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The DRIFT Dark Matter Project:
Directionality, Sensitivity, and
Environmental Backgrounds
N I V E R
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Steven James Sutherland Plank
School of Physics
The University of Edinburgh
A thesis submitted for the degree of
Doctor of Philosophy in the subject of Physics
2008
Dedicated to my family
Abstract
It is now largely accepted that dark matter, and more specifically, Weakly Interacting Massive Particles (WIMPs), constitute the majority of the mass in our
Universe. Within this thesis are presented: (i) an overview of the motivation
and evidence for the existence of dark matter; (ii) a detailed discussion of direct detection techniques and a worldwide review of WIMP search experiments;
and (iii) new experimental measurements and complementary detailed numerical
simulations, carried out by the author, to determine the performance of DRIFT
experimental technology. Collectively, this work explores the capability of DRIFT
technology to detect dark matter, and in doing so, to resolve one of the key open
questions of contemporary science.
The DRIFT programme consists of an array of direct dark matter search
detectors located in the Boulby mine. An important limitation to the experiment is the neutron and gamma-ray background. Experimental work presented
here has determined the U and Th content of the cavern rock to be 66 ± 6 ppb
and 145 ± 13 ppb respectively, clarifying ambiguities in previous estimations.
Through the use of a Monte Carlo simulation the neutron and gamma-ray background experienced by DRIFT has been determined and the experimental implications assessed. In addition, the activity of the main neutron calibration
source used to calibrate DRIFT modules has been measured and was found to be
11600 n s−1 ±5 % on the date of exposure, resolving an earlier discrepancy.
Analysis of experimental data has confirmed that the technology employed by
DRIFT detectors has the capability to provide directional information of recoiling
nuclei at the low energies of interest to dark matter searches. A Monte Carlo
simulation has then been employed to determine the WIMP-nucleon sensitivity
achievable using DRIFT detectors of the present performance, also examining
what would be achievable if this was supplemented by a realistic active neutron
veto detector. It is found that a CS2 -filled DRIFT type detector running at
a 500 NIP threshold (∼16 keV and ∼27 keV for C and S recoils respectively)
for 300 kg years, and surrounded by the proposed veto scheme, would expect to
observe a background of six un-vetoed events. The minimum positive signal above
this background (90 % C.L.) would correspond to a WIMP-nucleon sensitivity
limit of ∼1.75 × 10−9 pb. This identifies the realistic limit of what can be achieved
using gaseous CS2 as a target medium. An investigation into the limits achievable
using a similar array in which DRIFT modules act as self-vetoing detectors is
also examined providing insight into the future development and operation of the
DRIFT programme.
i
Acknowledgements
First and foremost, I would like to acknowledge and thank my supervisor, Dr
Alex Murphy, for his valued guidance throughout my Ph.D. His help and direction
has not gone without recognition and much appreciation.
My gratitude goes to all members of the UKDMC and DRIFT collaboration,
past and present, who have aided in my work and made my time as part of the
group an enjoyable experience. Within the UK contingent of the collaboration
I would like to extend special thanks to Mike Carson, Vitaly Kudryavtsev, Tim
Lawson, Phil Lightfoot, Graham Nicklin, Sean Paling, and Matt Robinson for all
of their assistance and all I have learnt from them. Much thanks is expressed
to all collaboration members in the US and in particular to Dan Snowden-Ifft at
Occidental College, Los Angeles, who provided valuable help with, and instruction
to, my research. A great deal of appreciation is given to Dan, his family, and
Josh Forbes for their generosity and hospitality during my visits. Gratitude is
also given to Dinesh Loomba at the University of New Mexico for his similarly
gracious hospitality. The entire collaboration as a whole must be commended for
their dedication, enthusiasm, and all the hard work they have contributed to the
field of dark matter research. Credit must also be given to EPSRC for funding
my research and to PPARC, Cleveland potash Ltd., and the US NSF for their
assistance with and support of the UKDMC and DRIFT programme.
Furthermore, I would like to acknowledge everyone in the Nuclear Physics
group at the University of Edinburgh. Chamkaur Ghag deserves a special mention
for the enormous help he has given me throughout my time here and for the joyful
work trips taken. Tom Davinson, Derek Glazier, Dan Watts, Phil Woods, and
all other members of the group have each contributed in one way or another. To
my old and new office mates – Cham, Claire, Alexis, Daria, Gavin, Emma, Tom,
Andrea, Jo, Mark, Paul, and Phil – your camaraderie has made the department
a particularly enjoyable place to work; tea breaks would not have been the same
without the many profound discussions on Michael Bay and Jerry Bruckheimer
movies.
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To all of my other friends and colleagues at Edinburgh or elsewhere (you know
who you are), I express my sincere gratitude for your friendship, encouragement,
and helpful distractions.
Lastly, I must thank my family. The continuous support and belief from
Natalie, Michael, and my parents have been invaluable.
Declaration
This thesis has been composed by myself and no portion has been submitted for
any other degree or professional qualification. The work presented in this thesis
was carried out within the School of Physics at The University of Edinburgh
and the institutions of the DRIFT collaboration. Chapters 1 and 2 describe
much of the background theory relevant to the field of research. A substantial
contribution to the work described in Chapter 3 and onwards was made by myself,
but since the DRIFT programme is a collaborative effort, much of the work must
be attributed to several workers at a time, or the group as a whole. Part of my
work involved assistance to the manufacture, commissioning, installation, and
operation of certain DRIFT-II modules and components. The administration of
all Monte Carlo simulations and analysis of data described within this thesis was
carried out by myself, except where otherwise stated.
Steven J. S. Plank
v
Contents
Abstract
i
Acknowledgements
iii
Declaration
v
List of Figures
xiii
List of Tables
xvii
1 Introduction to Dark Matter
1.1
Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.1.1
Matter Only Models of the Universe . . . . . . .
6
1.1.1.2
Dark Energy Models of the Universe . . . . . . .
7
1.1.1.3
The Benchmark Model . . . . . . . . . . . . . . .
9
Problems with the Big Bang . . . . . . . . . . . . . . . . .
9
1.1.2
1.1.2.1
Inflation Theory . . . . . . . . . . . . . . . . . .
13
The CMB . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.2.1
Type Ia Supernovae . . . . . . . . . . . . . . . . . . . . . .
19
1.2.2
The Form of Dark Energy . . . . . . . . . . . . . . . . . .
20
Matter Constraints . . . . . . . . . . . . . . . . . . . . . . . . . .
23
1.3.1
Rotation Curves . . . . . . . . . . . . . . . . . . . . . . . .
23
1.3.2
Gravitational Lensing . . . . . . . . . . . . . . . . . . . . .
24
1.3.3
Structure Formation . . . . . . . . . . . . . . . . . . . . .
27
1.3.4
X-Ray Emission Measurements . . . . . . . . . . . . . . .
28
1.3.5
Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . .
29
1.1.3
1.2
1.3
1
vii
viii
CONTENTS
1.4
Dark Matter Candidates . . . . . . . . . . . . . . . . . . . . . . .
30
1.4.1
Baryonic Dark Matter . . . . . . . . . . . . . . . . . . . .
31
1.4.2
Exotic Dark Matter . . . . . . . . . . . . . . . . . . . . . .
32
1.4.3
WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
1.4.3.1
The Standard Model . . . . . . . . . . . . . . . .
33
1.4.3.2
Supersymmetry (SUSY) . . . . . . . . . . . . . .
35
1.4.3.3
SUSY Candidates
. . . . . . . . . . . . . . . . .
37
1.5
Alternative Theories . . . . . . . . . . . . . . . . . . . . . . . . .
40
1.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
2 Direct Detection of WIMP Dark Matter
43
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.2
WIMP-nucleon Interactions . . . . . . . . . . . . . . . . . . . . .
43
2.3
Interaction Cross-Sections . . . . . . . . . . . . . . . . . . . . . .
45
2.3.1
Spin-Independent Interactions . . . . . . . . . . . . . . . .
46
2.3.2
Spin-Dependent Interactions . . . . . . . . . . . . . . . . .
46
2.4
The Nuclear Form Factor . . . . . . . . . . . . . . . . . . . . . . .
47
2.5
Detector Limitations . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.5.1
Efficiency and Energy Threshold . . . . . . . . . . . . . .
48
2.5.2
Energy Resolution . . . . . . . . . . . . . . . . . . . . . .
51
2.5.3
Target Composition . . . . . . . . . . . . . . . . . . . . . .
52
2.6
Relative Motion of the Earth . . . . . . . . . . . . . . . . . . . . .
52
2.7
Detection Techniques . . . . . . . . . . . . . . . . . . . . . . . . .
54
2.8
World Review of WIMP Dark Matter Experiments . . . . . . . .
56
2.8.1
Boulby (UK) . . . . . . . . . . . . . . . . . . . . . . . . .
57
2.8.2
Gran Sasso (Italy) . . . . . . . . . . . . . . . . . . . . . .
60
2.8.3
Kamioka (Japan) . . . . . . . . . . . . . . . . . . . . . . .
64
2.8.4
Modane (France) . . . . . . . . . . . . . . . . . . . . . . .
66
2.8.5
SNOLAB (Canada) . . . . . . . . . . . . . . . . . . . . . .
67
2.8.6
Soudan (USA) . . . . . . . . . . . . . . . . . . . . . . . . .
68
2.8.7
Other Experiments . . . . . . . . . . . . . . . . . . . . . .
71
Directional Sensitivity . . . . . . . . . . . . . . . . . . . . . . . .
71
2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
2.9
CONTENTS
ix
3 Environmental Backgrounds
75
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
3.2
U & Th Content of the Cavern Rock . . . . . . . . . . . . . . . .
75
3.2.1
Location of the Ge Run . . . . . . . . . . . . . . . . . . .
79
3.2.2
Modelling the Environment . . . . . . . . . . . . . . . . .
79
3.2.3
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
3.2.3.1
Experimental Rates . . . . . . . . . . . . . . . .
83
3.2.3.2
Simulated Rates . . . . . . . . . . . . . . . . . .
84
3.2.3.3
U and Th Concentrations . . . . . . . . . . . . .
85
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
3.3
Background Gamma-Rays . . . . . . . . . . . . . . . . . . . . . .
88
3.4
252
89
3.2.4
3.5
Cf Neutron Source Measurement . . . . . . . . . . . . . . . . .
252
3.4.1
The
Cf Source . . . . . . . . . . . . . . . . . . . . . . .
91
3.4.2
Experiment . . . . . . . . . . . . . . . . . . . . . . . . . .
92
3.4.3
Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . .
93
3.4.4
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
3.4.5
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4 DRIFT
97
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
4.2
Concept of DRIFT Detection . . . . . . . . . . . . . . . . . . . .
97
4.3
The DRIFT-II Detector . . . . . . . . . . . . . . . . . . . . . . .
99
4.3.1
The Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.2
Gas System . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.3
Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . 102
Central Cathode . . . . . . . . . . . . . . . . . . 102
4.3.3.2
Fieldcage . . . . . . . . . . . . . . . . . . . . . . 104
4.3.3.3
MWPCs . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.4
Slow Control . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.5
Data Acquisition System . . . . . . . . . . . . . . . . . . . 108
4.3.6
4.4
4.3.3.1
4.3.5.1
Grid DAQ . . . . . . . . . . . . . . . . . . . . . . 108
4.3.5.2
Anode DAQ . . . . . . . . . . . . . . . . . . . . . 110
Event Data . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Further DRIFT modules . . . . . . . . . . . . . . . . . . . . . . . 115
x
CONTENTS
4.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5 Analysis
117
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2
Gamma-Rays in DRIFT . . . . . . . . . . . . . . . . . . . . . . . 118
5.3
5.2.1
Background Gamma-Ray Rejection in DRIFT-I . . . . . . 118
5.2.2
Electron Recoil Characteristics . . . . . . . . . . . . . . . 121
5.2.3
CH2 Shielding . . . . . . . . . . . . . . . . . . . . . . . . . 124
60
5.2.3.2
Background Gamma-Rays . . . . . . . . . . . . . 127
Co Exposures . . . . . . . . . . . . . . . . . . . 124
Nuclear Recoils in DRIFT . . . . . . . . . . . . . . . . . . . . . . 128
5.3.1
Nuclear Recoil Energies and Track Lengths . . . . . . . . . 128
5.3.2
Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.3.3
5.3.4
5.4
5.2.3.1
5.3.2.1
Event Parameters . . . . . . . . . . . . . . . . . . 131
5.3.2.2
Data Reduction . . . . . . . . . . . . . . . . . . . 134
DRIFT-IIb Neutron Exposures . . . . . . . . . . . . . . . 139
5.3.3.1
Neutron Run . . . . . . . . . . . . . . . . . . . . 140
5.3.3.2
Collimated Neutron Run . . . . . . . . . . . . . . 141
Radon in DRIFT . . . . . . . . . . . . . . . . . . . . . . . 144
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6 DRIFT Directionality
149
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.2
Simulated Nuclear Recoils . . . . . . . . . . . . . . . . . . . . . . 149
6.2.1
Purpose-Built Monte Carlo . . . . . . . . . . . . . . . . . . 150
6.2.2
GEANT4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.3
DRIFT-IIa Data: Directional Analysis . . . . . . . . . . . . . . . 157
6.4
Pseudo-data: Directional Analysis . . . . . . . . . . . . . . . . . . 160
6.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7 Large Scale DRIFT Arrays
169
7.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.2
Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.3
Detector & Veto Configuration . . . . . . . . . . . . . . . . . . . . 170
7.4
Neutron Production . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.5
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
CONTENTS
xi
7.5.1
Detection Thresholds . . . . . . . . . . . . . . . . . . . . . 173
7.6
7.5.2 Scintillator Size . . . . . . . . . . . . . . . . . . . . . . . . 181
Possible Improvements . . . . . . . . . . . . . . . . . . . . . . . . 181
7.7
Alternative DRIFT Array . . . . . . . . . . . . . . . . . . . . . . 184
7.8
The Feasibility of Large Scale Operation . . . . . . . . . . . . . . 187
7.9
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8 Conclusions
191
A MICROMEGAS
195
Bibliography
199
List of Figures
1.1
Data for Hubble’s Law . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
The Big Bang . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3
Expansion of matter dominated universes . . . . . . . . . . . . . .
8
1.4
Constraints on the curvature and expansion the Universe . . . . .
10
1.5
The horizon problem . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.6
Grand Unified Theories . . . . . . . . . . . . . . . . . . . . . . . .
13
1.7
WMAP measurements of the CMB temperature fluctuations . . .
16
1.8
Combined CMB radiation power spectra . . . . . . . . . . . . . .
17
1.9
Luminosity measurements of type Ia supernovae . . . . . . . . . .
21
1.10 Rotation curve of spiral galaxy NGC 3198 . . . . . . . . . . . . .
24
1.11 Illustration of gravitational lensing . . . . . . . . . . . . . . . . .
25
1.12 A galaxy cluster lens: Abell 2218 . . . . . . . . . . . . . . . . . .
26
1.13 The Bullet Nebula . . . . . . . . . . . . . . . . . . . . . . . . . .
27
1.14 Big Bang nucleosynthesis constraints on Ωb . . . . . . . . . . . . .
30
1.15 Matter/Energy density make-up of the Universe . . . . . . . . . .
33
1.16 Running of the gauge coupling constants . . . . . . . . . . . . . .
37
1.17 WIMP-type candidates . . . . . . . . . . . . . . . . . . . . . . . .
38
2.1
SI form factors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.2
SD form factors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.3
The WIMP wind and Earth’s motion . . . . . . . . . . . . . . . .
54
2.4
Underground laboratory depths . . . . . . . . . . . . . . . . . . .
56
2.5
Excitation and ionisation in xenon
. . . . . . . . . . . . . . . . .
59
2.6
Dual phase xenon system . . . . . . . . . . . . . . . . . . . . . . .
59
2.7
SI WIMP-nucleon cross-section limits . . . . . . . . . . . . . . . .
69
2.8
SD WIMP-nucleon cross-section limits . . . . . . . . . . . . . . .
70
2.9
Diurnal fluctuations of WIMP direction . . . . . . . . . . . . . . .
72
xiii
xiv
LIST OF FIGURES
3.1
Boulby mine cross-section . . . . . . . . . . . . . . . . . . . . . .
76
3.2
U and Th decay chains . . . . . . . . . . . . . . . . . . . . . . . .
78
3.3
The underground facility at Boulby . . . . . . . . . . . . . . . . .
80
3.4
The JIF laboratory . . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.5
Simulation of the JIF laboratory . . . . . . . . . . . . . . . . . . .
82
3.6
Simulated geometry of the Ge detector . . . . . . . . . . . . . . .
82
3.7
Background gamma-ray spectrum in the LB lab . . . . . . . . . .
83
3.8
Gamma-ray emission from the cavern rock face . . . . . . . . . . .
89
3.9
Simulated background gamma-ray spectrum . . . . . . . . . . . .
90
3.10 Emitted neutron energy spectrum from a
252
Cf source . . . . . . .
3.11 Measured gamma-ray spectrum with and without the
252
Cf source
present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Geometry of the
252
92
94
Cf measurement run . . . . . . . . . . . . . .
95
4.1
Basic concept of DRIFT detection . . . . . . . . . . . . . . . . . .
98
4.2
DRIFT gas input system . . . . . . . . . . . . . . . . . . . . . . . 101
4.3
DRIFT-IIa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4
The DRIFT-IIa fieldcage . . . . . . . . . . . . . . . . . . . . . . . 105
4.5
The MWPC wire planes . . . . . . . . . . . . . . . . . . . . . . . 106
4.6
DRIFT-II
4.7
The grid DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.8
The anode DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.9
An example alpha particle event in DRIFT . . . . . . . . . . . . . 113
4.10 Example
55
55
Fe calibration system . . . . . . . . . . . . . . . . . . 107
Fe events . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.11 An example neutron event in DRIFT . . . . . . . . . . . . . . . . 114
5.1
Simulated DRIFT-I rock gamma-ray interaction rates per energy
bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.2
Simulated DRIFT-I energy deposition histogram from background
gamma-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.3
Simulated electron recoil track lengths in DRIFT-I produced from
background gamma-rays . . . . . . . . . . . . . . . . . . . . . . . 122
5.4
Simulated low energy electron recoil track lengths in CS2 . . . . . 123
5.5
Simulated number of electron recoils in DRIFT-IIb from a
60
Co
exposure as a function of CH2 shielding . . . . . . . . . . . . . . . 126
5.6
NIPs as a function of nuclear recoil energy in DRIFT . . . . . . . 129
LIST OF FIGURES
xv
5.7
C & S nuclear recoil ranges in 40 Torr CS2 . . . . . . . . . . . . . 130
5.8
5.9
DRIFT-II event parameters on a single channel waveform . . . . . 132
An example of a ‘ringer’ event . . . . . . . . . . . . . . . . . . . . 135
5.10 Modelled geometry of a DRIFT-IIb neutron exposure . . . . . . . 140
5.11 Event rates per energy bin for a DRIFT-IIb neutron exposure . . 141
5.12 Modelled geometry of a DRIFT-IIb collimated neutron source run 143
5.13 Event rates per energy bin for a DRIFT-IIb collimated neutron
source run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.14 Illustration of a GPCC event . . . . . . . . . . . . . . . . . . . . . 147
6.1
NIPs vs. R2 for DRIFT-IIa data and pseudo-data y-axis runs . . 163
7.1
Modelled geometry of a DRIFT vessel coupled to an active neutron
veto scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2
Neutron production spectrum for 1 ppb U in stainless steel . . . . 172
7.3
Neutron production spectrum for 1 ppb Th in stainless steel . . . 173
7.4
7.5
Simulated neutron rate per energy bin from the steel vacuum vessel 175
Typical DRIFT WIMP-nucleon cross-section limit curve . . . . . 179
7.6
WIMP-nucleon cross-section limits for a large DRIFT array . . . 180
7.7
Large scale self-vetoing DRIFT array . . . . . . . . . . . . . . . . 185
A.1 The design of MICROMEGAS . . . . . . . . . . . . . . . . . . . . 196
A.2 The drift and high amplification region of MICROMEGAS . . . . 197
List of Tables
1.1
The fate of a matter dominated universe . . . . . . . . . . . . . .
7
1.2
The Benchmark Model parameters . . . . . . . . . . . . . . . . .
11
1.3
Significant epochs in the Benchmark Model . . . . . . . . . . . . .
11
1.4
The fundamental particles of the Standard Model . . . . . . . . .
34
1.5
Generation of quarks and leptons in the Standard Model . . . . .
35
1.6
Properties of gauge bosons in the Standard Model . . . . . . . . .
35
1.7
Supersymmetric particles . . . . . . . . . . . . . . . . . . . . . . .
36
3.1
Measured rates for U/Th gamma-rays . . . . . . . . . . . . . . . .
84
3.2
Monte Carlo rates for U/Th gamma-rays . . . . . . . . . . . . . .
86
3.3
U concentrations with and without Rn progeny . . . . . . . . . .
86
3.4
U and Th content of the cavern rock . . . . . . . . . . . . . . . .
87
5.1
Simulated rock gamma-ray interaction rates in DRIFT-I . . . . . 119
5.2
Simulated electron recoils per energy decade in DRIFT-IIb unshielded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.3
Simulated electron recoils per energy decade in DRIFT-IIb fully
shielded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.4
Simulated rock gamma-ray interactions in DRIFT-IIb unshielded . 128
5.5
Simulated rock gamma-ray interactions in DRIFT-IIb fully shielded 128
5.6
Event rates for a DRIFT-IIb neutron exposure . . . . . . . . . . . 142
5.7
Event rates for a DRIFT-IIb collimated neutron source run . . . . 144
6.1
Summary of MC directional neutron runs . . . . . . . . . . . . . . 151
6.2
Monte Carlo significance effect . . . . . . . . . . . . . . . . . . . . 153
6.3
Summary of GEANT4 directional neutron runs . . . . . . . . . . 155
6.4
GEANT4 significance effect . . . . . . . . . . . . . . . . . . . . . 156
6.5
DRIFT-IIa directional analysis data . . . . . . . . . . . . . . . . . 159
xvii
xviii
LIST OF TABLES
6.6
DRIFT-IIa directional analysis significance effect
. . . . . . . . . 161
6.7
6.8
Directional analysis pseudo-data . . . . . . . . . . . . . . . . . . . 164
Directional analysis pseudo-data significance effect . . . . . . . . . 165
7.1
Neutron production from stainless steel . . . . . . . . . . . . . . . 172
7.2
7.3
Simulated neutron rate from the steel vacuum vessel . . . . . . . . 174
Simulated rejection capability of a DRIFT veto detector . . . . . 177
7.4
End location of background neutrons from the steel vessel . . . . 183
Chapter 1
Introduction to Dark Matter
“If the facts don’t fit the theory, change the facts.”
Albert Einstein
In the scientific community there has been a stunning realisation that the
Universe is not what we once believed. At one time it was widely accepted
that stars contributed to nearly its entire mass; this is no longer so. Current
astronomical studies indicate that luminous matter accounts for only 1 % of the
composition: not only is our planet minuscule on the cosmological scale, but the
entirety of what we see is merely a fraction of the physical Universe. Compelling
evidence suggests that the majority of mass in the Universe is ‘dark matter’ and,
although by definition non-luminous (or nearly so), its gravitational effects are
apparent. In this chapter the motivation and evidence for the existence of dark
matter are described and possible candidates for the true form of dark matter are
considered.
1.1
Cosmology
In short, cosmology is the study of the Universe as a whole. At the foundation of
modern cosmology lies the cosmological principle, which states “There is nothing
special about our location in the Universe.” The Universe is both isotropic and
homogeneous, but only on the largest scales. It is clear that our immediate
surroundings are neither isotropic nor homogeneous and this holds true on the
galactic scale. When dealing, however, with scales over 100 Mpc, patterns of
1
2
1. INTRODUCTION TO DARK MATTER
superclusters and voids do appear uniform. In the 1920s, Edwin Hubble [1]
studied the relationship between galaxy redshifts and their distance from us.
Interpreting his results he found that the velocity, ~v , of a galaxy is proportional
to its distance, ~r, from us, and takes the form of Hubble’s law:
~v = H0~r
(1.1)
where the constant of proportionality, H0 , is known as Hubble’s constant and
is the Hubble parameter, H(t), as measured today, i.e. the current epoch. Note
that the Hubble parameter is a function of time and would have had an entirely
different value in the early Universe. It is common practice to define the Hubble
parameter in terms of a dimensionless number known as the reduced Hubble
parameter, h, where
H(t) = 100h km s−1 Mpc−1 .
(1.2)
Current observations indicate the reduced Hubble parameter at present, h0 =
0.73 ± 0.03 [2]. A modern data set of recession velocity against distance is shown
in Figure 1.1.
Figure 1.1: A plot of distance versus velocity for a set of 1355 galaxies. Hubble’s
Law is given by the best fit to the data. Taken from [3].
1.1 Cosmology
3
With Hubble’s law, Hubble had shown that distant galaxies are in fact moving
away from us. Naı̈vely one may assume that this result violates the cosmological
principle and implies that we are at the centre of an expansion and thereby at a
special location in the Universe. In actuality, for an expanding Universe, this is
exactly what should be seen in accordance with the cosmological principle. An
observer at any other point in the Universe would also perceive distant galaxies
to be moving away from them. This observation naturally implies that at some
point in the past these galaxies were close together. This evidence leads to the
Big Bang model in which the Universe expands and cools from an initial state of
immense density and temperature to its current low density state (Figure 1.2).
This theory, along with the idea that the very fabric of space itself is expanding (as
opposed to matter simply spreading outwards in some kind of void), is consistent
with the General Theory of Relativity.
Strong support for the Big Bang theory is given by measurements of the
Cosmic Microwave Background (CMB) Radiation (described in Section 1.1.3).
The CMB was first discovered by Arno Penzias and Robert Wilson [5] in 1965,
at which time it was shown to have isotropic properties. With great accuracy
the Cosmic Background Explorer (COBE) satellite and Wilkinson Microwave
Anisotropy Probe (WMAP) experiment have more recently mapped small scale
temperature fluctuations in the CMB. These results have indicated the CMB to
be isotropic at the 1 part in 105 (COBE [2]) and 1 part in 106 (WMAP [6]) level.
1.1.1
Expansion
Given these observations of a developing cosmos, it is pertinent to apply a mathematical description conveying this evolution. For our Universe, which is both
isotropic and homogeneous, the cosmological expansion scale factor, a(t), can be
described through:
~r = a(t)~x
(1.3)
where ~r is the real distance between two points and ~x is the co-moving distance
i.e. the distance measured in units that expand along with the Universe. The comoving distance remains constant when measured in co-moving coordinates and
the scale factor represents the relative expansion of the co-moving coordinate
system.
4
1. INTRODUCTION TO DARK MATTER
Figure 1.2: A graphic illustration of the Big Bang evolution of the Universe.
Significant epochs are indicated. Taken from [4].
1.1 Cosmology
5
The Hubble parameter, as defined in Equation 1.1, can be expressed in terms
of the scale factor:
H(t) =
ȧ(t)
.
a(t)
(1.4)
Given the isotropy and homogeneity of the Universe, the cosmological model can
be described by the Robertson-Walker metric [7]
dr2
2
2
2
2
+ r (dθ + sin θdφ )
ds = c dt − a (t)
1 − κr2
2
2
2
2
(1.5)
where s is the proper distance between space-time points; c is the speed of light;
r, θ, and φ are co-moving spherical polar co-ordinates; t is the cosmological
proper time (often called the cosmic time); and κ is a parameter used to define
the spatial curvature of space-time. In this model κ has been scaled to have the
values κ = ±1, 0 covering the three possible curvatures: positive, negative or flat,
respectively.
In the early 20th century Albert Einstein published his work on General Relativity (GR). This theory essentially demonstrates how gravitation is related to the
curvature of space-time and how the mass-energy content governs this behaviour.
It is believed that the Universe, as described thus far, obeys the Einstein field
equations (EFE) [8] used in GR:
1
8πG
Rµν − Rgµν − Λgµν = − 4 Tµν
2
c
(1.6)
where Rµν is the Ricci tensor, R the scalar curvature, gµν the metric tensor,
Tµν the energy-momentum tensor, G the gravitational constant, and Λ the cosmological constant which represents a component of the Universe with negative
pressure. This Λ contribution aids the expansion of the Universe and is often
referred to as vacuum energy or dark energy (see Section 1.2). The left hand side
of Equation 1.6 contains a description of the space-time geometry and the right
hand side describes the mass-energy content of the Universe.
By describing the matter in the Universe as a fluid, with density ρ and pressure
p (both radiation and matter are included here such that ρ = ρm + ρr ), the EFE
yields the following relations
2
ȧ
κc2 Λ
8πG
+ 2 − =
ρ
a
a
3
3
(1.7)
6
1. INTRODUCTION TO DARK MATTER
known as the Friedmann equation, and
d(ρa3 )
p d(a3 )
+ 2
=0
dt
c dt
(1.8)
known as the equation of local energy conservation. Taking the time derivative
of Equation 1.7 and using Equation 1.8 gives the acceleration equation
2
ä
ȧ
κc2
8πG
2
+
+ 2 − Λ = − 2 p.
a
a
a
c
(1.9)
The evolution for distinct models of the Universe can now be described through
the above relations.
1.1.1.1
Matter Only Models of the Universe
As mentioned previously, the spatial curvature of the Universe can be described
as one of the following: negatively curved, represented by κ = −1; flat (κ = 0);
or positively curved, κ = +1. The simplest way to describe these scenarios is
to consider a matter only universe with no dark energy component i.e. Λ = 0.
The radiation dominated era in our early Universe was sufficiently brief so that its
effects can be ignored for this purpose. Here a density parameter, Ω, is introduced
to denote the matter density relative to the critical density of the Universe. The
critical density (see Equation 1.11) is defined as the density of matter required
for zero curvature (flat) in the absence of any dark energy component. It is
the dividing line between a collapsing and an ever expanding universe. Ω is
expressed generally in Equation 1.13 (see later) but is described here considering
only a matter component:
Ω(t) =
ρ(t)
ρc (t)
(1.10)
where at time, t, ρ(t) is the mean mass density and ρc (t) is the critical density.
From Equations 1.4 and 1.7 the critical density can be expressed as
ρc (t) =
3H 2 (t)
.
8πG
(1.11)
Note that the critical mass density is equivalent to what is often referred to as
the critical energy density, εc , where ρc = εc /c2 . The current value for the critical
density of our Universe is ρc (0) ≈ (9.2 ± 1.8) × 10−27 kg m−3 which corresponds
to approximately 6 protons m−3 [9]. This density may seem exceptionally low by
1.1 Cosmology
7
Table 1.1: Hypothetical matter dominated universes. The density of matter is
closely linked to the curvature and ultimate fate of the universe. The evolution of
the scale factor is shown for each example. See main text for further details.
Density Curvature
Ω<1
κ = −1
Ω=1
κ= 0
Ω>1
κ = +1
Scale Factor Ultimate Fate
a(t) ∝ t
Big Freeze
2
a(t) ∝ t 3
Big Freeze
a(t) → 0
Big Crunch
terrestrial standards but when considering that most of the Universe is comprised
of ‘empty space’ this value is close to the mean density of the Universe.
The expansion of a matter only universe can now be determined through
the possible values of the density parameter. If Ω < 1 then a universe is said
to be ‘open’ and will continue expanding outwards forever; in this scenario the
spatial curvature is said to be negative (κ = −1). If Ω > 1, i.e. the density
of a universe is so great that gravitational forces eventually cause the universe
to collapse back in on itself, then the universe is said to be ‘closed’ (positively
curved, κ = +1). A spatially ‘flat’ universe (κ = 0) lies between the two scenarios
where the expansion continues forever but at an ever decreasing rate in time. In
each example the density of matter determines whether the universe will collapse
back in on itself, known as the Big Crunch, or expand outwards forever, known
as the Big Freeze. All three scenarios are summarised in Table 1.1 and illustrated
graphically in Figure 1.3.
It is important to grasp that the model described so far only applies to the
special condition where Λ = 0. When a form of dark energy is introduced the
model becomes more complex: the spatial curvature of the Universe does not
solely determine its fate.
1.1.1.2
Dark Energy Models of the Universe
In practice, it is useful to define each component of the Universe (radiation r,
matter m, and dark energy Λ) relative to the critical density, ρc (defined in
Equation 1.11):
Ωr ≡
ρr
ρc
Ωm ≡
ρm
ρc
ΩΛ ≡
ρΛ
.
ρc
(1.12)
It should be noted that the matter component can be further divided into subcategories as later described in Section 1.3. The total density parameter, Ωtot , is
8
1. INTRODUCTION TO DARK MATTER
a(t)
Ω<1
open
Ω=1
flat
Ω>1
closed
t
Figure 1.3: The scale factor as a function of time for matter dominated universes.
The blue line shows a(t) for Ω < 1, this universe is negatively curved (κ = −1)
and is described as ‘open’; the green line shows a(t) for Ω = 1, this universe has
zero curvature (κ = 0) and is described as ‘flat’; the red line shows a(t) for Ω > 1,
this universe is positively curved (κ = +1) and is described as ‘closed’.
represented here by
Ωtot = Ωr + Ωm + ΩΛ .
(1.13)
The curvature constant, κ, can now be written in the form
κ=
a2 H 2
(Ωtot − 1).
c2
(1.14)
The density parameter, Ωtot , still relates to the sign of the curvature, κ, in
the same way as before (Ωtot < 1 corresponds to negative curvature (κ = −1);
Ωtot = 1 corresponds to a spatially flat geometry (κ = 0); Ωtot > 1 corresponds
to positive curvature (κ = +1)) but the ultimate fate of the Universe is not so
directly linked. The evolution of a universe containing radiation, matter, and dark
energy, depends on the relative size of each component. The different possibilities
are covered in Figure 1.4. For the possible combinations of Ωm and ΩΛ that lie
within the region marked ‘recollapses eventually’, each feasible curvature will
ultimately end in a Big Crunch. In the majority of this region ΩΛ < 0 and so,
along with gravitational forces arising from matter, the cosmological constant
aids the collapse of the universe. The area labelled ‘expands forever’ represents
the scenarios in which the universe will end in a Big Freeze, these universes can
also have any sign for their curvature. In addition to the ultimate fate, several
1.1 Cosmology
9
models exist in which the development of expansion could be very different. In
the ‘No Big Bang’ region the universe begins in a contracting state, at some time
later reaches a minimum scale factor, then expands outwards forever, and so is
described as a Big Bounce universe. Universes which lie on the ‘No Big Bang’
boundary are described as ‘loitering universes’. These universes spend a long
time with a scale factor that is approximately unchanging, eventually however,
they will reach a large enough size to allow an accelerated continuing expansion.
1.1.1.3
The Benchmark Model
Constraints on Ωm and ΩΛ from several experiments are shown in Figure 1.4.
Using the values for Ωr , Ωm , and ΩΛ , that best fit the current data available, we
have what can be referred to as the Benchmark Model or, equivalently, the Λ Cold
Dark Matter (ΛCDM) model. Tables 1.2 and 1.3 list a summary of parameters
and significant epochs in this model. The current values suggest that we live in
a Universe containing approximately 70 % dark energy, 30 % matter, and a small
contribution from radiation. The total density parameter is believed to be close or
equal to unity implying our Universe is spatially flat, or at least very close to flat,
at the current epoch. The evolution of the Benchmark Model contains significant
transitions, first from a radiation dominated era in the early Universe, then to
a matter dominated era, and now into the relatively early stages of a lambdadominated phase. The time dependence of the scale factor increases more rapidly
with each successive phase transition up to the current epoch where a(t) ∝ eKt
(see footnote1 ). This implies that the Universe is expanding at an accelerated
rate and is destined to end in a Big Freeze.
1.1.2
Problems with the Big Bang
Despite its remarkable successes in describing the Universe, several problems with
the Big Bang exist. These problems do not invalidate the Big Bang theory but
do create difficulties in explaining their solution. A few of these problems are
outlined in the following list.
1
K = H0 (1−Ωm,0 )1/2 where Ωm,0 is the matter density component measured at the current
epoch. Legitimately, the radiation contribution has been classed as negligible for this purpose.
10
1. INTRODUCTION TO DARK MATTER
Supernova Cosmology Project
3
Knop et al. (2003)
Spergel et al. (2003)
Allen et al. (2002)
No Big Bang
2
Supernovae
1
ΩΛ
CMB
expands forever
lly
recollapses eventua
0
Clusters
clo
se
t
fla
d
en
op
-1
0
1
2
3
ΩM
Figure 1.4: Curvature and expansion of universes containing both matter and a
cosmological constant, Λ. The closed region represents κ = +1, flat κ = 0, and
open κ = −1. The area marked as ‘No Big Bang’ represents a ‘Big Bounce’ type
expansion, the boundary of which represents a ‘loitering universe’ (see main text
for details). The highlighted regions indicate the best fitting values from CMB and
galaxy cluster data added to the Supernova Cosmology Project (SCP) results [10].
1.1 Cosmology
11
Table 1.2: Current values for the density parameter, Ω, in the Benchmark Model
of our Universe [9; 11]. The distinct constituents of the matter component are
described in Section 1.3.
Parameter
Total radiation
Baryonic matter
Non-baryonic dark matter
Total matter
Dark energy
Total density parameter
Value
Ωr = 8.4 × 10−5
Ωb = 0.046 ± 0.001
Ωnbdm = 0.22 ± 0.02
Ωm = 0.27 ± 0.04
ΩΛ = 0.73 ± 0.04
Ωtot = 1.02 ± 0.02
Table 1.3: Significant epochs in the Benchmark Model of our Universe [9]. The
transition from one era to the next is not abrupt but happens gradually over time.
The time of matter-lambda equality occurred ∼3.7 billion years ago but current
data indicate Ωm and ΩΛ are comparable to within an order of magnitude.
Era
radiation-matter equality
matter-lambda equality
Present day
Age of Universe
trm = 4.7 × 104 yr
tmΛ = 9.8 Gyr
t0 = 13.5 Gyr
The Flatness Problem: From the different scenarios of the expansion of the
Universe it can be seen that if the value of Ωtot is not exactly 1 at any time,
then it will rapidly be driven away from 1; either increasing in a closed universe or decreasing in an open universe. The very fact that current observations
imply Ωtot = 1 means that extrapolating back to the Planck time (∼10−43 s after the Big Bang) Ωtot would need to be unity to within 60 orders of magnitude
i.e. Ωtot = 1 ± 10−60 . The logical solution to this scenario is to set the initial value
Ωtot = 1, where it remains so indefinitely. The flatness problem now becomes a
question of why a value of precisely 1 is, or at least appears to be, inherent to
the Universe.
The Horizon Problem: The extreme uniformity of the CMB traversing the
entire sky implies that at some point in the past all points were in causal contact,
thus enabling them to reach thermal equilibrium. The horizon problem points
out that regions of the sky more than 1◦ apart are separated by distances greater
than light could have travelled during the entire age of the Universe i.e. these
12
1. INTRODUCTION TO DARK MATTER
points are causally disconnected (see Figure 1.5). Given that information (or energy, heat, etc.) cannot travel faster than the speed of light, the CMB uniformity
should not be possible.
r0
A
O
B
Figure 1.5: The horizon problem. The solid circle represents the observable Universe as seen from our location, O. The horizon distance, r0 , is the proper distance
to the surface of last scattering. It is the very edge of the visible Universe from
which the first light emitted has only just reached us. The dashed circles represent
the observable Universe as seen from points A and B respectively i.e. their cosmic
horizons. Although points A and B can both be seen in our observable Universe
they are causally disconnected.
The Monopole Problem: One goal of modern day physicists is to find a Grand
Unified Theory (GUT) that unifies the electromagnetic, weak and strong nuclear
forces into one Grand Unified Force. It is also hoped to take this one step further
and find a Theory of Everything (TOE) that unites the Grand Unified Force with
gravity (see Figure 1.6). This unification has been a great ambition for physicists since James Clerk Maxwell established that electricity and magnetism are
not due to distinct forces, as was once believed, but are in fact both caused by
the one force, electromagnetism. Grand Unified Theories state that prior to the
GUT phase transition the strong and electroweak forces were unified, but since
then have behaved as disparate forces. This GUT phase transition also gave rise
to topological defects such as magnetic monopoles. Magnetic monopoles are essentially an isolated north pole or south pole of a magnet. Theory states that
north and south poles annihilate each other just as particle and antiparticle pairs
1.1 Cosmology
13
do. GUT predicts the very early Universe created monopoles in extreme numbers
and, due to the low reaction cross-section and rapid expansion of the Universe,
monopoles should still exist in abundance today despite annihilation factors. The
monopole problem is that although there is no evidence that magnetic monopoles
are forbidden, they have never been observed. Magnetic poles only appear to exist in pairs: a north pole and a south pole. Simply cutting an existing magnet in
half only creates two smaller magnets, each with a north and south pole. This
lack of detection leads to the obvious possibility that magnetic monopoles may
not even exist. The inflationary theory, however, provides a solution to explain
the monopole, horizon, and flatness problems.
gravity
??
strong
TOE
GUT
weak
ew
−43
time (s)
10
T (K)
10
E (TeV)
10
32
16
−36
10
10
28
12
10
electromagnetic
−12
10
10
16
1
Figure 1.6: Unification theory of the four fundamental forces (adapted from [9]).
In the very early Universe all forces were unified but as the Universe expanded
and cooled it sustained several phase transitions. The corresponding energy, temperature, and time after the Big Bang for each phase transition is indicated. The
electroweak (ew) force has already been confirmed experimentally and by extrapolation, the GUT and TOE conditions have been estimated.
1.1.2.1
Inflation Theory
Inflation, first proposed by Guth [12] and Linde [13], is a theory which states
that the very early Universe underwent a period of accelerated expansion. The
exact details of the driving force behind inflation have yet to be agreed upon
but is described mathematically as a scalar field attributed to an inflation phase
14
1. INTRODUCTION TO DARK MATTER
dominated by some form of a cosmological constant, Λ. In one theory, inflation
begins when the GUT phase transition (at particle energies of 1015 GeV) caused a
release of energy throwing space itself into a state of exponential expansion. Once
the phase transition was complete, the Λ component quickly decayed allowing
the Universe to settle down into the post-inflation era in which the Universe has
continued to evolve according to the Benchmark Model.
Given an exponential rate of expansion, any curvature of the Universe is
exponentially flattened out. This inflation phase can be described through the
analogy of an inflating balloon. Consider a balloon with a wrinkled surface, as it
expands outwards the wrinkles are flattened out. Similarly, the inflation of the
Universe is so rapid that even a strongly curved geometry quickly goes to zero,
resulting in the flat Universe observed today. Ergo, the inflationary theory solves
the flatness problem.
Likewise, the horizon problem is also solved by inflation. The expansion of
space during this time was so quick it was even faster than the speed of light:
space is not bound by the universal speed limit that particles are. This immense
growth meant that distinct points, initially in causal contact, were driven away
from each other to distances outwith causal contact. To best emphasise this point
it is apt to put a scale to this inflationary growth. In one model the inflationary
period lasted for ∼10−34 s, in which time the Universe expanded by a factor ∼ e100
greater than it would have done without inflation [9]. During this inflationary
epoch, the horizon distance increased from 10−28 m to a staggering 1016 m (∼1 pc).
This is a growth of 44 orders of magnitude within a minuscule time frame. To put
this into context, consider our visible Universe. Presently, the proper distance
from the Earth to the surface of last scattering is estimated to be
r0 ≈ 4.34 × 1026 m ≈ 46.5 billion light-years1 .
(1.15)
The instant inflation ended, the proper radius of what would ultimately evolve
into the observable Universe was
rf ≈ 0.9 m.
1
(1.16)
The age of the Universe is estimated to be ∼13.7 billion years and so it is a common
misconception that the radius of the visible Universe is 13.7 billion light-years. When, however,
the expansion of the Universe is considered it is clear that although the light has taken 13.7
billion years to reach us, when it was emitted the corresponding proper distance was much less
than 13.7 billion light-years and has now expanded to a size much greater than 13.7 billion
light-years.
1.1 Cosmology
15
At that moment the mass-energy content of the Universe, en route to become all
the planets, stars, galaxy clusters and superclusters currently visible to us, filled
a sphere of around six feet in diameter, about the height of one man. At the
onset of inflation, this same portion of the Universe had a proper radius of
ri ≈ 3 × 10−44 m
(1.17)
a distance 29 orders of magnitude below the current size of a proton. Before
inflation took place this portion of the Universe was so small, much smaller than
the horizon size, thermal equilibrium could easily be reached thus explaining the
CMB uniformity we see today.
Inflation also addresses the monopole problem in a similar way. The number
density of magnetic monopoles created before or during inflation is exponentially
reduced. This dilution, along with the additional expansion of the Universe,
decreases the number of monopoles in our observable Universe to a level so low
the probability of detection is exceptionally small.
1.1.3
The CMB
The CMB has proven to be a useful tool for analysing the state of the early
Universe. Essentially, the CMB is a snapshot of the Universe at the time of
decoupling of photons from matter. According to the Big Bang theory, immediately prior to decoupling the Universe consisted of a hot plasma of photons,
electrons and baryons. These photons were continually Thomson scattering with
the plasma making the Universe opaque to radiation. At this point the very hot,
dense, opaque Universe contained photons with a typical blackbody spectrum.
As the Universe expanded it also cooled. Approximately 300,000 years after the
Big Bang the temperature had cooled to ∼ 3,000 K and it was then possible
for the electrons to combine with ionised baryons to form neutral atoms. The
blackbody photons were then free to travel through the now transparent Universe. This process is often referred to as either decoupling, relating to when the
photons decoupled from matter, or recombination, relating to when the electrons
combined with nuclei. Since then the Universe has continued to expand and cool,
redshifting the radiation, and what is now seen as a cosmic microwave background
was once a cosmic near-infrared background. Best measurements of this cosmic
background radiation now place the temperature at 2.725 ± 0.002 K [14], indeed,
16
1. INTRODUCTION TO DARK MATTER
the most precisely measured blackbody spectrum in nature. The very existence
of the CMB is arguably the best piece of evidence for the Big Bang theory as it
arises naturally in the aforementioned way, in a model such as the Steady State
universe, however, the CMB is not easily explained.
Figure 1.7: All-sky WMAP measurement of the CMB radiation temperature. The
lowest temperatures are depicted by blue regions with red indicating higher temperatures. The fluctuations shown are of a very small magnitude with the average
temperature measured to be 2.725 ± 0.002 K. Taken from [15].
The small scale temperature fluctuations in the CMB (Figure 1.7) were initially caused by quantum fluctuations in the extremely early Universe which,
amplified by inflation and expansion, gave rise to gravitational potentials from
which matter could clump together. These fluctuations, as discussed later in
Section 1.3.3, essentially provide the necessary initial conditions for all structure
formation seen in our Universe.
The small deviations in the primeval fireball of the Universe represent regions of enhanced signal which, when plotted as a power spectrum (Figure 1.8),
can be referred to as acoustic oscillations. These peaks represent the angular
scale of structure in the CMB. The properties of these peaks (location, spacing,
etc.) depends on the energy-matter content of the pre-recombination fluid and
post-recombination Universe. Fits to the observed power spectra data can be
achieved through several existing models of the Universe, a leading one of which
is the Einstein-de Sitter model containing a zero vacuum energy component. This
model, however, breaks down when additional evidence for the existence of dark
1.1 Cosmology
17
Figure 1.8: Power spectra of the CMB radiation as a function of angular scale
(top) and multipole number, lef f (bottom), as measured by several experiments
[16]. The vertical axis indicates the intensity of temperature fluctuations in the
CMB. Values of vacuum energy and cold dark matter best fitting the Benchmark
Model are used to produce the predicted red curve (ΛCDM). This ΛCDM model
is a good fit to the measured data.
18
1. INTRODUCTION TO DARK MATTER
energy (Section 1.2) is taken into account. The ΛCDM model thus remains as
the best fit to the current data depicting the following parameters:
WMAP three year data alone [2] yields
Ωm h2 = 0.1277+0.0080
−0.0079
Ωb h2 = 0.02229 ± 0.00073
h = 0.732+0.031
−0.032
and then combining WMAP with data from other experiments including 2dFGRS
measurements, Lyα forest data, and others [17], gives
Ωm = 0.27 ± 0.04
Ωtot = 1.02 ± 0.02
providing evidence for a spatially flat Universe containing a large vacuum energy
component. Here we briefly explore the Λ contribution, before more extensively
covering the matter component of the Universe.
1.2
Dark Energy
Dark energy is the name given to a hypothetical form of energy permeating
through ‘empty space’ that exerts a force aiding the expansion of the Universe.
The evolution of the Universe had been (and still is) a question of scientific
and theological debate when Einstein introduced the concept of a cosmological
constant into his EFE. At the time, Einstein added the term to allow for the
possibility of a static Universe. Without this cosmological constant, a universe
in dynamic equilibrium would contract due to the gravitational forces exerted
by matter1 . When evidence was found to show that the Universe was in actuality expanding, an observation consistent with Friedmann’s discovery of the
expanding-universe solution to the original general relativity field equations, Einstein famously abandoned the cosmological constant. In recent years, however,
1
Nowadays, the cosmological constant is no longer considered to provide a static universe
at equilibrium since it accommodates an unstable solution whereby any deviation slightly contracting or expanding results in a contracting or expanding universe respectively.
1.2 Dark Energy
19
evidence indicates that the Universe is in fact undergoing an accelerated expansion commonly believed to be a result of the mysterious dark energy. To account
for this dark energy, the cosmological constant (or vacuum energy) has been reintroduced as a leading candidate along with other hypotheses such as quintessence.
1.2.1
Type Ia Supernovae
The principal incentive for invoking the concept of dark energy arises from observations of type Ia supernovae. Traditionally, supernovae were categorised into
one of two groups: type I supernovae, which contain no evidence of hydrogen
absorption lines in their emission spectra; and type II supernovae, which show
strong evidence of hydrogen absorption lines. The presence of other elements in
the emission spectra and the characteristics of the stars’ respective light curves
are now also used for further subdivision1 . Although these different subcategories exist, all type II supernovae begin as relatively massive stars (at least 8
times greater than the mass of our Sun) then at the end of their lifetime reach a
state whereby the nuclear fuel is exhausted and the release of nuclear energy no
longer supports the star. At this point the core collapses rapidly, is eventually
brought to a halt by the strong force, infalling material from the outer layers then
rebounds and is expelled into space leaving behind a core which will ultimately
form either a black hole or neutron star depending on the respective mass2 . Type
Ib, Ic and type II are in fact all of a similar sort of ‘core collapsing’ supernovae.
Types Ib and Ic are categorised as massive stars whose outer shell of hydrogen has
either been shed or blown away by strong stellar winds or some other interaction.
The remaining core then collapses culminating in a supernova explosion leaving
behind a degenerate remnant.
Type Ia supernovae, in contrast, are triggered through an entirely different
mechanism. This type of supernovae can occur through any one of several distinct
models in which a carbon-oxygen white dwarf accretes mass from a companion.
This companion may be a red giant, main sequence star, or possibly even another
white dwarf (in this scenario it is believed the two white dwarfs actually merge
together). This accretion continues until the mass of the white dwarf reaches a
1
A light curve is simply a plot of luminosity as a function of time. This is commonly used
to classify the subcategories of type II supernovae.
2
If the mass is sufficiently large it is thought the star will directly form a black hole without
the associated supernova explosion. Other models also exist in which extremely massive stars
undergo a supernova explosion through an entirely different mechanism.
20
1. INTRODUCTION TO DARK MATTER
critical mass of ∼1.4 solar masses i.e. the Chandrasekhar limit. At this point,
electron degeneracy can no longer support the star against its own gravitational
forces and the internal temperature increases igniting a runaway thermonuclear
explosion blowing apart the entire white dwarf in a supernova explosion. These
‘standard candles’ only ignite when reaching the Chandrasekhar limit and so
all have an intrinsic brightness from which their distance can be inferred. The
peak luminosities of type Ia supernovae can actually occur within a range of
values but are closely linked to the characteristics of its light curve. Thus, as
a standard candle, this allows the distance of these objects to be determined.
These observations, together with redshift analysis, show that the expansion of
the Universe is not linear or decelerating, as would be expected in a matter
dominated model, but is in fact accelerating (Figure 1.9). This is the key piece
of evidence that demonstrates the necessity for a dark energy component.
1.2.2
The Form of Dark Energy
Although the existence of dark energy can be inferred, very little is actually
known about it. Its true nature remains one of the biggest problems facing modern physics. The two leading models encompass the basic concept of dark energy,
its requirement to have some form of negative pressure opposing gravity, but they
characterise it quite differently: the proposed cosmological constant is a homogeneous energy density field permeating throughout space, whereas quintessence is
a dynamic energy field varying in space and time [18].
The cosmological constant: Often referred to as vacuum energy, this form
of dark energy exists in the so called vacuum and remains constant throughout
space independent of time and location. The expansion or contraction of the
Universe does not affect its characteristics. Classically, the concept of some sort
of energy density field existing throughout a vacuum sounds like a contradiction.
Conservation of energy states that energy may change form but it cannot be
created or destroyed: “Nothing can come of nothing.”1 Opposingly, quantum
physics predicts vacuum fluctuations in which virtual particle-antiparticle pairs
are spontaneously created and then later annihilate each other. These vacuum
1
William Shakespeare, King Lear, Act I, Sc. 1.
1.2 Dark Energy
21
Supernova Cosmology Project
Knop et al. (2003)
ΩΜ , ΩΛ
0.25,0.75
0.25, 0
1, 0
24
Supernova
Cosmology
Project
effective mB
22
20
18
Calan/Tololo
& CfA
16
14
0.0
0.2
0.4
0.6
0.8
1.0
redshift z
Figure 1.9: The effective peak magnitude luminosities of type Ia supernovae versus
redshift, z, as taken by the SCP. The best fit to the data is matched by our flat
ΛCDM model of the Universe. As a basis for comparison the curves obtained
from two other cosmological models have been superimposed onto the data. Taken
from [10].
22
1. INTRODUCTION TO DARK MATTER
fluctuations give rise to the associated energy density of the vacuum. The cosmological constant problem is that quantum field theories predict values for this
energy density that are up to 124 orders of magnitude larger than the presently
determined Ωtot = 1. Within these theories it is therefore essential that a large
finely tuned term of opposite sign exist to facilitate the flat Universe observed.
Quintessence: In this model it is hypothesized that in the early Universe this
form of dark energy had the capability to shadow the radiation density until the
time of radiation-matter equality. At this point the quintessence increased and
eventually grew to dominate over radiation and matter as in the present Universe.
The resultant effect is that it predicts a slower expansion of the Universe than
would be achieved from the cosmological constant model. This tracking ability
helps to solve the problem that any dark energy component in the early Universe
needs to be adequately submissive so as to allow for the formation of small scale
structure, and hence for the evolution of life as we know it.
Another problem facing cosmology is the coincidence problem. As illustrated
in Table 1.3, the Universe has undergone several transitions from one domination
phase to another. It is, perhaps, a remarkable coincidence that we happen to live
in a period close to matter-lambda equality where dark energy has only recently
become the dominating influence. Of course these problems, along with many
others in physics and cosmology, can be viewed by proponents as support for the
anthropic principle. The anthropic principle asserts that the very existence of
intelligent observers in the Universe sets constraints on the fundamental dynamics
and structure to be compatible with that required for life: if the Universe were
different we would not be here to observe it and so we should not be surprised
that all the parameters and fundamental constants appear to be finely tuned so
as to support our creation. Critics of the anthropic principle, however, maintain
that it lacks scientific method and discourages physical explanation.
Although the observation of an accelerating Universe is the primary motivation for implementing dark energy, evidence for its existence (and Ωtot = 1) has
been supported through independent studies of the CMB, gravitational lensing,
Big Bang nucleosynthesis, large scale structure, and measurements of the Hubble parameter [19; 20; 21]. While individual measurements of parameters may
provide crude uncertainties in the make-up of our Universe, the amalgamation
1.3 Matter Constraints
23
of data illustrates a high level of confidence in their obtained accuracies. Concordantly, possible independent predictions for specific parameters, such as dark
matter, can be attained through several means.
1.3
Matter Constraints
Matter in the Universe can be divided into several categories. The mass that
we are all familiar with, i.e. the protons and neutrons that make up the atoms
we typically encounter on a day to day basis, comes under the relatively small
subgroup of matter constituents classified as baryonic matter (Ωb ). This material
not only provides the building blocks for all the visible mass in our Universe (stars,
galaxies, etc.) but, through objects that emit little or no light (baryonic dark
matter, Ωbdm ), contributes to a small fraction of the total dark matter content.
The remaining mass, believed to be the more massive constituent, is in the form
of non-baryonic dark matter (Ωnbdm ). Constraints on the relative abundance
of each component, and the total matter density, can be ascertained through a
number of distinct approaches. With a particular emphasis on dark matter, we
now discuss evidence substantiating the current depiction of matter composition
in our Universe.
1.3.1
Rotation Curves
The first evidence for the existence of dark matter is generally attributed to Fritz
Zwicky who, in the early 1930s, studied the velocity dispersion of galaxies in the
Coma cluster [22]. It was found that the high magnitudes of velocities measured
could not be accounted for by the gravitational potential well arising from the
luminous material alone. This evidence was further supplemented in the 1970s by
the study of spiral galaxy rotation curves. Under expected Newtonian mechanics
the rotational velocity, v(r), of a mass gravitationally bound in a circular orbit
of radius r is given by
r
GM (r)
(1.18)
r
where G is the gravitational constant and M (r) is the total mass enclosed within
v(r) =
radius r. This means that the rotational velocity should decrease with radius as
r−1/2 . Observational data (Figure 1.10) has shown that the rotational velocity of
stars in a spiral galaxy does not obey a Keplerian fall off, as would be expected
24
1. INTRODUCTION TO DARK MATTER
from the distribution of visible mass, but in fact flattens off at large radii. This
indicates that a considerable non-luminous matter component, distributed in a
large spherical halo, exists in these outer regions. Analysis of rotation curves
alone implies that ∼ 90 % of a spiral galaxy’s mass is attributed to the dark
matter halo [23].
Figure 1.10: Plot of radius versus rotation velocity for stars within galaxy NGC
3198 (adapted from [24]). The proposed contribution from dark matter (DM) is
used to explain the discrepancy between the observed data and the curve expected
from luminous matter alone.
1.3.2
Gravitational Lensing
Gravitational lensing exploits the fact that light is bent by the gravitational field
of massive objects (see Figure 1.11). This effect is similar to that of an optical
lens, hence the given name. A noticeable difference, however, is that with gravitational lensing, the bending of light is at a maximum closest to the centre of the
gravitational object and at a minimum furthest from the centre. This bending
effect, together with the relative position of the gravitational lens, can result in a
distortion of the image. Consider a bright object, gravitational lens, and an observer in a straight line. What the observer sees is in fact an Einstein ring of the
original light source. If the gravitational lens does not lie along the central line of
1.3 Matter Constraints
25
Figure 1.11: Gravitational lensing [25]. The gravitational potential well arising
from the large body of mass (2) bends the path of light emitted from the distant
source (1). An observer on Earth (3) may see multiple distorted images of the
light source in a ring type shape surrounding the gravitational lens.
26
1. INTRODUCTION TO DARK MATTER
sight, as is commonly found, the respective distance of the light paths differ resulting in multiple distorted images (Figure 1.12). Careful analysis of this distortion
can allow the mass, and hence dark matter component, of the gravitational lens
to be deduced. The application of this technique is thus a highly valued tool in
modern cosmology. The Cosmic All-Sky Survey (CLASS) project is just one of
the collaborations to utilise gravitational lensing and, through this method, has
estimated the total matter density, Ωm = 0.31+0.27
−0.14 [26]. Other groups such as the
Optical Gravitational Lensing Experiment (OGLE), Microlensing Observations
in Astrophysics (MOA), and the successor to the Massive Astrophysical Compact
Halo Objects (MACHO) collaboration: superMACHO, continue to search for and
set constraints on lensing objects. Results from such experiments have indicated
that baryonic dark matter alone cannot account for the total dark matter content
inferred from observations.
Figure 1.12: Hubble deep field image of the Abell 2218 cluster [27]. Light from
galaxies behind the massive cluster has been bent and focused towards Earth.
Many of the background galaxies are seen as multiple arc-shaped images of varying
brightness.
A recent piece of evidence, and a very convincing one, is the multiple wavelength plus weak lensing analysis of the Bullet Nebula. The distribution of different mass components after two galaxy clusters have collided can be seen in Figure
1.13. In this process, the visible and non-baryonic dark matter components of
1.3 Matter Constraints
27
the galaxies have effectively passed through one another unaltered. The hot gas,
however, which constitutes most of the normal baryonic matter, has collided thus
displacing it from the visible galaxies [28]. Through weak lensing observations it
can be seen that the majority of mass lies in the areas highlighted in blue thus
strongly implying a necessity for a dark matter component.
Figure 1.13: Composite image of the Bullet Nebula [29]. The distribution of
dark matter inferred from gravitational lensing is shown in blue. The majority of
baryonic material, which exists as hot gas, was determined from X-ray emissions
and is highlighted in pink. The distribution of visible material can be seen in
white.
1.3.3
Structure Formation
Current models indicate that dark matter played a vital role in the formation of
the Universe as we know it. Before the time of decoupling, during radiation domination, pressure forces prevented the baryonic material from collapsing below the
Jeans mass. The behaviour of dark matter, in particular cold dark matter (CDM),
was primarily governed by gravitation and was unaffected by the radiation pressure that was so critical to baryonic material. CDM refers to particle candidates
whose kinematical state would have been non-relativistic at the time of decoupling. Correspondingly, hot dark matter (HDM) would have been relativistic at
28
1. INTRODUCTION TO DARK MATTER
this time. These conditions allowed CDM to clump together following the primordial density perturbations created by quantum fluctuations in the very early
Universe. A drop in the Jeans mass, at the time of decoupling, allowed baryons
to follow suit and collapse into the gravitational over-densities created by CDM.
Dissipation of energy, owing to the electromagnetic interactions between baryons,
then allowed baryonic material to coalesce and form higher density regions. Thus
the presence of CDM was responsible for advancing the development of structure
in the Universe. This is where the distinction between CDM and HDM becomes
important.
When considering the formation of large scale structure, there is generally
accepted to be a bottom-up hierarchical progression, starting first with the development of smaller scales, such as galaxies, followed then by galaxy groups,
clusters, superclusters, and finally filament structure. Any growth beyond this
scale is now suppressed as dark energy-driven acceleration becomes increasingly
dominant. The formation of small scale structures, such as stars and planets, depended on the local densities of mass and happened at various stages throughout
the evolution of larger structures. In fact, simulations of large scale structure formation have shown that collisions taking place between galaxies not only formed
larger structures, but in certain cases also helped to coalesce mass and provide
energy to ignite star formation. If the dominant constituent of matter had been
fast moving particles, such as HDM candidates, then mass would have been unable to clump together on small scales and would even suppress the development
of other small scale structures. CDM, however, does allow for the predicted formation of small scale structure. Ordinary baryonic matter on its own would have
been at too high a temperature and too great a pressure after the Big Bang to
form small scale structures. To understand the evolution of the Universe it is
believed that there was in fact a mix of these different types of matter, comprised
of a substantial CDM component and a much smaller HDM component.
1.3.4
X-Ray Emission Measurements
In the centre of galaxy clusters it has been found that there exists an abundance
of very hot (107 − 108 K) baryonic gas now known as the intracluster medium
(ICM). The total mass of galaxy clusters is so great that the arising gravitational
forces provide infalling material (attracted to the galaxy centre) with sufficient
1.3 Matter Constraints
29
kinetic energy to create these high temperatures. This heat not only keeps the gas
in hydrostatic equilibrium with the cluster’s gravitational field, but also allows
for X-ray emission via Bremsstrahlung and atomic line emission. From this it is
possible to not only deduce the mass of the X-ray emitting baryonic matter, but
to also determine the total mass of the galaxy cluster.
The Chandra X-ray Observatory and BeppoSAX (Satellite per Astronomia X)
projects are two of the leading astronomy satellites providing X-ray emission data
sets utilised by many groups. When considering the standard CDM model, Nbody simulations have indicated that the dark matter density distribution at the
centre of galaxy clusters follows a power law behaviour: ρ(r) ∝ rα , where α lies
in the range 1-2 [30]. Observational evidence, however, from both gravitational
lensing and X-ray measurements have shown certain contradictory results. X-ray
constraints set by several groups seemingly agree with the CDM model [31; 32]
but other observations [30; 33], although showing an agreement within a 200 kpc
radius from the centre of galaxy clusters, demonstrate there is a discrepancy below
100 kpc radii. Results indicate that the mass density profile actually flattens off
at these scales. Although additional observations of several clusters indicate flat
cores [34] it should be noted that measurements of many other galaxy clusters
[35] are broadly consistent, although not perfect, with ΛCDM predictions.
1.3.5
Big Bang Nucleosynthesis
Big Bang Nucleosynthesis (BBN) refers to the production of light nuclei in the
early Universe. The high temperatures during the first few minutes after the Big
Bang allowed nuclear fusion to take place forming the stable nuclei 4 He, 2 H, 3 He
and 7 Li. The total mass density of these primordial nuclei, ρx , relative to the
total baryonic mass density, ρb , can be expressed as the primordial fraction
Yx =
ρx
ρb
(1.19)
where x represents a specific nucleus i.e. one of the following: 4 He, 2 H, 3 He or
7
Li. Note this ratio represents the abundance of an isotope in terms of mass but
it can also be expressed in terms of the number of nuclei.
By comparing the abundance of these primordial elements, predicted by the
Big Bang theory, to that deduced from observations, it is possible to determine
an estimate for the total baryonic content of the Universe. Figure 1.14 shows
30
1. INTRODUCTION TO DARK MATTER
the computed and experimentally observed abundance of specific elements as a
function of baryon density. This method sets constraints on Ωb within the limits
[7; 36]
0.017 . Ωb h2 . 0.021
(1.20)
Taking h = 0.73 ± 0.03, sets an upper limit of Ωb < 0.045; far below the total
matter density Ωm = 0.27 ± 0.04.
Figure 1.14: The number abundance relative to H of 4 He, 2 H (deuterium, D),
3
He and 7 Li as a function of baryon density [37]. The horizontal lines indicate
experimentally observed abundances and the curved lines correspond to computed
values. The grey vertical line highlights agreement between observation and theory.
1.4
Dark Matter Candidates
A great number of candidates and theories have been proposed to explain the
so-called missing mass problem of the Universe. Although the solution to this
problem remains an ongoing debate, known characteristics and constraints exist
1.4 Dark Matter Candidates
31
which favour certain possibilities over others. A brief overview of the commonly
mentioned dark matter candidates, and their validity, are outlined here.
1.4.1
Baryonic Dark Matter
MACHOs: The term Massive Astrophysical Compact Halo Objects (MACHOs)
can be used to cover numerous examples of massive astronomical bodies emitting
little or no light. Since they are effectively non-luminous they can be categorised
as dark matter. These include: stellar remnants such as M Dwarfs, red dwarfs,
white dwarfs, neutron stars, and stellar black holes; brown dwarfs1 , a class of
sub-stellar objects; snowballs, hydrogenous comet-like bodies; and unassociated
planetary objects.
SuperMassive Black Holes (SMBH): An SMBH is a black hole with a mass,
M > 105 M , where M is the mass of our Sun (∼1030 kg). There are several
means by which they can form: a stellar black hole can slowly accrete more mass,
a large gas cloud could condense into an extremely massive star which may then
collapse directly into a black hole, or they could be formed by density fluctuations
shortly after the Big Bang giving rise to primordial black holes surviving to this
day.
Gas Clouds: Baryonic particles, in the form of gas and dust, also constitute
dark matter. In fact, in many instances the majority of baryonic matter in a
galaxy cluster is in the form of such gas. The intracluster medium (described in
Section 1.3.4) is an example of hot baryonic gas. Since hot baryonic gas can be
detected through the radiation it emits, this mass contribution can be directly
observed. Cold gas, on the other hand, cannot be detected so easily.
The evidence set out in Section 1.3 constrains the total baryonic content of
the Universe to that which is far below the total matter content, and so it is
believed that baryonic dark matter, although known to exist, cannot explain the
mass discrepancies observed.
1
Brown dwarfs are often referred to as ‘Jupiters’ as they have similar characteristics to the
gas giant but also have distinct differences. Their mass is sufficiently large (13-75 times the
mass of Jupiter) to undergo thermonuclear fusion of deuterium but too low for the nuclear
fusion of hydrogen in their cores. They are therefore categorised as sub-stellar objects.
32
1.4.2
1. INTRODUCTION TO DARK MATTER
Exotic Dark Matter
The bulk of dark matter is thought to be in the form of non-baryonic material. To
fit observed constraints these particles must: be massive and abundant enough
to satisfy Ωnbdm = 0.22 ± 0.02, have long lifetimes, and be able to pass through
baryonic matter almost undisturbed. This exotic matter can also be further divided into cold dark matter and hot dark matter components.
Neutrinos: Neutrinos are elementary particles classed as leptons which come
under the broader term of spin 1/2 fermions. They have no charge, interact
through the weak force, but not the electromagnetic or strong nuclear forces, and
are believed to exist in similar abundances to the number density of background
photons (412 cm−3 [7]). Until the 1990s, neutrino masses were consistent with
zero but, through experimental observations of neutrino oscillations, are now confirmed to have mass. These characteristics qualify neutrinos as good non-baryonic
dark matter candidates. Constraints, however, set the neutrino matter density
contribution to be 0.001 < Ων < 0.05 [38] and so they cannot account for the
total dark matter content. Also, neutrinos are categorised as HDM and so would
have suppressed the formation of bottom-up large scale structure as explained in
Section 1.3.3.
Axions: Axions are hypothetical particles postulated to prevent CP violation
in quantum chromodynamics (QCD). It is expected that their mass lies in the
range 10−6 − 10−3 eV c−2 , with an estimated number density of 1012 − 1014 cm−3
at our location in the Galaxy [7]. Although their individual mass is relatively
low, should they exist, they qualify as CDM and so contribute to the dark matter
content of the Universe. It is predicted that in the presence of a strong magnetic
field, axions can be converted into photons. For a number of years, attempts to
experimentally detect axions through this technique have been undertaken but,
as yet, no axion detection has been confirmed [39].
SUSY WIMPs: Supersymmetric Weakly Interacting Massive Particles (SUSY
WIMPs) encompass a wide range of potential dark matter particles. These contain the generally favoured CDM candidates, the details of which are described
1.4 Dark Matter Candidates
33
in Section 1.4.3.
Figure 1.15 illustrates the accumulation of constraints on the total matter
composition and its individual components. This composition is consistent with
the ΛCDM model where the majority of mass is in the form of CDM.
Figure 1.15: The density of matter/energy constituents in the Universe normalised to the critical density. An overall account of the matter/energy content
is shown below the logarithmic axis and above a breakdown of the matter components. Adapted from [40].
1.4.3
WIMPs
WIMPs and WIMP-type candidates appear in supersymmetric (SUSY) extensions to the Standard Model (SM). It is therefore apt to first describe the SM
and extensions to it before describing in detail the specific WIMP-type candidates.
1.4.3.1
The Standard Model
In 1897, the first elementary particle, the electron, was discovered by J. J. Thomson. Since then a very successful Standard Model has emerged in the field of
particle physics. This theory describes fundamental particles and their interactions through the electromagnetic, strong and weak forces. In this model, leptons
and quarks, both spin 1/2 fermions, are the most basic constituents of matter
34
1. INTRODUCTION TO DARK MATTER
Table 1.4: The known leptons and quarks in the Standard Model. The corresponding anti-particles have equal mass but opposite charge and additive quantum
numbers.
Particle
Symbol
Electron Neutrino
νe
Electron
e−
Muon Neutrino
νµ
Lepton
Muon
µ−
Tau Neutrino
ντ
Tau
τ−
up
u
down
d
charm
c
Quark
strange
s
top
t
bottom
b
Charge (e) Mass (MeV c−2 )
0
< 3 × 10−6
-1
0.511
0
< 0.19
-1
106
0
< 18
-1
1777
+2/3
1.5-4.5
-1/3
5-8.5
+2/3
1000-1400
-1/3
80-155
+2/3
(174.3 ± 5.1) × 103
-1/3
4000-4500
so far discovered. A summary of these particles detailing their characteristics is
shown in Table 1.4. It can be seen that the distinct types of leptons differ greatly
in mass and each charged lepton has a neutrino as a neutral partner. Quarks
have fractional charge but have never been detected individually, they have only
been found in bound states of three (baryons) or bound states of two (mesons).
A proton, for example, is a bound state of uud quarks whilst a neutron consists
of udd quarks, giving an overall charge of +1 and 0 respectively. A meson is
composed of a quark-antiquark pair e.g. the charged pion π + is an ud¯ and π − is
an ūd bound state.
Both quarks and leptons are grouped into (three) generations, within which
they occur in pairs (Table 1.5). The ‘ordinary’ matter we are most familiar with,
i.e. the matter our world is made of, is contained within generation 1. Quarks
interact through all three forces in the standard model: electromagnetic, weak
and strong. Leptons, however, can be categorised into neutrinos, interacting
through only the weak force, and charged leptons, interacting through the weak
and electromagnetic forces. Each of these forces is mediated via the exchange of
gauge bosons, spin 1 particles, as detailed in Table 1.6. There is of course a fourth
fundamental force: gravity. It is significantly weaker than all other forces, in fact,
when dealing on the scale of quarks and leptons, its effects are immeasurable and
can therefore be neglected for these purposes. The mediating particle for gravity
1.4 Dark Matter Candidates
35
Table 1.5: The three generations of quarks and leptons and their interactions in
the Standard Model. Note that the generations are arranged in order of increasing
mass.
Generation:
1
2
Leptons:
νe
e−
Quarks:
u
d
νµ
µ−
3
c
s
ντ
τ−
Interactions
t
b
weak
weak & electromagnetic
electromagnetic,
weak and strong
Table 1.6: Gauge bosons (force carriers) and their interactions in the Standard
Model.
Gauge Boson
Symbol
8 Gluons
g
Photon
γ
Intermediate
Z0
Vector Bosons
W±
Charge (e) Mass (GeV c−2 )
Interaction
0
0
Strong
0
0
Electromagnetic
0
91.1876
Weak
±1
80.423
is known as the graviton but, as yet, has not been detected.
An additional particle predicted by the Standard Model, which has yet to be
observed, is the Higgs boson. If this particle does indeed exist, the implications
are considerable. It is known from quantum theory that fields have associated
particles. In the case of the electromagnetic field, the associated particle is the
photon. Similarly, it is proposed that there exists a Higgs field with an associated
Higgs boson. This field gives rise to the mechanism through which all particles
can acquire mass. If such a field was to permeate through all of space, then as
particles travel through this field they may interact with it. From this interaction
particles appear to gain mass. Discovery of the Higgs boson would thus mark a
pivotal moment in determining the origin of mass in our Universe.
1.4.3.2
Supersymmetry (SUSY)
Supersymmetry is a proposed extension to the SM that relates matter and force
particles i.e. fermions and bosons. This is achieved by invoking a superpartner for
36
1. INTRODUCTION TO DARK MATTER
Table 1.7: The Standard Model particles and their respective superpartners. Each
SM fermion has a bosonic superpartner and each SM boson has a fermionic superpartner. R represents the R-parity of each particle (see main text for details).
SM Particle
Quark
Fermions
Lepton
Gluon
W
Bosons
B
Z
Photon
q
`
g
W
B
Z
γ
Higgs bosons
Hu , Hd
Higgs
Spin
1/2
1/2
1
1
1
1
1
R
+1
+1
+1
+1
+1
+1
+1
Superpartner
Squark
q̃
Slepton
`˜
Gluino
g̃
Wino
W̃
Bino
B̃
Zino
Z̃
Photino
γ̃
Spin
0
0
1/2
1/2
1/2
1/2
1/2
R
-1
-1
-1
-1
-1
-1
-1
0
+1
Higgsinos
1/2
-1
H̃u , H̃d
every particle in the SM. The corresponding superpartners have the same internal
quantum numbers but differ with their SM counterparts by half a unit of spin and
are believed to be much more massive. The Minimal Supersymmetric Standard
Model (MSSM) represents the supersymmetric extension to the SM with the
minimal particle content (see Table 1.7). One problem within the SM is that
the gauge coupling constants, shown in Figure 1.16, do not converge at a single
point. In contrast, when the MSSM particle content is considered, these constants
converge at µ = 2 × 1016 GeV implying supersymmetric grand unification.
It is an attractive feature of the SM that baryon number and lepton number
are, to a good approximation, conserved in experiments. In the MSSM case, however, the presence of the superpartners allows for non-conserving baryon number
and lepton number terms. It is therefore necessary to introduce the existence of
an additional symmetry. The minimal way to do this is through the conservation
of a multiplicative quantum number called R-parity, defined here as
R = (−1)3B+L+2S
(1.21)
where S is the spin, B the baryon number, and L the lepton number. This
definition ensures that all the quarks, leptons and Higgs bosons have R = +1 and
all their superpartners have R = −1. Thus ordinary particles are distinguished
from their superpartners. An important implication of this is that annihilation or
creation of superpartners must occur in pairs. Ergo, R-parity ensures that once
created the Lightest Supersymmetric Particle (LSP) is absolutely stable with
1.4 Dark Matter Candidates
37
Figure 1.16: Running of the gauge coupling constants with energy in the SM
(left) and the MSSM (right) [41]. The gauge groups U(1), SU(2) and SU(3) represent the underlying symmetries of the electromagnetic, weak and strong forces
respectively. Considering only the SM, there is a poor convergence of the gauge
couplings, but when the effects of the MSSM are taken into account, they converge
at approximately 1016 GeV.
no possibility for decay. Given the characteristics of the LSP, it qualifies as an
excellent candidate for CDM.
1.4.3.3
SUSY Candidates
Within the exotic dark matter group there are a number of WIMP-type candidates (shown in Figure 1.17). These candidates have not simply been invented as
possible solutions to the dark matter problem, but have independently been predicted by the SM and supersymmetry. The neutrino and axion do not meet the
requirements necessary to be the favoured CDM candidate and so can be disregarded for the reasons outlined in Section 1.4.2. In addition, there is also another
class of relics named wimpzillas. These wimpzillas, should they exist, could have
been created by extremely high energies shortly after the Big Bang. It has been
postulated that these particles may also be responsible for ultra high energy cosmic rays [42] but recent data from the Pierre Auger Observatory disfavours this
hypothesis [43]. Wimpzillas may, indeed, contribute to the dark matter content
of the Universe but are not the favoured choice. The preferred CDM candidate
is believed to be the LSP for which the principal competitors are: the gravitino,
the axino, the sneutrino, and the neutralino.
The gravitino arises as a consequence of coupling SUSY to gravity, it is the
38
1. INTRODUCTION TO DARK MATTER
Figure 1.17: WIMP-type candidates [44]. mx is the mass of the candidate and σint
denotes an order of magnitude estimate of the interaction strength with ordinary
matter. It should be noted that the area labelled ‘WIMP’ covers several possible
candidates, one of which is the neutralino.
1.4 Dark Matter Candidates
39
fermionic superpartner of the hypothesised graviton. As shown in Figure 1.17,
the mass of the gravitino is predicted to lie in the keV to TeV range and has
an extremely low interaction strength with ordinary matter. If the gravitino is
unstable, then it no longer qualifies as the LSP. If the gravitino is stable then
a problem arises; the calculated density of these particles is predicted to exceed
that of the observed dark matter density. This problem may be overcome by
setting severe constraints on gravitino abundances and so this particle should not
be ruled out entirely [45]. Either way the gravitino is not the favoured candidate
for CDM.
The axino is the fermionic superpartner of the axion. Studies have concluded
that light axinos could constitute warm dark matter while more massive axinos
could qualify as CDM. The axino is electrically and colour neutral, weakly interacting, could potentially be the LSP, and is thus a good candidate for dark
matter.
The sneutrino is the bosonic superpartner of the neutrino. Despite a history
of being classed as a good dark matter candidate, results from direct dark matter
search experiments have ruled out the associated cross-section phase space and
so it is no longer considered a viable option [46].
The two gauginos, B̃ and W̃3 (superpartners of B and W3 respectively), and
the two higgsinos, H̃10 and H̃20 (superpartners of the Higgs bosons H10 and H20 )
can mix to form four mass eigenstates known as neutralinos. The lowest-lying
mass eigenstate of these, χ̃01 , is the favourite candidate to be the LSP and is
the focus of many experimental dark matter searches. It is thought that these
particles existed in equilibrium with the radiation in the early Universe, at a
time when kT mc2 (see footnote1 ). This equilibrium was maintained through
particle-antiparticle annihilation and their inverse reactions
χ + χ̄ p + p̄ (or γ + γ)
(1.22)
where χ is a neutralino, χ̄ is the neutralino’s antiparticle, p + p̄ represents a
different particle-antiparticle pair, and γ is a photon. Once the temperature, T ,
dropped below mc2 /k, the number of neutralinos decreased exponentially with
temperature, reducing the annihilation rate [47]. Evidence currently available
sets the mass of the lightest neutralino within the range 37−500 GeV c−2 [48; 49].
1
k is Boltzmann’s constant, T is the temperature of the Universe, m is the mass of the
particle, and c is the speed of light.
40
1. INTRODUCTION TO DARK MATTER
Given these conditions, their present density parameter is now estimated to be
Ωχ̃01 ∼ 1, a figure that fits our desired models well. The neutralino provides the
most promising solution to date for the dark matter problem.
1.5
Alternative Theories
It is important to appreciate that alternative theories to dark matter exist. One
theory is that of Modified Newtonian Dynamics (MOND) [50] proposed by Mordehai Milgrom. His theory states that Newton’s laws of gravitation are valid above
some critical acceleration but below this value they no longer hold. The force in
fact weakens in direct proportion to the distance and so thus falls off less rapidly
than Newton predicted. A major objection to MOND is that it lacks a priori
motivation. It is simply the best fit to the data presented. It is also found that
despite impressive results on studies of many different galaxies the model breaks
down on widespread analysis. It still holds well on the outer regions of galaxy
clusters but does not explain motion at the inner cores.
Another theory similar to that of MOND is the Non-symmetric Gravitational
Theory [51]. This is essentially a modification on Einstein’s General Relativity
whereby a massive antisymmetric field explains the motion of galaxy rotation
curves. This field affects the motion of stars in our galaxy but is not observable on
the planetary scale. Research into alternative theories to dark matter is ongoing
and should not be discounted.
1.6
Summary
A variety of observations have led to the widely accepted conclusion that we live
in a flat expanding Universe whose evolution can be described through the Big
Bang theory and is consistent, to the best of our knowledge, with the ΛCDM
model. In this model, the matter-energy content of the Universe is composed
of approximately 70 % dark energy, 30 % matter, and a small fraction radiation.
The amalgamation of a great deal of evidence indicates that the majority of
mass is in the form of non-baryonic cold dark matter and that its existence
both affects the current behaviour of ‘normal’ baryonic matter and played a
crucial role in the structure formation of our Universe. Many particles have been
put forward to explain the dark matter content of the Universe and, although
1.6 Summary
41
alternative theories to dark matter exist, the ΛCDM model remains the favoured
choice for which the lightest neutralino is the preferred dark matter candidate.
It should also be noted that the neutralino has not just been invented to explain
mass discrepancies, but has been independently proposed by supersymmetric
extensions to the standard model, a highly successful model found to describe
our Universe with great accuracy.
Chapter 2
Direct Detection of WIMP Dark
Matter
2.1
Introduction
The evidence for the existence of dark matter is highly persuasive but the true
solution to the dark matter problem has yet to be confirmed experimentally. It
is the goal of many collaborations worldwide to provide indisputable evidence
that dark matter, and more particularly CDM, does indeed exist. As described
in Section 1.4.3, the lightest neutralino is thought to be the leading candidate for
CDM and so this is where the direct detection effort is focussed. In this chapter,
the interactions between WIMPs and atomic nuclei, and the techniques required
for the direct detection of these WIMPs, are discussed, along with an overview
of the world’s foremost experimental searches. This then leads to the motivation
behind the technology utilised for the duration of this thesis.
2.2
WIMP-nucleon Interactions
The mechanism through which a WIMP signature is detected is similar in all direct dark matter searches. Occasionally, a WIMP traversing the detector volume
will have a weak interaction with one of the detector’s nuclei. That will then
recoil, depositing energy which can then be detected. This may be observed in
the form of photons (scintillation), charge (ionisation), heat (phonons), or some
other phenomena. Many experiments exploit only one detection method but
some employ a combination of techniques to improve event discrimination. To
43
44
2. DIRECT DETECTION OF WIMP DARK MATTER
fully comprehend and quantify the response of a dark matter detector it is therefore essential to understand the nature of these nuclear recoils. The differential
energy spectrum of such nuclear recoils can be expressed as
dR
R0 −ER /E0 r
=
e
dER
E0 r
(2.1)
where R is the event rate per unit mass of target, ER is the recoil energy, R0 is
the total event rate, E0 is the mean incident kinetic energy of a WIMP of mass
mχ , and the kinematic factor, r, is given by
r=
4mt mχ
(mt + mχ )2
(2.2)
where mt is the mass of the target nucleus [52]. Given typical WIMP galactic
velocities of ∼10−3 c and that WIMP mass estimates lie in the range 10−1000
GeV c−2 , it is expected the energy deposition from such a nuclear recoil would be
a few tens of keV.
Much time and effort is spent by experimentalists to reduce or disregard unwanted background events so as to reveal any hidden WIMP-induced signal. In
effect, what this is doing is reducing the left hand side of Equation 2.1. The right
hand side of Equation 2.1 represents a very much simplified version of the reality
behind these interactions and must be amended to account for the following:
i – The detector is not stationary relative to the galactic rest frame. The Earth
orbits the Sun and the solar system moves through the galaxy (see Section
2.6)1 .
ii – The detection efficiency for nuclear recoils and electron recoils could be
different i.e. the observed recoil energy and the true recoil energy may differ.
In this scenario a quenching factor needs to be taken into account (see
Section 2.5).
iii – The target medium may consist of more than one element. Each species
requires separate calculations for WIMP-nucleon cross-section limits (see
Section 2.5).
iv – Detector constraints, such as energy resolution and threshold effects, limit
its capability (see Section 2.5).
1
The effect of the Earth spinning on its own axis is discussed in Section 2.9.
2.3 Interaction Cross-Sections
45
v – Form factor corrections dependent on recoil energy and the nuclear radius
of the target must be considered (see Section 2.4).
vi – Predicted interaction cross-sections differ for spin-independent and spindependent interactions (see Sections 2.3.1 and 2.3.2)
Taking these conditions into account, Equation 2.1 can be re-written as
dR
|observed = R0 S(E)F 2 (E)I
dE
(2.3)
where S is the modified spectral function that includes the factors listed in points
i−iv, F is the form factor correction described in point v, and I is an interaction
function involving spin-dependent and/or spin-independent factors described in
point vi. R0 remains the unmodified rate for a static detector. These points are
now expanded on in the following sections.
2.3
Interaction Cross-Sections
Experimental searches aim to record nuclear recoils resulting from the elastic
scattering of WIMPs with atomic nuclei. The likelihood of this interaction is
expressed through the elastic scattering cross-section, σA , given as
σA = 4G2F µ2A CA
(2.4)
where GF is the Fermi coupling constant, µA = mt mχ /mt + mχ , and CA is an
enhancement factor dependent on the nucleus and form of the interaction. For a
comprehensive review and derivation of this cross-section refer to [47]. In general,
many forms of interactions exist which all contribute to the total cross-section.
When dealing, however, with WIMP-nucleon elastic scattering cross-sections, the
situation can be simplified. The two dominant interaction types to consider are:
spin-independent interactions, where the WIMP interacts with the mass of the
nucleus; and spin-dependent interactions, where the WIMP interacts with the
spin of the nucleus. The full interaction may be dependent on either contribution
or a mixture of the two.
46
2. DIRECT DETECTION OF WIMP DARK MATTER
2.3.1
Spin-Independent Interactions
For the spin-independent case the cross-section is proportional to the square of
the mass of the nuclei:
σSI = 4G2F µ2A CSI
(2.5)
1
(Zfp + (A − Z)fn )2
2
πGF
(2.6)
and CSI is given by
CSI =
where fp and fn are the WIMP-proton and WIMP-neutron couplings respectively,
Z is the number of protons, and A is the number of nucleons i.e. the mass number.
Neutralinos are Majorana particles and so it is predicted that fp ≈ fn giving
CSI ∝ A2 . Thus, heavy target nuclei provide a greater probability of interaction
over their lighter counterparts.
The WIMP-nucleon elastic scattering cross-section is generally dependent on
the magnitude of the momentum transferred to the nucleon. The characteristic
interaction length, λ, for this is dependent on the average momentum transfer,
q(v0 ), where v0 is the relative velocity of the two particles.
For values of mt and mχ between 10 − 1000 GeV c−2 , and v0 ' 10−3 c, λ '
10−14 − 10−15 m. This length is larger than the scale-size of a typical nucleus,
thus, the interaction must be with the nucleus as a whole. The scattering rate
can therefore be given as [53]
R0 (SI) ' 1.2r
N
2
2
kg−1 day−1
(2.7)
where N is the number of nucleons in the target nucleus. For different target
nuclei, the normalisation rate can be attained by dividing by N. In practice, it
is useful to compare the rate to that of a reference nucleus, commonly Ge, by
multiplying by A2Ge .
2.3.2
Spin-Dependent Interactions
For the spin-dependent case, where the nucleus has an odd number of neutrons
and/or protons, the cross-section is proportional to the spin value J:
σSD = 4G2F µ2A CSD
(2.8)
2.4 The Nuclear Form Factor
47
and CSD is given by
CSD =
(J + 1)
8
(ap hSp i + an hSn i)2
π
J
(2.9)
where ap and an are the WIMP-proton and WIMP-neutron couplings respectively,
hSp i and hSn i are the expectation values of the spin content of the proton group
and neutron group respectively, and J is the total angular momentum of the
nucleus. For all paired spins in the target nucleus the spin-dependent coupling
sums to zero and so the interaction rate is dependent on the spin-content of the
odd nucleon and whether it is a proton or a neutron. A more detailed discussion
on spin-dependent and spin-independent interaction rates can be found in [54].
2.4
The Nuclear Form Factor
When the characteristic interaction length, λ, is comparable to the nuclear radius, rn , the effective cross-section is reduced for increasing momentum transfer,
q. This even occurs for spin-dependent interactions where the interaction is effectively with a single nucleon. This modification is represented through a ‘form
factor’, F , described by [52]
σ(qrn ) = σ0 F 2 (qrn )
(2.10)
where qrn is a dimensionless quantity (in natural units) and σ0 is the fundamental
cross-section in the limit of zero momentum transfer.
Approximating with plane waves (first Born approximation), F (qrn ) is the
Fourier transform of the density distribution, ρ(r), of the nuclear scattering centres:
Z
4π ∞
F (q) =
r sin(qr)ρ(r)dr.
(2.11)
q 0
For the spin-independent case, where the interaction is with the nucleus as a
whole, ρ(r) can be approximated as that for a uniform solid sphere with
ρn for r ≤ rn
ρ(r) =
(2.12)
0 for r ≥ rn
where the nuclear radius is given by rn = 1.14A1/3 fm. The resultant form factor
obtained is given by
F (qrn ) =
3
[sin(qrn ) − qrn cos(qrn )].
(qrn )3
(2.13)
48
2. DIRECT DETECTION OF WIMP DARK MATTER
For the spin-dependent case, where the interaction is with a single nucleon,
ρ(r) can be approximated as that for a thin shell of material. The resultant form
factor is given by
sin(qrn )
F (qrn ) =
(2.14)
qrn
with rn = 1.0A1/3 fm. Equations 2.13 and 2.14 are commonly approximated by
2
F 2 (qrn ) = e−α(qrn ) .
(2.15)
For α = 1/3, this form factor is exactly that of a Gaussian scatter of rrms = rn
which, for small qrn , is an adequate approximation to Equation 2.14. α = 1/5
gives a comparable approximation to Equation 2.13 but only for qrn < 3−4.
In the spin-dependent case, detailed computations from [55] show the zeroes
of Equation 2.14 are partially filled when coupling to all ‘odd group’ nucleons is
taken into account. A suitable approximation for the form factor here is
(
sin(qrn )
qrn < 2.55, qrn > 4.5
F (q) = √qrn
(2.16)
0.047 2.55 ≤ qrn ≤ 4.5
where rn = 1.0A1/3 as before. The form factor as a function of qrn is shown
for the solid sphere approximation (spin-independent case) in Figure 2.1 and for
the thin shell approximation (spin-dependent case) in Figure 2.2. More accurate
calculations for the spin-dependent case are performed in [47; 55] and the spinindependent case is discussed in more detail in [52].
2.5
Detector Limitations
The management of WIMP-induced events described so far has not dealt with the
reality and limitations of experimental apparatus. In practice, detectors are never
perfect and so we must take into account the real life response of such equipment.
The effects considered in this section include: energy detection efficiency, detector
threshold, energy resolution, and target mass fractions.
2.5.1
Efficiency and Energy Threshold
In many detectors it is often found that the true recoil energy deposited in a
target volume is different from the observed recoil energy. The ratio of these
energies largely depends on the type of recoiling target particle. Predominantly,
2.5 Detector Limitations
49
Figure 2.1: The behaviour of the form factor represented by F 2 as a function of
qrn in the solid sphere approximation. The solid line shows the fit to Equation
2.13 (solid sphere approximation) and the dotted line is a rough approximation
based on Equation 2.15 with α = 1/5. Taken from [52].
Figure 2.2: The behaviour of the form factor represented by F 2 as a function of
qrn in the thin shell approximation. The dashed line fits Equation 2.14 (thin shell
approximation), the dotted line shows the rough approximation based on Equation
2.15 with α = 1/3, the solid line is an approximate fit to the single particle model
in which Equation 2.16 holds true, and the circles and stars represent the single
particle model fits for 131 Xe and Nb respectively. Taken from [52].
50
2. DIRECT DETECTION OF WIMP DARK MATTER
the difference between electron and nuclear recoils must be considered, but also
the distinction between varying species of target nuclei needs to be calculated.
For a given recoil energy deposition, ER , the velocity of a recoiling nucleus is less
than that of a recoiling electron. Therefore, and rather importantly, the mean
charge density along the track length will be higher, and recombination times will
be lower, for a nuclear recoil than it would be for the faster electron recoil. This
is a crucial distinction utilised for discrimination purposes in many detectors. It
should also be noted that, due to these characteristics, more ionisation along the
total length of the track will be produced if the recoiling particle was an electron
as opposed to a nucleus. The ratio of the ‘visible’ energy, Ev , to the actual energy
of the recoil, ER , is defined as the ‘quenching factor’, fn , and is given by
Ev = fn ER
(2.17)
and allowing for the dependence of fn with ER ,
dR
ER dfn
dR
= fn 1 +
.
dER
fn dER dEv
(2.18)
When the recoil energy, ER , drops below the threshold at which the maximum
energy transferred to target electrons is lower than that required to produce
ionisation there is a rapid drop in ionisation (or scintillation) efficiency. As a
result, there is a minimum energy, of the order Ec , below which the detector is
not expected to produce an observable signal. For nuclear recoils this is given by
mt
Eg
(2.19)
4me
where mt is the target mass, me the electron mass, and Eg is the ionisation
Ec =
potential. For electron recoils,
Ec =
p 2
m t p
Ee + Eg − Ee
4me
(2.20)
where Ee is the typical kinetic energy of electrons in the atoms or molecules of
the target medium. Below Ec , fn will fall rapidly to zero and the threshold region
0
can be approximated by multiplying the quenching factor accordingly to give fn ,
defined as
0
fn = fn 1 − e−ER /Et
(2.21)
where Et ∼ Ec is a constant for a given target material. Thus, the quenching
factor for a specific target medium can be expressed as a function of ER . See [56]
2.5 Detector Limitations
51
for an example of the quenching factor in a CS2 -filled ionisation detector (where
Ec = 10.08 eV).
In practice, it is useful to define the amount of ionisation liberated in terms
of the number of electron-ion pairs (NIPs) produced:
0
NIPs = fn (ER )ER /W
(2.22)
where W (commonly referred to as the ‘W factor’ for gaseous targets) is the
energy required to liberate a single electron-ion pair, and is ∼19 eV for CS2 . The
correlation between observed NIPs and recoil energy for carbon, sulphur, and
electron recoils in the DRIFT-II detector is discussed in Section 5.3.1.
2.5.2
Energy Resolution
In a hypothetically perfect detector, a monoenergetic source generating N events
0
of energy E would return an energy spectrum observed as a delta function. For
a detector of finite resolution the resulting energy spectrum can be approximated
by a Gaussian distribution. The observed energy spectrum transformation is thus
Z
dR
1 dR −(Ev −Ev0 )2 /2∆E 2 0
1
=√
e
dEv
(2.23)
dEv
∆E dEv0
2π
where ∆E is equal to the width of the peak, defined here as the standard deviation.
It is commonplace to express the energy resolution as the ratio of the width
of the peak at half maximum (FWHM) to the mean energy:
where ∆EFWHM =
√
∆EFWHM
E0
(2.24)
8ln2∆E ' 2.355 × ∆E.
It may be found that the detector signal in question (e.g. from a photo0
multiplier) consists of a discrete number of counts given by, n = E /ε where
ε = 11.5ER (keV )Z −7/3 . At low energies, and for an adequately small number
of counts, the Gaussian fit described in Equation 2.23 could lead to an inaccurate measurement of counts to unphysical negative energy. It is therefore apt to
exhibit the statistical component of the resolution through Poisson rather than
Gaussian statistics [52]:
dR
1
=
dEv
n!ε
Z
dR
dEv0
0
Ev
ε
n
0
0
e−(Ev /ε) dEv .
(2.25)
52
2. DIRECT DETECTION OF WIMP DARK MATTER
2.5.3
Target Composition
It is often found that the target medium in many detectors is composed of more
than one element. As mentioned in Section 2.5.1, for a given recoil energy, distinct
species of elements will produce varying levels of visible energy. Individual limits
on R0 are thus calculated separately for each element. Consider an element, A,
which makes up some fraction, fA , of the total target mass. For this element,
Equation 2.3 can be re-written as
dR
|observed (A) = fA R0 SA FA2 IA .
dE
(2.26)
From [56] the recoil rate is given by
2 NA ρ0
R0 = √
σ0 v0
π A mχ
(2.27)
where NA is Avogadro’s number, ρ0 is the local mean WIMP density, mχ is
expressed in units GeV c−2 , and v0 is the velocity of the Earth relative to the
WIMP ‘wind’ i.e. ∼ 220 km s−1 . These recoil rates can then be converted to
scattering cross-sections for each element and combined to give a total crosssection for the whole target.
2.6
Relative Motion of the Earth
In the simplest models, the dark matter halo in our galaxy is assumed to be
non-rotating. The Milky Way, however, is known to rotate and so the motion of
the solar system through the galactic rest frame creates a WIMP ‘wind’ relative
to the Earth. These velocities can be expressed through:
~uχ = ~vχ − ~v⊕
(2.28)
where |~uχ | = uχ is the WIMP speed relative to the detector, and, with respect
to the galactic rest frame, ~vχ is the WIMP velocity and ~v⊕ the velocity of the
Earth.
Ignoring the rotation of the Earth about its own axis, Equation 2.28 can be
used to relate the WIMP velocity distribution in the Earth’s rest frame, f⊕ (~uχ ),
to the local WIMP velocity distribution in the galactic rest frame, f0 (~vχ ). Given
that the Earth is orbiting the Sun at ∼ 30 km s−1 in a plane inclined at ∼ 60o to
2.6 Relative Motion of the Earth
53
the solar system’s galactic velocity vector, and the solar system orbits the galactic
centre at ∼ 220 km s−1 , |~v⊕ | is given by
|~v⊕ | ∼ 244 + 15sin(2πt) km s−1
(2.29)
where t is the time measured in years from the 2nd March.
The minimum WIMP speed that can generate a recoil of energy ER can be
shown to be
s
umin =
ER mA
2µ2A
(2.30)
and the maximum speed, umax , which is often set to infinity, should realistically
be set to the galactic escape velocity, vesc [57].
Assuming the local velocity distribution follows a Maxwell-Boltzmann form,
the differential recoil energy spectrum can be expressed as
(
h i
vmin −v⊕
vmin +v⊕
1
erf
−
erf
−
4v⊕
v0
v0
dR
ρ0 σA F 2 (ER )
=
2
2
dER
mχ µ2A
erf vesc − √2 vesc e−vesc /v0
v0
−
√1 e
πv0
2
vesc
2
v0
)
π v0
(2.31)
and, ignoring the form factor correction, the total rate, R, is given by
R = 4.9
ρ0 σA
g(v0 , v⊕ , vesc ) kg−1 day−1
mχ mt
(2.32)
where ρ0 is the local WIMP density measured in GeV c−2 cm−3 , σA is measured in
pb, and mχ and mt are measured in GeV c−2 . For a more comprehensive review
of this derivation and the function g(v0 , v⊕ , vesc ) refer to [58].
Considering target material typically used in dark matter detectors, such as
19
F, 32 S, and 131 Xe, it is found that the recoil energy spectrum peaks below
∼100 keV and the total event rate is expected to be . 0.01 kg−1 day−1 . This holds
true even for a heavy nucleus such as Xe and a WIMP-proton spin-independent
cross-section of 10−6 pb. The derivation of Equations 2.31 and 2.32 were carried
out assuming a constant value for v⊕ but, as shown in Equation 2.29, v⊕ modulates sinusoidally giving a higher WIMP-induced event rate in June and a lower
event rate in December. Figure 2.3 illustrates how the motion of the Earth and
solar system cause this annual modulation. The magnitude of the modulation
varies depending on the energy threshold set but is expected to have an amplitude
of up to ∼ 5 % of the mean recoil rate.
54
2. DIRECT DETECTION OF WIMP DARK MATTER
Figure 2.3: Depiction of the major velocity components affecting the WIMP wind.
The solar system’s orbit around the galactic centre provides a WIMP wind from
the approximate direction of Cygnus. The additional motion of the Earth orbiting the Sun introduces an annual modulation to the WIMP-induced event rate
providing strong support for the origin of such a signal.
2.7
Detection Techniques
To optimise an experiment for WIMP detection many factors and difficulties
must be considered and overcome. Given the expected range of WIMP masses,
a target material with a large atomic mass will help improve kinematic factors
and also increase reaction cross-sections. The choice of target element is also
crucial when considering the type of limit to be set: a spin-dependent crosssection limit relies on the net spin of the target, and a spin-independent limit
favours increased atomic mass. An expected WIMP-nucleon interaction rate of
. 0.01 kg−1 day−1 requires exposure, through both total target mass and running
time, to be maximal.
The recoil energy of a WIMP-induced event will be small and so it is necessary to set an adequately low energy threshold. This, however, increases the
rate of unwanted signals seen in the detector and, together with a sizeable exposure, may produce a problematic background. The potential backgrounds seen
may include: muon events, arising from cosmic ray interactions; alpha, beta,
and gamma events, from surrounding material; and, importantly, neutron events,
originating from a variety of sources. These neutron events could be a result
of muon interactions with nearby material, or may be produced from naturally
2.7 Detection Techniques
55
occurring decay chains (such as those from uranium and thorium isotopes) in the
local environment1 , or could occur through some other means.
As described in Section 2.5.1, the type of recoiling particle affects the characteristics of the event signature observed and so, by using this signature, many
unwanted interactions, such as muon and gamma events, may be disregarded
without the need to invoke shielding measurements. Neutrons, however, with
initial energies in the range E0 = 0.1 − 10 MeV, are expected to produce nuclear
recoil events of energy ER = 1 − 50 keV, the expected WIMP-induced range.
Given these energies, and that neither WIMPs nor neutrons interact through the
electromagnetic force, neutron events would leave a signature very similar to that
expected for a WIMP interaction and thus cannot be disregarded so easily. This
leads to the necessity for shielding. The shielding requirements are of course dependent on the environmental backgrounds and the specific techniques employed
by each detector and so appropriate measures are taken to reduce each type of
background accordingly. The first step taken is to place the detector in a low
background environment. This is largely done by locating the experiments in
underground laboratories which not only have the obvious advantage of heavy
shielding from cosmic rays, but often have very radiologically pure surroundings.
Scintillation detectors will traditionally have shielding such as lead and copper
castles erected to reduce unwanted gamma ray interactions. To minimise neutron
events, it is standard practice to surround detector vessels with a suitable form of
passive neutron shielding and, in addition, many systems also utilise the benefits
provided by installing active veto detectors.
At present, it cannot be said that there exists a single optimal technique for
WIMP detection, and so distinct methods are utilised by different collaborations.
Ionisation, scintillation, and phonons are among the most common employed.
Whichever technique is used, they all have similar strategies; once the detector has
been optimised, background rates reduced, and recoil discrimination applied, any
remaining signal is analysed. Ideally, it is hoped that the remaining signal would
match that of a WIMP-induced recoil distribution complete with annual modulation. If, however, no WIMP detection can be confirmed, and any observed signal
matches that expected from background, an upper limit on the WIMP-nucleus
elastic scattering cross-section (corresponding to theoretical WIMP masses) can
1
7.
Background from U and Th content is dealt with for specific examples in Chapters 3 and
56
2. DIRECT DETECTION OF WIMP DARK MATTER
be set. By continually building more sensitive, efficient detectors, the dark matter community continues to delve deeper into the predicted phase-space and will,
hopefully, identify and then confirm a WIMP signal in the near future.
2.8
World Review of WIMP Dark Matter Experiments
A large number of experiments around the world are attempting to prove the
existence of dark matter through the direct detection of WIMPs. These experiments are placed in underground laboratories, often located in mines or road
tunnel excavations, to shield the detectors from cosmic rays and resulting backgrounds which would otherwise swamp a surface based experiment. It is therefore
useful to express the depths of these sites in units of metres of water equivalent
(m.w.e.) as this provides an indication to the expected flux of cosmic ray muons,
shown in Figure 2.4. A brief overview of the main underground sites and their
experiments are outlined here.
Figure 2.4: The relationship between muon flux, Φµ , and underground depth
(m.w.e.) is shown. The corresponding position of many underground laboratories
across the globe are indicated. Taken from [59].
2.8 World Review of WIMP Dark Matter Experiments
2.8.1
57
Boulby (UK)
The Boulby underground facility is located in the north-east of England at the
Boulby mine, North Yorkshire. The mine itself, although housing several experiments, is currently in operation as a working rock-salt and potash mine managed
by Cleveland Potash Ltd. The depth of the mine ranges from 850 m to 1300 m
(the deepest in the UK) with the underground laboratory situated 1100 m below
the surface. From 1987−2007 Boulby mine was the base of operations for a series
of UK Dark Matter Collaboration (UKDMC) projects. Presently, however, the
UKDMC is no longer in existence but the latest experiments survive under their
new collaborative groups.
NaIAD
From 2000 to 2003, the UKDMC operated a dark matter search experiment
named NaIAD (NaI Advanced Detector). The physical set-up of the detector consisted of an array of six thallium-doped sodium iodide, NaI(Tl), crystals
providing a total target mass of 46 kg. Within copper boxes, each crystal was
centred inside a solid polytetrafluoroethylene (PTFE) reflector cage and coupled
to two long quartz light guides, each of which were also mounted in PTFE cages.
Photomultiplier tubes (PMTs), attached to the end of each light guide, were
used to detect scintillation light created from nuclear and electron recoils in the
target medium. A cooling system, in which chilled water was pumped through
surrounding copper coils, was installed to maintain the crystals at an approximate, constant, 10 ◦ C working temperature [60]. To shield the detector from
background radioactivity, these individual modules were positioned inside lead
and copper castles around which layers of wax and polypropylene were added.
With both low and high mass targets (23 Na and
127
I) NaI has the advantage
over many other experiments by being able to reduce related uncertainties in
nuclear physics calculations and being sensitive to both spin-independent and
spin-dependent interactions [60]. Figure 2.7 shows the spin-independent limit set
by NaIAD and Figure 2.8 the corresponding spin-dependent (proton) limit, the
world’s best at the time it was published.
ZEPLIN
ZEPLIN (ZonEd Proportional scintillation in LIquid Noble gases) is an ongoing
58
2. DIRECT DETECTION OF WIMP DARK MATTER
programme initially developed by the UKDMC. The ZEPLIN-I and ZEPLIN-II
experiments have since been decommissioned but the ZEPLIN-III detector, run
by the ZEPLIN-III collaboration, has recently started operation at the Boulby
facility. In each detector, cryogenic liquid xenon was used as a target material.
The sensitivity of Xe to both spin-independent and spin-dependent interactions,
and its high mass (atomic mass ∼131), make Xe a desirable target medium. The
first generation ZEPLIN detector, ZEPLIN-I, ran from 2001 to 2004 and was
a single phase scintillation detector (liquid only) that relied upon pulse shape
discrimination to disregard unwanted interactions. The detector consisted of a
3.2 kg target contained within an oxygen free copper vessel on top of which were
3 PMTs. The main detection unit was housed inside an active liquid scintillator
veto system with passive lead shielding around the entire vessel [61].
The second generation detectors, ZEPLIN-II and ZEPLIN-III, both utilise
dual phase technology (liquid and gas) that use scintillation and electroluminescence to provide proportional discrimination. The basic mechanism through
which a WIMP interaction generates scintillation in liquid xenon is illustrated in
Figure 2.5. A nuclear/electron recoil excites and ionises xenon atoms producing
electron-ion pairs (Xe+ and e− ) and excitons (Xe*). Additionally, recombination
of free electrons with Xe+
2 ions form even more excitons. The resulting Xe2 * excimer state de-excites producing VUV luminescence. In a single phase detector,
this scintillation pulse alone is used for analysis discrimination.
In the two phase system, shown in Figure 2.6, the primary scintillation pulse
is created in the liquid xenon as described previously. In the absence of an
electric field the majority of free electrons produced in the ionisation process
would simply recombine as shown in Figure 2.5. The presence of an electric
field, however, prevents this recombination (not fully) and causes the electrons
to drift toward the liquid surface where a number of these are extracted into the
gas phase. Electrons then drift through the gas layer and, in doing so, excite
the xenon gas atoms producing electroluminescence observed as a second light
output signal. The ratio of the two light pulses depends on the type of interaction
that occurred and can therefore be used to identify the particle responsible for
the initial recoil. For the case of a gamma interaction, the secondary pulse is
much larger than the primary; for a neutron interaction the ratio of these pulses
is much lower.
2.8 World Review of WIMP Dark Matter Experiments
59
Figure 2.5: The interaction processes in liquid xenon.
Figure 2.6: The dual phase Xe system. The top and bottom layers consist of gas
and liquid Xe respectively. See main text for details.
60
2. DIRECT DETECTION OF WIMP DARK MATTER
From 2005 ZEPLIN-II was underground and operational and has only recently
been decommissioned. The ZEPLIN-II detector consisted of a 30 kg liquid Xe
target contained within a tapered PTFE basin. Immediately above the target
were seven 5-inch PMTs situated for very efficient light capture [62]. An active
liquid scintillator veto system surrounded this unit and additional lead and wax
shielding was placed around the whole vessel. The ZEPLIN-II spin-independent
and spin-dependent WIMP-nucleon cross-section limits are shown in Figures 2.7
and 2.8 respectively.
ZEPLIN-III operates in much the same way as ZEPLIN-II but is essentially
a more advanced detector. An array of thirty one 2-inch PMTs are arranged in a
planar geometry and immersed in the liquid phase. This improves light collection
of the primary scintillation pulse by not only removing an interface (liquid-gas)
with mismatched refractive indices, but by also allowing the collection of additional light through total internal reflection. The secondary pulse is improved
upon by utilising a high electric field in the gas phase thereby increasing photon
emission per electron. The refractive index change from the gas to liquid phase
also effectively provides a focusing effect for light reaching the immersed PMTs
[63]. The projected spin-independent limits for ZEPLIN-III are shown in Figure
2.7.
DRIFT
The DRIFT (Directional Recoil Identification From Tracks) programme, previously run by the UKDMC, is today maintained by the DRIFT collaboration1 .
The DRIFT-I detector was in service at the Boulby facility from 2001 until 2004,
during which time the module demonstrated the successful operation of DRIFT
technology. The DRIFT-II programme, which forms the basis for much of the
work outlined in this thesis, is ongoing and is described in detail in Chapter 4.
2.8.2
Gran Sasso (Italy)
The Gran Sasso National Laboratory (Laboratori Nazionali del Gran Sasso (LNGS))
is situated on the east coast of Italy approximately 120 km from Rome. The underground facilities are located at a depth of 3500 m.w.e. inside a tunnel also
1
The University of Edinburgh, The University of Sheffield, The University of New Mexico,
Boston University, Massachusetts Institute of Technology (MIT), and Occidental College.
2.8 World Review of WIMP Dark Matter Experiments
61
built to accommodate a freeway passing underneath the Gran Sasso mountain.
It is the home to a great number of experiments involving many collaborative
groups from many different countries. A few of these programmes are briefly
outlined here but for a comprehensive and up to date review see [64].
DAMA, LIBRA and XeDAMA
DAMA (particle DArk MAtter searches with highly radio-pure scintillators at
Gran Sasso) is a WIMP dark matter search programme with several distinct
experiments. The first detector, usually referred to as DAMA/NaI, used a NaI
target similar to that of NaIAD. The detector consisted of nine 9.7 kg low radioactivity NaI(Tl) crystals with two PMTs attached to each crystal, one at either end.
These crystals were enclosed within a copper box maintained in a high purity nitrogen atmosphere. The copper box was then surrounded by a low radioactive
shield consisting of copper, lead, polyethylene and cadmium materials [65]. An
important distinction between DAMA/NaI and NaIAD was the way in which
recoil events were rejected. NaIAD utilised pulse shape discrimination whereas
DAMA/NaI analysed specific energy windows to try and identify an annual modulation, see [66; 67] for a review. The results presented by the DAMA group
showed an annual modulation consistent with a model-independent WIMP signal (for an acquired 107731 kgdays of non-continuous running) at 6.3 σ C.L. Since
then, several other experiments, namely XENON, CDMS, ZEPLIN, EDELWEISS
and CRESST, have probed this same WIMP-nucleon cross-section phase-space
and not identified a positive WIMP signal. Thus, the DAMA detection has yet
to be confirmed by another experimental group.
The next generation detector, LIBRA (Large Sodium Iodide Bulk for RAre
processes), often referred to as DAMA/LIBRA, is essentially a scaled up version
of DAMA/NaI with a total target mass of ∼ 250 kg. In addition to a larger
target volume, many other alterations make LIBRA an improved detector over
its predecessor. LIBRA began taking preliminary data in March 2003 and released its first results in April 2008. These first results referred to an exposure
of 0.53 ton years but when combined with the previous DAMA/NaI results provided a total exposure of 0.82 ton years. The cumulative data presented showed
an annual modulation consistent with a model-independent WIMP signal at 8.2 σ
C.L. within the 2−6 keV energy interval [68]. It has been proposed that mirror
62
2. DIRECT DETECTION OF WIMP DARK MATTER
dark matter may be able to reconcile this positive DAMA annual modulation
signal with the null results from other experiments [69]. These DAMA results,
however, presently remain a ‘hot’ topic of debate within the dark matter community.
XeDAMA, commonly referred to as DAMA/LXe, is again run by the DAMA
collaboration but utilises pure liquid xenon as its target medium. Scintillation
from the 6.5 kg target is measured by PMTs attached to the vessel. For a detailed review of the detector set-up and main features see [70]. The programme
has already completed its first two phases of operation with the third underway.
CRESST
CRESST (Cryogenic Rare Event Search using Superconducting Thermometers)
is a dark matter search programme which employs detection of scintillation light
simultaneously with the detection of non-thermal phonons. The simultaneous
combination of these two methods allows for powerful discrimination and a considerable reduction of unwanted interactions. The first phase of the detector,
CRESST-I, had four sapphire crystals each with a mass of 262 g and an energy threshold of 500 eV. These were enclosed inside a copper cold box, designed
to cool the crystals to 15 mK, around which layers of copper and lead shielding were constructed. Using this set-up, CRESST-I obtained a spin-independent
WIMP-nucleon cross-section limit of 10−3 pb and a spin-dependent WIMP-proton
cross-section limit of 101 pb [71].
In the second phase, CRESST-II implements a modular design which again
uses simultaneous detection of scintillation and phonons, but each module consists of a 300 g cylindrical CaWO4 target and a cryogenic light detector [72]. A
tungsten superconducting phase transition thermometer (W-SPT) and a superconducting quantum interference device (SQUID) are used as readout devices. A
net exposure time of 20.5 kgdays, obtained during 2004, gave a nuclear recoil rate
of 0.87 ± 0.22 kg−1 day−1 between 12 and 40 keV. Given that a neutron shield and
muon veto were not present at the time of running, this rate was consistent with
the expected neutron-induced background signal [73].
HDMS
2.8 World Review of WIMP Dark Matter Experiments
63
The HDMS (Heidelberg Dark Matter Search) detector, run by the HeidelbergMoscow group, consists of two high purity germanium crystals. The first is a 202 g
p-type enriched 73 Ge crystal which is surrounded by the second well-type natural
Ge crystal of mass 2.111 kg. These two crystals are separated by a 1 mm thick
vespel insulator and the entire set-up is mounted into a copper cryostat cooling
system around which background shielding is placed. The second crystal not only
acts as a low background material surrounding the first but, through coincidence
measuring, effectively reduces unwanted multiple scattering events. Enrichment
of the
73
Ge target, a naturally occurring isotope with non-zero spin, helps to in-
crease spin-dependent sensitivity. For a more detailed review see [74; 75].
GENIUS
The GENIUS (GErmanium NItrogen Underground Setup) experiment, again
run by the Heidelberg-Moscow group, is proposed to ultimately have a naked
76
Ge target of mass 100 kg. This involves running the high-purity germanium
detectors directly in liquid nitrogen, thus removing the necessity for additional
materials used when running in the usual manner. Ergo, the background levels
will be significantly reduced. Before the final detector set-up is realised it was
decided to first run a test facility detector named GENIUS-TF [76]. This experiment, installed in 2003, involved running four separate Ge crystals, each of mass
10 kg, in liquid nitrogen [77]. Then later, in 2004, GENIUS-TF-II was installed
underground. This second phase experiment consists of six 15 kg naked highpurity Ge detectors in liquid nitrogen. It has been predicted that the final 100 kg
GENIUS detector will reach sensitivities at the 10−9 pb level but many practical
problems have been encountered through running the test facility experiments
[78]. The long-term stability of a full GENIUS-type project is, at the moment,
uncertain but not ruled out.
XENON
The XENON programme is designed to detect WIMPs using liquid xenon as a
target material. Future plans involve running a tonne-scale experiment consisting
of an array of 10 individual modules each with a target volume of 100 kg [79]. To
realise this goal it was first decided to run a smaller module (XENON10), with
a target mass of at least 10 kg, as an intermediate step. The actual XENON10
64
2. DIRECT DETECTION OF WIMP DARK MATTER
module built is a dual phase xenon time projection chamber (XeTPC), similar to
that of the ZEPLIN programme, and contains a target mass of 15 kg. The simultaneous measurement of scintillation and ionisation from a single event allows the
detector to discriminate signal from background down to a 4.5 keV nuclear recoil
energy level. From a total exposure of 58.6 live days and a fiducial mass of 5.4 kg,
the experiment was able to set a WIMP-nucleon spin-independent cross-section
upper limit (90 % C.L.) of 8.8 × 10−44 cm2 for a WIMP mass of 100 GeV c−2 , and
4.5 × 10−44 cm2 for a WIMP mass of 30 GeV c−2 [80]. This limit further constrains parameter space previously unpublished, thus, XENON10 presently holds
the world’s leading spin-independent WIMP-nucleon cross-section limit as shown
in Figure 2.7.
2.8.3
Kamioka (Japan)
The Kamioka Underground Observatory was originally built in 1983 for the purpose of verifying GUTs through a nucleon decay experiment. At 1 km underground in the Mozumi Mine (located in Kamioka-cho, Gifu, Japan) it has an
equivalent depth of 2700 m.w.e. Today the laboratory, referred to as the Kamioka
Observatory, is the home to several experiments searching for dark matter.
XMASS
The XMASS (Xenon MASSive detector) programme uses liquid xenon as a
target material and, along with dark matter, aims to detect low energy solar
neutrinos and neutrinoless double-β decays of
136
Xe. The final phase of the pro-
gramme is proposed to have an ∼10 ton target mass with 4π detector coverage
of scintillation light [81]. As a first step toward this goal it was decided to run a
100 kg xenon detector housed in a cubic copper chamber. For scintillation detection, nine PMTs were positioned on each face of the chamber and the whole unit
was surrounded by background shielding. The second phase of the programme
is to run a 1 ton liquid xenon detector with the experimental focus primarily on
dark matter detection. The expected release date of results, or current status of
the programme, have not, at present, been publicised.
ELEGANT V
2.8 World Review of WIMP Dark Matter Experiments
65
ELEGANT V (ELEctron GAmma ray Neutrino Telescope: EL V) was predominantly developed to investigate rare neutrinoless and two-neutrino double-β
decays, but has also been deployed to search for a dark matter signal. The target medium was an array of twenty NaI(Tl) scintillators of total mass 662 kg.
Within the detector an array of plastic scintillator modules was used to act as a
veto system for the main target material. Results concluded that no indicative
annual modulation beyond statistical fluctuations was seen [82]. Results for the
spin-dependent sensitivity were set and can be viewed on Figure 2.8.
LiF
The LiF detector consisted of eight lithium fluoride bolometers totalling a target
mass of 168 g. Each LiF crystal was 2 cm3 in size and had a neutron transmutation doped (NTD) Ge thermistor attached. The bolometers were encased in
copper holders, cooled to 10 mK, and surrounded by background shielding. The
detector was operational from 2001 to 2002 during which time an exposure of
4.1 kg days was accumulated and a spin-dependent WIMP-proton cross-section
sensitivity of approximately 10 pb was achieved [83]. A second similar experiment, using sodium fluoride (NaF) bolometers of total mass 176 g, was run from
2002 to 2003 with a total exposure of 3.38 kg days. This result confirmed that of
LiF and complemented the result of NaIAD [84].
NEWAGE
The NEWAGE (NEw generation WIMP search with an Advanced Gaseous
tracking dEvice) programme is designed to use similar technology to that of
the DRIFT collaboration. NEWAGE utilises CF4 as a target medium which is
a non-zero spin target and is thus capable of producing a spin-dependent limit.
The detector itself is a micro time projection chamber (µ-TPC), named so as it
has a micro pixel chamber developed with fine spatial resolution for the detection of recoil tracks. From research and development runs of a µ-TPC it was
predicted that a 0.3 m3 volume, with a year’s exposure, could reach the leading spin-dependent sensitivity limits of current experiments [85]. Underground
operation and development of the NEWAGE programme is ongoing.
66
2. DIRECT DETECTION OF WIMP DARK MATTER
2.8.4
Modane (France)
The Laboratoire Souterrain de Modane (LSM) is located 1700 m underground
along the Frejus road tunnel which passes underneath the Alps on the FrenchItalian border. The rock overhead reduces the muon flux to that consistent with
a 4500 m.w.e. depth. The laboratory is home to a number of experiments investigating a range of phenomena including double-β decay searches, super heavy
element searches, measurement of extremely low radioactivity levels, and of course
the search for dark matter.
EDELWEISS
The EDELWEISS (Experience pour DEtector Les WIMPs En Site Souterrain)
experiment utilises cryogenic heat-and-ionisation Ge detectors to search for WIMPs.
The measurement of both charge and phonons provides a useful discrimination
technique used to disregard unwanted background events. The first phase detector, EDELWEISS-I, consisted of three 320 g Ge detectors cooled to a temperature
of 17 mK. To record ionisation, Al electrodes were attached to two faces of each
crystal, and neutron transmutation doped (NTD) Ge thermistors were added to
read phonon signals. With an achieved recoil energy threshold of 13 keV in the Ge
detectors and a total exposure of 62 kg days, a WIMP-nucleon spin-independent
cross-section limit of the order 10−6 pb was obtained [86]. Improvements for the
second phase detector, EDELWEISS-II, include: a much larger fiducial volume
made from 21 Ge detectors (ultimately capable of holding 120 units), 50 cm of
polyethylene shielding to reduce background neutron flux, a muon veto system
to tag muon induced neutrons created from interactions with the shielding, and a
more stringent selection of materials to reduce surface electron background. With
these changes EDELWEISS-II is expected to reach sensitivities at the 10−8 pb level
[87].
Future plans involve a merging of the CRESST and EDELWEISS collaborations (together with some new members) to form a new project named EURECA (European Underground Rare Event Calorimeter Array). This will be,
essentially, a scaling up of the CRESST and EDELWEISS experiments, reaching
target masses of several hundred kilograms and ranging up to 1 tonne. The experiment is currently still in the R & D phase with construction planned at the
Modane Underground laboratory.
2.8 World Review of WIMP Dark Matter Experiments
2.8.5
67
SNOLAB (Canada)
Originally built for the Sudbury Neutrino Observatory (SNO) programme, SNOLAB is an extension to the underground facility which is now home to several
experiments, two of which aim to directly detect dark matter particles. The laboratory is located in INCO’s Creighton Mine near Sudbury, Ontario, Canada. At
a 6010 m.w.e. depth (over 2 km physical depth) it is effectively the deepest dark
matter search facility in the world.
PICASSO
In the PICASSO (Program In CAnada to Search for Supersymmetric Objects)
experiment the target medium used consists of millions of tiny droplets of superheated liquid. The droplets range in diameter from 10 to 100 µm and are
composed of fluorine loaded active liquids such as C4 F10 and C3 F8 [88]. The basic concept of detection relies upon the fact that when a liquid has been heated
well above its boiling point, it is extremely unstable. A slight perturbation can
cause an abrupt change of phase from liquid to vapour. So, when an incoming
WIMP causes a target atom, such as F, to recoil, energy is deposited along its
track and, if enough energy is deposited, a tiny proto-bubble is created in the
droplet. The proto-bubble continues to grow until the entire droplet becomes a
vapour. This transformation gives off an acoustic pulse which can be detected
and used to determine the cause of the initial recoil. For a more detailed review
of this technology see [89]. For a WIMP mass of 29 GeV c−2 and a total exposure
of 1.98 ± 0.19 kg days, the experiment was able to set a spin-dependent WIMPproton cross-section limit of 1.31 pb and a WIMP-neutron cross-section limit of
21.5 pb at a 90 % C.L. [90].
DEAP
DEAP (Dark Matter Experiment using Argon Pulse-shape discrimination) is a
relatively new experiment run by collaborators from Canada and the US. The
first stage of the detector consists of a 7 kg liquid argon target and utilises pulse
shape discrimination of scintillation light to suppress unwanted interactions. Trial
runs of the detector were carried out at Queen’s University (Kingston, Ontario,
Canada) and as of October 2007, the detector has been moved to the underground
facility at SNOLAB. A second phase of the programme, a tonne-scale device, is
68
2. DIRECT DETECTION OF WIMP DARK MATTER
due to begin construction in 2008 and is expected to reach WIMP-nucleon crosssection limits at the 10−10 pb level [91].
2.8.6
Soudan (USA)
The Soudan Underground Laboratory is located in the Soudan Mine State Park,
Minnesota, USA. At a depth of 780 m (2090 m.w.e.) it is curently the leading deep
underground science and engineering laboratory in the US. Several experiments
at the facility, some of which are still under construction or in the planning stage,
will take advantage of the low background rates provided by the rock overhead.
One of their major programmes, already underway, is focussed on the search for
dark matter.
CDMS
Until recently, the CDMS (Cryogenic Dark Matter Search) collaboration held the
world’s best spin-independent WIMP-nucleon cross-section limit (currently improved upon by XENON10). The programme uses Ge and Si based Z-dependent
Ionisation and Phonon (ZIP) detetcors, cooled to mK temperatures, to record
nuclear recoils. Through the simultaneous measurement of phonons and ionisation in the detector, excellent discrimination of events can be achieved. The first
generation detector was successfuly operated in a shallow underground site at
a depth of only 16 m.w.e. The success of this detector led to the installation
and operation of the second generation detector, CDMS II, at the Soudan Underground Laboratory. This CDMS II experiment consists of Ge (each 250 g)
and Si (each 100 g) ZIP detectors shielded from background radiation by layers
of copper, lead and polyethylene. Placed around this set-up is a highly efficient
veto scintillator which tags > 99 % of muon-induced neutrons [92]. After a total exposure of 34 (12) kg days (for Ge (Si) targets respectively), averaged over
recoil energies 10−100 keV, no annual modulation beyond expected background
signals was seen. The Ge target thus set an upper limit on the spin-independent
WIMP-nucleon cross-section of 1.6 × 10−7 pb (90 % C.L.) for a WIMP mass of
60 GeV c−2 [93]. New limits announced at the DM 2008 conference improve this
limit to 6.6 × 10−8 pb (4.6 × 10−8 pb when combined with previous CDMS data)
at the 90 % C.L. for a WIMP mass of 60 GeV c−2 .
2.8 World Review of WIMP Dark Matter Experiments
69
Cross-section [cm2] (normalised to nucleon)
-40
10
-41
10
-42
10
-43
10
-44
10
-45
10
1
10
2
10
WIMP Mass [GeV/c2]
10
3
DATA listed top to bottom on plot
NAIAD 2005 final result
DAMA 2000 58k kg-days NaI Ann.Mod. 3sigma,w/o DAMA 1996 limit
CRESST 2004 10.7 kg-day CaWO4
Edelweiss I final limit, 62 kg-days Ge 2000+2002+2003 limit
ZEPLIN I (2005)
ZEPLIN II (Jan 2007) result
CDMS (Soudan) 2004 + 2005 Ge (7 keV threshold)
ZEPLINIII(yr 1) Proj. Sens.
XENON10 2007 (Net 136 kg-d)
ZEPLINIII(yr 3,with PMT upgrade) Proj. Sens.
Figure 2.7: Experimental upper limits on the spin-independent WIMP-nucleon
cross-sections as a function of WIMP mass (note the ZEPLIN-III limits are projected sensitivities). Produced from [94].
70
2. DIRECT DETECTION OF WIMP DARK MATTER
Cross-section [cm2] (normalised to nucleon)
-34
10
-35
10
-36
10
-37
10
-38
10
-39
10
10
1
2
10
WIMP Mass [GeV/c2]
3
10
DATA listed top to bottom on plot
CRESST 2001 spin dep., 1.51 kg-days, 262g sapphire
DAMA 2003 NaI SD-proton (est.)
ELEGANT V NaI spin dep. exclusion limit (OTO COSMO Observatory)
Edelweiss SD-neutron
NAIAD 2005 Final SD-proton
ZEPLIN I SD-neutron (preliminary)
ZEPLIN II SD-neutron
CDMS Soudan 2004+2005 Ge SD-neutron (Ressell form factor)
XENON10 SD-neutron (preliminary)
Figure 2.8: Experimental upper limits on the spin-dependent WIMP-nucleon
cross-sections as a function of WIMP mass. Produced from [94].
2.9 Directional Sensitivity
2.8.7
71
Other Experiments
In addition to the programmes outlined here there also exist a great many more
experiments with the aim or potential to directly detect dark matter. These
include the programmes: IGEX-DM [95], ANAIS [96], and ROSEBUD [97], all run
at the Canfranc underground facility in Spain, and the COURICINO & CUORE
[98], KIMS [99], ORPHEUS [100], ULTIMA [101], SIMPLE [102], and WARP
[103] detectors operated at various locations around the world. For a detailed
description of each experiment refer to the assigned reference or review [104] to
see a more comprehensive run-down of the world’s dark matter searches. Plots of
several experimental spin-independent and spin-dependent WIMP-nucleon crosssection limits are shown in Figures 2.7 and 2.8 respectively.
2.9
Directional Sensitivity
All the experimental searches described thus far have a similar approach to WIMP
detection: to either rule out the WIMP-nucleon interaction phase-space predicted
by theory, or to observe an annual modulation in nuclear recoils above the expected background level and thus identify a WIMP signal. The exceptions to
this are the DRIFT and NEWAGE programmes which additionally aim to identify the direction of the incoming WIMP signal. An annual modulation alone is
certainly favourable evidence for a dark matter signal but cannot unquestionably
confirm the source of origin. First of all, the predicted modulation should be no
more than ∼ 5 %, but it is also likely that any local background signals present
may have a seasonal modulation themselves and thus provide a false positive in
dark matter detection [105].
As described in Section 2.6, the WIMP wind relative to the Earth is roughly
coming from the direction of Cygnus. This, together with the angle of inclination
of Earth’s orbit, implies that due to the rotation of the Earth about its own axis,
the mean WIMP recoil direction for a detector located at the same latitude as
the Boulby underground laboratory will rotate from downwards to southwards
and back again in one sidereal day. Figure 2.9 depicts this effect. The capability to experimentally demonstrate this change in recoil direction would provide
very strong support that such an observed signal was galactic in origin and thus
72
2. DIRECT DETECTION OF WIMP DARK MATTER
WIMP-induced. Moreover, by translating the directions measured in the laboratory frame to the galactic coordinate system (thus removing the effect of the
Earth’s rotation) it would be possible to observe the primary anisotropy in the
distribution of recoil direction. In practice, the distribution of elastic scattering
events will reduce the anisotropy somewhat but the directional signal will still be
apparent.
Figure 2.9: The diurnal fluctuation in WIMP direction. As shown in Figure
2.3, the WIMP wind strikes the Earth from the approximate direction of Cygnus
but the Earth rotates about its own axis. Thus, a detector on Earth, fixed at a
latitude similar to that of the Boulby facility, would observe a daily modulation
in the relative direction of such a WIMP signal. Taken from [106].
To measure the direction of a nuclear recoil inside a target volume the orientation of the track must be reconstructed. This alone can show an asymmetry
in the recoil distribution of approximately 7−17 % for energy thresholds up to
Eth =
1keV
amu
A when considering a WIMP mass of 100 GeV [107]. Directional
capabilities can be further improved if head-tail discrimination is possible. This
means that the start (head) of the track can be differentiated from the end (tail)
of the track. Even without head-tail discrimination, the directional capability to
measure two directional signals (the sidereal modulation in the laboratory frame
and the primary anisotropy in the galactic coordinate system) implies the number of recoil events needed, and thus the overall exposure, will be less than that
2.10 Summary
73
for detectors observing only an annual modulation. The short period demands
on a directional detector would, therefore, be advantageous over the enduring
requirements necessary to show a confirmed annual modulation.
Furthermore, the application of directionality in a direct dark matter search
experiment would allow for investigation into the structure and dynamics of the
WIMP halo in our Galaxy. Deviations in the distribution of recoil direction
observed would provide insight into the true form of the WIMP distribution and,
thus, discrimination between different halo models would be made possible. Ergo,
the motivation for a directional detector such as DRIFT (the detector utilised in
this body of work) is clear. Although the NEWAGE experiment promotes similar
directional concepts, it is the DRIFT programme that currently runs the only
operational full size gaseous TPC with directional technology.
2.10
Summary
At present, direct dark matter search experiments aim to confirm the presence of
dark matter through the observation of WIMP-induced nuclear recoils in their target medium. Though the mechanism may be similar, several distinct techniques
are utilised to detect these interactions. Scintillation, ionisation and phonons
are among the most common methods employed. In the running of such experiments, and the analysis of accumulated data, a number of factors must be considered to account for the true behaviour of WIMP-nucleon interactions. These
include: the relative motion of the Earth, quenching factors, target composition,
detector energy threshold and resolution, form factors, and whether the interaction is spin-dependent or spin-independent. No single method of detection has
proven superior, thus, around the world, there exists a wide variety of unique
experiments.
At the discovery level, detection schemes aspire to observe an excess of nuclear
recoil events above the expected background. This, however, simply provides a
crude measurement of any supposed WIMP signal as its origin may be background in nature. Ideally, such a signal should be accompanied by an annual
modulation fitting the effects predicted by the Earth’s motion around the Sun,
but even this yearly modulation does not authenticate an observed WIMP signal;
the modulation is small and may be dependent on varying background rates or
74
2. DIRECT DETECTION OF WIMP DARK MATTER
detector reponse. Confirmation is required by other experiments reaching similar
sensitivities which, at present, has not come about.
A novel technique is to demonstrate the daily modulation in the directional
distribution of WIMP-induced recoil events. This would provide much more
compelling evidence that the observed signature truly is extraterrestial. Many
distinct programmes worldwide continue to exclude, and probe further into, uncharted parameter phase-space predicted by theory, and whilst other technologies
may be better suited for the initial detection of dark matter, genuine validation
will ultimately transpire from directionality. The only full size detector that is
currently operational and utilises directional capabilities is that of the DRIFT
collaboration.
Chapter 3
Environmental Backgrounds
3.1
Introduction
The bulk of the work outlined within this thesis is primarily focussed on the
DRIFT experiment. The Boulby underground facility is home to the DRIFT
programme and several other experimental projects, thus an understanding of
the environment and its background is essential. This chapter includes an investigation into the U and Th content of the cavern rock, which is believed to
be the dominant source of background neutrons in the laboratory, and describes
a detailed Monte Carlo simulation of the environment which was later modelled
and run to determine the background gamma-ray rejection factor of the DRIFT-I
detector. In addition to background rates, measurement of the activity level of
a
252
Cf neutron source, used for both the DRIFT and ZEPLIN programmes, is
described.
3.2
U & Th Content of the Cavern Rock
When dealing with experiments that require extreme sensitivities, such as those
necessary to search for dark matter in the form of WIMPs, the minutiae of background levels in a given environment suddenly become increasingly significant.
Every effort is made to ensure minimum contamination levels of both the apparatus and the laboratory, however, an accurate knowledge of any remaining background is vital in establishing expected detection rates and thus the necessary
shielding requirements. As shown in Figure 3.1, the rock above and surrounding
the Boulby facility includes a range of different materials. Potash is a generic
term given to a variety of potassium-bearing minerals. The caverns of the mine
75
76
3. ENVIRONMENTAL BACKGROUNDS
are contained within a layer of sylvinite (a mixture of sylvite1 (KCl) and halite
(NaCl, rock-salt) in varying proportions) dating back to the Permian age. Below
this sylvinite layer (commonly referred to as the potash bed) lies a thick layer of
strong, pure halite through which the main roadways are built to access current
and future mining areas. It is within this layer that the underground science
facility is located.
Figure 3.1: Cross-section showing the deposit and overlying strata at the Boulby
mine. Note the special shaft lining needed to exclude water from the aquifer.
Each layer of rock above the facility provides the obvious benefit of shielding
the detector from cosmic rays but does inherently produce its own radioactivity. The thick seam of NaCl in the immediate vicinity provides shielding from
the outer rock and so these exterior layers are of no consequence in the determination of background rates. It is thus the NaCl stratum that needs to be
considered. Background neutrons in the MeV range are produced primarily by
(α,n) reactions derived from the decay chains of U and Th (see Figure 3.2), and U
fission (approximately a factor of 10 lower). For an underground site at a depth
of ∼ 3000 m.w.e. (the case for the Boulby facility), the muon flux is estimated
1
Also known as sylvine.
3.2 U & Th Content of the Cavern Rock
77
at ∼ 3 × 10−8 muons cm−2 s−1 (a detailed investigation into the muon flux at the
Boulby mine can be found in [108]). Through the processes of absorption and
spallation, this muon flux results in a neutron production rate emitted from the
cavern rock of ∼ 3 × 10−11 n g−1 s−1 , three orders of magnitude lower than the
production rate due to U and Th. Thus, the rate of muon-induced neutrons is
negligible for these purposes. To accurately determine the expected neutron flux
from the cavern it is therefore necessary to first estimate the
238
U and
232
Th
content of the NaCl rock, hereby referred to as simply U and Th.
In previous years, estimates of the U and Th content were achieved via mass
spectrometry analysis of rock samples, or by the measurement of gamma-rays
emitted from the U and Th decay chains. In the latter case, individual rock samples were placed next to a Ge detector and the entire set-up was contained within
a shielding castle. The problem with both these methods was that variations in
the local concentration levels could skew overall estimates, i.e., although chemical
analysis of each sample is likely to be very accurate, a small individual sample is
not necessarily a good representation of the cavern as a whole. It was therefore
decided to employ a method in which the average U and Th concentrations in the
cavern walls were determined over a 4π solid angle. This would yield a much more
suitable result by mimicking the conditions and geometrical exposure experienced
by a dark matter detector. This was undertaken by exposing an unshielded Ge
detector in the open cavern and comparing the measured gamma-ray count of the
principal U and Th emission lines to that of a Monte Carlo simulation of known
U and Th concentrations. The results obtained are reported here, and can also
be found in [110]. In addition, a liquid scintillator unit was also used to directly
detect neutrons within certain areas of the cavern [111]. The entire accumulation of data, however, showed a certain level of discrepancy in results between
the different methods. This discrepancy may be explained by the specific difference in locations of each sample/measurement, or it was hypothesised that Rn
progeny plate-out could also affect results. This can occur since
in the decay chain of
238
222
Rn, produced
U, has a propensity to diffuse out of materials, in this
case the cavern walls, and thus allow subsequent Rn progeny to plate-out onto
nearby surfaces. The four most intense gamma-rays emitted from the decay of
238
U (the gamma-ray lines used for analysis) are actually produced in the decay
chain below 222 Rn. Although the absolute rate of gamma-rays emitted from such
Rn progeny plate-out is small relative to that emitted from the cavern rock, the
78
3. ENVIRONMENTAL BACKGROUNDS
Figure 3.2: Uranium and thorium decay chains. Several transitions are mediated
via alpha decay giving rise to (α,n) reactions with the surrounding NaCl rock.
This is the dominant source of background neutrons in the underground facility.
It should be noted that 235 U constitutes less than 1 % of the natural uranium
abundance. Image taken from [109].
3.2 U & Th Content of the Cavern Rock
79
exact position of this plate-out can have a notable effect. For example, if there
exists a thin layer of Rn progeny on the Ge detector head, or on the cavern walls
themselves, the emitted Rn progeny gamma-rays could skew detector measurements giving erroneous estimates of the U content in the rock. For these reasons
it was decided to repeat the unshielded Ge experiment using a more detailed
Monte Carlo simulation of the set-up.
3.2.1
Location of the Ge Run
Over the years a number of experiments have been conducted in several locations
around the undergound facility (see Figure 3.3) with the JIF area being home
to the most recent. The JIF facility itself is essentially a wooden structure with
walls primarily composed of plasterboard. In the construction of the building a
protective membrane layer was included to help minimise Rn contamination of
the laboratory. This, however, was not a fully preventative method but simply a
reduction technique. Rn testing of the laboratory and specific materials concluded
that Rn is indeed present within the JIF facility and has caused unwanted events
in the DRIFT-II module (discussed later in Section 5.3.4), thereby strengthening
the need to repeat the U and Th measurement.
The specific areas of the JIF laboratory are indicated in Figure 3.4. The
section of the JIF area housing the DRIFT and ZEPLIN programmes is a class
10,000 cleanroom. Within the JIF facility there is a specially designed low background laboratory (LB lab) with more stringent cleanroom standards; this is a
class 1,000 cleanroom. It is within this LB lab that gamma-ray measurements
using the Ge detector were made to determine the U and Th content of the cavern
rock.
3.2.2
Modelling the Environment
To achieve an accurate Monte Carlo, a GEANT4 simulation was set up to mimic
the real life geometry and exposure experienced by the detector. The resultant
simulation incorporated a vast improvement in detail and accuracy over previous
efforts to imitate the environment. The first step involved modelling the cavern
mine and laboratory. Figure 3.5 depicts a GEANT4 image of the modelled JIF
area; the white wire outline represents the main cavern in which the JIF building
is located. The entire volume lying outwith this wire frame is composed of NaCl
80
3. ENVIRONMENTAL BACKGROUNDS
Figure 3.3: Overview of the underground site showing the location of several areas used for scientific study in the past and present. The current experimental
programmes, including DRIFT, are situated in the JIF area.
3.2 U & Th Content of the Cavern Rock
81
Figure 3.4: The JIF laboratory in detail. The areas highlighted in red meet strict
cleanroom standards and may only be accessed by personnel through the air shower
indicated, except in emergency situations.
rock of density 2170 kg m−3 . An important point to note is that the JIF building
does not actually occupy all stubs but is shaped as illustrated in Figure 3.4.
For the purposes of this Monte Carlo, however, it was only necessary to model
the structure immediately surrounding the Ge detector i.e. the low background
laboratory. Here the walls and ceiling of the LB lab were modelled as 3 cm
thick plasterboard and the wooden floor was set as 2.5 cm thick fibreboard (more
commonly known as chipboard).
In modelling the Ge detector, particular attention was paid to the detector
head and Ge crystal contained within it. The most crucial aspect of this was
ensuring that the mass of the Ge crystal was indeed accurate. Shown in Figure
3.6, the detector head was set as a hollow aluminium cylinder, 1 mm thick with
outer radius 4.85 cm and length 17.8 cm, encapsulating the Ge crystal set in a
near vacuum. The crystal itself was modelled as HPGe of density 5.32 g cm−3 in
a cylinder shape of radius 3.7 cm and length 8.741 cm providing a total mass of
∼2 kg.
82
3. ENVIRONMENTAL BACKGROUNDS
Figure 3.5: GEANT4 image of the JIF area. The highlighted area indicates the
specially designed low background laboratory within the JIF facility. Scale sizes
are included in the image.
Figure 3.6: GEANT4 image of the Ge detector head in the LB lab. Left: the yellow
volume represents the HPGe crystal and the wire outline depicts the aluminium
head. Right: a more distant view showing the location of the Ge detector relative
to the LB lab. Scale sizes are included in each image.
3.2 U & Th Content of the Cavern Rock
3.2.3
Results
3.2.3.1
Experimental Rates
83
The unshielded Ge detector was set up inside the JIF LB lab and exposed for
24 hours of continuous running. In the obtained spectrum (shown in Figure 3.7)
the four most intense gamma-ray lines emitted from the U and Th decay chains
can be seen superimposed on the Compton continuum. Analysis of these peaks
above the baseline noise led to the observed rates shown in Table 3.1. In addition
to the peaks used for analysis, the 1461 keV peak (produced from the decay of
40
K) has also been marked on Figure 3.7. Although
40
K is a prominent source of
gamma-rays generated from the rock, it does not make a significant contribution
to the rate of background neutrons generated and is therefore not considered in
the analysis performed here; it is the U and Th content that is of interest.
Figure 3.7: 24 hour background gamma-ray spectrum obtained in the JIF low
background laboratory. The decay lines from U and Th are superimposed on the
Compton continuum. The principal gamma-ray emission lines used for analysis
are marked and shown in units of keV. The 1461 keV gamma-ray peak produced
from 40 K has also been marked (see main text for details).
84
3. ENVIRONMENTAL BACKGROUNDS
Table 3.1: Measured rates for the gamma-rays emitted in the decay chains of U
and Th in the cavern rock. The four most intense lines from each decay chain
have been analysed. The line strength indicated represents the intensity of the
emitted gamma-ray per parent decay of natural U and Th [112].
Line
(keV)
609
352
295
1765
Line strength
per parent decay
0.428
0.342
0.177
0.147
Observed events s−1
U
Parent decays g−1 s−1
(for 1 ppb)
1.29E-5
Th
4.06E-6
239
2615
583
911
0.436
0.356
0.304
0.266
0.0416 ± 0.0007
0.0359 ± 0.0007
0.0623 ± 0.0009
0.0560 ± 0.0008
3.2.3.2
0.2102 ± 0.0016
0.1952 ± 0.0015
0.0738 ± 0.0009
0.0509 ± 0.0008
Simulated Rates
In order to replicate the exposure experienced by the Ge detector it was necessary
to simulate the dominant gamma-ray contributions individually and then combine
the results to form a complete overall picture. The individual sources simulated
were as follows:
i – The NaCl cavern rock.
ii – The plasterboard.
iii – The Rn progeny plate-out on the laboratory surfaces.
Over 99.9 % of neutrons emitted from the cavern rock-face are produced within
the first 3 m depth of rock [113]. It is known, however, that 94 % of gamma-rays
originate within the first 25 cm of rock (see Section 3.3) and so, for the purposes
of reducing computation time, gamma-rays were only fired from a volume of rock
extending 25 cm into the cavern walls. This gave a total simulated active rock
mass of ∼ 500 tonnes. The rates of gamma-rays depositing energy in the Ge crystal were then scaled to correct for 100 % of the gamma-ray flux. For convenience
the simulated concentrations of U and Th in the rock were both set as 1 ppb. This
allowed for easy scaling when comparing the simulated results to that of the real
3.2 U & Th Content of the Cavern Rock
85
life measurement. For the case of simulating the plasterboard, independent measurements [114] found the U and Th concentrations to be 300 ppb and 100 ppb
respectively, thus, these values were used for the purpose of this study. Since the
plasterboard contains significant levels of U and Th, these concentrations must
be included here to obtain an accurate estimate of U and Th content of the rock.
When undertaking a comprehensive analysis of background neutron levels, the
full effect of the plasterboard must be considered, this includes the attenuation
of rock neutrons and the neutrons generated from the plasterboard itself. The
plasterboard is, however, relatively thin (∼2 g cm−2 ) and given its composition
(mainly the elements Ca, S, and O) has a lower neutron yield than the NaCl
cavern rock. In [114] the plasterboard is found to produce a net reduction of
∼ 8 % in the neutron flux entering the laboratory, thus the U and Th content of
the cavern rock remains the dominant factor in the level of background neutrons.
Using a specialised Rn detector, the activity of Rn found in the JIF facility
was measured to be 3 Bq m−3 [115]. This level of contamination was then used
to estimate an upper limit on the quantity of Rn progeny plate-out assuming
an even distribution over all surfaces in the LB lab. These surfaces not only
included the walls, ceiling, and floor of the laboratory but also the Ge detector
head, incorporated since it is in close proximity to the Ge crystal. In reality
much of the Rn progeny should escape through the ventilation system and so
this Monte Carlo represents an exaggerated scenario. Simulated results for the
dominant gamma-ray contributions are shown in Table 3.2. Since
produced in the decay chain of
3.2.3.3
238
222
Rn is only
U, the plate-out only affects the U estimate.
U and Th Concentrations
To estimate the U and Th content of the NaCl it was first necessary to obtain
a value for the measured activity produced solely by the contribution from the
cavern rock. This was done by first subtracting the simulated plasterboard rate
from the total measured rate and then separately including and excluding the
effects of Rn progeny plate-out. The resulting value was thus an estimate of the
detected rate of gamma-rays originating from the cavern rock. By comparing
this measured rate to that of the Monte Carlo (simulated using a nominal 1 ppb
for each element), the U and Th content of the rock was estimated for each
gamma-ray emission line. The results obtained are shown in Tables 3.3 and 3.4.
86
3. ENVIRONMENTAL BACKGROUNDS
Table 3.2: GEANT4 simulated rates. The contribution from each source is listed
separately. Note: the 222 Rn progeny plate-out only affects the U result.
Line
(keV)
609
352
295
1765
239
2615
583
911
Rock
(1 ppb U)
1.4E-3 ± 2E-4
1.5E-3 ± 2E-4
7.0E-4 ± 9E-5
3.3E-4 ± 6E-5
(1 ppb Th)
3.7E-4 ± 7E-5
2.1E-4 ± 5E-5
3.1E-4 ± 4E-5
3.1E-4 ± 4E-5
Monte Carlo rate (events s−1 ) from
plate-out onto
plate-out onto
Plasterboard
lab surfaces
Ge detector head
(300 ppb U)
0.0931 ± 0.0057 0.0072 ± 0.0003 0.0047 ± 0.0002
0.1045 ± 0.0060 0.0086 ± 0.0003 0.0053 ± 0.0002
0.0569 ± 0.0032 0.0047 ± 0.0002 0.0032 ± 0.0002
0.0156 ± 0.0016 0.0013 ± 0.0001 0.0009 ± 0.0001
(100 ppb Th)
0.0190 ± 0.0011
0.0036 ± 0.0005
0.0064 ± 0.0004
0.0052 ± 0.0004
Table 3.3: U concentrations of the cavern rock excluding and including
progeny plate-out.
Parent
U
Line Conc U
(keV) exc Rn progeny
(ppb)
609 82 ± 11
352 62 ± 9
295 24 ± 6
1765 106 ± 21
Mean
(ppb)
71 ± 6
Conc U
inc Rn progeny
(ppb)
74 ± 10
53 ± 8
13 ± 5
100 ± 20
Mean
(ppb)
66 ± 6
222
Rn
3.2 U & Th Content of the Cavern Rock
87
Table 3.4: Calculated U and Th concentrations in the NaCl cavern rock. The
effect of Rn progeny plate-out has been included in the U estimation.
Parent
U
Th
Line
(keV)
609
352
295
1765
239
2615
583
911
Conc U & Th Mean
(ppb)
(ppb)
74 ± 10
53 ± 8
13 ± 5
100 ± 20
66 ± 6
61 ± 12
154 ± 37
181 ± 26
165 ± 24
145 ± 13
The data indicates that although Rn progeny plate-out can have a notable
effect on the estimate of the U concentration, it does not determine or substantially alter the calculated concentrations; the results with and without Rn
progeny plate-out agree within errors. This is, in itself, an encouraging result
as it means Rn progeny plate-out does not govern the Ge detector’s response.
An undesirable observation, however, is that the concentrations corresponding to
each gamma-ray emission line are inconsistent with one another for both U and
Th. When interpreting these results it could be said that the lower energy peaks
have a biased weighting towards reduced estimates of the U and Th concentrations. It may be possible that when calibrating the Ge detector the efficiency was
inaccurately portrayed at low energies, thereby distorting valid detection rates.
Despite these discrepancies, the mean U and Th concentrations, including
and excluding Rn progeny, still agree within error to that of Smith et al. i.e.
67 ± 6 ppb U and 127 ± 10 ppb Th [110]. These are also consistent with additional
measurements in which a liquid scintillator unit was used to directly detect the
neutron flux within the cavern and thus determine the U and Th content, found
to be 95 ± 34 ppb U and 190 ± 69 ppb Th [111].
3.2.4
Conclusion
Several measurements of the U and Th content of the cavern rock, all using a
detection scheme in which a 4π coverage technique is employed, agree within
88
3. ENVIRONMENTAL BACKGROUNDS
errors. Furthermore, the analysis performed here dictates that Rn progeny plateout does not play a significant role in measurements made using the unshielded
Ge detector. The culmination of techniques utilised over the years implies that an
approach incorporating a 4π coverage provides a consistent reproducable method
of determining the U and Th content of the cavern rock. In addition, such a
technique is favoured over that in which a small sample of rock is analysed,
as was the case for mass spectrometry analysis and shielded Ge detector runs.
Through this work an important uncertainty in previous measurements has been
eliminated and, with the rejection of the small-sample technique, consistency
now established. The concentrations determined by Smith et al., confirmed here,
have since been used in many simulations for both DRIFT and ZEPLIN purposes.
This includes simulations to determine the volume of passive neutron shielding
required around the DRIFT-II vessels.
3.3
Background Gamma-Rays
The dominant contributions to background gamma-rays in the underground laboratory are derived from the decay of
238
U,
232
Th, and
40
K (1130 ppm [116])
contained within the NaCl rock. Using the known concentration levels of these
radioactive elements, the energy emission spectrum from the surrounding cavern
was generated using the SOURCES package and inserted into a GEANT4 Monte
Carlo of the environment. This Monte Carlo was then later used to simulate background events within the DRIFT I module1 allowing the detector’s gamma-ray
rejection factor to be deduced (see Chapter 5).
Before carrying out such simulations it was first neccessary to investigate the
depth of rock from which gamma-rays are produced and still penetrate the rocklaboratory boundary. Figure 3.8 shows the results of this investigation. It was
found that ∼ 94 % of the total gamma-ray flux entering the laboratory from the
cavern walls is generated within the first 25 cm of rock depth.
Using an active volume of rock extending 25 cm into the cavern walls, a Monte
Carlo simulation was carried out to reproduce the background gamma-ray spectrum obtained using the HPGe detector. This simulated spectrum, shown in Figure 3.9, is akin to the measured spectrum shown in Figure 3.7 and thus provides
additional support for the Monte Carlo’s authenticity. The basic shape of the
1
The design and concept of DRIFT modules is discussed in detail in Chapter 4.
252
Cf Neutron Source Measurement
Gamma ray flux (s-1m-2)
3.4
89
900
800
700
600
500
400
300
200
100
0
0
20
40
60
80
100
Active Rock Depth (cm)
Figure 3.8: Gamma-ray flux emitted from the cavern rock face as a function
of active rock depth. Approximately 94 % of the total gamma-ray flux originate
within the first 25 cm of rock.
spectra are the same and the large 1461 keV peak (produced from 40 K) is clearly
visible in the simulated results with other peaks beginning to emerge above background. Comprehensive reproduction of the full spectrum, however, is severely
limited by the computation time of the simulation; in reality an extremely large
number of gamma-rays, ranging throughout the whole energy emission spectrum,
are emitted from thousands of tonnes of rock and relatively few actually deposit
energy in the small 2 kg Ge crystal. Through increased statistics and improved
accuracy in the modelling of the rock gamma-ray production, it would be possible
to reproduce the finer attributes of the real background spectrum. For the case of
modelling the U and Th content, it was only necessary to simulate the principal
gamma-ray emission lines and thus computation time was greatly reduced.
3.4
252
Cf Neutron Source Measurement
When calibrating a detector with a radioactive source it is essential that certain
characteristics, such as the production rate and energy spectrum of the source, are
known as accurately as possible. For both the DRIFT and ZEPLIN programmes,
a 252 Cf neutron source was used to perform neutron calibration runs. This source,
90
3. ENVIRONMENTAL BACKGROUNDS
Figure 3.9: A Monte Carlo reproduction of the background gamma-ray spectrum
observed by the HPGe detector. See Figure 3.7 for the real life background spectrum.
3.4
252
Cf Neutron Source Measurement
91
when not in use, is housed inside a safe within the JIF store (indicated in Figure
3.4) and maintained at an appropriate distance from the detectors. The source
has been used, and will still be used, many times for calibration runs crucial to the
running and understanding of the DRIFT detector’s response to neutron events.
For this reason it was decided that, although the activity of the source was given
at the time of purchase, it would be prudent to verify the neutron production
rate. Also, some discrepancies in other results called in to question the activity
of the source, thereby providing added incentive for this evaluation.
The procedure to carry out this measurement first involved immersing the
source in a volume of CH2 big enough such that a significant fraction of neutrons
emitted by the source were thermalised and underwent neutron capture. Since
capture occurred almost exclusively on hydrogen nuclei, this was accompanied
by the emission of a 2.225 MeV gamma-ray, the energy equivalent to the “mass
defect” of the system. By detecting these gamma-rays with a HPGe detector
and then comparing the measured yield to that of a detailed Monte Carlo, the
source activity could be deduced. Details of the measurement are described in
the following sections and the results given.
3.4.1
The
252
Cf Source
Although the neutron source is composed almost entirely from
component of the source is made from
250
252
Cf. When acquired, the activity levels
for each isotope, quoted by the manufacturer, were given as:
• activity of
252
Cf in September 1994 = 1.80 × 106 Bq
• activity of
250
Cf in September 1994 = 5.55 × 104 Bq.
It is also known that each component has the following attributes:
•
252
Cf: half life = 2.645 years,
spontaneous fission branching ratio = 3.09 %,
neutron multiplicity per fission = 3.75
•
250
Cf, a small
Cf: half life = 13.08 years,
spontaneous fission branching ratio = 0.08 %,
neutron multiplicity per fission = 3.70
92
3. ENVIRONMENTAL BACKGROUNDS
By incorporating the attributes listed above, and assuming the source was manufactured at the end of September 1994, on the 20th October 2005 (the date the
Ge detector was exposed to the source) the respective neutron production rates
would have decreased to 11,487 n s−1 for
252
Cf and 91 n s−1 for
a total neutron production rate of 11,578 n s
−1
250
Cf, leading to
1
±5% .
250
Since the Cf component of the neutron source contributes to only a small
fraction of the total source activity, and is significantly less than the errors involved, for the purposes of this work the source was, justifiably, simulated as
emanating a
252
Cf spectrum only. The emitted neutron energy spectrum of the
Production Rate per 100 keV bin (neutrons s-1 cm-3)
source used in the Monte Carlo is shown in Figure 3.10. Here the neutrons are
predominantly produced by spontaneous fission.
×1018
30
25
20
15
10
5
0
0
2
4
6
Energy (MeV)
8
10
Figure 3.10: The neutron energy spectrum emitted by a 50 µCi 252 Cf source. This
spectrum was produced using SOURCES-4C.
3.4.2
Experiment
Before performing the
252
Cf measurement it was first necessary to calibrate both
the energy and efficiency of the HPGe detector. Efficiency calibration runs carried
1
5 % error quoted by the source manufacturer.
3.4
252
Cf Neutron Source Measurement
out using a
60
93
Co source were found to give close agreement to the performance
specifications quoted by the manufacturer. Extrapolation of these data provided
an estimate for the detector’s intrinsic peak efficiency at 2.225 MeV to be
Ei,p(2.225M eV ) = (12.6 ± 1.7) %.
The main sources of error in the calculation of this efficiency came from the
geometrical set-up and the extrapolation of data up to the 2.225 MeV energy
range.
In the dedicated LB lab within the JIF facility, the
252
Cf source (effectively
a point source permanently contained within a lead canister) was immersed in a
22 cm diameter, 41.5 cm high cylinder of polyethylene pellets (average density
0.6 gcm−3 ). Thermal neutron capture on hydrogen nuclei resulted in the emission
of 2.225 MeV gamma-rays. These gamma-rays were then detected with the well
calibrated HPGe detector set at a distance of 3.11 m away. Comparisons of the
Ge detector spectrum with and without the
252
Cf source present clearly showed
the presence of an additional photopeak at 2.225 MeV. The obtained spectra are
shown in Figure 3.11.
3.4.3
Monte Carlo
An extensive GEANT4 Monte Carlo was set up to exactly mimic the geometry
and physics of the experimental run. This included a detailed geometry of the
source, its permanent lead canister, the surrounding polyethylene, the HPGe
detector, the laboratory environment, and an extended volume of the cavern rock
surrounding the laboratory. Figure 3.12 shows a simulated image of the source
position relative to the detector. The fraction of neutrons captured within the
finite polyethylene volume, and the gamma-ray propagation from the capture
site to the surface of the detector, were incorporated within the Monte Carlo.
The GEANT4 neutron cross-section library included all relevant neutron capture
cross-sections.
3.4.4
Results
Within the Monte Carlo a total of 11.44 × 106 neutrons were fired from the
252
Cf
source. To determine the effect of the experimental uncertainty in source position, the simulation was repeated several times each with the source at varying
94
3. ENVIRONMENTAL BACKGROUNDS
Figure 3.11: The gamma-ray spectrum obtained when the 252 Cf source was immersed within the volume of CH2 . Inset: An enlarged section showing the spectrum obtained with the 252 Cf source removed (red) i.e. a background spectrum,
the spectrum obtained with the 252 Cf source present (green), and a subtraction of
one from the other (black). For clarity, the background spectrum and source spectrum have been offset by 200 counts and 100 counts respectively. The background
subtraction included a factor accounting for the slightly different live times of the
two data sets. The spectra clearly show the 2.225 MeV peak is not present in the
background run.
3.4
252
Cf Neutron Source Measurement
95
Figure 3.12: GEANT4 image of the Ge detector relative to the source position.
The 252 Cf source was placed inside the volume of CH2 pellets contained within a
plastic bin (coloured blue above).
positions within the volume of pellets. The error in position was simulated as
± 5 cm in the x-direction (the principal direction of distance between source and
detector) and ± 5 cm in the y-direction (vertical axis of the laboratory). It was
found that when compared to the original position, the average count per run did
not vary by more than 10-15 %. It is with high confidence that the actual error
in source position was much less than ± 5 cm in each direction, and so the error
in the simulated results is dominated by statistical uncertainties. Evaluating the
experimental results against that of the Monte Carlo, the neutron production rate
of the 252 Cf source on the 20th October 2005 was found to be 11,432 n s−1 ± 15 %,
a result consistent with the expected rate derived from the activity claimed by
the source manufacturer .
3.4.5
Conclusion
Verification of the source activity was an essential requirement for the collaboration, crucial to fully understanding the behaviour and response of DRIFT
modules. Measurement of the
252
Cf source indicates that the activity claimed
by the manufacturer was indeed accurate. The precision of the simulated results
could be improved through increased statistics but the final error is dominated
by the uncertainty in the intrinsic efficiency of the detector at 2.225 MeV.
96
3.5
3. ENVIRONMENTAL BACKGROUNDS
Summary
An investigation into the U and Th content of the cavern rock was consistent
with previous measurements and showed that Rn progeny plate-out does not
greatly affect the gamma-ray measurements made using the unshielded Ge detector. The measurement techniques employed here incorporated 4π coverage of
the surrounding environment and demonstrated that such a method provides reproducable results. Verification of the concentrations determined by Smith et al.
[110] (67 ± 6 ppb U and 127 ± 10 ppb Th) has provided added confirmation on
the validity of the many neutron background simulations carried out using these
values, for both DRIFT and ZEPLIN experiments.
Approximately 94 % of the gamma-rays contributing to the total gamma-ray
flux emitted from the cavern walls originate within the first 25 cm of rock. Derived
from the known concentration levels of
238
U,
232
Th, and
40
K, the background
gamma-ray energy spectrum emitted from the NaCl rock was integrated within
a GEANT4 simulation and used to reproduce the Ge detector background run
giving congruent results. A version of this Monte Carlo was then later adapted
to deduce the gamma-ray rejection factor of the DRIFT-I module, presented in
Chapter 5.
A measurement of the
252
Cf source, perennially used for neutron calibration
runs in DRIFT modules, was undertaken to verify its neutron production rate. By
immersing the source in a volume of polyethylene, a substantial fraction of emitted
neutrons underwent thermal capture on hydrogen nuclei giving off 2.225 MeV
gamma-rays which were then detected using a HPGe detector. Comparison of
these measured rates to that of a detailed Monte Carlo simulation confirmed
the manufacturer’s claim providing a definitive neutron production rate from the
source.
Chapter 4
DRIFT
4.1
Introduction
The DRIFT (Directional Recoil Identification From Tracks) programme, previously introduced in Section 2.8.1, ultimately aims to either confirm or rule out
the presence of a directional WIMP-induced signature. To achieve this goal, the
DRIFT collaboration continues to operate and develop detectors based on Time
Projection Chamber (TPC) technology. In this chapter, the basic concept of detection employed by DRIFT is described and then more precisely the design of
the DRIFT-IIa detector is given with further comments on later DRIFT-II modules. In addition, example data taken for specific recoil events and the response
of a DRIFT detector is illustrated.
4.2
Concept of DRIFT Detection
To provide a large overall target mass for WIMP detection, the DRIFT programme will, in the long term, consist of many modules set up in an array configuration. Each individual DRIFT module is a Negative Ion Time Projection
Chamber (NITPC) filled with a low pressure gas (currently CS2 ) and utilises the
phenomenon of ionisation to detect nuclear recoils. As shown in Figure 4.1, a
recoiling nucleus from a WIMP interaction creates an ionisation track inside the
target volume. The ionisation track produced is initially composed of electrons
which then attach themselves to CS2 molecules creating negatively charged CS−
2
‘anions’. In the presence of an applied electric field these negative ions drift towards a charge readout plane comprised of many individual wires arranged in a
97
98
4. DRIFT
grid layout. In the immediate region of the wire planes the high intensity electric field causes the electrons to be stripped from the anions and an avalanche of
charge is directed onto the readout plane. The final signal is then passed through
electronics and analysed. By considering the timing and location of each wire
hit, this signal can then be used to identify the energy, size, and direction of the
track thus making DRIFT a directional detector.
Figure 4.1: Negative ion drift inside a CS2 gas filled TPC. See main text for
details.
Due to the low energies involved, and the readout resolution capabilities of current technology, recoil ranges in solids and liquids are too short (around 10−8 m)
to provide any directional information. By using a low pressure gas, track ranges
reach the order of a few millimetres allowing directional information to be maintained. Individual DRIFT modules presently operate with CS2 gas at a pressure
of 40 Torr equating to a fiducial mass of 167 g per module. To detect a WIMP signal, however, a high target mass is desired and so a trade-off between sensitivity
and directionality must be made. In the case of DRIFT a large fiducial mass will
be realised by increasing the total number of modules. Gas targets, however, still
have their own limitations. As an ionisation track is drifted through the detector
volume towards the readout plane, diffusion occurs. If this diffusion is too great
then the track characteristics are lost and directionality cannot be achieved. The
diffusion effects experienced by the CS−
2 anions are less substantial than those
felt by electrons alone.
4.3 The DRIFT-II Detector
99
Consider the case of electron drift. Suppose an electron scatters off a particle
in the target gas; due to its low mass, the electron will scatter isotropically and
then, immediately after the collision, discard any preferential direction it may
have originally had. Before its next collision, the electron gains energy as it is
accelerated in the presence of an applied electric field. Ions, on the other hand,
have a much larger mass and a much lower charge-to-mass ratio than electrons.
In a given electric field, electrons will be accelerated more rapidly than ions and,
unlike ions, tend to lose very little energy through elastic collisions with target
gas atoms. Thus, on average, the electron momentum is randomised through
collisions and is therefore lost, whereas the ion momentum is not randomised as
much. The random energies of electrons can far exceed the energy of the thermal
motion, but for the case of ions the random energy remains mostly thermal. A
cloud of drifting electrons is thus subject to a much greater spatial spread (orders
of magnitude larger) than that experienced by drifting ions under comparable
drift fields and drift distances [117]. Using a mildly electronegative gas mixture,
such as CS2 , and a high electric field, long drift distances (' 50 cm in DRIFT)
are a viable option.
4.3
The DRIFT-II Detector
The first phase of the DRIFT programme, DRIFT-I, was run within the JIF
facility and successfully demonstrated the operation of DRIFT technology. For
a comprehensive review of DRIFT-I refer to [118]. The DRIFT-IIa module, as
with all other DRIFT modules, consisted of a 1 m3 fiducial volume inside a larger
stainless steel vessel. DRIFT-IIa was also operated in the JIF underground laboratory but has since been decommissioned. At present, the DRIFT-IIb detector
is fully operational at Boulby with the third module, DRIFT-IIc, set up and
functional at Occidental college, LA. There, DRIFT-IIc can be easily accessed by
members of the DRIFT collaboration and used for R&D or preliminary test runs
before future installation at Boulby where there exists space for up to 20 DRIFT
modules. Every module is composed of what is, essentially, two back-to-back
detectors each comprising a 0.5 m3 drift region and a Multi-Wire Proportional
Counter (MWPC) readout plane. In the following sections the specific design
of DRIFT-IIa is described but many of the features are generic or similar in all
DRIFT modules.
100
4.3.1
4. DRIFT
The Vessel
DRIFT vessels have a mass of approximately 1.9 tonnes and are constructed from
low background 304-grade stainless steel approximately 7 mm thick in the main
vessel walls and 12.5 mm thick in the hinged door [119]. The internal dimensions
are approximately 1.5 × 1.5 × 1.5 m3 with these internal walls being polished to
minimise gas absorption. Since these vessels need to withstand pressure differentials of at least 1.2 atmospheres, the cube shape is reinforced with strengthening
ribs at strategically calculated positions. From an engineering point of view, a
cubic shape is not, structurally, the strongest to use; a cylindrical shaped vessel is
intrinsically better suited to withstand large forces. The decision to manufacture
the vessel as a cube depended on a number of factors. For ease of manufacture,
low cost and simplicity, it was decided to use square shaped MWPC readout
planes which naturally lead to cube shaped vessels. The maximum size of the
vessels was dictated by transport requirements i.e. the vessels must fit through
mine shafts and any necessary surface buildings. By incorporating two MWPCs and creating two separate sensitive volumes back-to-back, the drift distance
is halved but the overall target mass is maintained. In manufacturing readout
planes the tensile strength of the wires sets a maximum unsupported length a
wire can span, which happens to be approximately 1 m. Therefore, to maximise
readout area a square design is favoured, again resulting in a cube shaped vessel.
Each vessel stands on tripod supports with adjustable height settings. This
is crucial for operation in an underground mine site where the floor, roof, and
walls of the cavern are constantly moving and changing due to the instability of
the mine environment. This is a natural and expected occurrence considering the
type of rock found in a salt and potash mine. As a necessity the vessel also has
several vacuum ports to provide: gas flow in and out, electrical connections for
signal pulses, high voltage feedthroughs to the central cathode and MWPCs, low
voltage feedthroughs for the
55
Fe source shutters, and a fitting for the pressure-
transducer.
4.3.2
Gas System
It was decided to operate a system in which the target gas is constantly circulated
through the detector volume. This provides certain benefits over simply sealing
the target gas inside the module. Firstly, in a static system, gas outwith the vessel
4.3 The DRIFT-II Detector
101
would seep in through any leaks present (a small fraction of CS2 gas would also
escape out), a continuous flow allows the overall target mass to be kept constant.
Secondly, the purity of the gas must be kept high, and a flow system helps to
avoid chemical deterioration and flush out any contaminants1 . The gas system
is set up in such a way that each DRIFT module has its own gas input system
but the entire array can be connected to a single output. The input system,
shown in Figure 4.2, includes a CS2 filled stainless steel container from which
liquid CS2 is evaporated and fed into the detector through a gas control system.
The CS2 bottle is suspended from a load cell to allow monitoring of CS2 loss.
The gas control system includes a mass flow controller (MFC), several isolation
valves, and a digital display showing pressure, pressure set-point, flow rate, and
CS2 weight.
Figure 4.2: The gas input system for a single DRIFT module. The capacitance
manometer, P, provides the pressure reading to the mass flow controller (MFC)
and the slow control computer. Taken from [119].
1
These contaminants largely come from leaks into the vessel.
102
4. DRIFT
To remove gas from the detector, the output system uses a dry rotary pump to
pull gas out through needle valves into a canister where the majority of vapour
condenses. Two charcoal filters, arranged in series, are then used to remove
any residual vapour and any excess beyond that is vented out into the cavern
mine air flow. Sensors continually monitor the level of CS2 exhaust giving a
safe and timely warning of the charcoal filters becoming saturated. These filters
can adsorb 5 kg of CS2 waste vapour equating to up to 190 days of continuous
running. The system can also be operated in a sealed mode for a short time
to allow the exchange of output filters or input canisters without the need to
cease data taking. Also included is a separate high-capacity rotary pump used
to pump-down or evacuate the vessel. In this process a liquid N2 trap is used to
freeze-out CS2 vapour and collect any residual oil-mist from the pump.
4.3.3
Inner Detector
A photograph of the inner DRIFT-IIa detector with all major components labelled
is shown in Figure 4.3. The 1 m3 fiducial volume is split in half by a central
cathode creating two separate drift regions. At opposite ends of each drift region
is an MWPC with a 1 m2 readout area. A fieldcage is present between each
MWPC and the central cathode. The purpose of these fieldcages is to provide a
steady electric field evenly incrementing in voltage from the central cathode to
the MWPCs. The fieldcages are kept in place by rigid Plexiglass supports and
the entire structure is held together by four Kevlar reinforced nylon rod tension
bolts with stainless steel threaded ends. The structure is set on top of a perspex
base so as to be insulated from the earthed vessel. This complete set-up rests on
a 15 mm thick stainless steel ‘skate plate’ fitted with roller units on the underside
to allow the whole assembly to be easily removed from the vessel and onto a
trolley unit.
4.3.3.1
Central Cathode
To operate the detector two high voltage systems are used: the ‘high high voltage’
(HHV) system, which sets the central cathode voltage and defines the drift field
within the fiducial volume; and the ‘high voltage’ (HV) system, which sets the
MWPC voltage and provides the avalanche field within the MWPC region. The
4.3 The DRIFT-II Detector
103
Figure 4.3: The DRIFT-IIa detector. This image was taken during the commissioning phase at Occidental College, LA. When referring to the left or right side
of the detector, the orientation is with respect to the perspective shown in this
figure.
104
4. DRIFT
central cathode consists of an open Plexiglass frame in turn composed of a ‘connector’ frame and a ‘cap’ frame, each with an outer dimension of 1210 mm and
an inner dimension of 1030 mm. This frame supports a wire plane of 512 20 µm
diameter stainless steel wires each spaced 2 mm apart. The wire plane is kept
in electrical contact with the HHV supply and, through spring-loaded electrical
contacts, both fieldcages. In running mode the central cathode is maintained at
approximately -34 kV with variations at less than 0.04 %.
4.3.3.2
Fieldcage
Each DRIFT-IIa fieldcage, one of which is shown in Figure 4.4, was constructed
from 31 tubular copper rings (in DRIFT-IIb stainless steel rings were used) held
15 mm apart by a rigid support structure composed of four acrylic legs bonded
to side panels. One of these legs houses a resistor chain facilitating the even
drift field between the central cathode and MWPC. The field rings were selected
to have a 6 mm diameter as this helps to minimise the field between adjacent
stages and limit the likelihood of corona discharge or electrical breakdown. Track
diffusion is inversely proportional to the square-root of the drift field (shown later
in Equation 6.2) and so it is desirable to operate the detector at a high drift field
but necessary to still maintain safe running. In DRIFT-II the mean operating
drift field is 624 ± 4 V cm−1 corresponding to a drift velocity of 4600 cm s−1 for
CS−
2 anions.
Parts of the detector at high voltage are only a few centimetres from the
grounded vessel and so electrical insulation must be added to protect against
breakdown. Two of the detector faces are shielded by the MWPCs themselves but
the remaining faces are covered by overlapping Plexiglass sheets with a thickness
of 6 mm. This shielding not only insulates the detector but also helps shield the
fiducial volume from any background radiation that may be emitted from the
inner surface of the vessel.
4.3.3.3
MWPCs
An individual MWPC, as depicted in Figure 4.5, is composed of three wire planes:
one anode plane sandwiched between two grid planes. Each grid plane consists
of 512 100 µm diameter stainless steel wires and the anode plane consists of 512
20 µm wires all separated by a distance of 2 ± 0.02 mm within their own plane
4.3 The DRIFT-II Detector
105
Figure 4.4: One fieldcage of the DRIFT-IIa detector sitting on the base section.
This makes up one half of the completed detector volume.
106
4. DRIFT
(the planes themselves are 10 mm apart). Due to electrostatic forces it is not
possible to position the wires closer than 2 mm to each other and maintain a
field capable of creating a sufficient avalanche region/gain. The wires of each
grid plane run perpendicular to those of the anode plane and they are all held
at tension between support bars mounted onto a Plexiglass ‘strongback’ of size
1.21 m × 1.21 m × 25.4 mm.
Figure 4.5: The wire planes of an MWPC. The anode plane is sandwiched between
two grid planes. As labelled, the outermost wires on each plane are set as either
veto wires or guard wires. Taken from [118].
The 20 outermost wires on each side of the grid planes are connected together
to provide a grid veto signal. The 11 outermost wires on the anode plane act
as guard wires where the voltage incrementally moves up from the grid voltage,
-2.98 kV at the outermost wire, to the anode voltage, set to 0 kV. These 11 wires
help to smooth electrostatic edge effects. The next 9 wires on the anode plane
act to provide an anode veto signal in a similar way to the grid veto. Veto wires
allow partially contained events, in particular alpha particles, to be rejected. The
2.98 kV potential maintained between the grid and anode planes during normal
running conditions results in a strong electric field surrounding the anode wires.
This in turn gives rise to an avalanche of charge entering the MWPC region and
a gas gain of ∼1000. The outer grid plane, also at -2.98 kV, helps to reduce end
effects due to the electric field.
When a recoil track is detected by the MWPC and analysed, each dimension
of the track is determined in a different way. The length of the track in the
4.3 The DRIFT-II Detector
107
x-direction, ∆x (this is parallel to the grid wires), is measured using the anode
wires and so the wire separation (2 mm) defines the spatial resolution in x. The
length in the z dimension, ∆z (parallel to the drift direction), is determined by
considering the deposition time of the event and noting that the drift speed is
constant. The y dimension, ∆y (parallel to the anode wires) is calculated by
reading the induced signal on the grid plane. From this the position of the centre
of the track is weighted against the size of the induced pulse. Using this technique
the spatial resolution in y is ≤ 0.1 mm.
The MWPCs also have another key feature, a 30 cm diameter hole located
in the centre of each strongback. This allows for
55
Fe energy calibration runs to
be carried out periodically during normal operation. These runs not only allow
for conversion of observed ionisation to calibrated NIPs, but are also essential
to monitor detector response and performance. The 100 µCi
55
Fe sources are
housed within stainless steel units mounted onto the outer faces of each MWPC
strongback. These units are equipped with electronic shutters, operated by the
data acquisition software, which open for 1 minute every 6 hours and expose the
fiducial volume to the 5.9 keV X-rays emitted from the source (see Figure 4.6).
Figure 4.6: The DRIFT-II energy calibration system. An
on the outside of each MWPC.
55
Fe source is mounted
108
4.3.4
4. DRIFT
Slow Control
Each DRIFT experiment is equipped with a slow control monitoring system to
read and record several attributes of the detector during normal operation. Approximately every five seconds, data are acquired from a variety of devices to
record: the vessel pressure, voltage and current of the MWPCs and central cathode, volume of CS2 remaining, gas flow rate, and temperature. A slow control
monitoring cut-off box acts as a fail-safe mechanism to automatically power down
the detector in the event of a problematic scenario. This may include a drop in
vessel pressure or a failure of the slow control computer. In the event the automatic shut-off fails, the detector can be powered down remotely by accessing the
slow control computer via internet or telephone line. The cut-off box can also be
operated manually if required. During normal running conditions the detector is
regularly monitored by collaboration members over a 24 hour period every day
(the ‘DRIFT-watch’), thus, any arising problems or anomalies are quickly spotted
and dealt with accordingly.
4.3.5
Data Acquisition System
The DRIFT-II data acquisition system is divided into two parts: the grid DAQ,
recording signals on the inner grid plane; and the anode DAQ, recording signals
on the anode plane. The grid DAQ provides information on the ∆y of an event
and the anode DAQ provides information on ∆x; both provide information on
the ionisation. Since a single DRIFT module has two DRIFT regions, and thus
two MWPCs (referred to as the left and right MWPCs), each module contains
two sets of anode signals and two sets of grid signals. An overview of the grid
and anode DAQs are given in the following sections.
4.3.5.1
Grid DAQ
The electronics and layout of the grid DAQ are illustrated in Figure 4.7. On each
MWPC, the 512 grid wires are grouped down to 32 channels which then pass
through front-end electronics contained inside shielded boxes mounted onto the
back of the MWPC strongback. These front-end electronics consist of 32 Amptek
A250 preamplifiers each with a charge sensitivity of 1 V pC−1 . Every eighth A250
output is summed together providing eight final signals which are each shaped
using two Amptek A275 shaping amplifiers. This means that the original 512
4.3 The DRIFT-II Detector
109
Figure 4.7: The grid DAQ system showing the location of the electronics within
and outside the vessel. Grid and veto signals from the right MWPC only are
shown. With the exception of shared items (e.g. the trigger inhibit circuit) an
identical arrangement exists for the left grid signals.
110
4. DRIFT
wires are effectively read out as sets of 8 adjacent wires with each set sampling a
16 mm distance. Given that a sulphur recoil of energy 40 keV has a typical range
of ∼ 2.7 mm in 40 Torr CS2 , a sampling size of 16 mm is more than adequate
to record all tracks of interest. The grouping of wires down to this level results
in a reduced necessity of components than when compared to a readout scheme
in which all 512 wires are read out individually. This not only produces a less
complex, more streamlined detector, but also provides a cost effective design. All
veto signals from each MWPC (two grid and two anode) also pass through an
A250 preamplifier, are then grouped to form one grid and one anode veto signal,
and are then passed through two A275 shaping amplifiers. The A275 amplifiers
give a shaping time of 4 µs and a gain of 40. On each of the channels the typical
noise observed is ∼14 mV.
All signals then move outside the vessel through BNC connectors in a specialised port on the vessel roof. The eight principal signal channels are then split
into two sets of eight, as shown in Figure 4.7, with one batch feeding into Adlink
PCI-9812 digitisers in the grid DAQ computer and the other batch entering an
Ortec 533 inverting summer unit which has been modified to accept eight inputs.
From there, this summed signal is passed into an NE 4684 discriminator which
produces a NIM-level logic pulse when a voltage threshold, set in software on
the slow control computer, is exceeded. Here, signals from either MWPCs are
accepted by a LeCroy 222 gate/delay generator and a TTL trigger pulse is provided. These pulses enter a trigger inhibit circuit to prevent further triggers being
accepted until the data acquisition from the current trigger has been completed.
The trigger signal, along with those for the anode and vetoes, is then passed to
the digitisers. All digitisers run at 2 MHz and have been specially modified for
a 3.3 V PCI bus. Bandwidth limits on the PCI bus of the grid DAQ computer
set an upper limit of 20 channels in total for both MWPCs i.e. eight principal
signals and two vetoes per MWPC.
4.3.5.2
Anode DAQ
The layout of the Anode DAQ electronics is shown in Figure 4.8. This data acquisition scheme involves much simpler wire grouping than the previously described
grid DAQ. Here, blocks of 32 anode wires are grouped down to 32 channels using a
4.3 The DRIFT-II Detector
111
Figure 4.8: The anode DAQ electronics. Only signals from the right MWPC are
shown.
112
4. DRIFT
32-way ribbon cable. These channels are then further grouped down to eight output signals and fed into customised preamplifier-shaper channels (CR-110 preamplifiers on CR-150 evaluation boards, followed by CR-2400-4 µs on CR-160 evaluation boards). These preamplifiers have a charge sensitivity of 1.4 V pC−1 , a
shaping time of 4 µs and a total gain of 6. These signals are then passed through
the vessel roof and into the PCI-9812 digitisers. This system also makes use of
the trigger supplied by grid DAQ, thus both the grid and anode are recorded at
the same time.
4.3.6
Event Data
When a signal received by one of the inner grid wire planes generates a pulse
large enough to trigger the grid DAQ (meeting the criteria previously described
in Section 4.3.5.1), data from the 8 anode, 8 grid, and 4 veto channels from each
MWPC are recorded and written to disk. During normal operation the trigger
level is set at -200 ADC counts (-100 mV) on the sum of the grid lines. The signal
on each channel is digitised and recorded from -1 ms to +4 ms relative to the
trigger time. Example data for several events are shown in Figures 4.9, 4.10 and
4.11. In each plot the left pane shows the signal output from the left MWPC and
the right pane shows the output from the right MWPC1 . A constant offset has
been added to successive traces in order to display them on the same plot. The
top eight channels on each pane are the grid signals with the ninth trace being
the grid sum. As demonstrated in Figure 4.10, the sum is useful for identifying
events with low ionisation such as 5.9 keV
55
Fe events. The next channels down,
in order, are the grid veto, anode veto, grid veto minus anode veto, the eight
anode signals, and lastly the anode sum. A grid veto minus anode veto is used
to cancel the effect of induced pulses resulting from events on nearby wires. An
authentic veto hit would leave a residual signal on this channel. A typical alpha
particle event, as shown in Figure 4.9, has a very long track length and thus
exceeds the length of eight wires several times over. Due to the cyclical grouping
of wires the final output is ‘wrapped round’ and seen as multiple hits on each
channel.
Typical X-ray events recorded during an 55 Fe calibration run are shown in Figure 4.10. It is known that a 5.9 keV
1
55
Fe interaction liberates ∼ 300 ± 40 NIPs
The orientation is defined earlier in Figure 4.3.
4.3 The DRIFT-II Detector
113
Figure 4.9: An alpha particle event in the right-hand-side drift region. Due to
the eightfold cyclical grouping of wires, a long track length, such as that shown
here from an alpha particle, causes the readout to ‘wrap around’ giving multiple
pulses on each line. The orientation of the ionisation track in 3 dimensions can
be determined from the timing of wire hits and the direction of the Bragg peak.
Figure 4.10: In this figure three 55 Fe X-ray events have occurred in the left MWPC.
Since these events produce very low ionisation the pulses are very small on the
individual lines but can just be seen on the grid sum line (ninth trace down).
114
4. DRIFT
in 40 Torr CS2 [120] and so these events can be used to calibrate the detector
to NIPs. During normal ‘WIMP mode’ runs the trigger level is set high enough
to prevent gamma-ray events, which intrinsically have a low dE/dx energy deposition, from triggering the system. For an
55
Fe run, however, the threshold is
lowered to allow the 5.9 keV X-rays emitted from the isotope’s decay to be identified. Interestingly, the capability of the detector to operate in such a mode also
allows for the possibility to search for Kaluza-Klein axions through identification
of the two gamma-rays produced in their decay [121].
Figure 4.11: A neutron-induced event in the left-hand-side drift region. The typical features include: the event appearing on only one or two adjacent anode wires
(due to the short track length), the flat section at the bottom of the peak, and no
trigger on the veto lines. This was taken during a 252 Cf calibration run.
As mentioned previously, the
55
Fe calibration runs were carried out periodi-
cally during normal operation. In addition, the detector was, from time to time,
also exposed to a
to
252
252
Cf neutron source and a
60
Co gamma-ray source. Exposure
Cf provides the obvious benefit of confirming the capability for neutron de-
tection and the
60
Co source allows for the observation of the detector’s response
to gamma-ray events in which electrons, rather than nuclei, recoil and deposit
energy. These runs were carried out by positioning the sources outside the vessel
in several distinct locations and exposing the unshielded detector for a set duration. The neutron runs are discussed in detail in Chapter 5. During normal
4.4 Further DRIFT modules
115
‘WIMP mode’ running the detector was surrounded by a shielding containment
infrastructure that was filled with CH2 polypropylene pellets of minimum depth
67 cm equating to 40 g cm−2 inclusive of the pellet packing fraction.
4.4
Further DRIFT modules
Except where mentioned, the description of DRIFT has been specific to the
DRIFT-IIa detector but with many of the attributes universal or similar in all
DRIFT modules. Some notable improvements in DRIFT-IIb, however, include
the successful implementation of a new grid amplification set-up using Cremat
amplifiers similar to those used for the anode DAQ system in DRIFT-IIa. Placement of these amplifiers outside the vessel allows for improved heat dissipation
and easier access for adjustment or maintenance. Not only are these amplifiers
cheaper than the Ampteks used previously, but they also have no signal-to-noise
compromise. The HV inputs have been fitted with improved filters thus reducing
the noise compared with that present in the DRIFT-IIa data. The use of DB50
internal cabling has reduced the number of feed-through flanges and an extension of the veto regions has decreased noise and improved rejection capability of
the detector. Also, an improved DAQ scheme has removed the need for NIM
units and provided better remote control of the system. Another alteration, as
mentioned previously, is that the DRIFT-IIb fieldcage has been constructed from
stainless steel rings as opposed to the copper rings used in DRIFT-IIa. Since the
decommissioning of DRIFT-IIa, several components from this module have been
retro-fitted or improved to provide what is essentially an entirely new detector,
DRIFT-IIc, currently in the commissioning phase.
4.5
Summary
DRIFT modules combine the concept of negative ion drift with TPC technology. In principle, when a WIMP interacts with the target medium a nucleus will
recoil leaving behind an ionisation track in a given direction. In the presence
of an applied electric field this track is drifted across the fiducial volume to an
MWPC readout plane where the directional information is extracted. Drifting
of this ionisation in the form of negative ions rather than electrons significantly
improves diffusion effects and thus maintains better directional information. The
116
4. DRIFT
design and function of a DRIFT module including its major components, electronics and gas system have been presented along with example data obtained
during typical operation. Manipulation and analysis of the data received allows
for discrimination between the types of recoiling particle. The detector’s response
and sensitivity to directional neutron runs is dealt with in the next chapter. The
first detector, DRIFT-I, demonstrated the successful operation of DRIFT technology. The design, electronics, and running of DRIFT-IIa, however, was a vast
improvement on that of the DRIFT-I module including the fidelity of accumulated data. Further enhancements have been made for DRIFT-IIb providing more
efficient electronics and a reduction of signal noise. Future plans for the DRIFT
programme envisage an array of several modules running back-to-back simultaneously providing a comparatively cheap direct dark matter search experiment.
Chapter 5
Analysis
5.1
Introduction
To set a WIMP-nucleon cross-section sensitivity limit, background rates seen in
the DRIFT data must be reduced to as low a level as possible. When dealing
with the low energy recoils involved in WIMP dark matter detectors, discriminating against non-nuclear recoils is essential. Gamma-ray interactions are a prime
example of the type of background event that can liberate electrons and cause unwanted detection rates. In many direct dark matter search experiments electron
recoils are removed in analysis, but in the case of DRIFT, as described previously, the detector is insensitive to electron recoils during normal operation. The
exception to this is if an electron recoil happens to occur within the MWPC region (detailed in Section 5.3.1). In the following sections, the response of DRIFT
detectors to gamma-ray interactions in their fiducial volumes is discussed and
in particular the gamma-ray rejection factor of DRIFT-I determined. This then
leads to an investigation of the effect of CH2 shielding on the gamma-ray event
rate seen by DRIFT detectors.
Of paramount significance in any WIMP direct dark matter search experiment
is the capability to identify nuclear recoil events. In this chapter the characteristics of nuclear recoil events in gaseous CS2 are discussed and an overview of data
analysis parameters and reduction techniques presented. Simulations to determine the response and efficiency of the DRIFT-IIb detector to neutron exposures
are presented and, finally, a discussion of a problematic population of events occurring in the DRIFT-IIa data set, believed to be a result of radon emanation
within the module, is given. Improvements made to minimise this unwanted event
117
118
5. ANALYSIS
rate in the DRIFT-IIb module are then reviewed.
5.2
5.2.1
Gamma-Rays in DRIFT
Background Gamma-Ray Rejection in DRIFT-I
The operation of DRIFT-I ceased in 2004. At that time an accurate simulation
of the detector’s response to background gamma-rays had not been undertaken.
This has now been performed and is presented here. Using trustworthy concentrations of 238 U, 232 Th and 40 K in the NaCl cavern rock, a background gamma-ray
production rate was determined using SOURCES and then utilised in a GEANT4
Monte Carlo simulation (as described in Section 3.3). This Monte Carlo was then
adapted and used to determine the gamma-ray rejection factor of the DRIFTI module1 . This was done by comparing the number of simulated gamma-ray
events in the fiducial volume to the recorded data taken during a background run
of the unshielded DRIFT-I module. The simulated detection rates at varying NIP
thresholds are shown in Table 5.1 and Figure 5.1. It should be noted that, due
to operational difficulties of the DRIFT-I module, only half the fiducial volume
was active when running and so the simulated rates shown are for a 0.5 m3 CS2
target volume as opposed to a full 1 m3 .
Considering the energy range of 1000-5000 NIPs, and given that the target
mass was 83 g, the expected rate of Compton electron energy depositions caused
by ambient background gamma-ray interactions in the unshielded detector was
estimated to be 3.4 × 106 kg−1 day−1 . Given the live-time and active volume
used on the background run of DRIFT-I, this yields a total number of expected
interactions of 1.1 × 107 events. In the data run itself only 47 background events
were recorded. Assuming all 47 of these events were gamma-rays (worst case
scenario) then the gamma-ray rejection factor is calculated to be 4.2 × 10−6 . The
characteristics of the recorded events, however, were not consistent with those
of gamma-rays and so assuming none of these were gamma-ray events (best case
scenario), then the gamma-ray rejection factor is improved to better than 2 × 10−7
at 90 % C.L. for 1000−5000 NIPs.
1
All GEANT4 simulations, of DRIFT modules, described in this thesis are adaptations
of Monte Carlo simulations originally developed by Chamkaur Ghag [113], Edinburgh. The
adaptation and administration of these simulations were carried out by the author.
5.2 Gamma-Rays in DRIFT
119
Table 5.1: The simulated interaction rates in DRIFT-I resulting from gamma-rays
emitted from the surrounding NaCl cavern rock. The second column indicates the
interaction rate corresponding to the minimum NIPs threshold listed in the first
column. Note: for this run the target mass of CS2 was 83 g. These results are
illustrated graphically (for discrete energy bins) in Figure 5.1.
NIPs Min.
0
20
100
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
1000-5000
Rate (day−1 ) Error (day−1 )
7.84E+05
1.74E+04
7.67E+05
1.72E+04
7.05E+05
1.65E+04
5.02E+05
1.39E+04
2.94E+05
1.06E+04
1.59E+05
7.82E+03
1.03E+05
6.28E+03
7.46E+04
5.35E+03
5.88E+04
4.75E+03
3.65E+04
3.75E+03
2.15E+04
2.88E+03
1.54E+04
2.43E+03
1.27E+04
2.21E+03
9.99E+03
1.96E+03
7.69E+03
1.72E+03
6.15E+03
1.54E+03
5.76E+03
1.49E+03
3.46E+03
1.15E+03
1.54E+03
7.69E+02
1.54E+03
7.69E+02
1.54E+03
7.69E+02
1.15E+03
6.66E+02
1.15E+03
6.66E+02
2.81E+05
1.04E+04
120
5. ANALYSIS
Figure 5.1: The simulated interaction rates in DRIFT-I resulting from gammarays emitted from the surrounding NaCl cavern rock. The rates shown here have
been calculated for discrete energy bins using the data presented in Table 5.1.
5.2 Gamma-Rays in DRIFT
5.2.2
121
Electron Recoil Characteristics
To observe additional characteristics of the response of DRIFT-I to background
gamma-ray events, the electron recoil track length, as well as the energy deposition, was also recorded within the Monte Carlo. The energy deposition of electron
recoils and the track ranges are shown in Figures 5.2 and 5.3 respectively.
Figure 5.2: Simulated energy deposition histogram of electron recoils in the
DRIFT-I module resulting from background gamma-rays produced in the cavern
rock. The mean energy deposition is 20.29 keV. Within the simulation a total of
4×108 gamma-rays were emitted from the cavern rock.
The energy spectrum of background gamma-rays emitted from the rock (shown
in Figure 3.7) extends up to the 3 MeV range. From Figure 5.2 it can be seen
that this results in energy depositions ranging up to ∼ 200 keV but with very few
events above the 100 keV range. The simulated mean energy deposition produced
by these background gamma-rays is 20.29 keV. The simulated mean track length
for electron recoils in DRIFT-I, as shown in Figure 5.3, was found to be 53.8 cm.
This length, however, was limited by the dimensions of the active fiducial volume i.e. only half the detector volume was active. Likewise, these dimensions
also brought about peaks at ∼50 cm and ∼100 cm for the electron recoil track
length. Similar simulations of electrons in the DRIFT-IIa detector (from a
60
Co
122
5. ANALYSIS
Figure 5.3: Simulated track lengths of electron recoils in the DRIFT-I module
resulting from background gamma-rays produced in the cavern rock. The peaks
at ∼50 cm and ∼100 cm arise due to the dimensions of the fiducial volume.
Note: only half the fiducial volume (0.5 × 1 × 1 m3 ) was active when the DRIFTI detector was operated. The histogram tail results from the addition of secondary
electron tracks to that of the primary electron recoil. For this simulated run the
mean track length is 53.8 cm. Within the simulation a total of 4×108 gamma-rays
were emitted from the cavern rock.
5.2 Gamma-Rays in DRIFT
123
exposure), which had a full 1 m3 active volume, produced a spectrum with a peak
at ∼ 100 cm and a mean electron recoil track length of 69.2 cm [113].
It has been shown that electron recoils in 40 Torr gaseous CS2 can have very
long track ranges but these results are for incoming gamma-rays up to the multiple
MeV range. When performing
55
Fe calibration runs, the emitted X-rays are of
energy 5.9 keV. Through analysis and previous simulation work, it is known that
when performing these calibration runs (the
55
Fe sources at the left and right
sides of the detector are exposed separately) events occur in both halves of the
detector volume, for example, 6.73 ± 0.07 % of the number of detected events in
the volume during a right MWPC 55 Fe calibration run are detected in the left half
[122]. This is due to the range 5.9 keV X-rays can travel in the fiducial volume
before interacting and generating electron recoils. Figure 5.4 shows the results of
GEANT4 simulations run to determine the average range of low energy electron
recoils in CS2 ; it is found that electron recoils of energy 6 keV (equivalent to
∼ 316 NIPs) have an average range of ∼ 8.7 mm.
Figure 5.4: Simulated electron recoil track lengths in CS2 as a function of recoil
energy. Only low energy recoils are considered here.
124
5. ANALYSIS
5.2.3
CH2 Shielding
CH2 shielding is erected around DRIFT vessels to perform the critical function
of attenuating ambient neutrons, thereby reducing the rate of background interactions in the detector. A minimum shielding thickness of 67 cm surrounding
the entirety of each vessel, equating to 40 g cm−2 inclusive of the pellet packing
fraction, was selected to reduce the interaction rate in DRIFT-II detectors caused
by background neutrons emitted from the cavern rock down to ∼ 1 year−1 [123].
Although the threshold of DRIFT detectors is set such that, in normal running
mode, gamma-ray interactions in the fiducial volume do not trigger the DAQ, it
is advisable to have an adequate knowledge of the influence this shielding may
have on gamma-ray interactions. This could be particularly useful in the event of
future DRIFT modules being coupled to active neutron veto detectors based on
scintillation. In such a scenario, CH2 shielding could play a vital role in reducing
the rate of unwanted events within the veto detector. To this end, a series of
GEANT4 simulations was carried out to first investigate the effect the shielding
has on
60
Co exposures and to then determine the result it has on background
gamma-rays emitted from the cavern rock.
5.2.3.1
60
60
Co Exposures
Co exposures have been conducted on past DRIFT modules to determine the
detector’s response to gamma-ray events and thus estimate the corresponding
gamma-ray rejection factor. In the decay of
60
Co, two principal gamma-rays
of energies 1.33 MeV and 1.17 MeV, respectively, are emitted. As expected, the
surrounding material can have a notable effect on the rate of electron recoil energy
depositions in the fiducial volume. This rate can differ significantly depending
on the specific location of the
60
Co source. For example, if the source were to be
placed directly into the active CS2 volume, gamma-rays would be able to interact
with the gas and liberate electrons that could then in turn deposit energy. If,
however, the source were to be placed behind one of the MWPCs (with respect to
the fiducial volume) the emitted gamma-rays would enter the perspex and, due to
the higher interaction cross-section, liberate more electrons through interactions
with the denser perspex than than the 40 Torr CS2 gas. Thus, placement of the
source in such a location would produce a higher event rate in the fiducial volume
than if the source had simply been placed directly into the target gas.
5.2 Gamma-Rays in DRIFT
125
For the purposes of the simulations described here, the 60 Co source was placed
a few centimetres outwith the CH2 shielding and aligned directly in front of
the DRIFT vessel door. Instead of simulating the source as isotropic, gammarays were fired directly towards the vessel along the x-axis direction. Given this
anisotropy, and close proximity of the source, gamma-rays entered the shielding
with little or no attenuation and were initially aligned along the most direct
path into the vessel. To observe the influence the shielding had on the event
rate within the fiducial volume, it was decided, by preference, not to alter the
volume of the shielding between the source and detector, but rather to alter the
simulated density of this shielding. The Monte Carlo was thus repeated several
times over: first, with no shielding present at all (equivalent to ∼ 0 % density) and
then again a number of times with the density evenly incrementing from 0 % up
to 100 % (600 kgm−3 including packing fraction). Since the only attribute altered
between runs was the shielding density, the exact position of the source relative
to internal components is of no consequence for the objective of this work.
The results illustrated in Figure 5.5(a) indicate that the CH2 shielding had
little effect on the total number of electron recoils in the fiducial volume. The
small effect that was present can be seen in the enlarged image, Figure 5.5(b). As
shown, at low values an increase in shielding density actually raises the number
of electron recoil depositions in the target gas. This is due to gamma-ray interactions within the CH2 liberating more electrons than when no shielding was
present, similar to the case in which a
60
Co source is placed behind an MWPC
strongback. As the density is increased further, the rate of electron recoil depositions begins to gradually fall due to the attenuation effect the CH2 has on
both the primary gamma-rays and the resulting electrons. In this set-up the
total shielding thickness equates to only 40 g cm−2 , and whilst this is sufficient
to attenuate neutron induced events in the fiducial volume, it does little to reduce the overall number of electron recoil energy depositions. This is due to the
two competing influences: firstly, the increase in CH2 density attenuates the incoming gamma-rays and provides more shielding against electrons entering the
fiducial volume; opposingly, however, the same increase in CH2 density results
in a greater number of liberated electrons and thus helps to increase the number
of electron recoils in the CS2 . Tables 5.2 and 5.3 are included to show that, for
this set-up, the number of electron recoil events in each energy deposition decade
is, similarly, not greatly affected by the shielding. It should again be noted that
126
5. ANALYSIS
(a)
(b)
Figure 5.5: Simulated number of electron recoils in DRIFT-IIb from a 60 Co exposure as a function of CH2 shielding. As shown in plot (a) the CH2 shielding has
little effect on the total number of electron recoils. Plot (b), however, shows an
enlarged view in which the effect of the shielding is apparent.
5.2 Gamma-Rays in DRIFT
127
Table 5.2: Simulated number of electron recoils per energy decade in the unshielded
DRIFT-IIb detector resulting from a 60 Co exposure.
Energy Threshold Number of counts
(keV)
0
20596
10
18208
100
682
Error
144
135
26
Table 5.3: Simulated number of electron recoils per energy decade in the fully
shielded DRIFT-IIb detector resulting from a 60 Co exposure.
Energy Threshold Number of counts
(keV)
0
19910
10
17552
100
625
Error
141
132
25
these results are for gamma-rays of energies 1.33 MeV and 1.17 MeV being fired,
from close proximity, directly into the shielding infrastructure and towards the
DRIFT detector. If the density of shielding was to be increased further, or a
broader energy spectrum sampled (as discussed in the following section), a more
notable effect might be expected.
5.2.3.2
Background Gamma-Rays
When dealing with direct dark matter search experiments, the detector will likely
require some form of gamma-ray shielding, often in the form of passive lead shielding. As described previously, gamma-ray events in the fiducial volume of DRIFT
can be eliminated by setting the DAQ threshold accordingly1 , thus lead shielding is not required. The passive hydrocarbon shielding will, however, provide a
certain level of attenuation for any incoming gamma-rays. Although Compton
scattering interactions in CH2 may be similar to that of lead, the attenuation
offered will be less effective per unit mass. This is due to the lower Z (atomic
number) which defers absorption to much lower energies. Investigated here is the
effect the shielding has on the event rate within DRIFT due to the background
1
Gamma-ray events occurring in the MWPC region can be rejected through analysis cuts
described in Section 5.3.2.2.
128
5. ANALYSIS
Table 5.4: Simulated rate of electron recoils per energy decade in the unshielded
DRIFT-IIb detector as a result of background gamma-rays emitted by the cavern
rock.
Energy Threshold Rate Error
(keV)
(Hz) (Hz)
0
20.00 0.59
10
14.27 0.50
100
0.52
0.09
Table 5.5: Simulated rate of electron recoils per energy decade in the fully shielded
DRIFT-IIb detector as a result of background gamma-rays emitted by the cavern
rock.
Energy Threshold Rate
(keV)
(Hz)
0
3.12
10
2.37
100
0.17
Error
(Hz)
0.23
0.20
0.05
gamma-rays emitted from the cavern rock. The GEANT4 Monte Carlo was thus
set up to emit the background gamma-ray spectrum previously described in Section 3.3 and then run with and without the CH2 shielding in place.
As can be seen from Tables 5.4 and 5.5, in this scenario the shielding plays
a significant role in reducing the rate of electron recoil energy depositions within
the fiducial volume. The large difference seen here, compared to the relatively
small effect shown for 60 Co exposures, can be attributed to the fact that gammarays produced by the rock have a much broader energy spectrum. The observed
rates indicate that a CH2 shielding density of 40 gcm−2 reduces the electron recoil
interaction rate in DRIFT (produced from rock gamma-rays) by a factor of ∼ 6
in the energy deposition range 0−100 keV and a factor of ∼ 3 at higher energies.
5.3
5.3.1
Nuclear Recoils in DRIFT
Nuclear Recoil Energies and Track Lengths
As discussed in Section 2.5.1, in any detector it is essential to know the relationship between the observed energy of a given event and its true recoil energy. In
gaseous CS2 , an energy of ∼19 eV is required to liberate a single electron-ion
5.3 Nuclear Recoils in DRIFT
129
pair (the ‘W factor’) and this value is used to convert the energy of an electron
recoil in keV to NIPs. When dealing with nuclear recoils, however, the relevant
quenching factor, specific to the type of recoiling nucleus, must also be taken into
account in accordance with Equation 2.22. The relationship between observed
NIPs and nuclear recoil energy is shown for carbon and sulphur recoils individually in Figure 5.61 . An important point to note is that the function obeys a
non-linear response at low energies.
10000
NIPs
8000
6000
4000
2000
0
0
50
100
150 200 250 300
Recoil Energy (keV)
350
400
Figure 5.6: Observed NIPs plotted as a function of nuclear recoil energy for carbon
(blue) and sulphur (red) recoils in a DRIFT detector filled with 40 Torr CS2 [120].
The relationships shown in Figure 5.6 are particularly useful when performing
GEANT4 Monte Carlo simulations of event rates within DRIFT. This is because
GEANT4 does not contain any information on the W factor for CS2 and thus
recoil energies are given in units of keV. The conversion of an energy deposition in
keV to observed NIPs, which takes into account the full response of the detector
and all relevant physics processes, is manually inserted into the simulation code.
The mathematical conversions performed follow the form of Figure 5.6 and were
calculated individually for distinct low energy regions.
For the most part, electron recoils in DRIFT are not seen due to their low
dE/dx energy deposition. Exceptions to this do of course take place during
1
Specific NIP thresholds and their keV energy equivalent are listed later in Table 7.2.
55
Fe
130
5. ANALYSIS
calibration runs in which the detector threshold is lowered specifically for this
purpose. In addition, if an electron recoil happens to occur within the high
electric field region of the MWPC, the resulting avalanche of charge, together
with the fact that the ionisation track will experience much less diffusion, may
lead to energy depositions on individual wires large enough to trigger the DAQ.
Therefore, gamma-ray events in the MWPC region can result in real detection
rates and so must be considered when analysing and simulating DRIFT data
runs.
For analysis, it is also vital to have an adequate knowledge of the expected
recoil track length. As indicated in Figure 5.3, electron recoil track lengths are,
relatively, very large, often spanning the entire length of the FV. Nuclear recoil
track lengths are, as expected, much shorter, of the order of a few millimetres. In
a WIMP search experiment it is the low energy nuclear recoils that are of interest
and, as shown in Figure 5.7, these have very small ranges. These characteristics
can, however, be used beneficially in data reduction.
10
9
Range (mm)
8
7
6
5
4
3
2
1
0
0
50
100
150
Recoil Energy (keV)
200
250
Figure 5.7: Nuclear recoil range as a function of carbon (blue) and sulphur (red)
recoil energy in 40 Torr CS2 gas [120].
5.3 Nuclear Recoils in DRIFT
5.3.2
131
Data Analysis
The analysis of DRIFT data is, for the most part, undertaken by several members
of the DRIFT collaboration1 using distinct analysis techniques. Despite their
differences, these algorithms follow similar methods for identifying and rejecting
unwanted events. The analysis techniques employed, by the author, in this thesis
were developed in collaboration with members of Occidental College, LA, and are
akin to those utilised for analysis of DRIFT-I data [120]. In the following sections
an overview of event parameters and cuts invoked to analyse data are described.
Once raw waveforms have been written to data files, the first step of analysis is
to implement a procedure designed to reduce noise and improve signal quality. By
applying a Fast Fourier Transform (FFT) to all these raw waveforms, excess power
at a frequency of ∼ 55 kHz, attributed to electrical pick-up from the laboratory
environment, was revealed and thus removed from the data before reconstructing
the waveforms. Useful parameters, including line voltage values, offsets (the
correction required for any baseline drifting that may be present), and regions of
interest (ROI), were then generated independently for each channel.
5.3.2.1
Event Parameters
Several key event parameters used in analysis are listed below and shown in Figure
5.8.
• tmin : the time at which the voltage reaches zero before crossing the software
threshold for the first time.
• tmax : the time at which the voltage reaches zero after crossing the software
threshold for the last time.
• Vmin : the minimum voltage on a channel within the ROI.
• Vmax : the maximum voltage on a channel within the ROI.
• tV min : the time at which Vmin occurred.
• tV max : the time at which Vmax occurred.
1
Including the author.
132
5. ANALYSIS
Figure 5.8: Depiction of several of the analysis parameters recorded on a single
channel waveform of a DRIFT-II detector. These statistics are used to apply
analysis cuts and reject unwanted events.
5.3 Nuclear Recoils in DRIFT
133
• Σ: the integral of the voltage on a single line with respect to time between
tmin and tmax , multiplied by -1. For any given channel where the signal does
not fall below the software threshold this value is set to zero. This statistic
is proportional to the ionisation falling on the line [124].
• Σsum : calculated as the integral of the voltage on a single line, as done for
Σ, but tmin and tmax are taken from the summed channel, and multiplied by
-1. This statistic is designed to identify and evaluate the ionisation present
on channels where the software trigger was not exceeded. In many instances
Σ is recorded as zero while Σsum still provides a measure of the ionisation.
• N F F W HM - Negative First Full Width at Half Minimum: Starting at
Vmin , this is the value of the first full width at half minimum. This characteristic can identify sparks (very fast pulses commonly arising when using
TPC technology) and events that occurred within the MWPC region (as
opposed to the main FV).
• Crossings: calculated as the number of times the voltage crosses the
software threshold value. This is a useful parameter used to identify long
recoil tracks, such as that of an alpha event shown in Figure 4.9 where the
signal is effectively ‘wrapped round’ eight channels several times over.
• SmoothedDerivativeCrossings: similar to crossings but, here, the
signal is first smoothed (to negate baseline noise fluctuations) and then
differentiated to determine the number of zero-crossings of the resulting
signal. Using this parameter, events classed as ‘ringers’ (see Figure 5.9
[120]), which are clearly distinguishable from neutron-induced nuclear recoil
events, may be identified and rejected.
• Risetime: the time interval between the times at which the pulse reaches
25 % and 75 % of its first amplitude where the software threshold is exceeded. This characteristic, as with the NFFWHM, can be used to identify
pulses too fast to be a neutron event.
• P reI: the ionisation present on a line outside the ROI. This parameter is
recorded since, in many instances, ionisation may have been deposited on
the channel outside of the ROI which was insufficient to trigger the DAQ.
This ionisation may, however, be large enough to determine that the main
134
5. ANALYSIS
pulse (within the ROI) is unreliable. Given the low probability of a WIMPnucleon interaction, it is extremely unlikely that two WIMPs will interact,
or a single WIMP will interact twice, in the detector volume so closely in
time.
• ∆x: the range of a recoil track in the x direction. This parameter is
calculated by multiplying the number of channels hit (defined as crossing
the threshold) minus one, by 2 mm (the pitch of the anode wires).
• ∆y: the range of a recoil track in the y direction. This parameter is
calculated using the induced signal on the grid wires. The position of the
centre of the track is weighted against the size of the induced pulse.
• ∆z: the range of a recoil track in the z direction. This parameter, as
discussed in Chapter 6, can be calculated in several ways. The principal
method of calculation is to subtract the earliest tmin (out of all the anode
wires hit) from the largest tmax (again out of all the anode wires hit), and
multiply this by the drift velocity.
• R2: the two dimensional projection of the track length on the x-z plane.
√
This parameter is calculated as ∆x2 + ∆z 2 .
• N IP s: the number of electron-ion pairs, initially described in Section 2.5.1.
From the anode, this value is calculated by summing the Σ parameter from
all the wires that crossed the threshold and then adding the Σsum from adjacent wires, multiplied by the NIPs conversion factor (discussed in Section
5.3.1). From the grid, this value is calculated by taking the Σ parameter
from the summed line and then multiplying by the NIPs conversion factor.
5.3.2.2
Data Reduction
Depending on the specfic data run carried out, and the type of analysis being performed, particular cuts are selected to meet the appropriate requirements. For
example, to determine the detector’s response and efficiency at detecting nuclear
recoils, data runs were conducted using the
252
Cf neutron source (the measure-
ment of which was described in Section 3.4). By comparing simulated theoretical
rates of such runs to the experimentally determined rates, the efficiency of the
5.3 Nuclear Recoils in DRIFT
135
Figure 5.9: A ‘ringer’ event in DRIFT occurring on the second from bottom
channel on the right pane. This type of event is characterised by the oscillatory
behaviour within a semi-Gaussian envelope. The origin of these events is at
present unclear.
136
5. ANALYSIS
detector can be estimated. Before doing this, however, suitable cuts are applied
to the neutron data such that as many unwanted events as possible are rejected
whilst all (or nearly all) neutron-induced nuclear recoils are kept in the data set.
To remove any background signal present, rates from background runs, either
immediately preceding or succeeding the neutron exposure, were passed through
identical cuts and then subtracted from the neutron data set. This is done independently for discrete energy bins as opposed to the entire data set as a whole.
Within the collaboration, this method of analysis is termed ‘proportional counter’
analysis and is quite distinct from ‘zero-background’ analysis. When performing
zero-background analysis much more stringent cuts are set to attempt to reject
all non-nuclear recoil events, thereby reducing the unshielded background rate
further than when compared to the proportional counter analysis. Applying identical cuts to the neutron data set inevitably removes a large number of legitimate
neutron-induced events. The corresponding neutron detection efficiency is thus
lower than that of the proportional counter mode. When attempting to identify a
potential WIMP signal (or at least set a WIMP-nucleon cross-section sensitivity
limit), it is, however, essential that these cuts are applied and all non-nuclear
recoil events are removed to the best levels possible. An overview of the analysis
cuts applied to DRIFT data is given here but for a more comprehensive review
the reader is directed to [124] and [120].
Proportional Counter Analysis Cuts
The following is a list of cuts applied to the data when performing proportional
counter analysis:
• LineCuts: a cut applied to each channel individually (not the entire
event) with the aim of eliminating induced signals that cross the threshold.
This cut is implemented since an induced signal can appear on the anode
lines, resulting in a pulse with an intial positive rise and then a negative
overshoot that may cross the threshold, falsely implying real ionisation.
There are two requirements of this cut: firstly, in a legitimate event, the parameter Vmax must not be more than twice the value of Vmin , thus targeting
events with large overshoots for rejection; secondly, in a legitimate event,
the negative part of the pulse must appear before the positive going part of
the pulse, thus targeting events where the apparent ionisation crosses the
5.3 Nuclear Recoils in DRIFT
137
threshold value and tV max is less than tV min . If an event fails to pass both
cuts, the NIPS value is set to zero and it is then later removed from the
data set.
• ZeroN ipCut: a cut applied to eliminate any event in which the sum of
the Σ’s for all channels was zero.
• SumCut: this cut removes events that are either too large (excessive Σ) or
too long (extending outwith the ROI) for the entire event to be adequately
recorded by the DAQ. This is particularly useful at removing alpha particle
events whose characteristics typically include long track lengths and a large
amount of ionisation.
• V etoCut: this cut will reject any event in which the veto channel has
been triggered i.e. any event that was not fully contained within the FV.
Again, this cut is useful at eliminating alpha particle tracks. This cut is
actually applied to the ‘veto sum’ line (the anode veto minus the grid veto),
as opposed to the individual grid and anode veto lines, since it is insensitive
to ‘false events’ that may be misconstrued from fluctuations in the baseline.
Zero-Background Analysis Cuts
When performing zero-background analysis, in addition to the proportional counter
cuts listed above, the following cuts are also applied to the data:
• RingerCuts: implemented to reject ‘ringer’ events, an example of which
is shown in Figure 5.9. This cut utilises the SmoothedDerivativeCrossings
parameter to identify these events. Using this parameter alone, however,
does not remove all ringer events since it is possible for these events to have
only one oscillation. Another characteristic utilised is that all the lines
on the anode, excluding any lines that received ionisation (principally the
triggered line), have negative NIPs values, which is in contrast to a genuine
neutron-induced event. Thus an additional cut is to reject any event with
less than -50 NIPs on any channel. A notable characteristic of neutron
events is that the ratio of NIPs recorded on the anode to that of the grid
is ∼ 1, this is not so for ringer events. By applying a further cut in which
the described ratio must lie within the range 0.768−1.176, any remaining
138
5. ANALYSIS
ringers are eliminated. These limits were set to retain 99.7 % (3σ) of the
data in a neutron run after all other cuts had been applied.
• SparkN M W P CCut: a cut designed to eliminate sparks and any event
that deposits sufficient charge within the MWPC high drift region. This
effectively acts as a veto for the two faces of the detector holding the MWPCs (the designated veto channels cover the other four faces). If an event
has an NFFWHM less than 28 µs it is rejected by this cut.
• EightLineCut: set to reject events, such as alpha particle events, which
fall below the threshold on all eight grid or anode channels. Since WIMPinduced events are expected to produce nuclear recoils of the order of tens
of keV, their recoil tracks would only span a few mm. Similarly, neutron
events of interest would also produce short recoil tracks and, thus, would
pass this cut unaffected. Refer to Figure 5.7 for the range of nuclear recoil
tracks in the low energy regime.
• AdjacentCut: a nuclear recoil depositing charge on more than a single
wire would deposit this ionisation on wires adjacent to one another. Thus, if
an event is seen with enough ionisation on non-adjacent or non-consecutive
wires to trigger those channels, the event is rejected.
• M issingN IP sCuts: a cut implemented to keep events in which the
NIPs value calculated from the anode sum channel is approximately equivalent to the summed total of the NIPs value calculated from each of the
eight anode channels. For legitimate neutron or WIMP-induced events the
ratio of this value will be ∼ 1. Events where this ratio lies outwith the range
0.879−1.181 are rejected. These limits were set to retain 99.7 % (3σ) of the
data in a neutron run after all other cuts had been applied.
• OtherSideCuts: set to reject events in which sufficient ionisation is deposited in both the left and right side of the FV i.e. ionisation is seen in
both MWPCs. If at least one channel is triggered in both MWPCs the
event is rejected. If the ionisation is insufficient to fall below threshold
a second order fit is made on the corresponding summed anode channel.
This fit is subtracted from the original waveform and a value for ‘other
side’ NIPs calculated. If this value is greater than 200 NIPs the event is
5.3 Nuclear Recoils in DRIFT
139
rejected. Since a neutron or WIMP-induced event is likely to have a very
short recoil track range, and is unlikely to interact twice within the fiducial
volume, legitimate WIMP or neutron events will, most probably, pass this
cut unaffected.
• P reIonisationCut: designed to reject events in which sufficient ionisation occured prior to the ROI. This is calculated by analysing the summed
anode line from the start of the event record up to the beginning of the
ROI.
The effect these cuts have on DRIFT data was included in the research of
other collaboration members. The number of events that are removed from an
example data set by each analysis cut are presented in [113].
5.3.3
DRIFT-IIb Neutron Exposures
When performing neutron exposures on DRIFT-IIa, the data were analysed using
proportional counter and zero-background reduction cuts. The rates found were
then compared to detailed GEANT4 Monte Carlo simulations of the corresponding runs. Likewise, similar simulations of DRIFT-IIb neutron exposures were
conducted by the author. In order to reduce computer processing time, and simultaneously improve statistics, the pressure of the CS2 gas within the simulated
geometry was increased from 40 Torr to 1000 Torr (a factor of 25 increase). At
this level, the neutron induced recoil rate obeys a linear relationship with the gas
density, scaling the pressure in this manner is therefore a legitimate technique
to employ [123]. The corresponding simulated neutron event rates were later
adjusted in a linear fashion to incorporate the true density. At pressures above
the 4000 Torr level, the probability of multiple scattering is non-negligible and
a linear correction would no longer be valid [123]. In the analysis of DRIFT-IIa
neutron run data, an energy window of 1000−6000 NIPs was selected as a region
of interest. Above 6000 NIPs, the long track ranges of carbon recoils meant that
many of these events were eliminated through reduction cuts, and also the number of detected events in both the simulation and experimental data becomes low
thereby reducing the statistical accuracy. The minimum value of 1000 NIPs was
selected as this was, essentially, the threshold of the detector for those particular
neutron exposure runs. Similarly, DRIFT-IIb data were analysed in a likewise
140
5. ANALYSIS
fashion. The simulated results of the DRIFT-IIb neutron exposures, presented
in the following sections, include 500 NIP energy intervals and also a summary
of the 1000−6000 NIPs energy region.
5.3.3.1
Neutron Run
On the 20th February 2007 the DRIFT-IIb detector was exposed to the
252
Cf
neutron calibration source. The configuration of the set-up is illustrated in Figure 5.10. At this time, five faces of the module were fully shielded with CH2
polypropylene pellets and the remaining face (the vessel door) was left unshielded
to allow direct access to the detector. For the run itself, the neutron source was
placed up against the centre of the vessel’s front door and slabs/bags of polypropylene pellets were positioned so as to surround the source.
Figure 5.10: Modelled geometry of the DRIFT-IIb 252 Cf neutron run on the 20th
February 2007. The lead canister containing the source is represented by the
yellow cylinder. For clarity, the CH2 shielding, vacuum vessel, laboratory walls,
and cavern rock are all transparent within this illustration. For demonstration,
the paths of several neutrons emitted by the source are also shown.
To show how the event rate varied with energy, the data were analysed in
500 NIP bins. This was done separately for the left and right halves of the detector and then combined to give a total detection rate. These were then compared
5.3 Nuclear Recoils in DRIFT
141
to simulated rates as discussed in Section 5.3.3. The results shown in Table 5.6
and Figure 5.11 represent the experimental and simulated rates for the whole detector. In addition to the errors listed, a 5 % systematic error should be applied
to all results to accommodate the uncertainty in source strength1 . After running
the experimental data through proportional counter cuts, the experimental rate
in the 1000−6000 NIPs energy range was found to be 0.28 ± 0.02 Hz2 . Comparing
this to the simulated rate for the same energy bin gives an exp/theory efficiency
of (67.85 ± 6.18 %(stat) ± 5 %(syst)) %. This result is slightly lower than the proportional counter efficiencies determined for DRIFT-IIa neutron exposures [113]
but, as shown in Figure 5.11, the experimental and theoretical rates are in good
agreement and follow a similar trend.
Figure 5.11: Experimental (blue) and simulated (red) rates per energy bin for a
DRIFT-IIb neutron exposure conducted on February 20th 2007. The rates shown
here are also presented in Table 5.6.
5.3.3.2
Collimated Neutron Run
An additional neutron exposure run, similar to that described in the previous
section, was carried out on the DRIFT-IIb detector and again simulated using
1
2
The 5 % error is quoted by the manufacturer of the source. See Section 3.4.
This analysis was performed in conjunction with Dan Snowden-Ifft, Occidental College.
142
5. ANALYSIS
Table 5.6: Experimental and simulated rates for a DRIFT-IIb neutron exposure
conducted on February 20 th 2007. The columns represent, from left to right: the
energy bins in units of NIPs, the experimental rates derived from neutron data
files, experimental rates derived from background (BG) data files, the background
subtracted neutron data rate (also known as the proportional counter (PC) rate),
the GEANT4 simulated proportional counter rates, and the ‘proportional counter’
efficiency (calculated as the experimental rate divided by the simulated rate). The
quoted percentage error represents the statistical uncertainty in the efficiency.
These results are illustrated graphically in Figure 5.11.
Energy
Bin
(NIPs)
0-500
500-1000
1000-1500
1500-2000
2000-2500
2500-3000
3000-3500
3500-4000
4000-4500
4500-5000
5000-5500
5500-6000
6000-6500
6500-7000
7000-7500
7500-8000
8000-8500
8500-9000
9000-9500
9500-10000
1000-6000
Neutron
Files
Rate (Hz)
9.1E-02
1.5E-01
1.0E-01
5.4E-02
4.0E-02
3.0E-02
2.3E-02
2.2E-02
1.9E-02
1.1E-02
1.4E-02
9.7E-03
1.1E-02
6.3E-03
8.2E-03
6.3E-03
8.8E-03
8.5E-03
7.2E-03
5.1E-03
3.3E-01
BG
Rate
(Hz)
2.9E-02
4.4E-02
2.5E-02
8.5E-03
3.4E-03
2.0E-03
1.5E-03
1.2E-03
9.4E-04
9.4E-04
1.5E-03
9.4E-04
9.4E-04
7.0E-04
8.2E-04
1.1E-03
4.7E-04
1.1E-03
7.0E-04
9.4E-04
4.6E-02
PC
Rate
(Hz)
9.1E-02
1.0E-01
7.8E-02
4.6E-02
3.7E-02
2.8E-02
2.2E-02
2.1E-02
1.8E-02
1.0E-02
1.2E-02
8.7E-03
9.6E-03
5.6E-03
7.3E-03
5.3E-03
8.3E-03
7.4E-03
6.5E-03
4.2E-03
2.8E-01
Sim
Rate
(Hz)
2.3E+00
2.4E-01
1.1E-01
7.4E-02
5.8E-02
3.9E-02
3.2E-02
3.0E-02
2.3E-02
1.8E-02
1.7E-02
1.5E-02
1.2E-02
1.2E-02
1.0E-02
8.0E-03
7.0E-03
6.9E-03
5.9E-03
3.6E-03
4.1E-01
Efficiency
(%)
Error
(%)
3.9
42.0
72.1
61.6
64.5
71.4
68.3
67.6
81.5
57.8
70.0
59.6
78.5
45.6
72.2
65.7
118.6
107.1
111.8
117.3
67.8
8
7
9
14
21
27
30
34
38
40
32
40
40
47
43
41
54
40
47
45
6
5.3 Nuclear Recoils in DRIFT
143
GEANT4. In this case, however, the neutron source was partially collimated due
to its placement within an open ended boron loaded wax container. Also of note,
for this particular run, was that only the left half of the fiducial volume was active.
The geometry for this run is illustrated in Figure 5.12. In this set-up, five faces
of the detector are again completely shielded using CH2 and the front face left
fully exposed. The
252
Cf source, placed within its wax container, was positioned
1.5 m away from the front face of the detector and directly in alignment with the
centre of the left half of the detector.
Figure 5.12: Modelled geometry of the DRIFT-IIb collimated neutron source run.
The 252 Cf neutron source is contained within an open ended boron loaded wax
container. The source is positioned 1.5m away from the front of the door in
alignment with the centre of the left half of the detector. Note: only the left side
of the detector was active during this run.
The experimental and simulated event rates for this collimated neutron source
exposure are shown in Table 5.7 and Figure 5.13. Due to low statistics, rates
beyond 6000 NIPs are not listed here. It should again be noted that a 5 %
systematic error should be applied in addition to the uncertainty quoted. In
analysing data for this run, zero-background analysis cuts described in Section
5.3.2.2 were applied. Zero-background rejection cuts eliminate events occurring
in the MWPC region and therefore, the simulated MWPC rate was ignored when
144
5. ANALYSIS
Table 5.7: Experimental and simulated rates for the DRIFT-IIb collimated neutron source run. The target mass for the run was 83 g. The quoted percentage
error represents the statistical uncertainty in the efficiency. These results are
illustrated graphically in Figure 5.13.
Energy Bin
(NIPs)
0-500
500-1000
1000-1500
1500-2000
2000-2500
2500-3000
3000-3500
3500-4000
4000-4500
4500-5000
5000-5500
5500-6000
1000-6000
Experimental
Rate (Hz)
0.0E+00
3.1E-05
7.1E-04
7.3E-04
4.5E-04
4.0E-04
3.0E-04
2.8E-04
2.7E-04
1.6E-04
8.0E-05
2.9E-05
3.7E-03
Simulated
Rate (Hz)
4.6E-02
4.0E-03
1.6E-03
1.4E-03
1.1E-03
7.9E-04
6.4E-04
7.0E-04
6.6E-04
4.3E-04
4.0E-04
3.0E-04
8.0E-03
Efficiency
(%)
0
0.78
45.05
50.41
41.43
50.76
46.95
39.84
40.9
36.62
19.77
9.73
46.08
Error
(%)
0
7.4
16.79
29.96
17.88
19.24
20.36
20.44
34.65
34.02
23.48
26.91
5.82
calculating the detector’s efficiency in this mode. For the energy window of 10006000 NIPs, the detector’s efficiency in zero-background mode was calculated to
be (46.08 ± 5.82 %(stat) ± 5 %(syst)) %. This is consistent with similar efficiency
measurements made on the DRIFT-IIa detector [113].
5.3.4
Radon in DRIFT
In the analysis of DRIFT-IIa data it was found that even after applying all cuts
to background data runs, a population of events remained. These events had the
characteristics of nuclear recoils similar to those expected from WIMPs (the reason for passing analysis cuts) and so, whilst being negligible for the purposes of
determining the neutron detection efficiency, they would be, however, problematic
in determining the WIMP-nucleon cross-section sensitivity (where absolute background rates are of utmost importance). The hypothesis for the cause of these
events is that they are a direct result of radon present within the detector. It is
believed that
222
Rn and
220
Rn, emitted from the detector’s internal components,
was able to diffuse into the fiducial volume where, if it then decayed, its progeny
could produce nuclear recoil events with all the characteristics necessary to pass
5.3 Nuclear Recoils in DRIFT
145
Figure 5.13: Experimental (blue) and simulated (red) rates per energy bin for a
DRIFT-IIb collimated neutron source run. The rates shown here are also presented in Table 5.7.
analysis cuts. These events were thus termed radon progeny recoils (RPRs). A
more thorough description of the radon hypothesis, and the analysis leading to
it, is given in [124] and [125] but is briefly outlined here.
Materials within the detector, such as the coaxial and ribbon cabling, have
been measured to emanate
222
Rn1 . With a half-life of 3.825 days, a fraction
of these atoms can drift into the fiducial volume. The
222
producing an alpha particle and a radon progeny atom,
Rn may then decay
218
Po. If the alpha
particle interacts with the CS2 and generates a nuclear recoil, it can be easily
rejected in analysis. The
218
Po atom, however, is positively charged and is thus
attracted to the central cathode [126]. The
218
Po atom, now within the vicinity
of the central cathode wires, may also decay via alpha emission leaving a
214
Pb
atom. Again, if the alpha particle interacts with the CS2 and generates a nuclear
recoil, it can be easily rejected in analysis. There is, however, a probability that
the alpha particle will be emitted directly into, and buried within, one of the
central cathode wires and thus be hidden from detection. In this case, the
214
Pb
atom is then left suspended in the fiducial volume alone and may generate a
1
This measurement was undertaken using a dedicated Rn detector [115].
146
5. ANALYSIS
nuclear recoil event with characteristics similar to those of a neutron or WIMP
event. Further RPRs can occur from the other daughter particles produced in
the
222
Rn, or also the
220
Rn, decay chains.
In addition to these RPRs, there will, of course, be a number of alpha particle
recoils that cross the central cathode and deposit energy in both the left and right
volumes of the detector (see Figure 5.14). Therefore, to verify the Rn hypothesis,
the rate of events in which an alpha particle deposited energy in both halves of the
detector volume and did not register the veto lines, termed gold plated cathode
crossing (GPCC) events, was searched for in analysis. By comparing the rate of
these GPCC events in the DRIFT-IIa data to that of DRIFT-IIb data, it was
found that replacing the offending coaxial and ribbon cables with radiologically
purer alternatives reduced the rate of GPCC by ∼ 92 %. Additional tests have
included replacing the central cathode entirely, thus reducing RPRs from longlived
210
Pb (22 year half-life), and running the detector at a higher CS2 flow rate
(8 vessel changes per day).
Longer term plans to solve the RPR problem involve finding ways to discriminate against RPRs. Possible ways to achieve this could be through determining
the absolute z-position of a recoil by measuring the diffusion of the ionisation
track, or by reading off the central cathode in some way to directly measure the
emitted alpha particle. One method of detection proposed is to replace the current central cathode with a slab of scintillating material. The outer surfaces of
this scintillator would, of course, need to be coated with an electrically conducting
material sufficient to act as the central cathode. When in operation, if an RPR
event was to occur, the emitted alpha particle (which would have previously gone
undetected) would now enter the scintillator and produce light which could then
be used to veto the entire event. Preliminary tests and simulations to determine
the detection capabilities of such a scintillator have indicated the proposed setup may be feasibile. Any new materials to be used in a DRIFT module are now
screened using a Rn emanation detection system and the HPGe detector (kept
inside the low background laboratory within JIF) to test for radiological purity.
5.4
Summary
In a direct dark matter search experiment it is of foremost importance that background levels are minimised to the best levels attainable. In normal running
5.4 Summary
147
Figure 5.14: Illustration of a gold plated cathode crossing (GPCC) event. An
alpha particle track has crossed the central cathode causing charge to be deposited
and subsequently drifted in opposite directions to each MWPC. The axis labels for
each side of the detector are different to account for the opposite drift direction
and thus represent the corrected orientation for calculation of ∆x, ∆y, and ∆z.
All dimensions shown are in millimetres. Taken from [125].
148
5. ANALYSIS
mode, DRIFT modules are set at a threshold appropriately high so as to be insensitive to electron recoils occuring within the main fiducial volume. Through
comparison of simulated event rates to those of real background data, the gammaray rejection factor of DRIFT-I was found to be better than 2 × 10−7 at 90 % C.L.
(best case scenario) for the energy range of 1000−5000 NIPs. Electron recoils generated from background gamma-rays are found to produce long ionisation track
lengths in 40 Torr CS2 gas, spanning up to the entire length of the fiducial volume. The CH2 shielding erected around the DRIFT-II vessels, at a thickness of
only 67 cm, does little to reduce the rate of electron recoils generated from a 60 Co
exposure. When dealing with background gamma-rays emitted from the cavern
rock, however, the CH2 shielding does have a notable effect. The difference seen
in the latter case is due to the broader, and of generally lower energy, energy
emission spectrum. To shield against a
60
Co source, a greater thickness of CH2 ,
or an alternative material, would be required; this, however, is not necessary in
the case of DRIFT.
Nuclear recoil events at the low energies of interest are known to have short
track lengths, of the order of a few millimetres. From knowledge of the typical ionisation track length of such recoils, and the relationship between observed
NIPs and true recoil energy, a number of parameters can be generated for each
recorded event and used to set analysis cuts on the data. Reduction of data
from neutron exposure runs on the DRIFT-IIb detector has been carried out
and used, along with detailed Monte Carlo simulations, to determine the ‘proportional counter’ efficiency (retention of events) of a neutron exposure run to
be (67.85 ± 6.18 %(stat) ± 5 %(syst)) %. The efficiency of a similar exposure run,
with much more stringent cuts applied, was found to be (46.08 ± 5.82 %(stat) ±
5 %(syst)) %, consistent with efficiencies calculated for ‘zero-background’ analysis
of DRIFT-IIa data.
Compelling evidence has led to the conclusion that an unwanted population of
events within the DRIFT-IIa data was caused by radon emanation from components within the vessel. Steps implemented to reduce events consistent with this
hypothesis proved successful and have thus been put in to force in the DRIFT-IIb
detector.
Chapter 6
DRIFT Directionality
6.1
Introduction
The principal motivation behind employing DRIFT in the field of WIMP detection is to exploit the directional capabilities of the technology. With progression
at each stage of development in the DRIFT programme, the directional sensitivity
will no doubt continue to improve, but to achieve these advances, the capabilities of current detectors must first be known and fully understood. This chapter
describes work carried out to estimate the theoretical capabilities of detecting
a directional signature using DRIFT and then compares this to real data results. This involved simulating nuclear recoils produced in directed neutron runs
and then, from this, generating pseudo-data which was run through real analysis cuts. Genuine DRIFT data from analogous directional runs were obtained,
passed through identical analysis cuts, and then compared to the pseudo-data.
The response and capability of current DRIFT modules are presented and discussed.
6.2
Simulated Nuclear Recoils
As discussed in Chapter 2, a detector capable of measuring the directional distribution of recoil events would, in theory, be able to observe the diurnal (and
annual) fluctuation of a WIMP signal. When dealing with real experiments, a
number of factors contribute to the detector’s directional capabilities, but before
looking at real DRIFT data it was decided to look at the theoretical distribution of
nuclear recoil tracks generated from directed neutron runs. This was achieved by
conducting two separate Monte Carlo simulations: a purpose-built Monte Carlo
149
150
6. DRIFT DIRECTIONALITY
package (hereby referred to within this chapter as the Monte Carlo), and the
GEANT4 simulation of the DRIFT-IIb detector previously utilised in Chapter 5.
In both scenarios, the simulations performed modelled directional neutron runs
along each of the principal axes: x, y, and z (the orientation of which is illustrated
in Figure 5.14). All results shown are for neutron induced nuclear recoils occurring in 40 Torr CS2 gas. Only the initial recoil tracks are generated within these
simulations; no diffusion effects are included.
6.2.1
Purpose-Built Monte Carlo
The purpose-built Monte Carlo is the first part of a larger simulation designed
to generate pseudo-data for the DRIFT experiment; the latter part is utilised
in Section 6.41 . When implemented, the code used a
252
Cf energy spectrum to
generate nuclear elastic scattering recoils spread over some angular distribution
and range of energies. Within the code, differential scattering data were taken
from [127] and recoil range scattering information exploited from SRIM [128].
In calculating the magnitude of recoil track ranges, a straight line was assumed from the start-point to the end-point of each track and the corresponding
size in each dimension worked out individually. In reality, straggling effects are
present and the actual path length a recoiling particle will travel is larger than
estimated using this technique, especially for low energy recoils, but to a first
order approximation a straight line fit is adequate. In addition, the analysis of
real DRIFT-IIa data calculates track ranges through the ionisation falling onto
the wire planes and, therefore, does not employ a true step-by-step measurement
approach that would be required to accurately deal with straggling effects. Table
6.1 summarises the Monte Carlo run details and calculated recoil track magnitudes in each dimension. The track sizes quoted have been calculated as the mean
value for all events within the specified energy ranges.
In comparing the results shown in Table 6.1, it can be seen that, as expected,
the track size is largest along the principal axis of orientation for that run e.g. for
the x-axis run, ∆x is larger than ∆y and ∆z. For simulated recoil track lengths,
these parameters can be compared in this way. In the analysis of DRIFT-IIa data,
however, ∆x, ∆y, and ∆z are calculated in entirely different ways (described in
1
This Monte Carlo was written by collaboration members at Occidental College, LA. A
description of the simulation can be found in [120]. The adaptation and implementation of the
code were conducted by the author.
6.2 Simulated Nuclear Recoils
151
Table 6.1: Summary of the Monte Carlo directional neutron runs. The mean
magnitude of recoil tracks in each dimension, and the corresponding number of
events, are listed for selected energy ranges. All recoil track sizes are quoted in
units of mm.
Monte Carlo: Run Summaries
x-axis run
Energy Bin
(NIPs)
All events
2500-5000
1500-5000
1500-3000
3000-7000
Number of
events
9901
1241
2170
1244
1436
Energy Bin
(NIPs)
All events
2500-5000
1500-5000
1500-3000
3000-7000
Number of
events
9901
1204
2128
1263
1390
Energy Bin
(NIPs)
All events
2500-5000
1500-5000
1500-3000
3000-7000
Number of
events
9901
1204
2129
1240
1369
∆x
∆y
∆z
5.23 ± 0.15
4.35 ± 0.11
3.30 ± 0.07
2.15 ± 0.06
6.08 ± 0.14
y-axis run
2.40 ± 0.06
3.16 ± 0.10
2.48 ± 0.06
1.78 ± 0.06
4.08 ± 0.12
2.35 ± 0.06
3.01 ± 0.10
2.36 ± 0.06
1.64 ± 0.05
4.00 ± 0.12
∆x
∆y
∆z
2.36 ± 0.06
3.02 ± 0.10
2.36 ± 0.06
1.68 ± 0.06
4.00 ± 0.12
z-axis run
5.37 ± 0.15
4.40 ± 0.04
3.23 ± 0.07
2.03 ± 0.06
6.36 ± 0.14
2.36 ± 0.06
3.03 ± 0.09
2.35 ± 0.06
1.67 ± 0.05
3.99 ± 0.11
∆x
∆y
∆z
2.50 ± 0.06
3.13 ± 0.10
2.41 ± 0.06
1.72 ± 0.06
3.93 ± 0.12
2.46 ± 0.06
3.20 ± 0.10
2.46 ± 0.06
1.76 ± 0.06
4.15 ± 0.12
5.45 ± 0.15
4.53 ± 0.11
3.30 ± 0.08
2.08 ± 0.06
6.30 ± 0.14
152
6. DRIFT DIRECTIONALITY
Section 5.3.2.1) and it is therefore unfair to compare these parameters against
one another; data analysis results for ∆x cannot be directly compared to ∆y or
∆z. For that reason, it was decided to present these results in such a way so as
to compare ∆x for one directional axis run against ∆x for another directional
run, and to similarly present ∆y and ∆z in a likewise fashion. With this purpose
in mind, a parameter used to illustrate the significance of the difference in track
size between directional runs, relative to the associated errors, was introduced.
This parameter is called the significance effect, S, and is calculated as follows.
Consider ∆x for the x-axis and y-axis runs, denoted as ∆x|x and ∆x|y , respectively. To measure the difference in magnitude between these values, one
is subtracted from the other. To measure the associated significance effect, this
difference is divided by the combined error:
∆x|x − ∆x|y
.
(error in ∆x|x )2 + (error in ∆x|y )2
S=p
(6.1)
Thus, the S parameter effectively gives a quantitative measure of a result’s significance; the larger the value of S, the larger the discrepancy between runs.
Table 6.2 lists the difference in recoil sizes and the corresponding significance
effect between each of the Monte Carlo runs. As expected, the S parameter
indicates that the magnitudes of track lengths for a given run are significantly
larger along the principal axis of orientation for that run.
6.2.2
GEANT4
In a similar way to the previous Monte Carlo, GEANT4 was utilised to generate
nuclear recoils induced from directional neutron exposures. A notable difference,
however, was that the GEANT4 simulation included the detailed geometry of
many of the detector’s internal and external components. Within this simulation,
nuclear recoils were not simply generated in 40 Torr CS2 gas, but neutrons (with a
range of energies mimicking a 252 Cf energy spectrum) were actually emitted from
a simulated isotropic point source and tracked through the modelled geometry
and into the detector’s fiducial volume. It should be noted that this was done
using a Monte Carlo simulation which had been extensively tested and shown to
perform well when held against real data results [113]. Table 6.3 summarises the
GEANT4 run details and calculated recoil range magnitudes for each directional
run. As can be seen, these results show track sizes distinctly shorter than those
6.2 Simulated Nuclear Recoils
153
Table 6.2: The significance effect (S) calculated using the purpose built Monte
Carlo results. See main text for the definition of S. The assigned letters denote
the direction of the run e.g. D.x represents the value of D for the x-axis run. All
recoil track sizes are quoted in units of mm.
Monte Carlo: Significance Effect (S)
∆x
Energy Bin
(NIPs)
All Events
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
All Events
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
All Events
2500-5000
1500-5000
1500-3000
3000-7000
∆x|x −∆x|y
S
2.875
1.331
0.946
0.474
2.080
17.87
8.91
9.71
5.80
11.28
∆y|y −∆y|x
S
2.971
1.235
0.752
0.251
2.280
18.08
11.62
7.64
3.00
12.37
∆z|z −∆z|x
S
3.097
1.512
0.944
0.443
2.300
19.09
10.05
9.62
5.49
12.47
∆x|x −∆x|z
S
∆x|y −∆x|z
S
16.91
8.14
9.13
5.14
11.66
-0.140
-0.112
-0.050
-0.038
0.070
-1.61
-0.80
-0.55
-0.47
0.41
S
∆y|x −∆y|z
S
17.77
11.39
7.92
3.17
11.99
-0.057
-0.040
0.022
0.013
-0.070
-0.66
-0.29
0.24
0.16
-0.41
∆z|z −∆z|y
S
∆z|x −∆z|y
S
3.085
1.498
0.950
0.410
2.310
19.09
10.11
9.8
5.11
12.97
-0.012
-0.013
0.006
-0.033
0.010
-0.14
-0.10
0.06
-0.43
0.06
2.734
1.219
0.896
0.436
2.150
∆y
∆y|y −∆y|z
2.914
1.195
0.774
0.265
2.210
∆z
154
6. DRIFT DIRECTIONALITY
presented from the previous Monte Carlo. This is most likely due to the angular distribution through which neutrons were simulated to enter the target gas.
Within the purpose-built Monte Carlo, the neutrons were modelled to have an
angular distribution of 15◦ centred around the principal axis for each particular
run. Within the GEANT4 simulation, the neutrons were emitted isotropically
from the source and therefore entered the fiducial volume with a complete angular distribution range. Thus, the nuclear recoils generated using GEANT4 had a
less weighted bias towards a particular axis of orientation. For these reasons, the
GEANT4 simulation represents a more realistic model of the true experimental
run, the data for which is presented in Section 6.3. It should also be noted that it
is the relative size of each track component, rather than the absolute magnitude
of each value, that is of importance when determining directional sensitivity.
Table 6.4 lists the significance effect summaries for the GEANT4 results in an
analogous fashion to that of the purpose-built Monte Carlo summaries (shown
in Table 6.2). For most energy bins, the GEANT4 results do present notable
significance effects in favour of the expected components for both the ∆x and ∆z
parameters. The exception to this occurs when analysing the “All events” energy
bin for ∆x. Through comparison of the data in Table 6.3 it is clear that the
“All events” energy bin is comprised mainly of low energy events and therefore
contains shorter track lengths with respect to other energy bins. Given that the
majority of events are of low energy, analysis of “All events” is, inherently, less
likely to extract reliable directional sensitivity.
The significance effect results for the ∆y parameter are less convincing. As
can be seen in Table 6.3, the y-axis run itself does, indeed, produce the largest
recoil track component in the y direction (when compared to the ∆x and ∆z
components for the y-axis run) but does not provide a significant result when
compared to the other axis runs. It can also be seen that despite the total number
of events for all runs being approximately equal, the number of events within each
energy bin is notably different between runs. The results across all energy bins
for all parameters are less consistent than those of the purpose-built Monte Carlo.
The discrepancy in statistics here may be, at least partially, responsible for the
anomalous significance results shown.
6.2 Simulated Nuclear Recoils
155
Table 6.3: Summary of the GEANT4 directional neutron runs. All recoil track
sizes are quoted in units of mm.
GEANT4: Run Summaries
x-axis run
Energy Bin
(NIPs)
All events
2500-5000
1500-5000
1500-3000
3000-7000
Number of
events
6487
365
670
413
393
Energy Bin
(NIPs)
All events
2500-5000
1500-5000
1500-3000
3000-7000
Number of
events
6653
280
504
317
306
Energy Bin
(NIPs)
All events
2500-5000
1500-5000
1500-3000
3000-7000
Number of
events
6602
727
1306
790
835
∆x
∆y
∆z
0.74 ± 0.03
1.67 ± 0.08
1.24 ± 0.05
0.84 ± 0.03
2.30 ± 0.10
y-axis run
0.49 ± 0.02
1.44 ± 0.06
1.05 ± 0.04
0.70 ± 0.03
1.88 ± 0.08
0.48 ± 0.02
1.49 ± 0.07
1.11 ± 0.04
0.79 ± 0.04
1.90 ± 0.08
∆x
∆y
∆z
0.37 ± 0.02
1.33 ± 0.07
1.01 ± 0.04
0.72 ± 0.04
1.81 ± 0.09
z-axis run
0.58 ± 0.03
1.36 ± 0.07
1.06 ± 0.04
0.78 ± 0.04
2.22 ± 0.10
0.38 ± 0.02
1.31 ± 0.06
1.03 ± 0.04
0.78 ± 0.04
1.96 ± 0.10
∆x
∆y
∆z
0.82 ± 0.02
1.24 ± 0.04
0.98 ± 0.03
0.69 ± 0.02
1.66 ± 0.05
0.79 ± 0.02
1.21 ± 0.04
0.92 ± 0.03
0.64 ± 0.02
1.64 ± 0.05
1.64 ± 0.05
1.78 ± 0.04
1.29 ± 0.03
0.81 ± 0.03
2.56 ± 0.06
156
6. DRIFT DIRECTIONALITY
Table 6.4: The significance effect calculated using the GEANT4 results. All recoil
track sizes are quoted in units of mm.
GEANT4: Significance Effect (S)
∆x
Energy Bin
(NIPs)
All Events
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
All Events
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
All Events
2500-5000
1500-5000
1500-3000
3000-7000
∆x|x −∆x|y
S
0.377
0.340
0.227
0.118
0.487
10.07
3.18
3.39
2.48
3.71
∆y|y −∆y|x
S
0.091
-0.078
0.014
0.078
0.348
∆x|x −∆x|z
S
∆x|y −∆x|z
S
-1.94
4.64
4.44
3.81
5.76
-0.455
0.090
0.029
0.031
0.153
-16.04
1.11
0.55
0.76
1.50
∆y|y −∆y|z
S
∆y|x −∆y|z
S
2.58
-0.86
0.25
1.62
2.79
-0.208
0.156
0.143
0.141
0.587
∆z
-5.77
2.01
2.86
3.44
5.27
-0.299
0.234
0.128
0.063
0.239
-10.05
3.11
2.67
1.64
2.56
∆z|z −∆z|x
S
∆z|z −∆z|y
S
∆z|x −∆z|y
S
1.156
0.291
0.184
0.017
0.656
22.60
3.69
3.48
0.37
6.44
1.260
0.474
0.260
0.025
0.604
24.99
6.05
4.95
0.56
5.4
0.104
0.183
0.077
0.008
-0.052
3.93
2.00
1.30
0.17
-0.41
-0.077
0.430
0.256
0.149
0.640
∆y
6.3 DRIFT-IIa Data: Directional Analysis
6.3
157
DRIFT-IIa Data: Directional Analysis
Directional neutron exposures on the DRIFT-IIa detector were conducted using
the
252
Cf neutron calibration source. Data taken from these runs were passed
through analysis cuts and used to determine the magnitude of nuclear recoil
range components parallel to each principal axis of the detector. The methods of
calculation for ∆x, ∆y, and ∆z are detailed in Section 5.3.2.1. For the DRIFTIIa data analysed, it was found that the ∆y measurement gave a rather crude
estimate of the component of recoil range in this direction and is, therefore,
not included within this work. In this case the poor ∆y measurement is due
to unsatisfactory reconstruction of the recoil track component. The poor ∆y
significance results for the GEANT4 data are independent of the results shown
here. Recent analysis of DRIFT-IIc data has also shown that the ∆y measurement
is indeed the least accurate out of all three dimensions. An important attribute
to consider, however, is the angle through which the WIMP signal is expected to
fluctuate. As illustrated in Chapter 2, it is predicted that a detector located at a
latitude similar to that of the Boulby facility will observe a diurnal fluctuation in
the relative direction of a WIMP signal. A DRIFT module can be orientated such
that the approximate alignment of this signal will oscillate between two axes of the
detector (see Figure 2.9). Due to the angular range of this fluctuation, oscillation
across all three axes is not possible. It is, therefore, only necessary to observe
the directional distribution along two axes. Naturally, it is preferable to utilise
the two axes of the detector with the most accurate measurement capabilities, in
this instance the x and z axes. For these reasons, when searching for a WIMP
signal, it would be advantageous to orientate future DRIFT modules such that
one of these axes runs parallel to the north-south line and the other axis points
in the direction of the surface normal i.e. perpendicular to the Earth’s surface.
Table 6.5 summarises the run details and recoil range components calculated
from DRIFT-IIa data sets. Since these results are deduced from real data, all
the detection and resolution factors inherent to real experiments are present.
Crucially, these attributes include the readout capabilities of the detector and
the diffusion effects experienced by the ionisation charge as it drifts across the
fiducial volume towards the MWPC. When compared to the GEANT4 simulated
results, it can be seen that the ∆x measurement is slightly larger. This is expected
since the effects of diffusion inflate the true recoil track range. The diffusion of
158
6. DRIFT DIRECTIONALITY
charged particles can be expressed through the relation [117]:
σ2 =
4L
3eE
(6.2)
where is the characteristic average energy of the electron or ion, L is the drift
distance, e is the charge of an electron, and E is the drift field. For the case of
electrons, varies from thermal energies at low drift fields to several eV at higher
E/P (where P is pressure). This non-linear relationship arises since electrons
have a much smaller mass than that of the target gas atoms and thus the energy
gained from the electric field is higher than that lost through collisions with the
gas. Ions, however, have masses comparable to that of the target gas atoms and
so remain well thermalised. Given an electric field strength of 624 ± 4 V cm−1
in the DRIFT-IIa detector (see Section 4.3.3.2), Equation 6.2 gives σ < 0.5 mm,
a result consistent with experimentally measured diffusion effects [129]. The
magnitudes of ∆x measurements deduced from DRIFT-IIa, therefore, reasonably
match those from the GEANT4 data when combined with expected diffusion.
The ∆z measurement, however, looks to be heavily inflated and so it was decided
to calculate this parameter using two further additional techniques. The first
technique, used to produce the nf f whm∆z parameter, is similar to the previous
method used to calculate ∆z with the exception of the start and end time criteria.
Rather than selecting tmin and tmax for this purpose, the earliest time at which
an nf f whm began (out of all the anode wires hit) is subtracted from the latest
time at which an nf f whm ended (again out of all the anode wires hit), and then
this value is multiplied by the drift velocity. In the second technique, the root
mean square time (rmst) between tmin and tmax is calculated for each channel.
rmst∆z is then calculated by subtracting the earliest rmst from the latest rmst
(out of all the anode wires hit) and multiplying by the drift velocity.
As expected, nf f whm∆z and rmst∆z both provide a reduced estimate of
the range component along the z-axis compared with the traditional method
of calculation. To compare the magnitude of these parameters with respect to
distinct axis runs, the significance effect must be considered. These results are
shown in Table 6.6. It should again be noted that since ∆x and ∆z are calculated in entirely different ways, these parameters cannot be directly compared
to one another; only a comparison of the same parameter between distinct runs
can be made. Within higher energy bins, where recoil track ranges are larger
and thus directional sensitivity more apparent, the significance effect for the ∆x
Number of
events
607
1298
881
471
Number of
events
472
1072
753
355
Number of
events
96
167
104
70
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
∆z
∆z
∆z
5.594 ± 0.147
5.207 ± 0.107
4.817 ± 0.120
6.092 ± 0.193
∆x
2.021 ± 0.140
1.605 ± 0.105
1.269 ± 0.106
2.286 ± 0.192
1.992 ± 0.057 5.702 ± 0.081
1.401 ± 0.038 5.039 ± 0.047
1.052 ± 0.038 4.674 ± 0.046
2.349 ± 0.072 6.014 ± 0.095
z-axis run
∆x
2.201 ± 0.056 5.681 ± 0.064
1.530 ± 0.037 5.051 ± 0.041
1.078 ± 0.035 4.623 ± 0.042
2.650 ± 0.070 6.140 ± 0.076
y-axis run
∆x
x-axis run
2.649 ± 0.035
2.611 ± 0.025
2.589 ± 0.036
2.692 ± 0.040
nf f whm∆z
2.672 ± 0.019
2.596 ± 0.011
2.547 ± 0.011
2.719 ± 0.021
nf f whm∆z
2.636 ± 0.014
2.562 ± 0.009
2.519 ± 0.010
2.682 ± 0.017
nf f whm∆z
DRIFT-IIa Data: Run Summaries
0.976 ± 0.012
0.971 ± 0.009
0.967 ± 0.012
0.995 ± 0.014
rmst∆z
0.986 ± 0.007
0.967 ± 0.004
0.957 ± 0.005
0.993 ± 0.008
rmst∆z
0.967 ± 0.005
0.950 ± 0.003
0.938 ± 0.003
0.984 ± 0.006
rmst∆z
Table 6.5: Summary of the DRIFT-IIa directional neutron runs. All recoil track sizes are quoted in units of mm.
6.3 DRIFT-IIa Data: Directional Analysis
159
160
6. DRIFT DIRECTIONALITY
measurement indicates that this component of recoil range is significantly larger
for a neutron exposure directed along the x-axis. The same conclusion cannot
be made for the ∆z parameter, these significance effect results are inconsistent.
Thus, for the DRIFT-IIa data analysis presented here, ∆z is not an appropriate
parameter to use when attempting to demonstrate the directional capabilities
of the detector. The results also indicate that whilst nf f whm∆z and rmst∆z
may provide a more closely matched magnitude to the true recoil track size, the
significance of the associated errors skew any positive confirmation of directionality across all energy bins. Within selected energy windows, in which the lowest
energy recoils are included, the measurements of nf f whm∆z and rmst∆z from
the z-axis run are indeed greater than those from the x-axis and y-axis runs. The
problem in demonstrating a definitive significance effect in favour of a directional
sensitivity appears to lie with the associated errors for the z-axis runs which are,
due to poorer statistics, higher than those of the x-axis and y-axis runs.
It should be emphasised that ∆x, ∆z, nf f whm∆z, and rmst∆z are crude
measurements of the true recoil track size components but do provide information on the relative track ranges with respect to runs of contrasting orientation.
Given that the important factor to consider is the relative size of these recoils, a
slightly more accurate measurement of the ∆z parameter, be it through improved
techniques, enhanced fidelity of data, or increased statistics, would provide the
necessary capability to confirm directional sensitivity along the z-axis. The directional analysis of DRIFT data, as described here for DRIFT-IIa, was extended
upon for the analysis of directional neutron runs conducted on the DRIFT-IIc
module. Very recent results have confirmed directional sensitivity along all three
axes of the DRIFT-IIc detector [130].
6.4
Pseudo-data: Directional Analysis
The pseudo-data described within this section were developed using the full
purpose-built Monte Carlo simulation package first described in Section 6.2.1.
From the nuclear recoil information generated in the first part of the Monte Carlo,
imitation voltage traces were produced to mimic those of the channel waveforms
created during a genuine DRIFT run. The pseudo-data were then passed through
analysis cuts identical to those of the real DRIFT-IIa data. Figures 6.1(a) and
6.1(b) show a plot of NIPs versus R2 (a track length parameter defined in Section
6.4 Pseudo-data: Directional Analysis
161
Table 6.6: The significance effect calculated using the DRIFT-IIa data analysis
results. All recoil track sizes are quoted in units of mm.
DRIFT-IIa Data: Significance Effect (S)
∆x
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
∆x|x −∆x|y
S
0.209
0.129
0.026
0.301
2.64
2.43
0.50
3.00
∆z|z −∆z|x
S
-0.087
0.156
0.194
-0.048
∆x|x −∆x|z
0.180
-0.075
-0.191
0.364
∆z
∆z|z −∆z|y
-0.54
-0.108
1.36
0.168
1.53
0.143
-0.23
0.078
nf f whm∆z
∆z|z −∆z|y
S
∆x|y −∆x|z
S
1.19
-0.67
-1.71
1.78
-0.029
-0.204
-0.217
0.063
-0.19
-1.83
-1.93
0.31
S
∆z|x −∆z|y
S
-0.64
1.44
1.11
0.36
-0.021
0.012
-0.051
0.126
-0.20
0.19
-0.82
1.04
S
∆z|x −∆z|y
S
-0.58
0.55
1.12
-0.60
-0.036
-0.034
-0.028
-0.037
-1.53
-2.39
-1.88
-1.37
∆z|z −∆z|x
S
0.013
0.049
0.070
0.010
0.34
1.84
1.87
0.23
∆z|z −∆z|x
S
∆z|z −∆z|y
S
∆z|x −∆z|y
S
0.009
0.021
0.029
0.011
0.69
2.21
2.34
0.72
-0.010
0.004
0.010
0.002
-0.72
0.41
0.77
0.12
-0.019
-0.017
-0.019
-0.009
-2.21
-3.40
-3.26
-0.90
-0.023
0.015
0.042
-0.027
rmst∆z
162
6. DRIFT DIRECTIONALITY
5.3.2.1) for genuine DRIFT-IIa data and the generated pseudo-data, respectively.
The highest density of events in both figures occurs around R2 = 0.5 cm. It can
also be seen that the pseudo-data plot has a greater number of events extending
into the higher energy region, this, combined with the more idealised set-up of the
Monte Carlo, results in a broader distribution of events. The agreement between
plots highlights the effectiveness of the simulation at producing imitation data
sets.
Table 6.7 details the run summaries for the pseudo-data sets. As expected,
the recoil track size is largest along the principal axis of orientation for each given
run. This is unsurprising since these results are derived from the Monte Carlo
recoils shown in Table 6.1. The ∆z parameter shown here appears much larger
than that of the DRIFT-IIa data results and is also much larger than the initial
recoil it is generated from. This discrepancy is too large to be explained through
diffusion effects. This result emphasises that ∆z represents a very crude estimate
of the true recoil size, rmst∆z and, in particular, nf f whm∆z are much more
accurate. Table 6.8 lists the corresponding significance effects for the pseudodata. As was the case for the real data analysis, the ∆x parameter provides
a positive confirmation of the directional sensitivity along the x-axis while ∆z
and nf f whm∆z fail to provide conclusive confirmation. The rmst∆z parameter
does, however, in this example at least, present a significant directional sensitivity
along the z-axis.
6.5
Summary
Before examining the directional capabilities of DRIFT it was first decided to investigate the theoretical distribution of neutron induced nuclear recoils in 40 Torr
CS2 gas. This was done, initially using a purpose-built Monte Carlo package in
which the incoming neutrons (with a
252
Cf energy spectrum) had an angular
◦
distribution of 15 , and again repeated using the GEANT4 simulation of the
DRIFT vessel, a simulation previously used to simulate neutron exposure runs
and shown to respond well when benchmarked against real data results. Within
the GEANT4 simulation, neutrons were fired isotropically (again with a
252
Cf
energy spectrum) and thus entered the vessel with the full range of angular distributions inherent to a true 252 Cf exposure. In both circumstances, the distribution of events showed that nuclear recoils were directed preferentially along the
6.5 Summary
163
1.5
0.0
0.5
1.0
R2 (cm)
2.0
2.5
3.0
Neutrons, y−axis
0
2000
4000
6000
8000
10000
8000
10000
Nips
(a)
1.5
0.0
0.5
1.0
R2 (cm)
2.0
2.5
3.0
x−NeuRec−neutrons
0
(b)
2000
4000
6000
Nips
Figure 6.1: NIPs versus R2 plot for: (a) a DRIFT-IIa y-axis neutron exposure, (b)
a pseudo-data y-axis neutron exposure. Results shown were obtained after applying cuts to both data sets. In comparing the analogous plots it can be seen that the
simulated results have a slightly broader distribution of events but, nonetheless,
have similar features to that of the real data.
6. DRIFT DIRECTIONALITY
164
Number of
events
586
987
560
609
Number of
events
468
778
449
509
Number of
events
391
708
422
369
nf f whm∆z
2.848 ± 0.079
2.474 ± 0.052
2.041 ± 0.040
3.198 ± 0.096
nf f whm∆z
2.857 ± 0.092
2.439 ± 0.056
2.042 ± 0.039
3.188 ± 0.116
nf f whm∆z
1.078 ± 0.019
0.960 ± 0.013
0.840 ± 0.010
1.231 ± 0.025
rmst∆z
1.026 ± 0.022
0.931 ± 0.014
0.819 ± 0.011
1.118 ± 0.027
rmst∆z
1.037 ± 0.026
0.931 ± 0.016
0.829 ± 0.011
1.127 ± 0.032
rmst∆z
x-axis run
∆z
3.041 ± 0.067
2.591 ± 0.045
2.134 ± 0.038
3.627 ± 0.088
∆z
∆x
8.392 ± 0.140
7.516 ± 0.087
6.658 ± 0.072
9.271 ± 0.165
∆z
1.803 ± 0.064 8.143 ± 0.142
1.614 ± 0.046 7.443 ± 0.096
1.385 ± 0.051 6.605 ± 0.075
2.016 ± 0.067 8.903 ± 0.174
z-axis run
∆x
2.348 ± 0.095 8.348 ± 0.167
1.946 ± 0.061 7.506 ± 0.104
1.550 ± 0.057 6.690 ± 0.075
2.650 ± 0.105 9.129 ± 0.209
y-axis run
1.792 ± 0.070
1.542 ± 0.048
1.214 ± 0.046
1.941 ± 0.074
∆x
Pseudo-Data: Run Summaries
Table 6.7: Summary of the pseudo-data directional neutron runs. All recoil track sizes are quoted in units of mm.
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
6.5 Summary
165
Table 6.8: The significance effect calculated using the pseudo-data analysis results.
All recoil track sizes are quoted in units of mm.
Pseudo-Data: Significance Effect (S)
∆x
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
Energy Bin
(NIPs)
2500-5000
1500-5000
1500-3000
3000-7000
∆x|x −∆x|y
S
0.545
0.332
0.165
0.634
4.76
4.35
2.16
5.09
∆z|z −∆z|x
S
0.044
0.010
-0.032
0.142
∆z|z −∆z|x
0.184
-0.257
-0.907
0.439
∆x|x −∆x|z
0.556
0.404
0.336
0.709
∆z
∆z|z −∆z|y
0.20
0.249
0.07
0.073
-0.31
0.053
0.53
0.368
nf f whm∆z
S
∆z|z −∆z|y
1.62
0.193
-2.82
0.117
-11.78
0.093
3.01
0.429
rmst∆z
S
∆x|y −∆x|z
S
4.71
5.20
4.59
5.52
0.011
0.072
0.171
0.075
0.12
1.08
2.49
0.75
S
∆z|x −∆z|y
S
1.25
0.56
0.51
1.53
0.205
0.063
0.085
0.226
0.93
0.45
0.80
0.83
S
∆z|x −∆z|y
S
1.86
1.70
1.68
3.29
0.009
0.374
1.000
-0.010
0.07
3.95
12.81
-0.07
∆z|z −∆z|x
S
∆z|z −∆z|y
S
∆z|x −∆z|y
S
0.041
0.029
0.011
0.104
1.27
1.41
0.74
2.56
0.052
0.029
0.021
0.113
1.80
1.52
1.41
3.06
0.011
0.0005
0.010
0.009
0.33
0.02
0.65
0.20
166
6. DRIFT DIRECTIONALITY
principal axis of orientation at a level capable of being measured experimentally.
Given that nuclear recoils produced as a result of exposure to a
252
Cf source are
similar to those expected from massive WIMP-induced nuclear recoil events, a
detector capable of demonstrating directional sensitivity here would, in principle,
also have the potential to observe a directional WIMP signal.
In the analysis of real data sets, the recoil track size components in each dimension are calculated in entirely different ways. It is therefore unfair to compare
each directional track size component against another. To this end, like parameters were only compared between distinct runs i.e. ∆x for the x-axis run was
set against ∆x for the y-axis run and then the z-axis run. Similarly ∆y for the
x-axis run was set against ∆y for the y-axis run and then the z-axis run, and so
on. To gauge the significance of any directional bias towards the given axes, a
parameter S, named the significance effect, was introduced.
In order to test the capability of DRIFT-IIa in observing this biased recoil
range distribution, a
252
Cf neutron source was placed at several locations around
the vessel in such a way so as to provide directional neutron runs along each of
the principal axes (x, y, and z). The presented results showed that a directional
sensitivity could be demonstrated along the x-axis. The ∆y measurement, at
that time and for the given data sets, proved too unreliable to determine any
conclusive results. Measurement of the recoil range along the z-axis, whilst not
definitive, demonstrated that directional information could be obtained. More
recent, improved analysis of DRIFT-IIc data, built upon the techniques described
here, has confirmed directional sensitivity along all three axes.
Work carried out using the complete purpose-built Monte Carlo package
showed that pseudo-data, closely mimicking genuine DRIFT data, can be generated. These data were then passed through identical analysis cuts and used
to determine the associated significance effect of the corresponding parameters.
The presented results were shown to produce an analogous, and slightly improved,
sensitivity bias along the x and z axes than when compared to the DRIFT-IIa
data sets. Further improvement of this simulation package, tailored more specifically towards the DRIFT-IIc module, and a very similar Monte Carlo, designed
to include the simulation of WIMP events, is already being undertaken by members of the DRIFT collaboration. Additional work in this field is set to utilise
the head-tail effect described in Section 2.9. It is predicted that head-tail discrimination will provide a more pronounced effect than simply considering the
6.5 Summary
167
magnitude of recoil track sizes. DRIFT-IIc analysis encompassing this work has
already shown that the head-tail effect is measurable within DRIFT.
Chapter 7
Large Scale DRIFT Arrays
7.1
Introduction
DRIFT technology has the potential to confirm that a supposed WIMP signal is
galactic in origin, but to achieve this goal the predicted WIMP-nucleon sensitivities must first be attained. When dealing with a low pressure gas, as in DRIFT,
a large overall exposure (target mass × time) can only be realised through operating a large number of detectors over a set time, or running fewer modules over
an extended period of time. Although the implementation of a vast array may be
an unavoidable consequence, it does not necessarily result in substantially greater
expense or difficulty of operation compared to alternative technologies. In this
chapter, a Monte Carlo simulation is employed to explore the sensitivity reach of
the present DRIFT technology supplemented by a realistic active neutron veto
detector and to then determine the factors constraining this sensitivity limit and
how it could be enhanced further. The conclusions presented here are based on
operating the proposed detection scheme set up in an extended array configuration. This then leads to an investigation of a comparable array in which DRIFT
modules act as self vetoing detectors. The overall aim within this chapter is to
establish the realistic sensitivity reach of this technology and thus provide insight
into the possible advancement of the DRIFT programme.
7.2
Assumptions
In modelling the set-up to examine the capabilities of a possible future DRIFT
array, several realistic assumptions must be made. Firstly, it is assumed that
the proposed DRIFT modules will be, in effect, completely shielded to external
169
170
7. LARGE SCALE DRIFT ARRAYS
neutrons. For a passively shielded detector within the JIF laboratory, rates of ∼1
neutron interaction per year due to ambient neutrons have already been demonstrated, and so for a dedicated facility, set up to operate a large scale array with
extensive passive shielding, it is reasonable to expect a significant improvement
upon this. Thus, the only remaining background source must come from the detector itself, namely the steel vacuum vessel. The vessel is the dominant internal
contributor since it has, by far, the largest mass of all module components. Also,
only components of low radiological impurities are selected for use within the vessel. Assuming concentration levels of radioisotopes consistent with the UKDMC
measurements [131], the neutron production spectra emitted from the stainless
steel vessels were generated via the SOURCES code.
Secondly, it is assumed measurements would be made using detectors based
on the current DRIFT-II design, but achieving detection thresholds a little better than presently demonstrated, reflecting what is believed to be a reasonable,
achievable prediction of progress.
Thirdly, it is assumed that these detector vessels would be enclosed within
an active veto, the precise design of which is immaterial, except that it does
not produce additional radioactivity, achieves 4π coverage, and has an attainable
detection threshold. Nominally this is simulated as a 20 cm thick boron loaded
liquid (BC-523-A) scintillator. Each module is then surrounded by an additional
2 m of passive water shielding. Overall, these assumptions represent a realistic
best case scenario.
7.3
Detector & Veto Configuration
Before deciding upon the specific design and technicalities of a large DRIFT
array, a single module running in an ultra-low background mode was simulated
to determine the sensitivity reach of such a set-up. The Monte Carlo included
a single DRIFT module surrounded by the assumed veto scheme and passive
shielding. This modelled detector was essentially a replica of a DRIFT-II module
(described in Chapter 4) incorporating the vacuum vessel, CS2 gas, stainless steel
field rings, the steel skate plate, the plastic wire plane supports, the MWPC
strongbacks, field ring combs, corner posts, HHV shielding and other plastic
parts. All steel was modelled as 304-grade stainless steel of density 8 g cm−3 .
An important point to note, however, is that the simulated vacuum vessel was
7.4 Neutron Production
171
modelled as a simple cube shape and did not include the additional steel support
ridges present on the outer surfaces of a real vessel, therefore the total simulated
mass was ∼ 867 kg as opposed to the actual ∼1900 kg of a current DRIFT module.
A GEANT4 image of the simulated geometry is shown in Figure 7.1.
Figure 7.1: Modelled geometry of a single DRIFT vessel coupled to an active
neutron veto scintillator. The liquid scintillator and walls of the vessel have
been made transparent for illustration purposes. The 2 m water shielding extends
outwith the scope of this figure.
7.4
Neutron Production
Given the level of passive shielding surrounding the DRIFT module, the dominant
source of background neutrons remaining is due to the U and Th contamination
of the steel components (as discussed in Section 7.2). Background neutrons are
generated from the steel in much the same way as they are generated from the
cavern rock1 ; alpha particles derived from the decay chains of U and Th, with a
small contribution from fission, give rise to (α,n) reactions creating an ambient
source of neutrons. The neutron production spectra, for 1 ppb U and 1 ppb Th,
1
Neutron production from the rock is described in Chapter 3
172
7. LARGE SCALE DRIFT ARRAYS
Table 7.1: The integrated neutron production rates estimated for 304-grade stainless steel containing 1 ppb U and 1 ppb Th.
Contaminant species
U (1 ppb)
Th (1 ppb)
−1
−3
−10
Integrated neutron production rate (s cm ) 1.474 × 10
5.164 × 10−11
Total (s−1 cm−3 )
2.0 × 10−10
were produced using the SOURCES package and are shown in Figures 7.2 and
7.3. As summarised in Table 7.1, the total neutron production rate was found to
be 2.0 × 10−10 neutrons s−1 cm−3 with the production rate from U being approximately 3 times greater than that of Th (when considering equal concentrations
of each).
Figure 7.2: The neutron energy spectrum generated from uranium contaminants
(1 ppb) in 304-grade stainless steel [132].
7.5
Results
To classify an observed number of events as a WIMP signal, an event rate that
is significantly in excess of background levels must be recorded. Such a signal
7.5 Results
173
Figure 7.3: The neutron energy spectrum generated from thorium contaminants
(1 ppb) in 304-grade stainless steel [132].
is defined here as being significant if it satisfies the 90 % confidence level of the
Feldman-Cousins tables [133]. These parameters are then used to establish the
WIMP-nucleon cross-section limit set by the experiment.
7.5.1
Detection Thresholds
Within the Monte Carlo, the steel vacuum vessel was simulated as a uniform
source of neutrons from which the neutron production spectra shown in Figures
7.2 and 7.3 were used to isotropically emit a total of 1.2 × 107 neutrons from the
steel. This is equivalent to an exposure of ∼8000 years for a single DRIFT module,
providing sufficient data to constrain statistical effects. All applicable physics
processes, such as elastic and inelastic scattering, and the generation and tracking
of any secondary particles produced, were included in the simulation. The Monte
Carlo described here is an adapted version of an extensively tested simulation
found to reproduce experimental data accurately to a very high degree [124].
Thus, this Monte Carlo provided a reliable indication of the detector’s response
to the neutron background level. This response is shown in Table 7.2. The data
174
7. LARGE SCALE DRIFT ARRAYS
Table 7.2: Simulated rate of nuclear recoil events occurring in the fiducial volume
of one DRIFT module as a result of background neutrons generated from the U
and Th content of the steel vacuum vessel. The nuclear recoil rate is shown for
carbon and sulphur recoils individually and collectively. The entry corresponding
to the 500 NIP threshold is indicative of a typical level of performance achievable
for a large scale array. These results are illustrated graphically (for discrete energy
bins) in Figure 7.4.
Threshold
(NIPs / keV (C) / keV (S))
0
0
0
20
0.7
1.1
100
3.3
5.6
500
16
27
1000
32
48
1500
42
62
2000
52
78
2500
65
95
3000
79
111
3500
93
127
4000
107
144
4500
120
160
5000
134
176
5500
148
192
6000
162
209
Nuclear recoil event rate
(C / S / Total)
(events kg−1 day−1 )
1.7 × 10−3 1.4 × 10−3 3.1 × 10−3
5.7 × 10−4 8.5 × 10−4 1.4 × 10−3
4.8 × 10−4 6.7 × 10−4 1.1 × 10−3
3.6 × 10−4 2.9 × 10−4 6.5 × 10−4
3.0 × 10−4 1.9 × 10−4 4.8 × 10−4
2.5 × 10−4 1.4 × 10−4 4.0 × 10−4
2.4 × 10−4 1.1 × 10−4 3.5 × 10−4
2.0 × 10−4 9.5 × 10−5 3.0 × 10−4
1.9 × 10−4 7.5 × 10−5 2.6 × 10−4
1.6 × 10−4 6.2 × 10−5 2.2 × 10−4
1.5 × 10−4 5.2 × 10−5 2.0 × 10−4
1.3 × 10−4 3.9 × 10−5 1.7 × 10−4
1.2 × 10−4 3.0 × 10−5 1.5 × 10−4
1.0 × 10−4 2.2 × 10−5 1.2 × 10−4
9.2 × 10−5 1.7 × 10−5 1.1 × 10−4
Error
(%)
2
3
3
4
4
5
5
6
6
7
7
7
8
9
10
are presented here as a rate of induced nuclear recoil events above set detection
thresholds, given in units of NIPs; the corresponding energy equivalent in keV
is indicated for carbon and sulphur recoils individually. Under the assumption
that no external neutrons penetrate the water shielding, Table 7.2 effectively
shows the minimum background levels attainable in a stand alone DRIFT module
using present day negative ion drift technology. The data in Table 7.2 are also
illustrated graphically in Figure 7.4 but with the rate expressed over discrete
energy bins.
As mentioned previously, the additional steel support ridges included in the
design of present DRIFT vacuum vessels results in a larger total mass of steel per
module than is included in the simulation, and so an upper limit of 2.19 times
7.5 Results
175
Figure 7.4: Simulated rate per energy bin of nuclear recoil events occurring in
the fiducial volume of one DRIFT module as a result of background neutrons
generated from the U and Th content of the steel vacuum vessel. The nuclear
recoil rate is shown for carbon (blue) and sulphur (red) recoils individually and
collectively (black). The rates shown here have been calculated for discrete energy
bins using the data presented in Table 7.2. For clarity, error bars are marked
only for the carbon + sulphur data points (black line).
176
7. LARGE SCALE DRIFT ARRAYS
the neutron production rate could be applied1 . It is, however, likely that when
constructing a large scale array, a steel with inherently low radioactivity will be
selected, such as grade 304L stainless steel, measured to have concentration levels
of 0.6 ppb U and 0.7 ppb Th [131]. Thus, the simulated vessel containing 1 ppb
U and 1 ppb Th is a good approximation for a potential array.
The data presented in Table 7.2 show the rate of induced nuclear recoils in
the fiducial volume of the DRIFT module. For many of these events there will
also be, in coincidence, an energy deposition in the surrounding veto detector
allowing a reduction of the primary data set, and thus improving the WIMPnucleon sensitivity reach (since true WIMP induced events would not produce
coincident veto signals). Table 7.3 shows the simulated rejection capability of the
veto scintillator. A 100 keV (electron equivalent) threshold is typical for a large
scintillator but it is thought that 50 keV could be achieved. For comparison, the
corresponding capability for a 0 keV and a 500 keV veto detector is also shown.
In all cases a quenching factor of 0.4 [134] has been applied to all nuclear recoil
events in the liquid scintillator.
As can be seen from Table 7.3, a high percentage of nuclear recoil events
occurring in the fiducial volume of the DRIFT detector could be rejected using
a veto system of this type. For the purposes of this simulation it has been
assumed that the DRIFT module is insensitive to gamma-rays at all thresholds.
Although this may be optimistic for a present day DRIFT module, it has already
been shown that an individual wire trigger threshold of 150 DFNIPs (DFNIPs
for delta function NIPs. This represents the instantaneous deposition of NIPs
to a single wire.) will remove the majority of gamma-ray events occurring in
the fiducial volume. Using data runs and analysis cuts specifically designed to
optimise gamma-ray data and then in turn neutron data, described in [120], it
was found that raising the software threshold from 25 DFNIPs to 150 DFNIPs
reduced the number of gamma-ray events (defined as having NIPs < 500 and
R2 > 0.5 cm) from 413 to 0, while the number of neutron events (defined as
having NIPs > 500) decreased by only 10 %. Successful operation and a high
degree of accuracy (experiment/theory) for neutron detection has already been
demonstrated in the DRIFT-IIa detector at a trigger threshold of 1000 NIPs [113],
1
This would be an upper limit since the additional steel support ridges are attached to the
outer faces of the vessel, away from the fiducial volume.
7.5 Results
177
Table 7.3: The simulated rejection capability of the veto detector at varying Fiducial Volume (FV) thresholds. All results shown are relative to the total FV rate
i.e. considering carbon and sulphur recoil events in DRIFT.
FV threshold
(NIPs)
0
20
100
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
Percentage of events in the FV also having an
event above threshold (as indicated) in the veto
0 keV
50 keV
100 keV
500 keV
95.38
92.57
90.70
79.66
96.41
93.93
92.34
84.21
97.03
95.07
93.46
85.47
97.30
96.10
94.90
87.41
97.58
96.37
95.77
89.11
97.55
96.32
95.59
89.46
97.18
95.77
95.49
89.01
97.06
96.08
95.75
90.20
97.03
95.91
95.54
90.71
96.51
96.07
95.63
92.58
97.07
96.59
96.10
92.68
97.19
96.63
96.07
92.70
96.69
96.03
95.36
92.72
96.03
95.24
94.44
92.86
96.40
95.50
94.59
92.79
178
7. LARGE SCALE DRIFT ARRAYS
and so it is reasonable to assume future advancements will lower this threshold
further.
Together, the results presented in Tables 7.2 and 7.3 give a simulated estimate of the irreducible background level achievable using the proposed detection
scheme. To claim detection of a WIMP signal, deduced purely from event rates
(no directional information is used here), an observed number of events would
have to be present at a level statistically above background. Here, the exposure
necessary to provide a signal satisfying the 90 % Feldman-Cousins confidence levels is estimated, and the corresponding WIMP-nucleon cross-section sensitivity
calculated. For a given set of parameters, such as target mass, running time,
scintillator threshold, and FV threshold, the WIMP-nucleon cross-section can be
plotted as a function of the incident WIMP mass (discussed in Chapter 2). Ideally the minimum of this curve occurs when the WIMP mass is equal to that of
the nucleus it scatters from. The WIMP mass at which the calculated minimum
cross-section occurs is, however, dependent on the detector threshold; the higher
the threshold, the larger the optimum WIMP mass. An example of such a limit
curve is shown in Figure 7.5; this is similar to the limit curves plotted in Figures
2.7 and 2.8. All WIMP-nucleon cross-section sensitivities quoted in the remainder
of this chapter refer to the minimum point of one of these curves.
When the exposure of an experiment is increased, be it through a larger target
mass or simply a longer running time, the sensitivity reach improves. In the
absence of any expected background, the estimated minimum WIMP-nucleon
cross-section sensitivity, σ, is inversely proportional to the exposure i.e. σ ∝
1/(target mass × time). This sensitivity reach improves more slowly when a
background subtraction is included. Figure 7.6 illustrates how the sensitivity
reach improves over time and the effect varying the DRIFT detector threshold
has.
The values shown in Figure 7.6 have been calculated for the larger mass of
steel as used in a present DRIFT module, and so represent conservative limits. A detection threshold of 50 keVee has been assumed in the veto detector.
As expected, the cross-section sensitivity was found to improve with increased
exposure, and the lower the DRIFT detector threshold, the better the sensitivity reach. Although it is true to say that a low detection threshold is desirable
for such an array, the benefits of an improved sensitivity are offset by worsening background levels (with a lower threshold, more background events can be
7.5 Results
179
Figure 7.5: The WIMP-nucleon cross-section sensitivity curve obtained by a
DRIFT-type detector with an exposure of 50 kgyears (40 Torr CS2 gas), a 500 NIP
threshold, and 1 background event observed. The calculated sensitivities satisfy
the 90 % Feldman-Cousins C.L.
seen). Also, the technical and analysis requirements necessary to operate at such
thresholds become increasingly demanding at lower energies. Thus, there would
be little benefit in lowering the threshold further.
The results indicate that, under these running conditions, a large scale array
of DRIFT modules is capable of probing parameter space down to the order of
10−9 pb. As with all detectors of this kind, the sensitivity reach of the array is
ultimately determined by the mass of the target material and the running time
of the experiment. In this case, however, the background levels dealt with are so
low that the sensitivity of the array is not governed by the rate of background
events i.e. the proposed veto system approaches the fundamental limit of what can
be achieved using gaseous CS2 as a target material. To quantify this, consider
a CS2 detector running at a 500 NIP threshold in an ideal, background free
environment and non-radioactive steel for 300 kg years with zero events seen,
this would produce a WIMP sensitivity limit of around 8 × 10−10 pb. A DRIFTtype detector running at a 500 NIP threshold for 300 kg years in a realistic
environement with a 20 cm thick veto scintillator (which leaves a background of
180
7. LARGE SCALE DRIFT ARRAYS
Figure 7.6: The minimum in the WIMP-nucleon cross-section sensitivity achieved
as a function of time for various detection thresholds in the DRIFT fiducial volume. All results shown are for a 100 kg CS2 target (equivalent to ∼600 modules
containing 40 Torr CS2 ) and a 20 cm thick liquid scintillator surrounding the
DRIFT module. Each data point corresponds to an integer background event.
The termination of the 20 NIPs limit curve occurs when the number of background events reaches 15. This is a direct result of the Feldman-Cousins table (at
90 % C.L.) terminating at 15 background events. For the corresponding FeldmanCousins limits refer to [133].
7.6 Possible Improvements
181
six events seen), would produce a WIMP-nucleon cross-section sensitivity limit
of around 1.75 × 10−9 pb, a level close to the fundamental limit.
7.5.2
Scintillator Size
In addition to varying the energy thresholds, varying the thickness of the surrounding scintillator also affects the rejection capabilities of the proposed veto
detector. Similar work carried out by Smith et al. [110], but which was not
specific to DRIFT, found that a veto thickness of > 10 cm can achieve a > 90 %
neutron rejection (for nuclear recoil energies of 5−200 keV) with > 20 cm being
preferable. Given this information, it was decided here to explore the effect of a
20 cm thick veto compared to that of 30 cm. Assuming a 500 NIP threshold in
the DRIFT fiducial volume and a 50 keVee scintillator threshold, the following
rates apply:
• For a 20 cm scintillator > 96.1 % of FV neutron events are tagged. At this
rate, the target mass required to leave 1 un-vetoed background event year−1
is 50 kg, equivalent to 300 modules running at 40 Torr for 1 year. This
corresponds to a minimum WIMP-nucleon cross-section of 6.46 × 10−9 pb.
• For a 30 cm scintillator > 97.4 % of FV neutron events are tagged. The
target mass required to leave 1 un-vetoed background event year−1 is 72 kg,
equivalent to 430 modules running at 40 Torr for 1 year. This corresponds
to a minimum WIMP-nucleon cross-section of 4.47 × 10−9 pb.
This shows that increasing the scintillator thickness from 20 cm to 30 cm
would not greatly affect the WIMP sensitivity limit achieved but would, however, greatly affect the practical implications of running such a detector array.
Therefore, when dealing with the proposed detection scheme in a large array
configuration, of the order of several hundred modules, the cost and technical
restrictions of an increased veto size (beyond 20 cm) would outweigh the experimental benefits.
7.6
Possible Improvements
Although the proposed veto scheme allows for sensitivities reaching the fundamental limit of what can be achieved using this technology, one of the principal
182
7. LARGE SCALE DRIFT ARRAYS
reasons for this work is to determine what factors constrain the sensitivity limit
and how it could be improved upon further. In this study, an investigation into
the propagation and confinement of background neutrons is carried out to determine what happens to the un-vetoed neutrons and the possible improvements
that could be made to reduce background rates further. Shown in Table 7.4 are
the results of a Monte Carlo simulation in which the propagation, tracking, and
final location of individual neutrons are recorded. The data presented displays
the output simulated for a single DRIFT module operated at 40 Torr for ∼ 8000
years and surrounded by a 20 cm thick veto detector with a 50 keVee energy
threshold. This large running time was chosen simply to provide a statistically
meaningful output. Without the presence of the proposed veto detector, similar
percentages of background neutrons would terminate in the vacuum vessel and
plastic components.
The results from Table 7.4 show that approximately equal numbers of unvetoed neutrons terminate in each of the three groups listed i.e. the plastic components, the steel vessel, and all other volumes combined. Therefore, to improve
the sensitivity reach beyond that already shown here, one or more of the following
must be done: reduce the mass of steel used to construct the vacuum vessel, reduce the mass of internal plastic components contained within the module, or use
lower background materials. The simple fact that all of these contributions are
approximately equal, and not one of them individually dominates the potential
for increased rejection capability, does, itself, present an additional challenge.
The plastic components used in the detector are there to perform important
functions, such as to support the wire planes or provide HHV shielding. The total
mass of plastic utilised is already quite minimal and a substantial reduction,
using the present DRIFT design concepts, would be extremely difficult, if not
impossible. The most natural and obvious way to lower background levels would
be to construct the vessel using materials that are radiologically very pure or,
more specifically, have a lower U and Th content; copper is a prime candidate
for this purpose. Contamination levels of 0.01 ppb U and 0.01 ppb Th have
already been measured for specific grades of copper confirming that it could be
used in place of steel [131]. It should also be noted that Young’s modulus for
stainless steel is 190 GPa, while for copper it is 120 GPa and so additional
strengthening struts would be required resulting in a larger overall mass than
that of a steel vessel. The low U and Th content of copper would, however,
7.6 Possible Improvements
183
Table 7.4: The simulated final end location of background neutrons generated in
the steel vacuum vessel. Column 2 lists the number of induced nuclear recoil
events seen in the DRIFT FV; column 3 lists how many of these events did not
also leave, in coincidence, an energy deposition (above 50 keV) in the veto; and
columns 4, 5, and 6 indicate the volumes in which the neutrons terminate.
Number of un-vetoed
events that terminate in:
Threshold
of FV
(NIPs)
0
20
100
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
∗
Number of nuclear recoil events
In FV and not Plastic Vessel
In FV
seen in veto
3161
235
82
96
1450
88
24
36
1177
58
19
24
667
26
8
9
496
18
6
6
408
15
4
5
355
15
4
5
306
12
3
4
269
11
3
4
229
9
3
3
205
7
2
3
178
6
1
3
151
6
1
3
126
6
1
3
111
5
1
3
Other∗
57
28
15
9
6
6
6
5
4
3
2
2
2
2
1
Mainly the steel skate plate but also includes the field rings and energy depositions
in the liquid scintillator below 50 keV.
184
7. LARGE SCALE DRIFT ARRAYS
generate a much lower neutron production rate, calculated using the SOURCES
code to be 1.32 × 10−12 s−1 cm−3 [132]. Even assuming that twice the mass of
copper would be required for structural integrity, this still results in a neutron
production rate per vessel of ∼ 85 times less than that produced from a present
steel vacuum vessel.
Alternatively, a new veto design could be implemented in which the veto
system is contained within the steel vessel. This design concept would, however,
require careful consideration as the veto system itself may produce undesirable
levels of background radioactivity. Another possible improvement technique could
be the installation of a MICROMEGAS-type readout in place of the existing
grid and anode systems. MICROMEGAS technology, described in Appendix
A, essentially offers a higher resolution readout and thus gives way to superior
directionality and head-tail discrimination. Depending on the specific design of
such a readout, this could bring about a large reduction in the overall mass of
internal components and, in this way, improve background rejection capabilities.
The refined readout resolution would provide the capability to resolve shorter
track lengths and therefore fill each detector to a higher gas pressure which in
turn would lead to larger target masses per module and, by extension, would give
rise to an improved sensitivity.
When dealing with extremely low background levels, as described for this large
scale array, further reduction of background rates alone does little to improve the
WIMP-nucleon cross-section limits achieved. What it does allow is the construction and operation of large arrays over greater exposure periods, be it through
larger target masses or increased running time. It is this increased exposure which
will ultimately improve the sensitivity reach of a large scale array.
7.7
Alternative DRIFT Array
In planning any large scale experiment it is advisable to consider alternative options and in doing so it may become apparent that a different design is more
efficient, structurally simpler, or possibly even just more cost effective. Since
DRIFT modules are essentially highly sensitive neutron detectors, one proposed
alternative was to set up a large scale self-vetoing array in which the DRIFT
modules themselves double as neutron veto detctors. To investigate the effectiveness of such an array, a GEANT4 simulation was composed to model a 5 × 5 × 25
7.7 Alternative DRIFT Array
185
configuration of DRIFT detectors as illustrated in Figure 7.7. It is assumed that,
in operational mode, such an array would be adequately shielded from external
neutrons and the dominant background source would again be produced from
internal components, principally the stainless steel vessels. Thus, for the purpose
of this simulation, background neutrons were fired isotropically from all stainless
steel vessels using the neutron energy emission spectra for 1 ppb U and 1 ppb Th
as previously described in Section 7.4.
Figure 7.7: A 5 × 5 × 25 self-vetoing DRIFT array in which modules are positioned 50 cm apart from one another. For simulation purposes the entire array
has been placed inside a large cavern with sufficient space to simulate various
shielding infrastructures. The modelled NaCl walls have a thickness of 3 m,
adequate to produce over 99.9 % of neutrons that penetrate the rock-laboratory
boundary in the JIF facility.
Within the Monte Carlo, a total of ∼ 8.6 × 105 neutrons were emitted from
the stainless steel. Each time a nuclear recoil energy deposition occurred in any
of the modules’ fiducial volumes, the event data were recorded and outputed to
an ASCII file. In order to determine the array’s potential for vetoing events, the
186
7. LARGE SCALE DRIFT ARRAYS
data were analysed and used to calculate the number of multiple scatters occuring within the total target mass. In this Monte Carlo the design of each DRIFT
module was identical to that of the previous simulation, the critical distinction
between modelled geometries being, of course, that no veto scintillator existed
in this set-up thus providing a higher probability of multiple vessel scatters than
compared to the previously proposed array. Since identical energy emission spectra were emitted in both simulations, the relative rates of carbon and sulphur
recoils are expected to be similar. As a first pass analysis, only total event numbers were looked at and the following observed.
For the given number of neutrons fired there were 16,360 nuclear recoil energy
depositions within the total target mass. The large majority of these were single
scatter events i.e. a single neutron entered one of the fiducial volumes and produced only one nuclear recoil. Out of the total number of nuclear recoils, 800 of
these were multiple scatter events. By multiple scatter events it is meant, here,
that a single neutron entered one of the fiducial volumes and produced two or
more nuclear recoils within the whole array’s target mass, very often within one
module’s fiducial volume. The number quoted (800) represents the cumulative
total of these scatters. Since it is highly unlikely that a WIMP will interact twice
within the array’s sensitive volumes, multiple scatter events can be rejected. In
the best case scenario, all 800 of these could be vetoed equating to ∼ 5 % of all
nuclear recoil events being vetoed. If only multiple vessel scatters were to qualify
as being suitable for rejection purposes, that is to say a single neutron being
fired generates two or more nuclear recoils in distinct vessels, this would give a
corresponding veto efficiency of ∼ 1 %.
These results, although preliminary, indicate that the proposed self-vetoing
array would have a very poor neutron event rejection capability. The problem
here is that, although individual DRIFT modules are highly sensitive to neutron
events that do occur within their fiducial volumes, the target mass is too low
to act as an effective veto system; put simply, there just aren’t enough multiple
scatters in the sensitive volumes. It is apparent that the previously proposed
array, in which a separate veto detector is coupled to each DRIFT module, would
be far more effective. That is not to say, however, that the liquid scintillator
set-up is optimum. Other alternatives or improvements could involve using slabs
of strategically located plastic scintillator, a different target medium other than
CS2 in certain modules, or, perhaps, loading particular materials with gadolinium
7.8 The Feasibility of Large Scale Operation
187
(selected due to its high neutron capture cross-section). The work presented here
provides a good introduction into the capabilities of large scale DRIFT arrays
but there remains much scope for further investigation into the potential of other
configurations.
7.8
The Feasibility of Large Scale Operation
Ideally, a large scale WIMP search experiment would be built and operated to
such an extent so as to exploit the full potential of the technology being utilised.
In reality, this is not always feasible; many factors, be it mechanical or financial, may hinder or prohibit a project. The question of whether or not a large
scale DRIFT array could be competitive with alternative technologies, or even
realistically come to fruition, is a debatable one. From past and present DRIFT
modules it has already been demonstrated that a single module can be operated
continuously, at room temperature, for long periods of time (months). Careful
monitoring of the detector can be done remotely with only occasional physical
access required (∼ weekly), and even then only to supply fresh CS2 canisters. It
is now standard practice in many physics experiments to enclose detectors within
large liquid scintillators and it has even been proposed that an entire underground facility could be encompassed by a large passive water shield providing
an extremely low background environment [135].
The exact design and layout of a large array would require careful consideration and planning in order to accommodate the high number of modules required
and still leave sufficient space for all the additional utilities necessary (gas system, data acquisition, power supply, etc.). Given the accumulated knowledge and
expertise of the DRIFT collaboration, the construction and installation of new
DRIFT modules can be carried out at a relatively low cost. The total expense occurred for the latest DRIFT module was approximately £20,000. For a large scale
array of the order of, say, 500 modules, the total cost, including that of the liquid
scintillator (should it be required), could reach up to tens of millions of pounds.
At first glance this expense may seem excessive but would actually be financially
competitive with proposed tonne-scale alternative technologies, and would have
the huge potential benefits offered by directional technology as well as the operational advantages of the DRIFT programme, in particular the detectors would
not require low temperature running conditions. Using present technology and
188
7. LARGE SCALE DRIFT ARRAYS
the current design of a DRIFT-type array to reach WIMP-nucleon cross-sections
lower than that presented within this chapter, may be mechanically feasible but
will likely prove too expensive or require physical demands too great to be accomodated at a single facility. The realisation of a large scale array may depend on
the availability of a suitable location rather than the physics limitations of such
an experiment.
7.9
Summary
The future development and continuation of the DRIFT programme will no doubt
encompass the installation and running of a large scale detector array. To investigate the potential capabilities of such a scenario, Monte Carlo simulations have
been carried out using an adapted version of an extensively tested GEANT4 simulation. The first array concept modelled, involved simulating a single DRIFT
module, coupled to an active neutron veto detector, in an ultra-low background
environment for an extensively long live time, intrinsically equivalent to simulating many modules over a shorter running time. Assuming passive shielding suppresses external background neutrons to a sufficient degree, the dominant source
of background neutrons remaining is the stainless steel vacuum vessel. Using
measured concentration levels of 1 ppb U and 1 ppb Th, the rate of induced
nuclear recoils in the DRIFT FV and veto detector were simulated and used to
produce an estimate of the irreducible background rate achieveable from such a
set-up. Using these event rates, and Feldman-Cousins limits at the 90 % C.L.,
the WIMP-nucleon cross-section sensitivities were calculated at varying thresholds and scaled to accommodate the progression over time. It was found that a
DRIFT-type detector running at a 500 NIP threshold for 300 kg years coupled
to a 20 cm thick veto scintillator would produce a WIMP-nucleon cross-section
sensitivity limit of around 1.75 × 10−9 pb, approaching the fundamental limit of
what can be achieved using gaseous CS2 as a target material.
Increasing the thickness of the veto detector beyond 20 cm would create little
benefit in reducing the un-vetoed background rate. Other improvements to the
system, such as reducing the overall mass of plastic within a DRIFT module,
or reducing the mass of steel used to construct a vacuum vessel would, again,
result in only a small improvement to the rate of un-vetoed induced nuclear
recoils. The simplest way to reduce background levels would be to manufacture
7.9 Summary
189
a vacuum vessel from a more radiologically pure material, such as copper. Even
then, at this level, any further reduction makes little difference towards improving
the sensitivity reach of the experiment. It does, however, lead to the increased
exposure of large arrays which in turn provides an improved WIMP-nucleon crosssection limit. Future advancement of the DRIFT programme will likely include
a replacement of the existing readout system tailored specifically to incorporate
an enhanced readout resolution, such as MICROMEGAS. This would not only
improve the directional capabilities of the detector but would also lead to an
increased target mass per module. Also investigated was the capability of a
large scale 5 × 5 × 25 array in which DRIFT modules themselves double as veto
detectors. The results found from this work indicate that the proposed setup would be inadequate at serving as a self-vetoing system. The potential for
alternative array configurations, or improvements to the proposed arrays, are
open to further investigation.
Given the low cost of a single DRIFT module, a large scale DRIFT array,
as presented here, could be financially competitive with proposed tonne-scale alternative technologies and offer the potential benefits of directional technology.
When attempting to reach cross-sections at even lower orders of magnitude, however, it is apparent that the physical and financial demands using present day
DRIFT technology may prove too costly.
Chapter 8
Conclusions
Strong evidence leads to the conclusion that much of the Universe is in the form
of dark matter, thought to be largely composed of WIMPs. A great deal of
time and effort is made by the many collaborative groups around the world to
validate this theory. The practical benefits dark matter detection may have on
day to day life cannot be certain, but the advancement of science rarely is: “It’s
for discovery.”1 A confirmed detection of WIMPs would no doubt further our
understanding and knowledge of the Universe which in turn may lead to greater
progression. Although a number of experiments aim to directly detect dark matter, it is thought that true confirmation must come from a direction sensitive
detector; this is where DRIFT technology has the advantage over many other
experimental searches.
Each individual DRIFT module is a negative ion time projection chamber
filled with low pressure CS2 gas. When an incoming particle causes a target
nucleus (or electron) to recoil, ionisation charge is deposited along the recoiling
particle’s track. By drifting this ionisation across the fiducial volume and onto
an MWPC readout plane, the energy, size, and direction of the track can be
determined. Analysis of the resulting channel waveforms allows the type of particle that caused the initial interaction to be deduced. Using this technique, a
DRIFT detector has the potential to observe the directional signature of WIMPinduced recoil events. The design, development, and advancement of the DRIFT
programme has been, and still is, a collaborative effort owing to the work of
many individuals over several years. The successful operation and stability of
1
Aaron Sorkin, The West Wing, Season 3, Ep. 16 (Dead Irish Writers).
191
192
8. CONCLUSIONS
DRIFT technology has been demonstrated and improvements, in both the technical design and fidelity of data, continue to be made with the introduction of
each DRIFT module.
As with all direct dark matter search experiments, background rates seen
within a given data set are an important factor to consider, inherent to the limit
setting and discovery capabilities of the detector. At a depth of over 1 km, the
Boulby mine provides an environment for the experiment which is not only low
in natural radiological impurities but is also well shielded from cosmic rays which
would otherwise overwhelm a surface based experiment. Within the JIF facility,
the dominant source of background neutrons critical to the detection rates seen
within DRIFT (neutron events leave a signature very similar to that expected
from WIMP interactions), are believed to be produced as a direct result of the
U and Th content inside the NaCl cavern rock. Work outlined within this thesis
has determined this U and Th content to be 66 ± 6 ppb and 145 ± 13 ppb respectively, clarifying previous discrepancies and confirming the validity of many
background neutron simulations carried out by the collaboration. An investigation into background gamma-rays emitted from the cavern walls found that,
using the known concentrations of
238
U,
232
Th, and
40
K, approximately 94 % of
the total gamma-ray flux originates within the first 25 cm depth of rock.
Of the utmost importance pertaining to the DRIFT experiment is its response
to, and capability in dealing with, neutron exposures. In measuring the detector’s
efficiency and verifying analysis methods, the detector is perennially exposed to
a
252
Cf neutron source. It is therefore vital that the neutron production rate
from the source is known to a high degree of accuracy. With this in mind,
an experiment was undertaken to measure the activity of the source which was
found to be consistent with that claimed by the manufacturer (11,600 ns−1 ±5 %),
resolving ambiguities in previous work.
In order to keep track of the detector’s behaviour and maintain a consistent
performance, it is routine to periodically execute
55
Fe energy calibration runs.
During these calibrations, the trigger threshold of the detector is set to an appropriately low level so as to record the energy depositions generated by the 55 Fe
5.9 keV X-rays. An attractive feature of DRIFT, however, is that by adjusting
this threshold level accordingly, the main fiducial volume of the detector is made
insensitive to gamma-ray events. Comparison of data analysis to that of a detailed GEANT4 Monte Carlo simulation found the gamma-ray rejection factor of
193
the unshielded DRIFT-I module to be better than 2 × 10−7 at 90 % C.L. (best
case scenario) for the energy range of 1000-5000 NIPs. Although it is neutron
rates that are of key interest in DRIFT, and despite having excellent gammaray rejection capabilities, it is prudent to accumulate an adequate knowledge of
background gamma-ray events occurring in the detector and the effect neutron
shielding erected around the vessel may have. Previous work by the collaboration
has already shown that the level of CH2 shielding added reduces the rate of rock
neutron induced events down to less than 1 year−1 . Here it was found that the
polypropelyne shielding has little effect on reducing the number of electron recoils
generated from a
60
Co exposure but does, however, due to the broader energy
spectrum, play an influential role on reducing the number of events generated by
gamma-rays emitted from the cavern rock.
Simulations and data analysis of neutron exposures carried out on the DRIFTIIb vessel found the ‘proportional counter’ efficiency to be (67.85 ± 6.18 %(stat) ±
5 %(syst)) %. When applying more stringent cuts, so as to suppress background
rates to a level suitable for ‘WIMP running’, the experiment’s efficiency at detecting neutron events is reduced down to (46.08 ± 5.82 %(stat) ± 5 %(syst)) %. The
efficiency measurements determined here are similar to those calculated for the
DRIFT-IIa module. In addition, it is believed that the presence of radon within
the DRIFT-IIa detector led to a population of unwanted events that prevented
the reduction of background rates to zero. Implementing techniques to reduce
events consistent with the radon hypothesis proved successful and have since been
enforced in subsequent modules.
Given the theoretical distribution of the range through which a directional
WIMP signal is expected to fluctuate, a detector capable of directional sensitivity
along two axes (in Cartesian coordinates) has the potential to observe this sidereal
change. Analysis of experimental data taken from the DRIFT-IIa detector, first
presented here, has demonstrated that directional information can be attained
using DRIFT technology, with sensitivity along the x and z axes favoured. Using
a purpose-built Monte Carlo simulation, it is possible to generate pseudo-data
with characteristics mimicking that of real data to an exceptionally high level.
Additional work by the collaboration is set to utilise the head-tail effect associated with recoil tracks. It is predicted that head-tail discrimination will provide
a more pronounced result than simply considering the magnitude of recoil track
sizes alone. Analysis of DRIFT-IIc data, by the collaboration, has already shown
194
8. CONCLUSIONS
that the head-tail effect is measurable within DRIFT. A notable benefit directional sensitivity provides over conventional direct dark matter searches, is the
requirement of a significantly shorter exposure (mass × time) period.
It is envisaged that the future of the DRIFT programme will involve large
scale operation comprised of many individual DRIFT detectors set up in an array format. Here, the first detailed Monte Carlo simulations of a DRIFT module
coupled to an active neutron veto system were conducted to determine the potential of such a set-up. With extensive passive shielding surrounding the detector,
sufficient in size to reduce external background neutrons to a negligible level,
the dominant source of background neutrons remaining are produced from the
detector components themselves, principally the stainless steel vessel. Assuming
modules of present technological capabilities, it was found that a DRIFT-type detector operating at a 500 NIP threshold for 300 kg years, in conjunction with the
proposed veto scheme, would set a spin-independent WIMP-nucleon cross-section
sensitivity limit of ∼ 1.75 × 10−9 pb (90 % C.L.). This value approaches the fundamental limit of what can be achieved using gaseous CS2 as a target medium,
thus highlighting the excellent rejection capabilites of the proposed veto scintillator. The most effective way to reduce background rates even further would be
to manufacture the detector vessel from a more radiologically pure material such
as copper. At such low background rates, however, even this would do little to
extend the sensitivity reach. Only through increased exposure would the limit
setting capability be improved significantly. A likely addition to the technology
already utilised would be to replace the current readout system with one which
incorporates a higher readout resolution, such as that of MICROMEGAS. Simulations of a large scale array in which DRIFT modules double as self-vetoing
detectors were found to show that the proposed array would have an inadequate
vetoing efficiency. Investigation into the potential for large array configurations
is ongoing and given the comparatively low cost of a single DRIFT module, large
scale operation could be financially competitive with tonne-scale alternative technologies.
Appendix A
MICROMEGAS
The MWPC technology utilised by DRIFT (see Section 4.3.3.3) has a readout
resolution determined by the spacing of grid and anode wires: 2 ± 0.02 mm within
their own plane. Due to electrostatic forces, the resolution of this technology
cannot be significantly improved upon. Therefore, to obtain a refined readout
of the order of a few hundred micron pitch, it is necessary to employ another
technology. One such technology is that of MICROMEGAS (MICROMEsh
GAseous Structures), the design of which is shown in Figure A.1. The principles
behind this detection scheme rely upon a high amplification region existing within
a narrow space (∼ 50−100 µm) between two parallel plates, a cathode and anode
plate respectively, making possible gains up to 105 . This high amplification region
is set between the metallic micromesh (cathode) and the conducting microstrip
readout (anode) shown in Figure A.1. The micromesh layer is typically a few
microns thick and is comprised of a Kapton film coated with a Cu or Ni layer
on one side. Small holes (30−40 µm) are etched into the micromesh at a pitch
of ∼ 50 µm. In Figure A.1, the readout plane is shown as being comprised of a
microstrip set-up but may, alternatively, utilise a pixelated format. To maintain a
uniform electric field, and thus consistent avalanche of charge, it is essential that
the distance between the cathode and anode plates is kept constant over the entire
active area. This is achieved by positioning small insulating (Kapton) pillars
between the two layers. The drifting and amplification of charge is illustrated in
Figure A.2.
In addition to the high resolution readout offered, MICROMEGAS has several
195
196
A. MICROMEGAS
Figure A.1: The basic design of MICROMEGAS. A high amplifictoin region is
maintained between the micromesh and microstrip readout plane, the distance
between which is kept constant by Kapton pillars. The third electrode shown
defines a larger gas-filled drift region. Taken from [136].
197
Figure A.2: The drift and high amplification region of MICROMEGAS. The ionisation charge is drifted through the main gas-filled fiducial volume of the detector
and avalanche occurs within the micromesh-microstrip region. Charge is then
induced on the anode microstrip elements and on the cathode micromesh.
benefits over alternative technologies: it is inexpensive and easy to manufacture;
resiliant to spark damage; and, due to its design structure, individual units may
be tiled together to create larger active areas. The research and development of
this technology is one of the many ongoing aspects undertaken by the DRIFT
collaboration. This work has included the design and testing of a charge readout
board built specifically for use in MICROMEGAS and is described in [113]. For a
more comprehensive review of MICROMEGAS technology the reader is directed
towards [136; 137; 138].
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