I plot the ratio of McAdam to LA flux density as a function of
the LA flux density. Here it can be seen that as the LA flux increases the agree-
ment between the McAdam flux and the LA flux improves. This is especially
obvious for the AMI002 sources.
177
5.8 Survey Source Properties
 0
 10
 20
 30
 40
 50
 60
 70
 80
 90
 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
C
o
u
n
t
McAdam/LA
 0
 10
 20
 30
 40
 50
 60
 70
 80
 0  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6
C
o
u
n
t
McAdam/LA
Figure 5.49: A histogram of the McAdam source flux divided by the LA fluxes.
The histogram has been fitted with a Gaussian. On the left are the results from
the AMI002 field, the amplitude of the Gaussian is 81, the peak is at 0.94 and
σ = 0.18. On the right are the results from the AMI005 field, here the amplitude
is 71, the peak is at 0.98 and σ = 0.18.
178
5.9 Conclusions
 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2
 0.1  1  10  100
M
cA
d
a
m
 f
lu
x/
L
A
 f
lu
x
LA flux (mJy)
 0
 0.2
 0.4
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 0.1  1  10  100
M
cA
d
a
m
 f
lu
x/
L
A
 f
lu
x
LA flux (mJy)
M
cA
d
a
m
 f
lu
x/
L
A
 f
lu
x
Figure 5.50: The McAdam source flux divided by the LA fluxes as a function of
the LA flux. On the left are the AMI002 sources and on the right are the AMI005
sources.
Both Figures 5.49 and 5.50 demonstrate that there is no systematic offset
between the LA and SA source fluxes. The histograms plotted in Figure 5.49 are
well fit by Gaussians with a standard deviation of 20%. However, these Gaussian
fits underestimate the tails of the histograms. These fits show that using a 40%
prior on the LA flux density measurement is reasonable but in practice a 20%
prior could be used without significant effects on the source fluxes.
5.9 Conclusions
During the course of my investigations I analysed two deg2 fields of the AMI
blind survey data. I have conducted pointed follow-up SA observations for all
candidates that were discovered. I found the following:
• In analysis of the AMI002 survey data, nine candidates were discovered
with p values greater than 0.3. These have significances on the map of
3σSA,SUR to 6σSA,SUR. Follow-up observations of these candidates revealed
that several false positives were detected and that candidates 5 and 9 were
179
5.10 Future Work
not detected in the follow-up observations. The other seven candidates were
again detected with p > 0.3 and significances between 3σSA and 8σSA.
• In the AMI005 survey data only three candidates were discovered with
derived p values greater than 0.3. In the follow-up observations none of
these three candidates were detected by McAdam and no meaningful p
values were derived. The most promising is candidate 2, which was detected
at 3σSA in the follow up observations.
• The follow-up observations have proved vital for checking the candidates in
the survey field, especially for clusters originally detected with low p values.
All 12 candidates were followed-up; in these pointed observations, five of
the candidates disappeared and seven remained. Several of these seven
remaining candidates would benefit from deeper observations with the aim
of obtaining more definite results.
• Two cluster candidates discovered in the AMI002 field were particularly
convincing – candidates 1 and 2. These had the highest derived R values
(4.4 × 104 and 9.5 × 102 respectively) of all the clusters detected in the
survey and were the highest signal-to-noise detections were in the follow-up
observations (5σ and 8σ respectively).
• The McAdam derived source fluxes agree well with the LA measurements.
A Gaussian with a standard deviation of 20% of the source flux will be
suitable for future analyses of the AMI survey data.
5.10 Future Work
• The analysis of the AMI002 field would be more robust if more pointed
observations were obtained towards candidates 3, 4, 7 and 8.
• AMI005 candidate 2 would benefit from additional observations at an hour
angle chosen to make the synthesized beam of the concatenated data more
circular.
180
5.10 Future Work
• Follow-up observations with other instruments must be obtained for all can-
didates. This is not only necessary to confirm the existence of candidates
but also to determine their redshifts. I have applied for CARMA observa-
tions of the AMI002 candidate 2.
• I have analysed only two fields out of 12. A thorough analysis needs to be
performed on the remaining 10 fields.
• Once the AMI survey is complete and we have a firm understanding of the
selection function and have obtained redshifts for our candidates, then we
can constrain N(M, z).
181
Chapter 6
SZ Observations of LoCuSS
clusters with AMI: High X-ray
Luminosity Sample
I present observations from the SA of eight high X-ray luminosity galaxy clus-
ter systems selected from the Local Cluster Substructure Survey (LoCuSS). The
SZ effect is detected towards seven of these clusters; for three this is the first
published SZ image. For the detected clusters I present posterior probability
distributions for large scale (close to the virial radius) cluster parameters such
as mass, radius and temperature (TSZ,MT ). Combining this sample with that
of AMI Consortium: Rodr´ıguez-Gonza´lvez et al. (2011) provides the first fully
Bayesian analysis of a sizeable, mostly LX limited sample of clusters. By as-
suming priors on fg and the cluster redshift I estimate the value of the cluster
average temperature, TSZ,MT , from the SZ data alone. Where suitable X-ray
spectroscopic temperatures, TX , are available I compare TX with TSZ,MT , an im-
portant scaling relation. I find that there is reasonable correspondence between
TX and TSZ,MT values at low TX , but that for clusters with TX above around
6keV the correspondence breaks down with TX exceeding TSZ,MT .
In this chapter I first highlight the differences between SZ and X-ray obser-
vations, I then describe the cluster sample, the observations and the analysis.
I present maps and derived parameters before comparing the TSZ,MT with TX
measurements from the literature.
182
6.1 X-ray emission and the SZ Effect
6.1 X-ray emission and the SZ Effect
The gas within galaxy clusters has a temperature between 107K and 108K; at
this temperature the thermal emission from the cluster gas appears in the X-ray
part of the spectrum. The emission is predominately from bremsstrahlung and
the X-ray flux density is described by
SX =
1
4pi(1 + z)4
∫
n2eΛ(Te)dl, (6.1)
where Λ(Te) is the electron cooling function and is proportional to the square
root of the electron temperature T
1/2
e (Sarazin 1986).
The observable signal that arises due to the SZ-effect is a change in the ap-
parent temperature of the CMB and is given by Equation 1.26.
The SZ effect is linear in ne and Te, whereas the X-ray emission varies as
n2eT
1/2
e . Hence, from either the properties of the X-ray emission or the SZ effect
the parameters ne, Te and other cluster properties such as the gas mass Mg can
be determined. Due to the differences in the X-ray and SZ effect signals it is
useful to compare the SZ effect observed cluster parameters with those derived
from X-ray observations.
6.2 The LoCuSS Cluster sample
The Local Cluster Substructure Survey (LoCuSS see Smith et al. 2003, 2005)
contains 164 clusters with redshifts between 0.142 and 0.295. The LoCuSS pro-
vides a near-snapshot of clusters in z. It aims to measure the relationship between
the structure of galaxy clusters and the evolution of the hot gas and galaxies that
inhabit them using gravitational lensing data and other observations spanning
the electromagnetic spectrum from the radio to X-ray. In this thesis I focus on
LoCuSS clusters with a declination greater than 20◦ and an X-ray luminosity
(LX) greater than 11 ×1037W over the 0.1-2.4 keV band in the cluster rest frame
(according to Ebeling et al. 1998, 2000, using h50 = 1). Radio source contam-
ination can make it difficult to observe the SZ effect at 16 GHz and I have not
studied the clusters with sources brighter than 10 mJy/beam within 10′ of the
cluster X-ray centre. Note that our redshifts correspond to those cited in Ebeling
183
6.3 Observations
et al. (1998, 2000). I present results from the analysis of eight galaxy cluster
systems; Table 6.1 shows the coordinates, redshifts and X-ray luminosities of
the selected LoCuSS clusters. In AMI Consortium: Rodriguez-Gonzalvez et al.
(2011) AMI observations of LoCuSS clusters with an X-ray luminosity in the
range 7-11 ×1037W (h50 = 1) are presented.
Table 6.1: Coordinates, redshifts and X-ray luminosities of the observed LoCuSS
clusters. Note that Abell 1758B is included even though it is below our luminosity
cut; this is because it is within the field of view of our Abell 1758A observations.
Redshifts and X-ray luminosities are taken from Ebeling et al. (1998, 2000).
Cluster Right ascension Declination Redshift X-ray luminosity
(J2000) (J2000) in 1037W
(h50 = 1)
Abell 586 07:32:12 +31:37:30 0.171 11.12
Abell 611 08:00:56 +36:03:40 0.288 13.60
Abell 773 09:17:54 +51:42:58 0.217 13.08
(or RXJ0917.8+5143)
Abell 781 09:20:25 +30:31:32 0.298 17.22
Abell 1413 11:55:18 +23:24:29 0.143 13.28
Abell 1758B 13:32:29 +50:24:42 0.280 07.25
Abell 1758A 13:32:45 +50:32:31 0.280 11.68
Zw1454.8+2233 14:57:15 +22:20:34 0.258 13.19
(or Z7160)
RXJ1720.1+2638 17:20:10 +26:37:31 0.164 16.12
6.3 Observations
SA pointed observations centred at the X-ray cluster position (Table 6.1) for our
eight clusters were taken during 2007-2010. The observation lengths were in the
range 20-90 hours per cluster before any flagging of the data; the noises on the
SA maps reflect the actual observation time used.
With the SA I observed phase calibrators every hour and used bi-daily ob-
servations of 3C48 or 3C286 for amplitude calibration. With the LA I typically
184
6.4 Bayesian Analysis
conduct 61+19pt hexagonal raster observations centred on the cluster X-ray po-
sition. The 61 pointing centres are separated by 4′; the inner 19 pointings are
observed for approximately six times longer than the outer 42 pointings. Phase
calibrators were observed every ten minutes. Observations were taken over 2009-
2010 and each cluster was observed for 10-25 hours before any flagging of the
data.
All our cluster data were passed through the reduce pipeline which is detailed
in Section 2.6. Thermal noise levels for the SA and the LA maps (σSA and σLA
respectively), and phase calibrators that have been taken from the Jodrell Bank
VLA Survey (Patnaik et al. 1992, Browne et al. and Wilkinson et al.) are
summarised in Table 6.2.
Source finding was carried out in exactly the same manner as for the AMI
blind cluster survey (see Section 5.8).
Table 6.2: Details of AMI observations of LoCuSS clusters.
Cluster σSA σLA Number of LA LA phase calibrator
(mJy) (mJy) 4σLA sources
Abell 586 0.172 0.09 23 J0741+3112
Abell 611 0.106 0.07 23 J0808+408
Abell 773 0.133 0.09 09 J0903+468
or J0905+4850
Abell 781 0.116 0.07 24 J0925+3127
or J0915+2933
Abell 1413 0.130 0.09 17 J1150+2417
Abell 1758A 0.115 0.08 14 J1349+536
Abell 1758B 0.130 0.08 14 J1349+536
Zw1454.8+2233 0.100 0.10 16 J1513+2338
RXJ1720.1+2638 0.084 0.10 17 J1722+2815
6.4 Bayesian Analysis
The priors that I use in our Bayesian analysis differ from those used to analyse
the survey fields. These differences arise because the redshift and the position of
185
6.5 Maps and Derived Cluster Parameters
Table 6.3: Priors used in our Bayesian analysis of LoCuSS clusters.
Parameter Prior
Source position (xs) + or ×: Delta-function using the LA positions.
△: Gaussian centred on the LA positions with σ=5′′.
Source flux densities × or △: Gaussian centred on the
(S0/Jy) LA continuum value with a σ of 0.4S0.
+: Delta-function on the LA value.
Source spectral index (α) × or △: Gaussian centred on the value calculated
from the LA channel maps with σ as the LA error.
+: Delta-function on the LA value.
Redshift (z) Delta-function on the X-ray value (Table 6.1).
Core radius (rc/h
−1
100kpc) Uniform between 10 and 1000.
Beta (β) Uniform between 0.3 and 2.5.
Mass (MT,r200/h
−1
100M⊙) Uniform in log space over,
(0.32− 50) × 1014M⊙h−1100.
Gas fraction (fg) Gaussian prior centred on 0.086, σ=0.02
(Komatsu et al. 2010).
Cluster position (xc) Gaussian prior on the X-ray position,
σ=60′′ (Table 6.1).
the LoCuSS clusters are known. The priors that I have used for these pointed
observations towards known clusters are shown in Table 6.3.
6.5 Maps and Derived Cluster Parameters
For each cluster I present SA maps before and after source subtraction, and
posterior probability distributions of the large-scale cluster parameters obtained
from running the SA data through McAdam. The derived cluster parameters
are given in Table 6.4. I also present Chandra images taken from the Chandra
Data Archive. In Section 6.6 I compare our derived cluster temperatures with
large-radius X-ray temperatures (r ≈ 500kpc) taken from the literature.
I present the source-subtracted maps with a uv taper of 600kλ (a Gaussian
taper of value 1.0 at 0kλ falling to 0.3 at 600kλ) since the shorter SA baselines
186
6.5 Maps and Derived Cluster Parameters
are more sensitive to the large angular size of the SZ-effect signal. Maps before
source subtraction have been cleaned with a single box over their total extents,
whilst source-subtracted maps have been cleaned with a tight box around the
SZ signals. All maps are contoured at ±2σ, ±3σ, ±4σ etc ., where σ is stated in
the caption that is output with the aips image. For pre-source subtracted maps
σ is also stated in Table 6.2. On all AMI maps negative contours are dashed and
positive contours are solid.
6.5.1 Abell 586
Our SA maps and the parameters that have been measured are presented in
Figure 6.1. I have overlayed our map on an X-ray Chandra image; the cluster
centroids match and an extension of the cluster towards the south is observed.
The SZ effect from Abell 586 has previously been observed with OVRA/BIMA
by LaRoque et al. (2006) and Bonamente et al. (2006). LaRoque et al. apply an
isothermal β-model to SZ and Chandra X-ray observations and find Mg(r2500) =
2.49 ± 0.32 × 1013M⊙ and Mg(r2500) = 2.26+0.13−0.11 × 1013M⊙ respectively (using
h70 = 1). In addition, they determine an X-ray spectroscopic temperature of the
cluster gas of ≈ 6.35keV between a radius of 100kpc and r2500; r2500 is the radius
at which the average cluster density falls to 2500 times the critical density at
that redshift and is determined from Chandra observations by Bonamente et al.
(2006). In comparison, Okabe et al. (2010) use Subaru to calculate the cluster
mass from weak lensing by applying a Navarro, Frenk & White (NFW; Navarro
et al. 1995) profile. They find MT(r2500) = 2.41
+0.45
−0.41 × 1014M⊙, whilst at large
radii they find MT(r500) = 4.74
+1.40
−1.14 × 1014M⊙ (using h70 = 1).
Abell 586 has been studied extensively in the X-ray e.g. Allen (2000) and
White (2000). A recent analysis of the temperature profile (Cypriano et al.,
2005) shows how the temperature falls from ≈ 9 keV at the cluster centre to
≈ 5.5keV at a radius ≈ 280′′. Cypriano et al. have used the Gemini Multi-
Object Spectrograph together with X-ray data taken from the Chandra archive
to measure the properties of Abell 586. They compare mass estimates derived
from the velocity distribution and from the X-ray temperature profile and find
that both give very similar results, Mg ≈ 0.46 × 1014M⊙ within 1.3h−170 Mpc.
187
6
.5
M
a
p
s
a
n
d
D
e
r
iv
e
d
C
lu
ste
r
P
a
r
a
m
e
te
r
s
Table 6.4: Derived values for cluster parameters.
Cluster name MT (r200) MT (r500) Mg(r200) Mg(r500) r200 r500 fg(r500) TSZ,MT (r200)
×1014 ×1014 ×1013 ×1013 ×10−1 ×10−1
h−1100M⊙ h
−1
100M⊙ h
−2
100M⊙ h
−2
100M⊙ h
−1
100Mpc h
−1
100Mpc h
−1
100 keV
Abell 586 5.1± 2.4 2.1± 1.1 4.3± 2.0 2.6± 0.8 1.2± 0.2 6.6± 1.1 1.4± 0.4 5.2± 1.6
Abell 611 4.0± 0.8 2.0± 0.5 3.5± 0.6 2.8± 0.3 1.1± 0.1 6.3± 0.5 1.5± 0.4 4.5± 0.6
Abell 773 3.6± 1.3 1.7± 0.7 3.1± 1.1 2.1± 0.5 1.1± 0.1 6.0± 0.8 1.4± 0.4 4.1± 1.0
Abell 781 4.1± 0.8 2.0± 0.5 3.6± 0.6 2.9± 0.4 1.1± 0.1 6.3± 0.5 1.5± 0.4 4.5± 0.6
Abell 1413 4.0± 1.0 1.9± 0.6 3.5± 0.8 2.7± 0.4 1.1± 0.1 6.6± 0.7 1.5± 0.4 4.4± 0.8
Abell 1758B 4.4± 2.2 2.2± 1.2 3.7± 1.8 2.2± 0.6 1.1± 0.2 6.4± 1.2 1.2± 0.4 4.6± 1.5
Abell 1758A 4.1± 0.7 2.5± 4.4 3.6± 0.5 3.4± 0.4 1.1± 0.1 6.8± 0.4 1.4± 0.3 4.5± 0.5
RXJ1720.1+2638 2.0± 0.4 1.2± 0.2 1.7± 0.3 1.6± 0.3 0.9± 0.1 5.6± 0.4 1.4± 0.3 2.8± 0.4
188
6.5 Maps and Derived Cluster Parameters
They suggest that the cluster is spherical and relaxed with no recent mergers.
The elongation of the SZ signal on our map (Figure 6.1) suggests non-sphericity.
6.5.2 Abell 611
The SA maps, large-scale cluster parameters and a Chandra image of Abell 611
in Figure 6.2. The Donnarumma & Ettori (2011) analysis of the Chandra achieve
data shows that the X-ray isophotes are quite circular, the surface brightness
profile is smooth and the brightest cluster galaxy lies at the centre of the X-ray
emission. These results indicate that the cluster is relaxed. From the X-ray
data, the cluster mass was estimated using an NFW profile, spherical symme-
try and hydrostatic equilibrium to be 9.32±1.39×1014M⊙ (within a radius of
1.8±0.5 Mpc). However, the Donnarumma et al. analysis of strong lensing data
indicates that the cluster mass could be closer to 4.68±0.31×1014M⊙ (within a
radius of 1.5±0.2 Mpc. Note that the values quoted from Donnarumma et al.
are an example of their mass estimates; from fitting different models they find
that the estimated mass varies significantly (between 9.32–11.11×1014M⊙ for the
X-ray mass and between 4.01–6.32×1014M⊙ for the lensing mass). Their mass
estimates use h70 = 1. Several other analyses of Chandra data produce compa-
rable mass estimates (e.g. Schmidt & Allen 2007, Morandi et al. 2007, Morandi
& Ettori 2007 and Sanderson et al. 2009).
Romano & et al (2010) perform a weak lensing analysis of Abell 611 using
data from the Large Binocular Telescope. With an NFW profile they estimate
MT,r200 = 4–7×1014M⊙ and r200 = 1400 − 1600kpc, for h70 = 1. These are in
agreement with the values obtained from Subaru weak lensing observations by
Okabe et al.
Using GMRT observations Venturi et al. (2008) concluded that Abell 611 has
no radio halo at 610MHz. Abell 611 has also previously been observed in the SZ
at 15 GHz by Grainger et al. (2002) and Zwart et al. (2010), and at 30 GHz by
Bonamente et al. (2004), Bonamente et al. (2006) and LaRoque et al.
From the analysis of the AMI SA observations of Abell 611 presented in this
paper I find that MT,r200 = 4.0
+0.3
−0.4×1014M⊙. Note that the mass obtained is
significantly smaller than the result given in Zwart et al. (2010); however, their
189
6.5 Maps and Derived Cluster Parameters
Abell 586
0.05 0.1 0.15
fgas,r
200
/h−1
y 0
/a
rc
se
c
−100
−50
0
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−50 0 50
0.05
0.1
0.15
y0/arcsec
−100−50 0
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.1: The top left image shows the SA map before subtraction, the map in
the middle left has had the sources removed, the top right panel shows the cluster
parameters that are sampled from in our Bayesian analysis and the middle right
plot presents several cluster parameters derived from our sampling parameters.
The image at the bottom shows the Chandra X-ray map overlayed with SA
contours.
190
6.5 Maps and Derived Cluster Parameters
MT estimates are biased high. The bias occurs because they used a low-radius X-
ray temperature as a constant temperature throughout the cluster, as is explained
by them and in Olamaie et al. (2010). The SZ maps presented in this paper are
similar to those in Zwart et al. (2010); both sets of observations indicate that
the cluster is extended in the NW direction. However, the analysis presented in
this paper differs from that by Zwart et al. (2010) who sample from temperature
and Mg,r200 and derive MT,r200 under the additional assumption of hydrostatic
equilibrium. Instead MT,r200 and fg,r200 have been sampled from and T has been
calculated using the M-T scaling relation given in Rodr´ıguez-Gonza´lvez et al.
(2010). The differences between these two models are described in detail by
Olamaie et al. who demonstrate that the mass estimated using the technique
in this paper produces a more reliable value and that the Zwart et al. (2010)
analysis underestimates the values for Mg,r200 and fg,r200. The values of β and
rc/h
−1
100kpc presented here agree with those in the Zwart et al. (2010) analysis.
There is no significant contamination from radio sources and we detect the
cluster with a high signal-to-noise ratio. A comparison of the SZ-effect image
and the Chandra map shows that the centres of the SZ and X-ray emission are
coincident.
6.5.3 Abell 773
In Figure 6.3 I show the AMI SA maps of Abell 773, a Chandra X-ray map
and the cluster parameters derived from our analysis. The SZ effect associated
with Abell 773 has been observed several times (Grainge et al. 1993, Carlstrom
et al. 1996, Saunders et al. 2003, Bonamente et al. 2006, LaRoque et al.). Most
recently, Zwart et al. (2010) observed the cluster and found a cluster mass of
MT,r200 = 1.9
+0.3
−0.4×1015M⊙ using h70 = 1; however, their MT estimates are biased
high – see Section 6.5.2.
Inspection of a 10′×10′ region of the Sloan Digital Sky Survey (SDSS1 ) centred
1Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation,
the Participating Institutions, the National Science Foundation, the U.S. Department of Energy,
the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max
Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site
is http://www.sdss.org/.
191
6.5 Maps and Derived Cluster Parameters
A611
0.06 0.1 0.14
fgas,r
200
/h−1
y 0
/a
rc
se
c
−20
0
20
40
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−20 0 20
0.06
0.08
0.1
0.12
0.14
y0/arcsec
−20 0 20 40
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.2: The top left image shows the SA map before subtraction, the map in
the middle left has had the sources removed, the top right panel shows the cluster
parameters that are sampled from in our Bayesian analysis and the middle right
plot presents several cluster parameters derived from our sampling parameters.
The image at the bottom shows the Chandra X-ray map overlayed with SA
contours. 192
6.5 Maps and Derived Cluster Parameters
on Abell 773 reveals a complex galaxy distribution with some EW extension.
Our observations support this extension, but there is no detailed correspondence
between the galaxy and gas distributions. The Chandra observations appear to
show little if any such extension. There is no significant contamination from radio
sources and we detect the cluster with a high signal to noise ratio.
For this cluster, Barrena et al. (2007) present an intensive study of the optical
data from the Telescopio Nazionale Galileo (TNG) telescope and X-ray data from
the Chandra data archive. They find two peaks in the velocity distribution of the
cluster members which are separated by 2′ along the E-W direction. Two peaks
can also be seen in the X-ray, although these are along the NE-SW direction.
Barrena et al. estimate the virial mass of the entire system to be Mvir = 1.2-
2.7×1015h−170 M⊙. Giovannini et al. (1999) reported the existence of a radio halo in
Abell 773. This feature, typical of cluster mergers, was confirmed with 1.4 GHz
VLA observations by Govoni et al. (2001). Zhang et al. (2008) used XMM-Newton
to study Abell 773 and found M500 = 8.3 ±2.5 ×1014M⊙, where r500 = 1.33Mpc;
they assumed isothermality, spherical symmetry and h70 = 1. Govoni et al.
(2004) present a Chandra temperature map and an X-ray image of Abell 773;
they estimate a mean temperature of 7.5±0.8 keV within a radius of 800 kpc
(h70 = 1).
6.5.4 Abell 781
AMI SA maps, derived parameters and a Chandra observation of the Abell 781
cluster are presented in Figure 6.4. From X-ray observations with Chandra and
XMM-Newton (Sehgal et al. 2008) it is apparent that Abell 781 is a complex
cluster system. The main cluster is surrounded by three smaller clusters, two
to the East of the main cluster and one to the West. They estimate the mass
of the clusters assuming a NFW matter density profile; the results indicate that
the cluster mass of Abell 781 within r500 is 5.2
+0.3
−0.7×1014M⊙ from XMM-Newton
andChandra X-ray observations or 2.7+1.0−0.9×1014M⊙ from the Kitt Peak Mayall
4-m telescope lensing observations (where r500 is 1.09
+0.04
−0.04 and 0.89
+0.10
−0.12 respec-
tively). Alternatively, Zhang et al. use XMM Newton observations to estimate
193
6.5 Maps and Derived Cluster Parameters
Abell 773
0.05 0.1 0.15
fgas,r
200
/h−1
y 0
/a
rc
se
c
−50
0
50
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−50 0 50
0.05
0.1
0.15
y0/arcsec
−50 0 50
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.3: The top left image shows the SA map before subtraction, the map in
the middle left has had the sources removed, the top right panel shows the cluster
parameters that are sampled from in our Bayesian analysis and the middle right
plot presents several cluster parameters derived from our sampling parameters.
The image at the bottom shows the Chandra X-ray map overlayed with SA
contours. 194
6.5 Maps and Derived Cluster Parameters
M500 = 4.5 ±1.3 ×1014M⊙, where r500 = 1.05Mpc, assuming isothermality and
spherical symmetry. Both Zhang et al. and Sehgal et al. use h70 = 1.
The main cluster of Abell 781 is also known to contain a diffuse peripheral
source at 610MHz; this was observed with the GMRT by Venturi et al. (2008).
6.5.5 Abell 1413
The SA maps before and after source subtraction are shown in Figure 6.5 together
with derived cluster parameters and an overlay of our SZ image on a Chandra X-
ray map. Abell 1413 has been observed in the X-ray by XMM-Newton (e.g. Pratt
& Arnaud 2005), Chandra (e.g. Vikhlinin et al. 2005 and Bonamente et al. 2006)
and most recently by the low background Suzaku satellite (Hoshino et al. 2010);
SZ images have been made of Abell 1413 with the Ryle Telescope at 15 GHz
(Grainge et al. 1996) and with OVRO/BIMA at 30 GHz (LaRoque et al. and
Bonamente et al. 2006). These analyses indicate that Abell 1413 is a relaxed clus-
ter with no evidence of recent merging despite its elliptical morphology. Between
the X-ray observations there is good agreement in the temperature and density
profiles of the cluster out to half the virial radius. Hoshino et al. measure the vari-
ation of the electron temperature with radius, finding a temperature of 7.5keV at
the centre and 3.5keV at r200. They assume spherical symmetry, an NFW density
profile and hydrostatic equilibrium to calculate MT,r200 = 6.6±2.3×1014h−170 M⊙;
where r200 = 2.24h
−1
70 Mpc. Zhang et al. use XMM-Newton to study Abell 1413
and find M500 = 5.4 ±1.6 ×1014M⊙, where r500 = 1.18Mpc; they assume isother-
mality, spherical symmetry and h70 = 1.
Recent VLA observations (Govoni & Murgia 2009) indicate that there is dif-
fuse 1.4-GHz emission associated with the cluster – this may be due to a mini-halo
around the cluster.
In the SA observations the SZ decrement has been detected at high signifi-
cance. The cluster mass has been determined to beMT,r200 = 4.0
+0.3
−0.6×1014h−1100M⊙
and r200 = 1.14
+0.4
−0.5h
−1
100kpc; both these values are comparable with the Hoshino
et al. results.
The source environment around the cluster at 16GHz is reasonable: the
brightest source is 14mJy (11:55:36.63 +23:13:50.1), but this is 700′′ from the
195
6.5 Maps and Derived Cluster Parameters
A781
0.06 0.1 0.14
fgas,r
200
/h−1
y 0
/a
rc
se
c
20
40
60
80
100
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
0 20 40
0.06
0.08
0.1
0.12
0.14
y0/arcsec
50 100
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.4: The top left image shows the SA map before subtraction, the map in
the middle left has had the sources removed, the top right panel shows the cluster
parameters that are sampled from in our Bayesian analysis and the middle right
plot presents several cluster parameters derived from our sampling parameters.
The image at the bottom shows the Chandra X-ray map overlayed with SA
contours. 196
6.5 Maps and Derived Cluster Parameters
cluster X-ray centre. After this bright source is subtracted from our data it is left
with a low level of residual flux density on the map; it is unlikely that this resid-
ual flux significantly contaminates our cluster detection or parameters. Both the
X-ray map and the SZ image indicate that the cluster is elliptical and extended
in the N-S direction.
6.5.6 Abell 1758
An analysis of ROSAT images clearly shows that this system consists of two inter-
acting clusters, Abell 1758A and Abell 1758B, separated by 8′ (Rizza et al. 1998).
In Figure 6.6 I present a single map that contains combined data from observa-
tions towards both clusters and the derived parameters for cluster Abell 1758A.
I present the derived parameters for cluster Abell 1758A and X-ray maps from
both the Chandra data archive and ROSAT 1. In Figure 6.7 I show the derived
parameters for cluster Abell 1758B.
A detailed analysis of XMM-Newton and Chandra by David & Kempner
(2004) indicates that the clusters Abell 1758A and Abell 1758B are likely to
be in an early stage of merging and that both of these clusters are also undergo-
ing major mergers with other smaller systems. A recent analysis of Spitzer/MIPS
24µm data by Haines et al. (2009) classifies Abell 1758 as the most active sys-
tem they have observed at that wavelength. They also identify numerous smaller
mass peaks and filamentary structures, which are likely to indicate the presence
of infalling galaxy groups, in support of the David & Kempner observations.
Zhang et al. use XMM-Newton to study Abell 1758A and found M500 = 1.1 ±0.3
×1015M⊙, where r500 = 1.43Mpc. They assume isothermality, spherical symmetry
and h70 = 1.
6.5.7 Zw1454.8+2233
Several sources are detected close to the cluster centre – a point source with a
flux density of 7.97 mJy at 14:56:59.11 +22:18:55.97 and a 4.67 mJy source at
14:57:25.38 +22:37:33.03. No SZ effect is detected from this cluster even though
1I acknowledge the use of NASA’s SkyView facility (http://skyview.gsfc.nasa.gov) located
at NASA Goddard Space Flight Center.
197
6.5 Maps and Derived Cluster Parameters
Abell 1413
0.04 0.08 0.12
fgas,r
200
/h−1
y 0
/a
rc
se
c
−120
−100
−80
−60
−40
−20
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−40 0 40
0.04
0.06
0.08
0.1
0.12
0.14
y0/arcsec
−120 −80 −40
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.5: The top left image shows the SA map before subtraction, the map in
the middle left has had the sources removed, the top right panel shows the cluster
parameters that are sampled from in our Bayesian analysis and the middle right
plot presents several cluster parameters derived from our sampling parameters.
The image at the bottom shows the Chandra X-ray map overlayed with SA
contours. 198
6.5 Maps and Derived Cluster Parameters
Abell 1758A
0.06 0.1 0.14
fgas,r
200
/h−1
y 0
/a
rc
se
c
150
160
170
180
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−120 −100 −80
0.06
0.08
0.1
0.12
0.14
y0/arcsec
160 180
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.6: The top left image shows the SA map before subtraction, the map in the
middle left has had the sources removed. The maps shown here are primary beam
corrected signal-to-noise maps cut off at 0.3 of the primary beam. The noise level is
≈ 115µJy towards the upper cluster (Abell 1758A) and ≈ 130µJy towards the lower
cluster (Abell 1758B). The source subtracted uv tapered map at the middle left has
a noise level ≈ 20% higher. The top right panel shows the cluster parameters that
are sampled from in our Bayesian analysis and the middle right plot presents several
cluster parameters derived from our sampling parameters. The image at the right
bottom shows the ROSAT PSPC X-ray map overlayed with SA contours, whilst the
bottom left shows a Chandra image with SA countours.
199
6.5 Maps and Derived Cluster Parameters
Abell 1758B
0.05 0.1 0.15
fgas,r
200
/h−1
y 0
/a
rc
se
c
−340
−320
−300
−280
−260
−240
−220
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
0 50 100
0.05
0.1
0.15
y0/arcsec
−340−300−260−220
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.7: On the left I show the cluster parameters that I have sampled from
and on the right I present some cluster parameters derived from our sampling
parameters.
a detection was expected, given the low noise levels of our SA maps. The SA
maps and derived parameters are shown in Figure 6.8. The derived parameters
for this non-detection are as expected: it is found that MT,r200 approaches our
lower prior limit (0.32 × 1014M⊙h−1100) and thatMg shows simliar behaviour; both
r200 and TSZ,MT are well constrained because both these parameters are derived
from MT,r200 which itself is well constrained at the value of its lower prior limit.
Zhang et al. used XMM Newton to study Zw1454.8+2233 and found M500 =
2.4 ±0.7 ×1014M⊙, where r500 = 0.87Mpc. They assumed isothermality, spherical
symmetry and h70 = 1. Venturi et al. (2008) observed the cluster with the GMRT
at 610MHz and found that the cluster contains a core-halo source. This is in
agreement with the value obtained from Subaru weak lensing observations by
Okabe et al. The Chandra X-ray observations (Bauer et al. 2005) also reveal
that Zw1454.8+2233 is a cooling core cluster; these are often associated with
core-halos.
200
6.5 Maps and Derived Cluster Parameters
Zw1454.8+2233
0.040.080.12
fgas,r
200
/h−1
y 0
/a
rc
se
c
−100
0
100
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−100 0 100
0.04
0.06
0.08
0.1
0.12
0.14
y0/arcsec
−100 0 100
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.8: The null detection of Zw1454.8+2233 in SZ. The top left image is the SA
map before subtraction, showing the challenging source environment. the map in the
middle left has had the sources removed, however, no decrement is visible. The top
panel on the right shows the sampling parameters and on the middle right panel I show
the derived cluster parameters, these parameters are what would be expected from a
null detection, they indicate mass with a high probability of being 0.0. The image at
the bottom shows the Chandra X-ray map.
201
6.6 Cluster Temperatures
6.5.8 RXJ1720.1+2638
At 16 GHz the source environment around the cluster is challenging: in our LA
data there is a 3.9 mJy source at the same position as the cluster, and several other
sources with comparable flux densitites < 500′′ from the cluster centre. However,
using our Bayesian analysis to accurately model the positions, flux densities and
spectral indices of these sources such that, after they are subtracted from our SA
maps, a significant decrement is seen. The AMI SA maps before and after source
subtraction are shown in Figure 6.9, as are the derived cluster parameters and
a Chandra image of the cluster. Our SZ-effect map shows that the cluster may
have an irregular shape; there is low signal-to-noise emission to the SE and NW
of the cluster X-ray centroid; however, the centre of the SZ emission is coincident
with the X-ray centroid.
Chandra observations (Mazzotta et al. 2001) indicate that, although the clus-
ter does not have an irregular shape or elongation, it has discontinuities in its
density profile; this may indicate it is in the latter stages of merging. The largest
discontinuity is observed in the SE sector of the cluster and is noted to have
a structure similar to a cold front observed in other merging systems such as
Abell 2142 and Abell 3667. Mazzotta et al. determined the mass profile for the
cluster assuming hydrostatic equilibrium using two distinct regions (SE and NW)
to model the cluster density profile: each region was separately analysed and used
to calculate M1000kpc = 4 ± 10 ×1014h−150 M⊙.
6.6 Cluster Temperatures
In Figure 6.10 I compare the AMI SA observed cluster temperatures within r200
(TSZ,MT ) with large-radius X-ray values (TX) from Chandra or Suzaku that I have
been able to find in the literature. Large radius X-ray temperature values are
used as these ignore the complexities of the cluster core and are representative
of the average cluster temperature within ≈1Mpc which is measured by AMI.
In this plot I have included the derived parameters from the AMI Consortium:
Rodriguez-Gonzalvez et al. (2011) analysis of 11 medium luminosity LoCuSS
clusters. Before comment on these I deal with two technical points. First, for
202
6.6 Cluster Temperatures
RXJ1720.1+2638
0.06 0.1 0.14
fgas,r
200
/h−1
y 0
/a
rc
se
c
−80
−60
−40
r c
/h
−
1 k
pc
200
400
600
800
1000
β
0.5
1
1.5
2
2.5
M
T(r
20
0)/
h−
1 M
Su
n
2
4
6
8
10
x0/arcsec
f ga
s,
r 20
0/h
−
1
−20 0 20 40
0.06
0.08
0.1
0.12
0.14
y0/arcsec
−80 −60 −40
r
c
/h−1kpc
500 1000
β
0.5 1.5 2.5
MT(r200)/h
−1MSun
5 10
2 4 6 8 10
x 1014MT(r500)/h
−1MSun
2 4 6 8 10
x 1013Mg(r500)/h
−2MSun
2 4 6 8 10
x 1013Mg(r200)/h
−2MSun
0 0.1 0.2 0.3
fg(r500)/h
−1
0.5 1 1.5
r500/h
−1Mpc
0.5 1 1.5
r200/h
−1Mpc
0 2 4 6 8 10
T/KeV
Figure 6.9: The top left image shows the SA map before subtraction, the map in
the middle left has had the sources removed, the top right panel shows the cluster
parameters that are sampled from in our Bayesian analysis and the middle right
plot presents several cluster parameters derived from our sampling parameters.
The image at the bottom shows the Chandra X-ray map overlayed with SA
contours. 203
6.6 Cluster Temperatures
Abell 611, I have plotted two X-ray values (from Chandra data); one from the
ACCEPT archive (Cavagnolo et al. 2009) which is higher than our AMI SA
measurement, while the second X-ray measurement from Chandra (Donnarumma
et al.) is consistent with our measurement. Secondly, the ACCEPT archive
r= 475-550kpc temperature for Abell 1758A is 16±7keV and for clarity is not
included on the plot.
Evidently Abell 586, Abell 611 (with the Donnarumma et al. X-ray tem-
perature) and Abell 1413 have corresponding SZ and X-ray temperatures while
Abell 773, Abell 1758A and RXJ1720.1+2638 have X-ray temperatures signifi-
cantly higher than their SZ temperature. The position is made clearer by com-
bining the values with those in Rodr´ıguez-Gonza´lvez et al. (2011). The combined
data are shown in Figure 6.11, in which there is reasonable correspondence be-
tween SZ and X-ray temperatures at lower X-ray luminosity, with excess (over SZ)
X-ray temperatures at higher X-ray luminosity. An exception to this is Abell 1413
which despite its high X-ray luminosity is in good agreement with our SZ value,
but for this cluster I have been able to use Suzuka measurements over r= 700-
1200kpc. It is noteworthy that Abell 773, Abell 1758A and RXJ1720.1+2638 are
major mergers.
In Smith et al. (2005) Chandra temperatures (0.1-2.0Mpc) are compared with
lensing masses within 500 kpc for 10 clusters. The results indicate that disturbed
clusters have higher temperatures. However, Marrone et al. (2009) compare the
SZ Yspherical to lensing masses within 350 kpc for 14 clusters, and find no dis-
crepancy between relaxed and disturbed clusters. Marrone et al. (2009) suggests
that SZ measurements are less sensitive than TX to the complexities of the intra-
cluster medium even at low radius. Our analysis has found that major mergers
have a larger TX (500-700 kpc) than TSZ,MT averaged over the whole cluster. This
suggests that even at large radius mergers affect n2e-weighted TX measurements
more than ne-weighted TSZ,MT measurements. Such an affect could be due to
shocking or clumping.
204
6.6 Cluster Temperatures
 2
 3
 4
 5
 6
 7
 2  4  6  8  10  12
AM
I t
em
pe
ra
tu
re
 (k
eV
)
X-ray temperature (keV)
A586(11.1)
A773(13.1)
A611(13.6)
RXJ1720.1+2638(13.2)
A1413(13.3)
A611*(13.6)
Figure 6.10: The AMI mean temperature within r200 versus the X-ray tempera-
ture, each point is labelled with the cluster name and X-ray luminosity. Most of
the X-ray measurements are large-radius temperatures from the ACCEPT archive
(Cavagnolo et al. 2009) with 90% confidence bars. The radius of the measure-
ments taken from the ACCEPT archive are 400-600kpc for Abell 586, 300-700kpc
for Abell 611, 300-600kpc for Abell 773 and for RXJ1720.1+2638 r = 550-700kpc.
The A1413 X-ray temperature is estimated from the 700-1200kpc measurements
made with the Suzaku satellite (Hoshino et al. 2010), this value is consistant with
Vikhlinin et al. 2005 and Snowden et al. 2008. The Abell 611* temperature is
the 450-750kpc value with σ error bars (Donnarumma & Ettori 2011). The AC-
CEPT archive temperature for Abell 1758A is 16±7keV at r= 475-550kpc with
SZ temperature 4.5±0.5, for clarity this has not been included on the plot.
205
6.6 Cluster Temperatures
 2
 3
 4
 5
 6
 7
 2  4  6  8  10  12
AM
I t
em
pe
ra
tu
re
 (k
eV
)
X-ray temperature (keV)
A586(11.1)
A773(13.1)
A611(13.6)
RXJ1720.1+2638(13.2)
A1413(13.3)
A611*(13.6)
A1423(10.0)
A2111(11.0)
A2146(9.0)
A2218(9.3)
Figure 6.11: The AMI mean temperature within r200 versus the X-ray tempera-
ture including values from Rodr´ıguez-Gonza´lvez et al. (2011). Again Abell 1758A
is not shown.
206
6.7 Conclusions
6.7 Conclusions
I have performed a detailed analysis of eight LoCuSS clusters and found the
following:
• I have obtained good SZ detections for eight clusters and a non-detection for
Zw1454.8+2233. The observed SZ decrements are not spherical but show
significant spatial structure.
• For the seven detected clusters with LX > 11×1037W (h50 = 1), β profiles
have been fit to the cluster signals to findMg,r200 values of 1.7-4.3×1013h−1100M⊙
and values MT,r200 of 2.0-5.1×1014h−1100M⊙.
• For Abell 611 and Abell 773 our values of Mg,r200 and MT,r200 are lower
than those in Zwart et al. (2010) which are thought to be biased high, be-
cause they use a high value for TSZ,MT (estimated from a low-radius X-ray
measurement) and assume this value to be constant throughout the cluster.
• For the six clusters in the work of this paper for which I have found large-
radius r ≥ 500kpc X-ray spectroscopic temperatures in the literature, it
is apparent that the TX and TSZ,MT values correspond reasonably well for
Abell 586, Abell 611 (with the Donnarumma et al. X-ray temperature
rather than the ACCEPT archive value) and Abell 1413, but that cor-
respondence falls away for Abell 773, Abell 1758A and RXJ1720.1+2638
which have a high TX , for these, TSZ,MT is less than TX .
• The picture seems to become clearer – although all of this work involves
only very small numbers – when I add in the data of Rodr´ıguez-Gonza´lvez
et al. (2011). I find that there is reasonable TX :TSZ,MT correspondence for
the six clusters at lower TX but that the correspondence breaks down at
high TX . However, two points are evident. The more general one is that
207
6.7 Conclusions
the breakdown of the TX :TSZ,MT correspondence tends to be associated with
high LX and with major mergers. The more specific one is that Abell 1413
has values of TX and TSZ,MT that correspond yet has high LX : but I have
used TX measured by the Suzaku at very high radius.
• I suspect this points to agreement between large-radius SZ estimates and
larger-radius spectroscopic temperature measurements, but that substantial
mergers bias TX measurements more than TSZ,MT ; however I stress again
that our sample from that and our companion paper is very small.
208
Chapter 7
Conclusions
In this thesis I have outlined the achievements of my work using AMI. Here I
present the conclusions and possible extensions of the work described in previous
chapters.
7.1 Commissioning and Calibration
The performance of both the SA and the LA has been improved by characterising
the lags on the correlators and refining our measurements of the arrays geometry.
Additionally, I have implemented important new routines into the standard data
reduction pipeline, these correct for time average smoothing and significantly
reduce the interference from geostationary satellites.
Importantly, I have produced what are currently the most accurate measure-
ments of the SA and LA primary beams. Knowledge of these beams is essential
in order to obtain accurate flux-density measurements of sources away from the
phase centre. Throughout my time in Cambridge I have assisted with testing and
automating the present standard data reduction pipeline.
I have developed several very useful routines to concatenate and simulate data,
subtract sources and to test for systematics. These routines are regularly used
throughout the AMI Consortium.
Improving and monitoring the performance of the interferometers and the
data reduction pipeline is an ongoing task. For example, inter-array flux-density
calibration is a priority.
209
7.2 AMI blind survey
7.2 AMI blind survey
I have for the first time applied our Bayesian analysis to search blindly for clusters
in the SA survey data. After significant effort testing and characterising the
analysis I have been able to obtain the first blind SZ detections with AMI. In two
deg2 regions the two most significant detections that I have found lie at 3:01:14.70
+26:16:40.78 and 03:00:15.50 +26:14:2.25
There are a further 12 fields of AMI survey data to analyse. Using programs
and techniques that I have developed for this first analysis I hope to continue to
collaborate with the AMI Consortium with the aims of publishing a final cluster
catalogue and coordinating follow-up observations with other instruments.
7.3 Pointed SZ observations
The images and derived parameters from the SZ observations of eight high lu-
minosity LoCuSS clusters when combined with those from AMI Consortium:
Rodriguez-Gonzalvez et al. (2011) provide a significant sample of clusters, which
is a luminosity limited near-snapshot in z. Such observations are excellent for
constraining cluster scaling relations and I have investigated the scaling between
Tx and TSZ . I found an overall agreement in the derived temperatures for relaxed
clusters, and larger discrepancies for major mergers.
AMI has observed all observable LoCuSS clusters with luminosities exceed-
ing 7 ×1037W which have insignificant source contamination. There are many
LoCuSS clusters at lower luminosities and currently we are in the process of
observing these. Additionally, I am in the process of conducting pointed SZ ob-
servations towards the hottest (T > 5keV) clusters in the XCS cluster sample
(Mehrtens et al. 2011). The results from this analysis will be compared to those
obtained from the LoCuSS sample.
210
Appendix A
The Friedmann Equation
In this appendix I present a derivation of the Friedmann equation from the Ein-
stein field equation. A similar derivation can be found many standard text books,
e.g. Peacock (1999) and Peebles (1993).
The Einstein Field Equation is
Guv = Ruv − 1
2
guvR = 8piGTuv, (A.1)
where Guv is the Einstein tensor. I shall begin by calculating the Ricci Tensor
(Ruv) and proceed by calculating the Ricci scalar (R). guv is described according
to the Friedmann-Robertson-Walker metric (Equation 1.7) and the stress energy
tensor, Tuv, is described in Equation 1.10. Throughout the derivation I set c = 1.
The Ricci Tensor (Ruv) is given by
Ruv = Γ
α
uv,α − Γαuα,v + ΓαβαΓβuv − ΓαβvΓβuα, (A.2)
where I have used
Γαuv,α =
δΓαuv
δxα
. (A.3)
Computing the Ricci tensor is time consuming and requires calculations of
many Christoffel symbols. Not all these calculations shall be presented here
however, apart from the the R00 and Rii terms all components reduce to zero. I
shall demonstrate the calculation of the R00 term.
R00 = Γ
α
00,α − Γα0α,0 + ΓαβαΓβ00 − Γαβ0Γβ0α. (A.4)
211
Because Christoffel symbols are equal to zero if both the bottom indices are 0
this can be simplified to
R00 = −Γα0α,0 − Γαβ0Γβ0α. (A.5)
Christoffel symbols are calculated according to
Γuαβ =
guv
2
(
δgαv
δxβ
+
δgβv
δxα
+
δgαβ
δxv
)
. (A.6)
Therefore,
Γα0α =
gαv
2
(
δg0v
δxα
+
δgαv
δx0
+
δg0α
δxv
)
, (A.7)
where guv is the inverse of guv and we know guv from the Friedmann-Robertson-
Walker metric (Equation 1.7). As guv is a diagonal matrix then g
uv is zero if
u 6= v, is -1 at u = v = 0 and 1
a2(t)
at the other points where u = v. This implies
that in Equation A.7 unless v = α, Γα0α = 0.
Γα0α =
gαα
2
(
δg0α
δxα
+
δgαα
δx0
+
δg0α
δxv
)
(A.8)
The first and last term on the right hand side reduce to derivatives of g00 which
is a constant (-1) and hence its derivatives are zero. Hence
Γα0α =
gαα
2
(
δgαα
δx0
)
. (A.9)
The derivative in the above equation is not equal to zero for the spatial coordinates
(3 ≥ α ≥ 1) but for the time coordinate (α = 0) it is zero. The spatial derivatives
can be calculated as follows:
Γ101 =
g11
2
(
δg11
δx0
)
=
1
2a2(t)
δa2(t)
δx0
=
a˙
a
, (A.10)
where x0 = t. The calculation performed above can be use to demonstrate the
property that
Γi0j = Γ
i
j0 = δij
a˙
a
, (A.11)
where here δij is a delta-function and is zero if i 6= j and one if i = j. It is now
possible to substantially simplify Equation A.5 to give
R00 = −δii δ
δt
(
a˙
a
)
− δijδji
(
a˙
a
)2
. (A.12)
212
Using the Einstein summation I note that both δii and δijδji imply a sum over
the three spatial indices. Hence δii = δijδij = 3.
R00 = −3 δ
δt
(
a˙
a
)
− 3
(
a˙
a
)2
(A.13)
Using the quotient rule the time derivation can be determined:
δ
δt
a˙
a
=
a¨a− a˙a˙
a2
=
a¨
a
− a˙
2
a2
. (A.14)
Therefore, the 00 component of the Ricci Tensor is
R00 = −3
(
a¨
a
− a˙
2
a2
)
− 3
(
a˙
a
)2
= −3 a¨
a
. (A.15)
By applying similar working it can also be determined that
Rij = δij(2a˙
2 + aa¨). (A.16)
Hence, if i 6= j then Rij = 0, otherwise,
Rii = 3(2a˙
2 + aa¨). (A.17)
The Ricci scalar can be dervied from Ruv according to
R = guvRuv. (A.18)
Using an Einstein summation and noting that off diagonal terms in both guv and
Ruv are equal to zero we find
R = −R00 + 1
a2
Rii. (A.19)
Putting in R00 and Rii from Equations A.15 and A.17 respectively gives
R = 3
a¨
a
+
1
a2
3(2a˙2 + aa¨) = 6
(
a¨
a
+
a˙2
a2
)
(A.20)
We can now solve the Einstein Field Equation (Equation A.1) for the time
component (00) of the Universe.
G00 = R00 − 1
2
g00R = 8piGT00 (A.21)
213
G00 = −3 a¨
a
− 1
2
(−1)6
(
a¨
a
+
a˙2
a2
)
= 3
(
a˙
a
)2
= 8piGT00 (A.22)
Recalling that T00 = ρ (Equation 1.10) implies
(
a˙
a
)2
=
8piGρ
3
(A.23)
This solution of the Einstein Field Equations is known as the Friedmann equation.
Note that similarly the acceleration equation (1.17) can be derived from the
trace of the Einstein Field Equation.
214
Appendix B
AMI002 LA Source Properties
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
03:01:37.66 +25:41:58.77 21.78* 0.49
03:01:05.45 +25:47:15.96 13.6 0.4
03:01:38.08 +25:21:48.20 13.55 0.82
02:59:55.14 +26:27:25.95 8.36 0.38
03:02:43.07 +26:07:59.01 8.3 0.65
02:58:03.29 +25:31:10.63 5.39 1.0
02:57:18.26 +26:54:07.93 4.51 0.12
03:00:15.82 +26:54:59.54 4.49 -0.0
03:02:20.25 +25:49:40.57 3.67 0.31
02:59:10.70 +25:54:31.31 3.44 1.21
02:58:17.27 +25:38:18.82 3.43 1.67
03:01:39.31 +26:29:31.87 2.98 0.24
03:01:55.72 +27:02:06.25 2.96 1.11
02:57:05.63 +26:07:10.07 2.88 0.64
02:58:34.96 +26:32:16.11 2.84 1.05
02:59:17.30 +27:04:01.64 2.79 0.4
02:56:52.95 +26:55:30.80 2.78 -0.03
03:01:36.46 +25:33:51.90 2.6 1.69
03:01:46.75 +27:00:46.04 2.44 0.64
02:59:32.31 +26:39:51.24 2.35 0.1
03:00:35.40 +26:34:24.95 2.32 1.29
215
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
03:00:27.04 +26:57:34.78 2.31 1.78
02:58:25.30 +26:16:59.79 2.29 1.02
02:57:01.71 +26:51:20.02 2.23 1.14
02:58:33.66 +26:32:51.31 2.13 -0.11
03:02:00.27 +26:45:57.57 2.03 1.11
03:02:36.83 +26:25:54.60 1.99 0.35
03:02:02.42 +26:00:17.81 1.97 0.88
03:00:52.02 +25:20:38.85 1.94 0.72
03:00:46.96 +26:44:11.31 1.91 1.27
02:56:35.91 +25:33:30.01 1.85 0.57
03:00:01.29 +26:21:00.66 1.83 -0.09
03:01:40.53 +26:56:21.42 1.69 1.03
02:59:41.05 +26:02:20.29 1.67 1.13
02:58:55.86 +26:54:49.96 2.37* 1.98
02:57:07.78 +25:56:35.05 1.64 -1.81
02:59:57.18 +25:53:55.96 1.63 2.41
03:02:44.36 +26:55:54.23 1.5 0.95
02:58:45.52 +26:30:48.72 1.47 0.49
03:01:16.32 +26:47:13.02 1.45 1.19
03:02:10.93 +26:18:44.78 1.42 1.46
03:00:29.47 +26:18:39.88 1.41 0.53
02:57:19.14 +25:29:20.26 2.19* 2.74
02:57:35.36 +25:28:41.70 1.39 0.79
03:00:59.25 +25:56:48.61 1.36 0.07
02:57:58.11 +25:59:47.15 1.34 0.01
03:00:21.67 +25:36:36.83 1.32 1.69
02:56:49.80 +25:23:23.17 1.31 1.51
03:02:15.65 +25:25:09.66 1.31 0.38
03:01:49.89 +26:40:13.47 1.27 1.12
03:00:35.26 +26:35:21.31 1.69* 1.46
03:02:12.00 +26:33:42.35 1.27 0.83
03:00:24.55 +26:19:40.64 1.2 1.4
02:58:28.52 +25:55:59.38 1.2 0.17
02:58:58.39 +25:44:57.82 1.68* 1.91
02:57:19.57 +26:11:20.65 1.15 0.91
03:00:33.35 +25:17:36.88 1.15 0.28
03:00:44.06 +26:54:31.04 1.14 0.02
216
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
03:00:15.21 +26:19:25.25 1.11 1.87
03:02:33.31 +25:59:31.01 1.07 0.7
03:01:30.19 +26:45:36.81 1.06 1.84
02:58:39.33 +25:47:54.29 1.05 0.35
03:02:09.80 +26:25:46.42 1.03 1.36
03:01:13.43 +27:03:05.56 1.03 0.45
02:59:26.31 +27:03:07.09 1.02 0.54
03:00:09.89 +26:31:00.88 1.02 0.91
03:01:55.47 +25:57:46.89 1.01 0.02
03:01:57.80 +25:26:47.56 0.98 0.18
03:00:16.51 +26:33:46.57 0.97 -0.29
02:58:29.18 +25:57:19.60 0.96 2.01
02:58:12.01 +26:20:54.06 0.96 1.2
02:58:41.82 +25:22:23.95 0.94 -0.09
03:00:09.98 +25:45:11.05 0.92 0.29
02:58:57.32 +26:24:49.28 0.91 1.22
03:02:05.76 +26:36:20.41 0.83 -0.16
02:56:35.67 +25:42:09.01 0.8 1.09
03:01:33.84 +26:13:19.71 0.8 2.45
02:59:24.23 +26:52:12.84 0.78 1.95
02:59:39.69 +25:53:22.67 0.78 -0.52
02:58:46.58 +25:27:31.40 0.75 -0.29
02:57:41.23 +25:22:36.82 0.73 0.15
03:01:19.63 +26:30:57.57 0.73 0.59
02:58:41.62 +26:54:10.96 0.72 -0.86
02:56:41.92 +25:22:30.81 0.72 1.2
03:02:37.36 +26:01:09.45 0.71 -0.05
03:02:14.25 +25:34:55.15 0.69 0.27
03:01:43.00 +26:39:05.99 0.69 0.37
02:58:23.50 +25:24:60.00 0.68 0.39
03:00:49.26 +26:15:05.07 0.68 0.73
02:59:20.14 +26:50:42.80 0.68 -1.16
03:01:55.90 +25:49:06.62 0.68 1.58
02:57:37.70 +25:27:06.24 0.68 0.01
02:59:38.93 +25:20:26.24 0.68 1.95
03:01:57.75 +25:21:19.72 1.24* 0.7
02:57:55.07 +25:38:28.19 0.67 -0.14
217
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
02:59:35.41 +26:17:25.68 0.67 0.78
03:01:01.33 +25:31:10.67 0.65 1.77
03:01:18.86 +26:03:52.86 0.65 0.37
02:58:32.31 +26:07:46.34 0.65 -0.2
02:59:34.39 +25:24:10.43 0.63 0.59
02:58:07.69 +25:36:39.55 0.61 -0.4
02:56:51.23 +26:46:33.71 0.6 1.09
03:00:49.22 +26:06:43.78 0.59 1.0
03:01:12.53 +26:30:57.78 0.58 -0.6
02:58:38.02 +25:28:35.49 0.57 1.27
02:57:03.04 +26:47:12.04 0.57 -1.32
02:58:15.74 +26:19:58.02 0.56 1.02
03:02:17.82 +26:12:25.88 0.56 -1.61
02:57:51.01 +25:27:17.41 0.56 0.27
02:57:11.31 +25:43:36.62 0.55 0.84
02:59:10.48 +26:31:25.81 0.55 -0.07
03:02:13.24 +25:57:24.84 0.54 1.17
02:58:22.26 +25:35:23.91 0.54 -1.01
03:00:23.05 +26:26:04.58 0.53 0.63
03:01:31.99 +26:21:44.81 0.53 -1.37
02:58:36.95 +26:42:20.87 0.52 -0.19
03:01:18.72 +26:05:05.60 0.52 1.44
03:01:24.17 +27:00:49.43 0.51 -0.2
02:58:44.02 +25:23:39.99 0.51 0.11
02:57:43.57 +25:58:58.65 0.51 1.06
03:00:21.16 +26:44:58.86 0.51 -0.5
02:58:29.79 +26:48:45.88 0.5 -0.92
02:59:50.12 +26:25:21.21 0.5 1.67
02:57:03.68 +25:38:39.42 0.5 1.1
03:02:13.87 +25:42:12.16 0.5 0.74
02:57:46.66 +26:43:18.39 0.49 -0.08
02:59:11.22 +26:57:10.94 0.49 -0.27
02:57:31.51 +25:41:35.88 0.49 -0.06
02:58:24.68 +25:35:25.67 0.49 1.08
03:01:32.33 +25:40:17.79 0.48 -0.12
03:02:02.99 +25:35:29.91 0.48 0.06
02:56:43.40 +25:54:45.30 0.9* 0.69
218
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
02:59:06.91 +26:15:30.41 0.46 0.73
03:02:09.97 +25:35:21.96 0.46 1.47
03:00:51.20 +25:56:15.20 0.46 0.95
03:01:40.66 +26:36:03.18 0.45 0.06
03:01:28.05 +26:16:46.80 0.7* 0.25
03:00:57.87 +26:26:50.43 0.45 -0.2
03:01:12.96 +25:51:59.42 0.44 0.48
03:01:38.54 +26:19:22.17 0.44 1.03
03:01:11.84 +26:50:22.74 0.44 2.26
02:58:55.70 +26:53:32.20 0.43 1.67
02:58:05.39 +25:38:55.44 0.43 -0.07
02:59:10.65 +26:45:24.71 0.42 1.74
03:01:01.61 +25:45:18.49 0.63* -0.84
02:56:41.13 +26:16:13.95 0.41 -0.53
02:59:39.72 +26:05:57.71 0.41 1.39
02:58:27.53 +25:47:13.44 0.41 1.28
02:56:58.80 +25:57:39.72 0.41 0.67
03:01:32.85 +26:31:27.70 0.4 -1.21
03:02:14.00 +26:42:55.36 0.4 1.08
02:57:21.56 +26:19:42.69 0.39 1.03
02:59:51.51 +26:42:52.91 0.38 0.39
02:59:23.54 +26:05:54.53 0.38 0.59
02:59:51.47 +25:42:14.50 0.37 2.06
02:57:50.69 +26:00:38.22 0.36 0.37
03:00:29.60 +25:41:36.57 0.35 -0.81
02:58:42.66 +26:01:33.80 0.35 -0.53
02:59:55.87 +26:39:23.19 0.51* 2.68
02:58:20.37 +26:36:56.09 0.35 -0.26
02:58:03.49 +26:38:53.78 0.34 -0.8
02:57:43.15 +25:57:19.26 0.33 -0.64
02:58:07.02 +25:48:35.56 0.31 -0.42
02:58:38.38 +26:09:24.04 0.31 0.28
03:00:57.85 +26:07:04.17 0.29 -0.9
02:59:17.90 +26:23:44.17 0.29 0.15
03:01:28.30 +26:06:58.69 0.29 0.64
02:58:24.00 +25:53:48.22 0.29 0.58
02:58:13.53 +26:28:09.74 0.29 0.76
219
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
02:59:53.84 +26:30:09.90 0.28 1.61
02:59:29.86 +26:09:47.26 0.28 1.25
03:00:26.67 +25:45:12.14 0.28 0.66
03:01:12.65 +26:18:23.51 0.28 0.86
02:59:31.23 +25:54:10.70 0.28 -0.8
03:00:40.27 +25:50:51.95 0.27 1.84
03:00:30.71 +26:24:06.76 0.26 1.14
03:01:15.44 +26:08:45.35 0.25 -0.77
02:59:42.22 +26:05:02.75 0.25 0.2
03:01:20.99 +25:47:04.94 0.25 0.85
03:00:14.84 +26:40:30.91 0.25 0.68
03:01:05.55 +25:45:06.08 0.32* 0.97
02:59:55.91 +26:08:41.13 0.25 2.13
02:58:34.24 +26:01:50.14 0.24 0.4
03:01:06.53 +25:48:53.38 0.24 0.14
03:00:06.30 +25:42:59.57 0.24 1.4
03:00:48.44 +26:41:09.81 0.23 -1.49
02:59:05.66 +25:51:40.50 0.23 0.39
03:00:53.30 +25:41:45.27 0.23 0.22
03:00:29.35 +25:57:34.53 0.33* 0.54
02:58:16.15 +26:35:08.80 0.22 0.72
03:01:12.19 +25:50:39.41 0.21 1.35
02:59:14.18 +26:07:12.26 0.21 0.34
03:00:31.69 +26:10:12.17 0.21 -0.74
02:58:32.81 +26:04:06.62 0.21 -0.02
03:00:10.64 +26:27:40.91 0.21 0.71
03:00:47.73 +26:27:44.50 0.21 -0.05
02:59:42.85 +26:35:00.46 0.21 -0.65
03:01:09.43 +25:42:18.72 0.21 0.89
02:58:44.16 +26:32:06.94 0.21 1.63
02:59:49.71 +26:32:47.66 0.21 0.41
03:01:05.37 +25:43:29.94 0.21 2.16
03:01:06.22 +25:41:53.57 0.2 0.72
02:58:23.97 +25:52:39.51 0.2 0.51
02:59:56.17 +25:45:05.57 0.19 1.68
03:00:19.09 +25:58:10.07 0.19 -0.28
03:00:20.57 +26:30:30.60 0.19 2.07
220
B.1 AMI005 LA Source Properties
Table B.1: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
03:00:24.93 +26:17:54.64 0.25* 0.92
02:58:43.89 +25:44:24.13 0.18 0.39
02:59:10.10 +25:44:39.30 0.18 0.6
03:00:50.02 +26:13:44.30 0.14 1.25
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:37:06.19 +32:06:57.11 46.83 0.46
09:42:08.84 +32:06:42.54 20.7 1.19
09:36:36.87 +32:03:34.35 18.74 1.23
09:35:59.46 +31:27:26.17 16.98 -0.21
09:41:46.66 +31:54:59.88 23.2* 1.08
09:38:26.59 +30:35:12.56 13.74 0.54
09:40:42.10 +32:01:29.03 11.48 1.35
09:41:07.44 +31:26:56.28 9.01 1.53
09:40:59.49 +31:25:36.88 13.61* 1.51
09:39:50.86 +31:54:15.16 8.14 1.46
09:36:11.92 +30:23:49.63 7.9 -0.1
09:40:53.05 +30:43:51.94 6.16 1.71
09:37:58.06 +31:43:43.22 5.59 1.12
09:39:53.78 +31:22:41.34 6.94* 1.74
09:41:47.45 +31:46:48.59 5.34 -0.42
09:37:18.16 +31:04:44.68 4.87 2.81
09:37:37.89 +31:22:41.08 4.86 0.28
09:38:17.39 +31:18:54.03 4.5 0.52
09:37:01.32 +31:29:40.91 4.32 1.06
09:41:16.67 +30:57:28.86 4.24 2.65
09:36:58.06 +31:29:31.31 3.95 0.08
221
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:37:39.56 +32:09:10.99 3.74 2.45
09:36:41.78 +30:33:55.15 3.73 0.5
09:36:52.68 +31:18:24.46 3.61 1.59
09:39:48.40 +31:34:00.15 3.27 1.55
09:37:22.10 +32:01:08.03 3.03 0.98
09:41:18.05 +31:58:51.31 2.84 0.87
09:39:31.91 +31:54:00.35 2.75 0.13
09:38:27.65 +30:28:01.18 2.7 0.49
09:42:12.23 +32:09:30.49 2.68 1.35
09:38:13.88 +31:31:47.79 2.66 1.14
09:37:13.91 +32:11:32.41 2.58 2.88
09:41:04.10 +30:27:48.15 2.52 2.7
09:37:25.66 +30:31:45.07 2.45 -0.3
09:41:45.83 +32:00:18.91 2.44 0.88
09:37:33.62 +31:18:15.62 2.42 2.16
09:42:09.50 +30:57:18.67 2.4 1.66
09:38:46.38 +31:37:59.78 2.36 1.08
09:41:50.78 +31:52:59.16 2.29 -0.87
09:40:48.10 +31:49:58.86 2.27 -1.05
09:39:21.35 +30:46:31.58 2.24 1.85
09:38:43.76 +31:05:35.30 2.21 1.04
09:37:44.33 +31:12:18.00 2.2 0.8
09:36:44.11 +32:11:28.57 2.17 -0.44
09:37:03.77 +31:56:41.11 2.12 -0.05
09:41:00.40 +30:50:51.51 2.11 2.06
09:39:48.86 +31:15:26.35 2.09 0.09
09:42:26.71 +31:27:07.11 2.09 2.22
09:39:39.83 +31:01:06.82 2.04 0.36
09:40:13.89 +31:21:45.67 1.89 1.33
09:38:07.34 +30:34:40.67 1.85 2.92
09:38:32.11 +30:24:05.80 1.83 1.94
09:38:39.02 +31:03:58.91 1.72 0.32
09:41:21.10 +31:25:42.70 1.69 -0.53
09:40:29.13 +31:58:05.15 1.68 3.49
09:39:09.34 +30:57:56.00 1.62 3.32
09:36:22.48 +31:08:37.12 1.58 2.99
09:37:01.95 +32:06:19.17 1.53 -3.01
222
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:39:13.06 +32:08:58.60 1.52 0.65
09:37:57.17 +31:13:14.13 1.51 0.01
09:36:55.25 +32:11:28.27 1.49 2.99
09:39:17.42 +31:39:40.39 1.48 1.81
09:37:22.94 +31:16:48.34 1.47 0.36
09:37:37.22 +31:59:08.74 1.45 1.46
09:38:59.96 +31:11:21.81 1.44 0.64
09:37:08.33 +32:08:05.39 1.39 -0.61
09:37:05.78 +30:21:48.59 1.38 -0.74
09:37:30.80 +30:29:46.60 1.37 -0.11
09:37:46.16 +30:28:39.38 1.34 0.09
09:39:37.49 +32:07:01.94 1.31 1.88
09:37:59.96 +30:41:28.14 1.31 4.98
09:37:46.28 +30:26:12.45 1.3 -0.44
09:37:11.82 +32:07:32.01 1.29 0.56
09:37:12.04 +32:10:06.66 1.29 1.84
09:41:26.10 +32:06:23.08 1.29 1.83
09:37:20.27 +30:39:02.75 1.29 1.43
09:37:25.71 +31:09:38.73 1.27 1.69
09:37:19.85 +30:51:22.26 1.26 0.48
09:36:10.42 +30:25:05.36 1.25 0.08
09:37:00.19 +32:03:41.84 1.18 -0.38
09:41:07.94 +30:27:11.66 1.17 -1.33
09:40:02.66 +30:22:21.50 1.16 0.29
09:37:22.10 +32:08:16.07 1.6* 0.16
09:36:18.70 +31:29:21.82 1.14 1.73
09:41:39.82 +30:27:02.46 1.08 -0.09
09:41:38.59 +32:06:17.04 1.05 -0.74
09:38:20.34 +31:31:27.68 1.05 0.02
09:37:59.69 +30:44:58.18 1.05 1.56
09:37:02.36 +32:04:59.42 1.05 1.4
09:38:38.58 +31:25:34.57 1.04 0.72
09:37:45.09 +31:34:22.86 1.03 1.33
09:39:40.84 +31:46:35.86 1.01 -1.67
09:38:33.11 +30:57:54.12 1.0 0.39
09:42:11.00 +30:49:22.20 1.0 0.86
09:41:11.15 +31:48:53.47 0.99 -0.09
223
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:37:06.04 +32:10:49.20 0.96 0.28
09:37:08.70 +31:17:55.26 0.94 0.49
09:36:44.52 +31:55:14.05 0.94 1.75
09:37:11.24 +32:08:46.95 0.93 1.87
09:36:51.44 +32:05:22.35 2.07* 4.11
09:41:26.14 +32:01:12.39 0.91 1.11
09:38:02.16 +31:11:32.77 0.9 1.88
09:41:12.06 +31:04:36.89 0.9 0.98
09:42:10.51 +32:05:52.44 0.9 0.42
09:36:17.77 +30:45:35.86 0.88 1.11
09:37:01.77 +32:07:37.64 0.88 0.09
09:41:08.64 +32:00:44.11 0.86 2.0
09:42:08.52 +31:38:01.97 0.84 0.36
09:36:37.39 +30:24:35.03 1.45* 1.42
09:37:44.54 +30:35:24.53 0.83 0.9
09:39:27.43 +31:16:29.85 0.83 -0.08
09:36:59.24 +32:08:25.99 0.83 1.09
09:36:34.78 +32:04:49.81 0.83 -0.03
09:37:04.03 +32:05:29.69 0.82 -0.79
09:36:56.33 +32:08:50.35 0.82 -0.14
09:37:25.50 +30:59:38.55 0.81 0.54
09:38:52.16 +31:20:18.70 0.8 0.89
09:42:11.15 +31:35:18.67 0.79 0.78
09:36:21.83 +30:31:27.75 0.79 1.53
09:36:46.89 +31:17:55.20 0.77 -1.73
09:37:08.04 +32:04:32.45 0.76 1.27
09:36:49.84 +32:08:12.73 0.75 0.19
09:37:14.19 +31:32:06.06 0.75 0.22
09:41:35.10 +31:55:30.33 0.69 1.4
09:42:20.25 +30:50:27.52 0.68 1.52
09:37:30.25 +30:31:16.34 0.66 0.96
09:36:36.18 +30:50:09.42 0.66 2.51
09:38:09.11 +32:07:00.54 0.65 0.33
09:40:45.02 +30:52:09.98 0.64 2.0
09:38:15.74 +30:39:13.45 0.63 -0.19
09:39:33.85 +31:56:19.41 0.63 0.97
09:36:40.17 +32:02:50.58 0.62 0.94
224
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:37:13.05 +32:05:19.62 0.62 -0.31
09:40:48.49 +31:22:39.36 0.62 1.93
09:41:03.53 +31:14:47.56 0.61 0.7
09:39:08.41 +31:36:11.24 0.61 1.52
09:41:29.95 +30:38:25.11 0.6 1.29
09:40:51.61 +31:33:53.06 0.6 0.57
09:42:27.30 +30:54:32.43 0.6 1.83
09:41:04.62 +31:20:24.23 0.59 -0.01
09:39:53.21 +31:16:14.65 0.59 -0.71
09:41:43.96 +31:55:56.09 0.59 0.56
09:42:05.52 +32:04:48.14 0.59 -0.01
09:42:10.27 +32:04:28.83 0.94* -0.37
09:39:30.41 +31:24:11.60 0.58 1.28
09:41:25.29 +30:35:33.46 0.58 0.82
09:38:31.54 +30:27:28.47 0.57 0.49
09:36:33.37 +30:28:34.94 0.56 1.58
09:39:28.53 +30:30:49.33 0.56 0.63
09:41:53.11 +30:34:35.34 0.56 1.0
09:41:48.99 +31:57:51.22 1.59* 0.26
09:38:43.61 +30:34:55.62 0.55 -0.76
09:40:29.14 +31:59:15.20 0.55 0.54
09:40:21.11 +32:04:58.04 0.54 -0.76
09:41:51.51 +31:02:23.40 0.54 -0.89
09:41:35.27 +31:50:14.53 1.05* 1.5
09:40:07.14 +32:02:43.44 0.54 0.53
09:42:03.35 +31:55:35.44 0.53 -1.03
09:40:47.30 +30:47:36.87 0.53 0.72
09:39:05.28 +31:55:13.44 0.51 -0.19
09:37:10.02 +32:03:32.34 0.5 0.23
09:42:18.69 +32:02:18.86 0.49 1.02
09:39:16.30 +31:15:09.33 0.49 1.53
09:37:37.19 +30:45:23.77 0.49 -0.99
09:40:14.28 +31:40:04.65 0.48 0.62
09:40:14.82 +31:34:38.50 0.47 2.08
09:41:06.74 +31:22:16.70 0.47 1.09
09:38:26.01 +31:28:39.92 0.46 -1.38
09:39:02.74 +30:41:23.01 0.46 2.97
225
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:39:45.84 +31:48:55.28 0.45 0.67
09:39:26.10 +31:27:29.23 0.44 0.28
09:39:28.75 +31:02:56.64 0.43 0.64
09:39:09.45 +31:38:28.63 0.42 0.91
09:37:48.86 +30:46:41.93 0.42 0.5
09:37:57.10 +30:56:18.69 0.42 0.69
09:41:12.68 +30:42:18.80 0.4 0.95
09:38:12.38 +31:12:42.65 0.39 3.16
09:37:38.70 +31:39:01.65 0.39 0.75
09:37:28.21 +31:09:01.96 0.39 0.38
09:38:17.97 +31:47:04.35 0.39 0.3
09:37:24.77 +31:33:36.35 0.36 0.04
09:38:54.61 +31:18:41.27 0.35 0.84
09:40:29.53 +31:46:50.73 0.35 1.44
09:39:00.07 +30:45:25.34 0.35 0.82
09:41:20.07 +30:50:28.15 0.34 0.85
09:41:11.52 +31:34:08.89 0.32 0.55
09:40:58.51 +31:40:07.97 0.31 -0.08
09:41:16.47 +31:22:35.11 0.6* 2.91
09:40:59.36 +31:29:44.24 0.31 1.52
09:41:07.04 +30:57:26.16 0.3 -0.05
09:41:14.42 +31:24:03.57 0.3 0.38
09:40:41.56 +30:53:24.26 0.3 -0.64
09:39:36.48 +31:21:08.72 0.3 0.59
09:38:14.17 +31:10:32.55 0.29 1.01
09:39:44.21 +31:31:00.81 0.29 1.48
09:40:25.20 +31:35:01.00 0.29 1.86
09:37:51.54 +30:47:51.47 0.28 1.98
09:39:38.90 +31:11:24.29 0.28 -0.16
09:38:14.14 +30:53:40.19 0.28 -0.27
09:38:52.79 +31:37:43.52 0.28 -0.66
09:41:09.41 +31:23:21.18 0.28 0.71
09:37:43.75 +31:32:47.01 0.26 2.06
09:39:54.94 +31:20:40.45 0.26 0.73
09:40:43.57 +30:59:14.70 0.26 0.46
09:37:47.12 +31:20:02.00 0.25 1.26
09:39:29.34 +30:44:58.72 0.25 1.04
226
B.1 AMI005 LA Source Properties
Table B.2: * extended source, quoting integrated LA flux
Right ascension Declination Flux Spectral Index
(mJy)
09:37:45.46 +31:26:57.71 0.25 0.27
09:41:01.87 +30:53:14.69 0.24 0.84
09:37:49.19 +31:43:52.16 0.24 -0.22
09:39:06.59 +30:58:53.79 0.24 2.15
09:40:49.79 +30:57:33.59 0.24 -0.11
09:39:36.99 +31:34:03.92 0.24 1.12
09:38:01.04 +31:02:37.76 0.23 0.03
09:39:14.33 +31:11:15.84 0.23 0.29
09:40:59.41 +31:02:21.92 0.23 0.83
09:37:47.74 +31:39:28.50 0.23 1.07
09:38:54.67 +30:48:55.00 0.23 -0.01
09:37:46.70 +31:44:26.89 0.23 1.16
09:39:43.88 +30:53:29.08 0.23 -1.98
09:37:52.69 +30:50:06.65 0.23 0.43
09:38:53.14 +31:10:15.90 0.22 0.87
09:39:33.27 +31:37:01.75 0.22 -0.33
09:37:54.56 +30:51:42.55 0.22 -0.45
09:39:51.04 +31:14:10.11 0.22 0.93
09:40:50.50 +31:40:42.61 0.22 1.09
09:39:50.21 +31:23:35.16 0.22 0.05
09:37:54.45 +31:02:57.13 0.21 1.38
09:41:11.05 +31:09:54.18 0.41* -0.58
09:40:06.17 +31:30:10.68 0.21 -1.18
09:39:04.09 +31:41:40.27 0.21 0.76
09:39:50.39 +30:46:49.31 0.21 -1.0
09:39:58.99 +30:55:13.62 0.21 2.16
09:38:50.60 +30:51:33.58 0.2 0.48
09:38:46.90 +31:12:30.95 0.2 0.21
09:40:45.57 +31:27:32.09 0.2 1.71
09:38:41.95 +31:00:40.54 0.2 0.73
09:38:08.03 +30:49:42.51 0.19 0.06
09:39:19.60 +30:57:25.85 0.19 0.12
09:39:24.38 +31:36:38.49 0.19 0.62
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