Chiba University
Graduate School of Science and Engineering
Master’s Thesis

Detection eﬃciency of next
generation IceCube opticalmodule, D-Egg, and its
sensitivity to opticalproperties of the Antarctic
ice with the GEANT4 based
precise photon simulation
Submitted in March, 2020
Division of Advanced Science and Engineering
Department of Physics
Ayumi Kiriki

Abstract
IceCube is a cubic-kilometer neutrino detector located at the geographic
South Pole, which consists of 5160 optical modules in the Antarctic ice sheet.
These optical modules detect Cherenkov radiation induced by charged particles produced by neutrinos interacting in the Earth. Deployment of IceCube’s optical modules utilises a hot water drill, where the optical modules
are dropped into the water to be re-frozen in the deep ice. While the optical properties of the glacial ice have been well documented, studies of the
man-made refrozen ice, called “hole ice”, remain inconclusive. This has
resulted in large systematic uncertainties in the angular reconstruction ofneutrinos with energies between 1–10 GeV. The IceCube Upgrade array isplanned for construction in the 2022/2023 South Pole Summer, involving
the deployment of a new specially-designed optical module called the DEgg. One of the important topics of the Upgrade is measurements of the
optical properties of the hole ice. A GEANT4 based precise photon propagation simulation was developed and the angular dependence of the D-Egg’s
Cherenkov photon detection eﬃciency was calculated. Furthermore, a detailed hole ice simulation was performed with D-Eggs as the chosen opticalmodules. A maximum likelihood was constructed using various hole ice parameters, the results of which increase current understanding of the hole ice
and improve on previous measurements. This simulation study shows thatthe D-Egg will allow IceCube to measure the optical properties of the hole
ice when combined with an artiﬁcial light source, located inside the D-Egg
module.

ii

Acknowledgments
Firstly, I would like to thank my supervisor Prof. Ishihara for her continuous support and leading me in the right direction in my research. I would
like to thank to Prof. Yoshida for his accurate advises on my research. I
would also like to thank Assistant Prof. Mase for his support and knowledgeof the calibration of IceCube.
I would also like to thank all the members of IceCube Chiba group.
Postdocs taught me a lot of things from the basics and helped me do research.
Students helped me do experiments and I had a great time with them.
Finally, I want to thank my family, especially my parents for providing
me an environment where I could concentrate on my research.

Contents
1 Introduction

1

2 IceCube
2.1 Introduction to high-energy neutrino astronomy . . . . . . . .
2.1.1 High-energy astrophysical neutrinos . . . . . . . . . .
2.2 The IceCube experiment . . . . . . . . . . . . . . . . . . . . .
2.2.1 Detector . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1.1 IceCube array . . . . . . . . . . . . . . . . .
2.2.1.2 DOM—Digital Optical Module . . . . . . . .
2.2.1.3 Construction . . . . . . . . . . . . . . . . . .
2.2.2 Neutrino detection principle in IceCube . . . . . . . .
2.2.2.1 Neutrino interactions . . . . . . . . . . . . .
2.2.2.2 Cherenkov light . . . . . . . . . . . . . . . .
2.2.3 Event types . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3.1 Track like event . . . . . . . . . . . . . . . .
2.2.3.2 Cascade event . . . . . . . . . . . . . . . . .
2.2.3.3 Double Bang . . . . . . . . . . . . . . . . . .
2.2.4 Ice properties . . . . . . . . . . . . . . . . . . . . . . .
2.2.4.1 Bulk ice . . . . . . . . . . . . . . . . . . . . .
2.2.4.2 Hole ice . . . . . . . . . . . . . . . . . . . . .
2.3 IceCube Upgrade . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
4
4
5
5
5
7
7
7
8
9
9
9
9
10
10
10
12

3 D-Egg
14
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 Linearity response curve . . . . . . . . . . . . . . . . . 21
3.2.3 Detection uniformity . . . . . . . . . . . . . . . . . . . 21
3.2.4 Darknoise rate . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Glass and gel . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

iii

CONTENTS
3.4

Flasheriv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

4 Detector simulation
27
4.1 DOMINANT . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 DOMINANT for D-Egg . . . . . . . . . . . . . . . . . . . . . 27
4.3 Eﬀective area calculation . . . . . . . . . . . . . . . . . . . . 27
5 Sensitivity to the hole ice
32
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2 Simulation of photon propagation in ice . . . . . . . . . . . . 33
5.2.1 Modeling hole ice . . . . . . . . . . . . . . . . . . . . . 33
5.2.2 Modeling of Mie scattering . . . . . . . . . . . . . . . 33
5.2.3 Toy simulation . . . . . . . . . . . . . . . . . . . . . . 34
5.2.4 Photon detection with D-Egg . . . . . . . . . . . . . . 40
5.2.4.1 Simulation framework . . . . . . . . . . . . . 40
5.2.4.2 Light source . . . . . . . . . . . . . . . . . . 40
5.2.4.3 Detection eﬃciency . . . . . . . . . . . . . . 41
5.2.4.4 Results – Hole ice parameter dependence of
NPE . . . . . . . . . . . . . . . . . . . . . . . 42
5.3 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . 46
5.3.1 Detector response . . . . . . . . . . . . . . . . . . . . 46
5.3.2 Alignment of the D-Eggs . . . . . . . . . . . . . . . . 46
5.3.3 Flasher LED proﬁles . . . . . . . . . . . . . . . . . . . 47
5.3.4 Cable shadow . . . . . . . . . . . . . . . . . . . . . . . 47
5.3.5 ⟨cos θ⟩ . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4 Extraction of hole ice parameters . . . . . . . . . . . . . . . . 48
5.4.1 Analysis method . . . . . . . . . . . . . . . . . . . . . 48
5.4.1.1 Likelihood construction . . . . . . . . . . . . 48
5.4.1.2 Test statistic . . . . . . . . . . . . . . . . . . 50
5.4.1.3 Test data . . . . . . . . . . . . . . . . . . . . 50
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.5.1 Case study – Three scenarios . . . . . . . . . . . . . . 52
5.5.2 A case when the geometrical information is available . 52
5.5.3 A case when no external information is available . . . 53
5.5.4 Final result: all systematic uncertainties included . . . 53
5.5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6 Conclusion

60

References

60

List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7

Sketch of the IceCube detector. . . . . . . . . . . . . . . . . .
A schematic of the DOM. . . . . . . . . . . . . . . . . . . . .
Cherenkov light yield. . . . . . . . . . . . . . . . . . . . . . .
Depth dependence of the scattering and absorption length. .
Hole ice forming images. . . . . . . . . . . . . . . . . . . . . .
Camera image looking downward into the established hole ice.
Sketch of the planned IceCube Upgrade array. . . . . . . . . .

6
6
8
10
11
12
13

3.1
3.2
3.3
3.4

Latest prototype of a complete D-Egg. . . . . . . . . . . . . . 15
Latest prototype of a lower half D-Egg. . . . . . . . . . . . . 15
8” Hamamatsu R5912-100-70 PMT. . . . . . . . . . . . . . . 16
QE of all PMTs planned for the IceCube Upgrade measured
by Hamamatsu. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.5 Example of a SPE waveform. . . . . . . . . . . . . . . . . . . 18
3.6 Example of a PMT’s charge distributions. . . . . . . . . . . . 19
3.7 Example of a PMT’s charge resolution and peak to valley ratio. 20
3.8 Example of a PMT’s high voltage dependence of gain. . . . . 20
3.9 Example of a PMT’s linearity response curve. . . . . . . . . . 22
3.10 2D uniformity measurement setup. . . . . . . . . . . . . . . . 23
3.11 Example of a PMT’s detection uniformity. . . . . . . . . . . . 23
3.12 Example of a PMT’s darknoise rate. . . . . . . . . . . . . . . 24
3.13 Transmittance of the glass and gel of the D-Egg comparedwith the DOM. . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.14 Prototype of the ﬂasher module. . . . . . . . . . . . . . . . . 26
4.1
4.2
4.3

Designs and geometries of the D-Egg implemented into DOMINANT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wavelength dependence of the absorption length of the bulk
ice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Depiction of the simulation. . . . . . . . . . . . . . . . . . . .

v

28
29
30

LIST OF FIGURES
4.4

5.1

Zenith angle dependence of the eﬀective area of the DOM andthe D-Egg. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

31Photon propagation with λe = 30 cm, D = 45 cm, and thelight source inside the bubble column. . . . . . . . . . . . . . 36
5.2 Photon propagation with λe = 100 cm, D = 45 cm, and thelight source inside the bubble column. . . . . . . . . . . . . . 37
5.3 Photon propagation with λe = 30 cm, D = 100 cm, and thelight source inside the bubble column. . . . . . . . . . . . . . 38
5.4 Photon propagation with λe = 30 cm, D = 45 cm, and thelight source outside the bubble column. . . . . . . . . . . . . 39
5.5 Illustration of the simulation and position parameters r and ϕ. 41
5.6 Angular proﬁle of LED XRL-400-5O. . . . . . . . . . . . . . . 42
5.7 Detection uniformity of PMT SQ0262. . . . . . . . . . . . . . 43
5.8 λe and D dependence of NPE. . . . . . . . . . . . . . . . . . 44
5.9 r and ϕ dependence of NPE. . . . . . . . . . . . . . . . . . . 45
5.10 Angular proﬁle of the LEDs. . . . . . . . . . . . . . . . . . . . 47
5.11 Cameras in a D-Egg. . . . . . . . . . . . . . . . . . . . . . . . 48
5.12 Example of a PDF of NPE. . . . . . . . . . . . . . . . . . . . 49
5.13 Example of the test statistic distribution. . . . . . . . . . . . 51
5.14 Example of the PDF of R. . . . . . . . . . . . . . . . . . . . . 51
5.15 True scenarios tested. . . . . . . . . . . . . . . . . . . . . . . 52
5.16 Results of likelihood ﬁt tests where rtrue , ϕtrue are known. . . 54
5.17 Results of likelihood ﬁt tests where rtrue , ϕtrue are unknown. . 55
5.18 P-values for test data from LEDs with +30% of −30% ofbrightness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.19 P-values for test data from LEDs with a diﬀerent angular
proﬁle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.20 P-values for test data from three LEDs out of four. . . . . . . 56
5.21 p-values for test data from ⟨cos θ⟩. . . . . . . . . . . . . . . . 56
5.22 Results of likelihood ﬁt tests where rtrue , ϕtrue are unknown
and the systematic uncertainties are included. . . . . . . . . . 58

CHAPTER 1. INTRODUCTION

1

Chapter 1

Introduction
The ﬁrst concrete ideas to search for astrophysical neutrinos were proposed in 1960 by K. Greisen [1]. The ﬁrst discovery of a PeV-energy astrophysical neutrino ﬂux was made by IceCube in 2013 [2], which opened a
new ﬁeld of astroparticle physics, high-energy neutrino astronomy. Neutrinos are unique messengers that carry information about their parent cosmic
ray particles to the Earth without being absorbed or deﬂected. The mostinteresting outcome from neutrino astronomy would be the identiﬁcation ofneutrino or cosmic ray sources and elucidation of acceleration mechanismsof cosmic ray particles. In 2018, the IceCube collaboration found evidenceof the blazar TXS0506+056 being a cosmic neutrino source, and thus also
likely a cosmic ray source [3].
The IceCube Neutrino Observatory is the worlds largest neutrino detector built at the geographical South Pole. The optical modules deployed in
the deep ice observe neutrinos by detecting Cherenkov light from charged
particles produced in the interactions of neutrinos with the ice. Neutrinos
are reconstructed from the amount and timing of the detected light, which
relies on the properties of the detection medium. Precise knowledge of thedetection medium for very large volume neutrino telescopes is one of thebiggest challenges, as the medium is usually in a remote location and not
man-made. In IceCube, the optical modules are equipped with light emitting
diodes (LEDs) as artiﬁcial light sources for measuring the optical propertiesof the ice. Previous measurements performed in IceCube have measured theproperties of the undisturbed glacial ice (bulk ice) [4], while the propertiesof the re-frozen ice, called “hole ice”, are still inconclusive due to a lack ofsuitable devices.
The IceCube Upgrade, planned for deployment in the 2022/2023 South
Pole Summer, will involve deployment of new optical modules, aimed at

CHAPTER 1. INTRODUCTION

2

improving the precision of neutrino measurements. One type of new optical module is the “Dual optical sensor in an Ellipsoid Glass for Gen2”(D-Egg). The D-Egg has an improved photon detection eﬃciency and optimized calibration devices, including LEDs, for measurements of the hole ice
properties.
To understand the performance of the calibration devices, a GEANT4
based simulation was performed to parameterize the hole ice system. A
maximum likelihood ﬁt was performed to calculate the sensitivity to various hole ice parameters. The results show the D-Egg’s hole ice calibration
system has the potential to characterize the hole ice more precisely than inprevious measurements. Improved understanding of the hole ice properties
will enable the better angular reconstruction of GeV energy neutrinos, which
is currently limited by systematic uncertainty of the hole ice properties [5].
Long-term improvements to angular reconstruction and overall reductionof ice modeling systematic errors will greatly beneﬁt all IceCube analyses
including neutrino astronomy and cosmic ray source searches.
An overview of IceCube is described in Chapter 2 of this thesis. Chapter 3 describes the D-Egg and Chapter 4 introduces the GEANT4 based
D-Egg simulation. Chapter 5 presents the simulation study of hole ice measurement with the D-Eggs and discusses practical considerations. Chapter 6
summarizes this thesis and discusses the scientiﬁc reach of this work.

CHAPTER 2. ICECUBE

3

Chapter 2

IceCube2.1

Introduction to high-energy neutrino astronomy

High energy primary cosmic rays are believed to be accelerated by astrophysical objects such as supernova remnants, active galactic nuclei andgamma ray bursts, however their origin and the acceleration mechanism is
not fully known. Charged cosmic rays are generally composed of protons(90%), α (9%), and heavier nuclei. Other cosmic rays include gamma-rays
and neutrinos. These cosmic rays can be produced up to very high energies,
arriving at Earth with up to 100 EeV [6]. By detecting either primary or
secondary cosmic rays, IceCube is able to discover more about these extragalactic sources.
In the case of charged primary cosmic rays, they interact with magnetic
ﬁelds. This is important for two reasons. Firstly, the directions of primarycosmic rays are altered by magnetic ﬁelds as they propagate towards the
Earth, obscuring their true origins. Secondly, cosmic rays can be conﬁned
with magnetic ﬁelds at the source. However protons, for example, can collide with ambient matter, which results in another challenge for detecting
primary charged cosmic rays.
A common interaction mode for the cosmicly accelerated proton resultsin either hadronuclear pion production:()
p + p → π + X π = π±, π0 ,(2.1)
or in photohadronic pion production from interactions with the radiativeﬁeld in the source region:{
π0 + pp + γradiation →(2.2)
π+ + n .

CHAPTER 2. ICECUBE

4

The pions subsequently decay producing electrons and neutrinos:
π 0 → γγπ± →(−)µ± ν µ ,
+
+

(2.3)
(2.4)

µ → e ν̄µ νeµ− → e− νµ ν̄e .

Each of the three neutrinos produced in the decay of a π ± Eq. (2.4) car1
ries approximately 20of the energy of the parent proton. In addition to
Eq. (2.3), high energy gamma rays can be produced by Inverse Compton
scattering. In the regions of strong cosmic magnetic ﬁelds, a high densityof electrons and photons, produced via synchrotron radiation, react andproduce high energy gamma rays:e− + γradiation → e− + γhigh energy .

(2.5)

However, these photons acquire energy by Inverse Compton scattering up
to 10–100 TeV, but unlikely to PeV-level energies. Observations of PeV
gamma rays produced by the reaction in Eq.(2.3), therefore, can be a proof of
hadronic acceleration. However, the PeV gamma rays are highly attenuatedduring propagation by the cosmic microwave background (CMB):γPeV + γCMB → e+ + e− ,(2.6)

making their detection extremely challenging.

2.1.1

High-energy astrophysical neutrinos

Neutrinos are nearly massless leptonic particles with no charge and onlyinteract weakly, meaning they mainly propagate through the universe to
the Earth without absorption or deﬂection. As neutrinos from astrophysicalsources can be traced back to their origins, such neutrinos can be used
to improve our understanding of charged cosmic rays—their origins andacceleration processes. To compensate for the small interaction probability
large volume detectors and high exposure times are required.

2.2

The IceCube experiment

The IceCube Neutrino Observatory [7] is a cubic-kilometer neutrino detector built in the South Pole ice between depths of 1450 m and 2450 m,
designed to detect GeV–EeV neutrinos. The large volume of transparent,

CHAPTER 2. ICECUBE

5clear and deep ice is perfect for a neutrino detector. The detector construction was completed on December 18, 2010, and the full operation started
in May 2011. IceCube has been primarily aiming to discover high-energy
astrophysical neutrinos and identify their sources, in addition to the searchfor dark matter, the study of neutrino oscillations and the observation of
Galactic supernova explosions [8]. The ﬁrst discovery of high-energy astrophysical neutrinos was achieved in 2013 [2] [9]. In 2018, an origin of
the astrophysical neutrinos was identiﬁed for the ﬁrst time, by gamma ray
follow-up observations to detect a gamma-ray ﬂare [3].

2.2.1

Detector

2.2.1.1

IceCube array

The detector array is composed of 5160 digital optical modules (DOMs)
across 86 vertical strings, with 60 DOMs on each string. In Figure 2.1 theDOMs are mostly deployed with a vertical spacing of 17 m, and a horizontalof 125 m. This sparse spacing is suﬃcient due to the long optical attenuation length of the South Pole ice. Eight strings out of 86 at the center of
the IceCube array compose a dense sub-array called DeepCore [10], mainly
aimed at measurements of neutrinos with energies of 10–100 GeV, and theindirect detection of dark matter. In DeepCore the DOMs are placed below
the depth of 2000 m with a vertical separation of 7–10 m and a horizontal
separation of 41–105 m.
2.2.1.2

DOM—Digital Optical Module

A DOM has a downward-facing 10” photomultiplier tube (PMT) in apressure-resistant glass sphere with a diameter of 35 cm, along with related
circuit boards for processing the PMT pulses and communicating with computers on the ice surface (Figure 2.2). The DOM also contains an LED
ﬂasher board for calibration. 12 LEDs are mounted to the edge of theﬂasher board, divided into six pairs with a 60◦ separation. One LED ineach pair emits light in the horizontal plane and the other 48◦ above thehorizontal, which is close to the Cherenkov angle in the ice. The LEDs
were selected to have 399 nm wavelength to match the typical wavelength of
Cherenkov photons the DOMs detect. The ﬂasher pulses are programmableand can produce pulses detectable by other DOMs located up to 0.5 km
away, making the LEDs useful for various calibration studies. These studies
include determining the detector geometry, PMT performance time oﬀset
and resolution, and the optical properties of the ice [11].

CHAPTER 2. ICECUBE

6

Figure 2.1: Sketch of the IceCube detector. The IceCube Laboratory at thesurface has the overall detector operation systems, where all the cables connectedto the DOMs are gathered.

Figure 2.2: A schematic of the DOM.

CHAPTER 2. ICECUBE
2.2.1.3

7

Construction

In order to build IceCube’s DOM array, 86 boreholes of 2500 m depth in
the glacial ice were created. It was achieved by hot water drilling which ismore time and fuel eﬃcient than a conventional drill.
The 5 MW Enhanced Hot Water Drill (EHWD) was designed for the
IceCube detector construction [12]. The drill head delivers 88◦ C hot waterwith a pressure of 7600 kPa. The head was equipped with instrumentation to
make a precise hole, such as calipers to measure the hole diameter, a pressure
sensor to measure depth, two liquid pendulums to measure tilt relative tovertical, and a ﬂuxgate compass to measure horizontal orientation. The holediameter was optimized to balance the cost and the rate of water freezing
and was decided to be 60 cm.
After the drill was withdrawn from the hole, the hole was ﬁlled withwater, though the water in contact with the outer ice starts freezing immediately. In order to place 60 DOMs at the planned depth, they were allconnected to one cable of 2505 m length with a diameter of 46 mm, together
with four 100 pound weights. The water in the hole then freezes the DOMs
in place. The ice in the hole created as a result of hot water drilling is called
the “hole ice”, discussed in Section 2.2.4.2 and Chapter 5.

2.2.2

Neutrino detection principle in IceCube

2.2.2.1

Neutrino interactions

Charged-current (CC) neutrino-nucleon interactions produce a leptonl = e, µ, τ :(−)ν l N → l∓ X ,(2.7)

where N denotes the target nucleon and X the hadronic ﬁnal state. The
lepton carries an average of 50% to 80% of the neutrino energy dependingon the neutrino’s energy, and the remaining energy is transferred to the
nucleon. In the case of IceCube, both the lepton and the hadronic shower
emit Cherenkov radiation.
Neutral current (NC) neutrino-nucleon interactions do not produce acharged lepton:(−)(−)
ν lN → ν lX .

(2.8)

The neutrino transfers a fraction of its energy to the target nucleon, producing a hadronic shower only.

CHAPTER 2. ICECUBE

8

3.0
2.5

dN
dλ

2.0
1.5
1.0
0.5
0.0 300

350

400

450 500
Wavelength[nm]

550

600

650

Figure 2.3: Cherenkov light yield (Eq. (2.10)) with β = 1, x = 1 cm.

2.2.2.2

Cherenkov light

When a neutrino interacts with a nucleus in the ice, charged particles
are generated (see Eq. (2.7) and (2.8)). When the charged particles movefaster than the speed of light in ice, they can travel through the IceCube ice
emitting Cherenkov photons, which are detectable by the DOMs near the
trajectory of the charged particle.
Photons are emitted at a characteristic angle relative to the charged
particle composing the so called “Cherenkov cone”. This characteristic angle
is called the Cherenkov angle and is given bycos θc =1,βn (λ)(2.9)

where β is the speed of the charged particle in units of the speed of light andn (λ) is the phase refractive index of the medium. In IceCube the refractive
index of the ice is n (λ) = 1.55749 − 1.57988λ + 3.99993λ2 − 4.68271λ3 +2.09354λ4 [13]. The number of photons emitted per unit length x for acharged particle with charge ze is wavelength (λ) dependent and given by
the Flank-Tamm formula:
(
)
d2 N
1
2πz 2 α1− 2 2,(2.10)=dλdx
λ2
β n (λ)where α = 1/137 is the ﬁne structure constant (Figure 2.3). IceCube mainly
detects photons with a wavelength from 300 to 600 nm.

CHAPTER 2. ICECUBE

2.2.3

9

Event types

Three diﬀerent event topologies are observed in IceCube, depending on
the neutrino interaction channel and energy.
2.2.3.1

Track like eventνµ CC interactions cause track like events. Muons have a long life timesuch that they can travel through the IceCube detector from end to end,
emitting Cherenkov radiation along its trajectory. This enables reconstruction of the muon arrival direction, resulting in an angular resolution to better
than 1◦ for the muon, and hence the incident neutrino with energies above
the TeV range [14]. Furthermore, an upward-going track is an unambiguous signature of neutrinos, since no other particle can penetrate the Earth.
Therefore, this event type is ideally suited for identiﬁcation of astrophysicalneutrino sources. On the other hand, since the muon track can be too long
to be fully contained within the IceCube detector, it is diﬃcult to reconstruct the full energy of the neutrino, coupled with the large background of
atmospheric νµ .
2.2.3.2

Cascade event

Cascades are formed by particle showers near the neutrino vertex withlengths of order 5–20 m. CC interactions of νe and ντ produce both hadronicand electromagnetic showers. NC interactions of all ﬂavors produce exclusively hadronic showers. The total energy deposited in the detector is
proportional to the cascade energy, and thus provides a more direct measurement of the neutrino energy with about 15% accuracy, which is muchbetter than for muon tracks. However, the precision of the angular reconstruction for cascades is worse than for tracks, since the lever arm for ﬁtting
the direction is small. Moreover, the strong scattering of photons in the refrozen ice further blurs the original direction information contained in the
Cherenkov cone.
2.2.3.3

Double Bang

At PeV energies, the CC interaction of ντ cause a third type of event,as the lifetime of τ leptons is suﬃciently long to travel up to hundreds ofmeters before decaying. This event is called the double bang, composed of
two cascades connected by a rather dim tau track: one cascade is produced
when the ντ interacts, and the second when the τ decays. However, a clear
double bang event has not been observed so far.

CHAPTER 2. ICECUBE
(a)

10
(b)

Figure 2.4: Depth dependence of the scattering (a) and absorption (b) length ata wavelength of 400 nm taken from [4]. The solid lines show the latest results withestimated uncertainties shown as gray bands.

2.2.4

Ice properties

As photons propagate to the DOM’s PMT, they are aﬀected by absorption and scattering in the ice. These eﬀects must be implemented into both
simulation and reconstruction of IceCube data. The optical properties of
the ice have been measured using ﬂasher LEDs in the DOMs.
2.2.4.1

Bulk ice

The optical properties of the undisturbed glacial ice (bulk ice) is parameterized by considering the absorption and scattering [4]. To determine thebulk ice parameters, measurements were performed with the IceCube detector. Photons were emitted by the ﬂasher LEDs located inside the DOMs,
and the total number of detected photons and the photon arrival times wererecorded by other DOMs. The measurement was performed for all depths
where DOMs are located, and the wavelength and depth dependence of thescattering and absorption length was determined to be less than 20 m and
5 m, respectively, at 400 nm wavelength (Figure 2.4).
2.2.4.2

Hole ice

A camera system, called the Swedish camera, was deployed on one of the
86 strings to monitor how the water in the drill hole refreezes and observe
the optical properties of the hole ice. It consists of two rotatable video
cameras with LED lamps and four lasers housed in separate glass spheres
5.8 m apart, located at the bottom of the string. The camera images tell thefollowing:• The water froze from the outside inwards (Figure 2.5(a), 2.5(b), 2.5(c)).

CHAPTER 2. ICECUBE

11(a) 22 December 2010(b) 26 December 2010(c) 31 December 2010(d) 1 January 2011

Figure 2.5: Hole ice forming images over nine days, 4 days after the deployment.
a) The hole still holds a large volume of water, which looks transparent, and theice wall is clearly identiﬁed. The circle ring spacer serves as a landmark in the later
images. b) The boundary of the ice and water has moved toward the inner part of
the hole. c) The water freezing has evolved so that the boundary of the ice and thewater (seen on the right) is observed from the frozen ice. d) The ice of the outerhole is so transparent that the green laser originating from the upper right on theimage can reach the spacer.

• The outer region of the hole ice is as clear, or more transparent, thanthe bulk ice (Figure 2.5(d)).
• A portion of ice includes a lot of impurities in the hole ice (Figure 2.6).
When the water from the drill, containing various impurities such as air
bubbles, still-liquid or dust, froze, the impurities condensed into the central area. This resulted in a central ice column with an enhancement of
impurities remaining after re-freezing, called the bubble column.
Since the PMT in a DOM faces downward, the increased scattering in the
bubble column leads to detection of more photons than expected. Althougheﬀorts have been made to measure the precise hole ice properties utilizing

CHAPTER 2. ICECUBE

12

Figure 2.6: Camera image looking downward into the established hole ice. The
bubble column is found on the center right. It looks opaque because of the Miescattering of the light on the impurities.

the ﬂasher LEDs [15], the properties of the hole ice are still inconclusive,
because the DOM LEDs cannot illuminate the hole ice directly. This leads
to one of the largest systematic uncertainties in the angular reconstructionof cascade events.

2.3

IceCube Upgrade

The IceCube Upgrade aims to improve the precise measurement of neutrino interactions. The IceCube Upgrade [16] is planned for deployment in
the 2022/2023 South Pole Summer, as a stepping stone to the next generation IceCube detector [17]. In the upgrade, an additional 700 new optical modules (OMs) will be deployed together with calibration modules at
a depth between 2150 m and 2425 m, across seven new strings inside the
DeepCore sub-array (Figure 2.7).
Several types of new OMs have been developed, including the mDOM [18]and the D-Egg [19]. They have an improved overall photon detection eﬃciency compared with the current IceCube DOM, and will be deployed witha vertical separation of 2.7 m and a horizontal separation of 20 m, which ismuch denser than the DOMs’ spacing in IceCube, even in DeepCore. These
will enable even more precise measurement of GeV energy neutrinos. The
IceCube Upgrade also targets better understanding of the optical propertiesof the ice, especially the hole ice. The new OMs hold optimized calibration
devices for this purpose, such as vertically illuminating LEDs and cameras.

CHAPTER 2. ICECUBE

13

Figure 2.7: Sketch of the planned IceCube Upgrade array, including the current
DOM spacing for IceCube and DeepCore as well as a zoom towards the DeepCore
region, where the narrowly spaced D-Egg and mDOM modules are planned for
deployment.

CHAPTER 3. D-EGG

14

Chapter 3

D-Egg
3.1

Overview

One type of new optical module for the IceCube Upgrade is called the
D-Egg, as seen in Figure 3.1. 300 D-Eggs are planned for deployment as
part of the IceCube Upgrade. The D-Egg has a similar structure to thecurrent IceCube DOM, but has been designed to have an improved photon
detection eﬃciency.
The basic idea for the D-Egg is to combine two PMTs for an egg likemodule. The size of the D-Egg is determined by its glass housing. The
housing is composed of two halves each 30 cm in diameter and combine to
be 53 cm tall. The upper and the lower sides have an almost symmetricalstructure. Both have PMTs as an optical sensor in the pressure-resistantglass hemisphere. A high voltage (HV) board is attached to each PMT,
which includes a driver circuit for the PMT and a HV module that increases
the input voltage by a factor of 400 to supply to the PMT. Silicone elastomer(gel) between the PMTs and the glass plays a role in ﬁxing the PMT inside
the glass and coupling them optically. A magnetic shield made of FINEMET[20] (Hitachi Metals) covers the PMT dynodes avoiding its cathode surface
to minimize the impact of the magnetic ﬁeld on the performance of the
PMT.
In addition the lower half has a ﬂasher module, camera module, mainboard and penetrator (Figure 3.2). The ﬂasher and camera modules are
installed for the purpose of calibration. The mainboard primarily controls
the electronics readout and communication between surface control units
and deep ice optical modules through the penetrator. The two half D-Eggs
are sealed by vacuuming inside the glass, and then locked in place by awaistband, which has harnesses to hang the D-Egg.

CHAPTER 3. D-EGG

Figure 3.1: Latest prototype of a complete D-Egg.

Figure 3.2: Latest prototype of a lower half D-Egg.

15

CHAPTER 3. D-EGG

16

Figure 3.3: 8” Hamamatsu R5912-100-70 PMT. The yellow hemispherical surface
is the photocathode made of bialkali and it is vacuum inside.

3.2

PMT

Each D-Egg holds two 8” Hamamatsu PMTs of R5912-100-70 (Figure 3.3).
The photocathode is grounded and a positive voltage is applied to thedynodes by the HV board. When a photon hits the photocathode, it excites
an electron on the photocathode surface and emits a photoelectron. This
photoelectron has a production probability inﬂuenced by the PMT’s quantum eﬃciency (QE). The intensity of Cherenkov light is higher at shorter
wavelengths (see Section 2.2.2), which motivates the selection of PMTs sensitive to 300–650 nm wavelength light and their maximum QE at 350–400 nm(Figure 3.4).
Individual PMTs have unique responses, and several quantities thatcharacterize the PMT response [21] have been measured in the laboratory
during the development stage. Before mass-deployment, 10% of the PMTs
for the IceCube Upgrade will undergo detailed calibration before being installed into D-Eggs.

3.2.1

Gain

A photoelectron generated at the photocathode is collected by the ﬁrst
dynode according to the potential diﬀerence. When the photoelectron hits
the ﬁrst dynode, secondary electrons are produced. The secondary electrons
are then multiplied when they hit each of the subsequent nine dynodes, andeventually between 106 and 107 electrons are collected by the anode to be
output, depending on the applied voltage. The electron multiplication factor

CHAPTER 3. D-EGG

1740643 PMTs
Average35

QE [%]

30
25
20
15
10
5
0 300 350 400 450 500 550 600 650
Wavelength [nm]Figure 3.4: QE of all PMTs planned for the IceCube Upgrade measured byHamamatsu. The maximum QE for each PMT is more than 32%.

is called the gain.
The total charge Q for a given waveform (Figure 3.5) is calculated using:∫V
Q = dt ,(3.1)
R
where t is time, V is the voltage, and R is the impedance, whose nominal
value is 50 Ω.
If we know the gain of the PMT G for the given supply voltage, thenumber of photoelectrons (NPE) accepted by the PMT is calculated fromthe charge of the output signal:
NPE =

Q
,
eG

(3.2)

where e is the elementary charge.
The PMTs are operated at G = 107 in IceCube, however we do not know
the value of the supply voltage a priori. To determine the supply voltage
needed for 107 gain, a range of supply voltages are applied in the laboratory.
In the measurement, 10000 waveforms are recorded for a dim input light withconstant intensity, and the charge of each waveform is calculated. Mostof the waveforms show no pulse, which constitute pedestal events, while
the others mostly are SPE events. The charge distribution is ﬁtted witha function containing nine parameters (Eq. (3.3)). Eq. (3.3) includes asum of Gaussian functions for pedestal, SPE and two photolectron (2PE)

CHAPTER 3. D-EGG

18

0.000

voltage [V]

0.002
0.004
0.006
0.008
0.010
0.4

0.2

0.0

0.2 0.4
time [s]

0.6

0.8

1.0

1e 7

Figure 3.5: Example of a waveform when a single photoelectron (SPE) is acceptedby the PMT.

events, and an exponential function describing failed multiplication events(Figure 3.6):)((Q − µpede )2
f (Q) = Apede exp −(3.3)
2σpede 2))((
Q1
Aexp exp (−Q/τ ) 1 + erf √+22σpede()(Q − µSPE )2+ ASPE exp −2σSPE 2()(Q − 2µSPE )2+ A2PE exp − (√)2 ,2 2σSPE
where A is a normalization constant for each component, µpede , σpede are themean charge and the standard deviation for pedestal distribution, µSPE , σSPE
are the mean charge and the standard deviation for SPE distribution. An
example of this combined ﬁt is shown in Figure 3.6 for charge distributions
collected from a D-Egg PMT. The various ﬁt parameters are given in theplots where [p0, p1, p2, p3, p4, p5, p6, p7, p8] corresponds to [ASPE , µSPE ,σSPE , A2PE , Apede , µpede , σpede , Aexp , τ ].
The ratio σSPE /µSPE is referred to as the charge resolution (Figure 3.7(a)).
The ratio of the frequency of observing a charge at the peak of SPE andthe valley between the pedestal and the SPE is also a feature quantity of a
PMT, called the peak to valley ratio (P/V) (Figure 3.7(b)). This provides

CHAPTER 3. D-EGG

19(b)
Entries

Entries

(a)
h_spe

103

Mean
χ2 / ndf
p0
p1
p2
p3
p4
p5
p6
p7
p8

102

10

0.1341
292.2 / 65
55.57
47.78
47.49 ±± 2.43
2.31
1.047 ± 0.020
1.028
0.3956 ± 0.0214
0.40950.02153.872 ± 0.728
3.864
0.703
1258
1004±±16.9
0.60.002525 ± 0.000784
0.002399
0.001699
0.13680.147±±0.0011
0.001
5.809 ± 0.936
3.817
0.250
0.16
0.2±±0.05
0.0

h_spe

103

102

10

1

0.1736331.6 / 79
73.66
42.06
45.64 ±± 1.83
1.51
1.336 ± 0.025
0.019
0.48370.429±±0.0222
0.003
2.999 ±± 0.459
2.391
0.421
1247
988±±18.7
0.5
0.0035 ± 0.0014
0.00280.00160.1484 ± 0.0013
0.13790.00094.619
5.311 ± 0.866
0.190
0.24
0.2± ±0.04
0.0

1
0

1

2

3

4

5

6

7
8
Charge [pC]

0

1

2

3

4

5

6

7
8
Charge [pC](d)
Entries(c)
EntriesMeanχ2 / ndf
p0
p1
p2
p3
p4
p5
p6
p7
p8

h_spe

103

Mean
χ2 / ndf
p0
p1
p2
p3
p4
p5
p6
p7
p8

102

10

0.2071480.3 / 86
95.68
42.87 ± 1.49
35.63
1.45
1.603 ± 0.024
1.627
0.027
0.59060.429± ±0.0209
0.001
3.248
1.83±±0.431
0.41
1257
968.8±±16.8
0.50.002656
0.002125 ±± 0.001664
0.000861
0.14720.1357 ±± 0.0009
0.0011
6.262 ± 1.612
5.185
0.142
0.24
0.2± ±0.07
0.0

h_spe

103

Mean
χ2 / ndf
p0
p1
p2
p3
p4
p5
p6
p7
p8

102

10

0.257774.44 / 104
30.48 ± 1.31
1.984 ± 0.027
0.6736 ± 0.0240
1.817 ± 0.342
1263 ± 16.7
0.003724 ± 0.000904
0.1355 ± 0.0011
5.678 ± 1.769
0.5457 ± 0.1146

1

1

0

1

2

3

4

5

6

7
8
Charge [pC]

0

1

2

3

4

5

6

7
8
Charge [pC]

Figure 3.6: Example of a PMT’s charge distributions for a voltage a) 1440 V, b)
1480 V, c) 1520 V, d) 1560 V. Data are shown as a blue histogram and is ﬁtted with
Eq. (3.3) shown as a red solid line. Red dashed lines from left to right correspondto the ﬁrst, second, third and forth term of the ﬁtting function, respectively.

an estimate of the PMT’s signal to noise performance.
The gain for a given PMT at a known supply voltage is calculated fromthe SPE mean charge µSPE :G = µSPE /e .

(3.4)

After measuring the SPE spectrum at various supply voltages, the voltage
V dependence of the gain is obtained by ﬁtting the data points with twoparameters:(
G (V ) =

V
a0

) 1

10a1

.

(3.5)

For example in Figure 3.8, the supply voltage needed to achieve 107 gain
can be extracted directly from the ﬁt.

CHAPTER 3. D-EGG

20

(b)

(a)

40.0

Peak to valley ratio

Charge resolution [%]

42.5
37.5
35.0
32.5
30.0
27.5
0.6 0.7 0.8 0.9 1.0 1.1 1.2
1e7
Gain

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.00.6 0.7 0.8 0.9 1.0 1.1 1.2
1e7
Gain

Figure 3.7: a) Example of the charge resolution versus the gain. b) Example of
the gain dependence of the P/V.

1e7

Gain

1.2
1.0
0.8
0.6
1425 1450 1475 1500 1525 1550 1575
HV [V]
Figure 3.8: Example of a gain measurement result, where the gain is plotted as afunction of high voltage. The four black circle points are measured data, ﬁtted with
Eq. (3.5) shown as a red curve. Once the voltage to achieve 107 gain is extracted
from the ﬁtting function, the gain measurement is repeated for the voltage withmore samples (40000 waveforms), shown as the black square.

CHAPTER 3. D-EGG

3.2.2

21

Linearity response curve

The D-Egg PMTs exhibit a linear behavior between the incident amountof light and the output up to several tens of photoelectrons (PEs) over a
period of one nanosecond. However, when the PMT detects a huge numberof photons within a short time, it saturates and the linearity is lost. In orderto estimate the true NPE generated at the photocathode from the output
waveform, the linearity of the peak current and NPE is measured in thelaboratory from a known input source (Figure 3.9). Waveforms are recorded
for six incident lights with diﬀerent known brightness (Figure 3.9(a)), where
the dimmest light is tuned to make a few tens of PEs on the photocathode.
The data for the dimmest light is used as an anchor point, assuming it iswithin the region where the PMT response is perfectly linear. Therefore,
the ideal peak current and unsaturated NPE are calculated. Particularly,
the ideal current is written as a function of the actual peak current x using
three parameters p0 , p1 , p2 :f (x) =

3.2.3

1
(
(
( )3 )( )1 )
2
1
1
x/ ln 1 + px2
x + p0 ln 1 + p1

(3.6)

Detection uniformity

The probability that a photoelectron is multiplied at each dynode depends on the electrons’ trajectory. This is called the collection eﬃciency(CE). It largely depends on the incident photon interaction point on thephotocathode. However, the CE cannot be measured directly, since the position dependence of the QE cannot be separated in the measurement. If
assuming the QE is uniform over the photocathode, the CE is obtained byjust scaling the measured photon detection eﬃciency. In the laboratory, amovable light source (Figure 3.10) enables the measurement of the photon
detection eﬃciency in 2D with respect to the incident position of the lightsource (Figure 3.11). The overall performance of the PMT is referred to as
the detection uniformity.

3.2.4

Darknoise rate

Even if no light is around the PMT, radioactive decays in the PMT glass
or elsewhere can generate an SPE which is detected in the PMT. This iscalled darknoise. Such PEs can limit the overall sensitivity of a PMT to
SPE events and are therefore important to understand. However, because

CHAPTER 3. D-EGG

22

(a)

0

Amplitude [V]

1
2
3
4
5
50

0

50
100
Time [ns]

102

101

0
1010
0

200

101

102
103
Ideal NPE [pe](c)Observed NPE [pe]Observed peak current [pe/ns]

(b)

150

101
102
103
Ideal peak current [pe/ns]

104

103
102
101
0
1010
0

104

105

Figure 3.9: Example of the linearity measurement results. a) Average waveforms
for various input light source intensities. Colors correspond to the input intensities
brightness in the order of brown, purple, red, green, orange, blue. Notice how the
PMT waveform becomes distorted as the intensity increases. b) The peak of theobserved current versus the ideal peak current. The data are ﬁtted with Eq. (3.6)
shown as the blue line. Note the departure from the linear region as the ideal
peak current increases. c) Number of total PEs detected versus input. This is also
demonstrates the linear and non-linear regions.

CHAPTER 3. D-EGG

23

Figure 3.10: 2D uniformity measurement setup. The light source output moves
along the curve of the metal semi-circle and rotates to fully sample the PMT surface.

90°

1.05

45°

10

180°

40
20 30

0.90
50

Relative sensitivity

135°

0.75
0°

0.60
0.45

225°

315°
270°

0.30
0.15
0.00

Figure 3.11: Example of the detection uniformity of a PMT. The relative sensitivity can be referred to as CE, given that the QE is uniform over the photocathode.

CHAPTER 3. D-EGG

24
0.25 p.e. threshold

35

Counts / second

30
25
20
15
10
5
09

8

7

6

5
4
log10 (dt [s])

3

2

1

0

Figure 3.12: Example of a darknoise measurement result. The distribution of timeintervals, dt, between peaks exceeding a 0.25 PE threshold when no light source ispresent is shown here. This measurement is not sensitive to below dt = 10−8 s andabove dt = 10−3 s. This is due to resolution and time window limitations in themeasurement, respectively.

radioactivity is largely an irreducible background, it is important to characterize these events through laboratory measurements. In the laboratory,
the rate of the darknoise is measured under the temperature of −30◦ C so as
to duplicate the situation where the D-Egg will be deployed (Figure 3.12).
At cold temperatures electronics noise is also reduced.

3.3

Glass and gel

The glass houses the components, protecting them from the pressure in
the deep water or glacial ice. The gel ﬁlls the gap between the PMT andglass so that the PMT sticks to the glass and, moreover, is optically coupled
to the glass. Both the glass and gel have been developed to have a hightransmittance of ultraviolet light, since the Cherenkov radiation intensity isinversely proportional to the emission wavelength. This was achieved mainly
by reducing the thickness and selecting more transmitive materials.
The thickness must balance both the photon transparency and the mechanical strength. The glass is 10 mm thick at the top or bottom, whichis thinner than the 12.7 mm DOM’s glass. The gel is 5 mm thick at the
top or bottom, which is half the thickness of the DOM’s gel, and 70 mm
deep, which covers almost the entire photocathode of the PMT. As a resultof the optimization of the thickness and the material, the transmittance issigniﬁcantly improved compared with the IceCube DOM (Figure 3.13).

CHAPTER 3. D-EGG

25

1.0

Transmittance

0.8
0.6

D-Egg glass 10 mm
D-Egg gel 5 mm
D-Egg top
DOM glass 12.7 mm
DOM gel 10 mm
DOM top

0.4
0.2
0.0250

300

350
400
Wavelength [nm]

450

500

Figure 3.13: Transmittance of the glass and gel of the D-Egg compared with the
DOM.

3.4

Flasher

The D-Egg includes 12 LEDs for calibration purpose (Figure 3.14). All
LEDs are mounted to a printed circuit assembly board and are inserted
into a special rectangular cup to ﬁx their orientation relative to the D-Egg.
These LEDs and the circuit board constitute the “ﬂasher”, which is madeto surround the PMT on the gel surface of the lower half D-Egg. XRL-4005O [22] has been selected as the LED for the IceCube Upgrade ﬂashers. It
has a 15◦ viewing angle and peak wavelength at 400–410 nm.
Eight of the 12 LEDs are pointing in the horizontal plane, mounted
on the ﬂasher board with a 45◦ interval so that they can emit light in all
directions. They will be used to calibrate the orientation of the opticalmodules, as is done currently in IceCube (see Section 2.2.1.2).
The other four LEDs are pointing downward and will be used to calibrate
the hole ice properties. Although the IceCube DOM also has ﬂasher LEDs
for measuring the optical properties of the ice, they are all horizontal ortilted by 45◦ , not fully vertical. As such, they are not ideal to measure thehole ice properties. The D-Egg with the fully vertical LEDs has potential
to perform more direct hole ice measurements.

CHAPTER 3. D-EGG

(a)

26

(b)

Figure 3.14: a) Prototype of the ﬂasher module. b) Flasher module on the gel ofthe lower half D-Egg, surrounding the PMT.

CHAPTER 4. DETECTOR SIMULATION

27

Chapter 4

Detector simulation
4.1

DOMINANTThe development of a new detector beneﬁts greatly from a detailed detector simulation. This was also the case for the D-Egg, including understanding how photons interactions in the ice propagate to the PMT. Such anunderstanding is needed to reconstruct neutrino properties from data takenby the PMTs in each OM. In order to understand the photon absorption, reﬂection and refraction inside the D-Egg including the glass, a precise D-Egg
simulator was developed, inheriting the DOM simulator called DOMINANT[23].
DOMINANT is an IceCube internal full Monte-Carlo simulator basedon GEANT4 [24], which traces a photon path directly to the photocathode,including the optical processes of absorption, reﬂection and refraction.

4.2

DOMINANT for D-Egg

The DOM in DOMINANT has been replaced with the D-Egg, changing
the geometry based on Figure 4.1, and the optical properties of the glass andgel (see Section 3.3). Note that adding even more detail such as surrounding
ice with diﬀerent properties and the cables which D-Eggs are hung is also
possible.

4.3

Eﬀective area calculation

The primary purpose of DOMINANT is to derive the eﬀective area ofthe detector. The DOMINANT simulation allows to access the informationof photons when they arrive at the photocathode. After the photons hit

CHAPTER 4. DETECTOR SIMULATION(a) Glass outer surface(c) PMT28(b) Glass inner surface(d) Electrical boards

Figure 4.1: Designs and geometries of the D-Egg implemented into DOMINANT.
The D-Egg solid is modeled as an ensemble of parts of simple shapes such as acylinder, sphere, and torus.

Absorption length[m]CHAPTER 4. DETECTOR SIMULATION

29

100
80
60
40
20
0

300

400

500

600
700
Wavelength[nm]Figure 4.2: Wavelength dependence of the absorption length of the bulk ice.

the photocathode, DOMINANT does not trace them any more, however,the PMT response is taken into account in the eﬀective area estimation
to conclude more realistic detector performance. The eﬀective area of the
D-Egg was calculated from simulations incorporating the measured PMT
responses, QE and uniformity.
The zenith angle dependence of the eﬀective area of D-Egg is calculated
by placing it in a large volume of bulk ice with a wavelength dependent absorption length (Figure 4.2). A circular parallel beam with a radius Rbeam
equal to half the D-Egg height (26.7 cm) consisting of 1000 photons is injected from 35 cm away from the center of the D-Egg, aiming at the centerof the D-Egg with a zenith angle θ from 0◦ to 180◦ (Figure 4.3). The eﬀectof the photon absorption is negligible since the distance from the incident
position to the surface of the D-Egg is much shorter than the absorption
length of the bulk ice (Figure 4.2).
The probability that a photon generates a photoelectron at the photocathode and is then collected at the PMT dynode can be calculated fromseveral factors measured in the laboratory (see Section 3.2). The probability
depends on the photon hit position on the photocathodes, which is recordedin the simulation. For a given PMT, the photoelectron detection probability
PNPE to the input from zenith angle θ is calculated byN

PNPE (θ) =

hit
Σi=0

(θ)

QE × CE (ri (θ))
,
Nbeam

(4.1)

where Nhit is the number of photons that arrive at the photocathode, Nbeamis the number of simulated photons and ri is the ith hit photon’s positionon the photocathode.
The eﬀective area Aeﬀ , including the PMT response, is then calculated

CHAPTER 4. DETECTOR SIMULATION

30

Figure 4.3: Depiction of the simulation. Green lines show the photons paths
injected from the upper right. Photons are reﬂected or refracted at the boundaryof diﬀerent materials such as the glass and the surrounding ice. Photon tracing isterminated after the step where the photon enters the PMT from the photocathodesurface.

CHAPTER 4. DETECTOR SIMULATION(a) DOM(b) D-Egg
Wavelength

320 nm
340 nm
380 nm
500 nm80
60
40
20
00 20 40 60 80 100 120 140 160 180
Zenith angle [deg]100
Effective area [cm2 ]100
Effective area [cm2 ]

31

80
60

Wavelength

320 nm
340 nm
380 nm
500 nm40
20
00 20 40 60 80 100 120 140 160 180
Zenith angle [deg]Figure 4.4: Zenith angle dependence of the eﬀective area of the DOM (a) andthe D-Egg (b). Zenith angle is 0◦ when the beam aims at the module from thebottom. This study includes a narrow wavelength simulation of photons at 320,
340, 380, and 500 nm as denoted by their colors. a) The eﬀective area is the largest
at a zenith angle of 0◦ since the DOM’s PMT faces downward. The eﬀective area issmall for low wavelengths due to the low transparency of the glass. b) The dashedlines show the contribution from each of the upper and lower PMTs, while the solidline is a summation of the two components. At small zenith angles the lower PMT
contributes most strongly and at large zenith angles from the upper PMT. The sumof the two PMTs is shown as the solid lines. Performance of the D-Egg is greatly
enhanced at lower wavelengths due to increased attention during development of
the glass and gel. The D-Egg performance is worse at 500 nm, which is contributed
from the geometrical area of the PMTs, although the transmittance of the glass
and gel and the QE are still better for the D-Egg than for the DOM.

from the averaged multiple photoelectrons over the input beam area,
Aeﬀ (θ) = PNPE (θ) · Abeam ,

(4.2)

2
where Abeam = πRbeamis the area of the beam. As long as Rbeam ≥ 26.7 cm,
the eﬀective area is always obtained to be the same. The zenith angle dependence of the eﬀective area for various wavelengths is shown in Figure 4.4 incomparison with the standard IceCube DOM. The D-Egg is twice or more as
sensitive to light from the side as the DOM, and it has the same sensitivity
to light from top as bottom, while the DOM is not sensitive to light fromthe bottom. Additionally, higher PMT QE, more transparent glass and gel
optimized for low wavelengths, results in an overall larger eﬀective area for
the D-Eggs even from the top or bottom where almost no photon is detectedby the PMT facing the other side. This is despite the geometrical area of
the D-Egg’s 8” PMT being smaller than DOM’s 10”.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

32

Chapter 5

Sensitivity to the hole ice
5.1

Introduction

The re-frozen ice in the drill holes, called “hole ice”, has diﬀerent opticalproperties from that of the bulk ice (see Section 2.2.4). The bulk ice has∼20 m long scattering length for optical light [4], while the hole ice has amuch shorter scattering length. The hole ice is composed of two regions:a central column containing some amount of impurities, called the bubble
column, and a clear outer region. Impurities in the bubble column serve
as targets of Mie scattering for optical photons. Therefore, the propertiesof the hole ice can be characterized by two parameters; scattering in the
bubble column and the bubble column size. Current IceCube DOMs do
not have fully vertical LEDs, which are not optimal for directly measuring
the hole ice properties. Combined with the large spaces between DOMs
(17 m vertically, 125 m horizontally), previous measurements of the hole ice
properties remain inconclusive. The lack of understanding regarding thehole ice properties is a dominant source of uncertainties to the directional
reconstruction for all neutrinos, and is particularly relevant for νe , ντ , andneutral current interactions in the GeV region.
As described in Section 3.4, the D-Egg has four LEDs useful for the hole
ice measurement. The light emitted by the downward-facing LEDs will thenbe detected by the D-Eggs in the same hole. Because the optical propertiesof the hole ice largely depend on the size of the bubble column and theposition of the D-Egg relative to the center, using all four LEDs can reduce
the overall uncertainty of the hole ice properties. Speciﬁcally, measurementswith the D-Eggs will determine the bubble column diameter D and theeﬀective scattering length of the bubble column λe . Although D-Eggs will
only be deployed in future IceCube expansions, the entire IceCube data

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

33

taken since 2011 can be reanalyzed using the updated hole ice parameters.

5.2

Simulation of photon propagation in ice

5.2.1

Modeling hole ice

To achieve the precise hole ice property measurement that can extract
the bubble column diameter D and the eﬀective scattering length of the
bubble column λe , the hole ice model includes the bubble column and theclear outer region, as observed by the Swedish camera. A simple situationis considered in this study.
• The drill hole is a perfectly vertical cylinder with a diameter of 60 cm.
• The bubble column is also a perfectly vertical cylinder at the centerof the hole.
• Photons undergo Mie scattering only in the bubble column.
• The bulk ice does not scatter photons at all.
• The hole ice outside the bubble column has the same optical property
as the bulk ice; the hole ice does not scatter photons at all and there
is no optical boundary between them.
• The absorption length is the same for all ice as for the bulk ice (Figure 4.2).

5.2.2

Modeling of Mie scattering

The Mie scattering in the bubble column is implemented through theHenyey-Greenstein (HG) scattering function [25], a common approximationand easy to introduce to the Monte Carlo simulation. In the HG approximation, Mie scattering is parameterized by an average scattering angle of⟨cos θ⟩ and a geometrical scattering length λs , the average distance between
scatters. The scattering angle θ follows the normalized density function:()
1
1
1 − ⟨cos θ⟩2−. (5.1)p (cos θ) =2 ⟨cos θ⟩
1 + ⟨cos θ⟩2 − 2 ⟨cos θ⟩ cos θ 1 + ⟨cos θ⟩In this study ⟨cos θ⟩ = 0.95 was chosen since it is comparable to what wasused in the study of bulk ice properties [26]. The sensitivity of the result tothe value of ⟨cos θ⟩ was studied as a part of systematics (see Section 5.5.4).
Mie scattering exhibits strongly forward peaked anisotropic scatters, which

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

34

means the eﬀective scattering length λe is much greater than the geometricalscattering length λs . In general, the average cosine of the direction after the
ith scattering ⟨cos θ⟩i can be expressed as a power of scattering times:⟨cos θ⟩i = ⟨cos θ⟩i .

(5.2)

As 0 < ⟨cos θ⟩ < 1, the average transport distance of photons experiencing
the Mie scattering n times is approximately obtained by
λe = λsn∑⟨cos θ⟩i .

(5.3)

i=0

Therefore, by taking the limit as n → ∞, the eﬀective scattering length isdeﬁned as
λe = λs / (1 − ⟨cos θ⟩) .

(5.4)

The scattering in the bubble column is now parameterized by only one variable, λe .

5.2.3

Toy simulation

To verify the conﬁguration described above, simple simulations of photon propagation in the ice were performed using GEANT4. Figure 5.1–5.4
show the photon propagation and the position of photons after propagating
upwards and downwards, for diﬀerent scenarios. These scenarios include
variations in the scattering length λe , bubble column size D and position ofa light source. In Figure 5.1, λe = 30 cm, D = 45 cm, and the light source isinside the bubble column.
Figure 5.2 considers a longer scattering length than Figure 5.1. Comparing Figure 5.2(b) with Figure 5.1(b), the longer the scattering length,
the fewer photons reach the upper plane. On the contrary, a comparison of
Figure 5.2(c) with Figure 5.1(c) shows that the longer the scattering length,
the more photons reach the lower plane. This is because photons must be
scattered to reach the upper plane, while less scattered photons arrive on
the lower plane. A long scattering length makes photons less scattered on
average, and it results in fewer photons going upward and more photons
going downward.
Figure 5.3 illustrates the results for a thicker bubble column than used in
Figure 5.1. Comparing Figure 5.3(b) with Figure 5.1(b), and Figure 5.3(c)with Figure 5.1(c), the thicker the bubble column, the more photons reachboth the upper and the lower planes. In this case the thick bubble column

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

35

provides a ﬁeld where photons undergo scattering, trapping the photons
inside. If a photon escapes, the inﬁnitely long scattering length in the outside
ice ensures no photons re-enter in this model.
In Figure 5.4, the light source is located outside the bubble column, unlike Figure 5.1. Comparing Figure 5.4(b) with Figure 5.1(b), fewer photons
reach the upper plane when the light source is outside the bubble column
than inside, because photons have a low chance to enter the bubble column and then undergo scattering. Photons that are not scattered directly
go downward, which makes the area dense with photons as seen in Figure 5.4(c).

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

36

(b)

(a)

(c)

Figure 5.1: Photon propagation with λe = 30 cm, D = 45 cm, and the light source
inside the bubble column. a) Depiction of the simulation: gray column at the center
represents bubble column and green lines show tracks of 100 photons emitted fromthe light source on the upper right in a 120◦ downward viewing angle. b, c) Greendots show the hit position of photons on the horizontal plane at 180.5 mm above
the light source (b) and at 2433 mm below (c), when 106 photons are emitted ata wavelength of 405 nm. The positions of the upper and lower planes correspondto the upper PMT of the D-Egg which has an LED at the position of the lightsource and the upper PMT of the D-Egg 2.7 m below the D-Egg. The yellow star
represents the position of the light source, and the black dashed circle represents
the bubble column edge.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

(b)

(a)

(c)

Figure 5.2: Same as Figure 5.1, but with λe = 100 cm.

37

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

(b)

(a)

(c)

Figure 5.3: Same as Figure 5.1, but with D = 100 cm.

38

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

39

(b)

(a)

(c)

Figure 5.4: Same as Figure 5.1, but with the light source outside the bubble
column.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

5.2.4

Photon detection with D-Egg

5.2.4.1

Simulation framework

40

DOMINANT has been expanded so that the performance of hole ice
measurements with D-Eggs can be evaluated. As in Section 5.2.3, in thelarge volume of bulk ice, the 60 cm diameter hole ice including the bubble
column with a diameter of D is generated, as modeled in Section 5.2.1. Two
D-Egg modules are simulated perfectly aligned in the 60 cm diameter hole
ice with a vertical spacing of 2.7 m. The relative position of the D-Eggs
to the center axis of the bubble column is characterized by the distance r
from the bubble column center to the center of the D-Egg module and therotation around the bubble column center ϕ (Figure 5.5(b)).
When the downward-pointing LED ﬂashes, two diﬀerent PMTs detect
the photons. Both the upward-facing PMT in the lower D-Egg (forward
PMT) and the upward-facing PMT in the D-Egg from which the photons
originate (backward PMT) can receive these photons (Figure 5.5(a)). But
the way in which the photons arrive to the PMTs are very diﬀerent. Thisdepends primarily on the scattering processes the photons undergo as seenin Section 5.2.3.
However, inaccuracy in calibration of the absolute LED intensity would
lead to a large uncertainty in the measurements of amount of light. To
minimize the eﬀect of the variation in absolute LED intensity, the ratio of
the amount of light detected at the forward PMT and the backward PMT istreated as an observable in this study. Although taking the ratio reduces theinformation from the measurement, the ratio is still sensitive to the hole ice
properties, as the hole ice property dependence of the amount of detected
light are diﬀerent for these two PMTs.
Multiple diﬀerent setups were simulated with regards to the bubble column eﬀective scattering length, the size of the bubble column, and the position of the D-Egg modules. This was done to investigate the eﬀects of λs ,D, r and ϕ over a large range of values.
5.2.4.2

Light source

Each of the D-Egg ﬂasher LEDs is capable of producing a pulse with awidth less than about 8 ns including 1 × 106 to 1 × 109 photons/ﬂash, with apeak wavelength at 400–410 nm. The LEDs have an 15◦ viewing angle witha dip at the center of the angular proﬁle as shown in Figure 5.6.
In this simulation, the downward-pointing LED produces 2×107 photons
and no timing information is used. The LED is modeled as a dimensionless

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

41

(a)

(b)

Figure 5.5: a) Illustration of the simulation: two D-Egg modules are located(partially) inside the bubble column. Photons from the LED originating fromthe upper D-Egg module are Mie scattered in the bubble column. b) Position
parameters r and ϕ. The stars represent the four downward-facing LEDs, LED1–4.
ϕ = 0 when LED1 is the furthest from the center.

light source at a wavelength of 405 nm. The initial directions of photons(θ, ϕ) are sampled from two uniform distributions; uniform in θ from 0◦ to
30◦ and in ϕ from 0◦ to 360◦ . The photons are weighted in order to mimic
the target angular proﬁle afterward. The conﬁguration in Figure 5.6 is usedas the default proﬁle in this study.
5.2.4.3

Detection eﬃciency

The photons emitted from the LED experience absorption in the gel,glass, and ice, as well as reﬂection and refraction at the boundary between
diﬀerent materials (see Section 4.2). Importantly, the photons also undergoscattering in the bubble column as modeled in Section 5.2.2. In the simulation, when the photons hit the photocathode of either the forward or
backward PMT, their initial direction θ and the hit positions on the photocathode r are recorded. After the simulation, the hit photons are weighted
to mimic the angular proﬁle of the LED (see Section 5.2.4.2). The weight isCHAPTER 5. SENSITIVITY TO THE HOLE ICE

42

0.10

PDF

0.08
0.06
0.04
0.02
0.000

5

10
15
20
Angle [deg]25

30

Figure 5.6: Angular proﬁle of LED XRL-400-5O measured by Jack Nuckles [27].
Although the measurement was performed for both sides (angle 0◦ to 30◦ and 0◦ to−30◦ ), their average is shown since the intensity is considered to be uniform overazimuth.

calculated using the photon’s initial direction θ (0◦ ≤ θ ≤ 30◦ ):w(θ) = pLED (θ)/psim (θ) ,(5.5)

where pLED is a probability density function (PDF) of the angular proﬁle ofthe XRL-400-5O, and psim is a PDF of θ in the simulation, thus psim (θ) =1−1
30 [deg] .
In addition, the hit photons are weighted to be converted into photoelectrons (PEs) by including the PMT response. The weight for a photon
which arrives at the position on the PMT cathode r is given as
w(r) = QE × CE(r) .

(5.6)

The PMT SQ0262 is assumed in this study since it has a typical performance
among the PMTs measured in the laboratory, which has 36.725% QE at awavelength of 405 nm and CE averaged over azimuth shown in Figure 5.7.
The NPE detected by the forward PMT and the backward PMT is thencalculated by summing the weighted photons, to eventually extract the hole
ice parameters.
5.2.4.4

Results – Hole ice parameter dependence of NPE

From the simulation the expected NPE has been calculated over a large
range of the eﬀective scattering length in the bubble column λs , bubble

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

1.05

90°

0.90

45°

10 20

50
30 40

0.75

60
0°

Relative sensitivity

135°

180°

43

0.60
0.45
0.30

225°

315°
270°

0.15
0.00

Figure 5.7: Measured detection uniformity of PMT SQ0262 averaged over azimuth, normalized to the center. In this study the relative sensitivity is assumed
to be equal to the uniformity (see Section 3.2.3).

column diameter D, and the position of the D-Eggs r, ϕ, for both the forward
and backward PMTs nF and nB , respectively(see Figure 5.5(b)).
Figure 5.8 shows the NPE dependence on λe and D, where the D-Eggs
are at the center of the bubble column (r = 0). Figure 5.8(a) indicates thatthe bubble column diameter dependence of nF changes after D exceeds approximately 20 cm. In cases when the bubble column is smaller than around
20 cm, the smaller bubble column detects more PEs, as the majority of photons hit the PMT directly, avoiding the bubble column entirely. However if
D ≳ 20 cm, the bubble column covers the LED, trapping the photons, resulting in increased detection for thick bubble columns. Figure 5.8(b) shows
the backward PMT detects more PEs when the scattering length becomesshorter as well as when the bubble column becomes larger. This is independent of whether the LED is inside or outside the bubble column, because
the backward PMT observes photons which have undergone scattering in
the bubble column.
Figure 5.9 describes the NPE dependence on the position r and ϕ where
the bubble column is 20 cm in diameter and LED1, which is located in
the direction of ϕ = 0◦ (see Figure 5.5(b)), ﬂashes. In the case of theCHAPTER 5. SENSITIVITY TO THE HOLE ICE

3.0
1.5

102

0.0
1.5
101
10

20 30 40 50 60
Bubble column diameter [cm]

3.0
4.5

6.0
4.5
3.0
1.5

102

log10(NPE)

6.0
4.5

Effective scattering length [cm](b) NPE at the backward PMT

log10(NPE)

Effective scattering length [cm](a) NPE at the forward PMT

44

0.0
1.5
101
10

20 30 40 50 60
Bubble column diameter [cm]

3.0
4.5

Figure 5.8: λe and D dependence of NPE out of 2 × 107 photons incidence whenr = 0.

forward PMT, the NPE increases as the LED moves further from the bubble
column, because of reduced photon scattering. Conversely, the backward
PMT detects more PEs as the LED approaches the bubble column, because
the bubble column acts as a light-guide to the PMT.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE(a) NPE at the forward PMT(b) NPE at the backward PMT

225°

90°

135°

log10(NPE)

180° A

6.0
45°
4.5
r
B
10 15
cm cm 3.0
5 cm
1.5
0°
0.0
1.5
3.0
315°
4.5
270°

180° A
225°

Geometry configuration at A
30
20
10
0
10
20
3030 20 10 0 10 20 30
x [cm]

φy [cm]y [cm]

φ

6.0
45°
4.5
r
B
10 15
cm cm 3.0
5 cm
1.5
0°
0.0
1.5
3.0
315°
4.5
270°

log10(NPE)

90°

135°

45

Geometry configuration at B
30
20
10
0
10
20
3030 20 10 0 10 20 30
x [cm]

Figure 5.9: Top: r and ϕ dependence of NPE out of 2 × 107 photons incidence
when λe = 30 cm, D = 20 cm and LED1, which is represented as the blue star,ﬂashes. Bottom: geometry conﬁguration of the bubble column and the D-Egg’s
four LEDs when the center of the D-Eggs is at A and B marked in the top ﬁgures.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

5.3

46

Systematic uncertainties

The eﬀect of the detector response, the position of the D-Eggs in thehole, the brightness of the LEDs, the angular proﬁle of the LEDs, lightobstruction from the main cable and the choice of ⟨cos θ⟩ are consideredin this study. The detector uncertainties are included in both the pseudo
experiments and the test data, meaning they have been taken into accountthrough the entire analysis. The uncertainty in the position of the D-Eggs
in the hole is included by introducing the nuisance parameters r and ϕ (seeSection 5.2.4.1), considered in Section 5.5.3 and beyond. The impact of theother uncertainties are quantiﬁed independently using test data generated
from each extreme scenario in Section 5.5.4.

5.3.1

Detector response

PMT saturation can be dealt with by lowering the gain of the PMTs.
Alternatively, the NPE for the target incident photons can be obtained byﬂashing the LED with dimmer brightness more times. These ways are left,
but this study conservatively assumes that the PMTs do not readout morethan 300 PEs, which is almost in the range where the PMT response is linear
at the normal gain 107 (see Figure 3.9(c)).
A Gaussian distribution with a standard deviation of 20% is applied tothe other overall detector uncertainties such as the detection uniformity andthe charge resolution of the PMTs.

5.3.2

Alignment of the D-Eggs

As shown in Section 5.2.4.4, the NPE largely depends on the positionof the LEDs, relative to the hole central axis, although the exact position
is not the parameter of interest in the hole ice calibration. Therefore theposition parameters r, ϕ are included as nuisance parameters in this study.
That said, the orientation of the D-Eggs can also cause a large modiﬁcation to the NPE. This systematic uncertainty will be solved by the
inclinometer mounted to the D-Egg module, providing extra information
regarding the alignment of the D-Eggs. However this uncertainty is notconsidered in this study. This systematic uncertainty is considered as anaddition to the situation.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

5.3.3

47

Flasher LED proﬁles

Brightness Recent studies on the D-Egg’s ﬂasher system indicate thatthe brightness is consistent with a standard deviation of 4% and a mean
drift of less than 1% [28]. However, the mean brightness of each LED isdiﬃcult to be calibrated accurately and has a variation of approximately
30%. The eﬀect of the variance in LED by LED brightness is included bygenerating test data from the LEDs with a brightness of 70% or 130% of theassumption with a nominal brightness of 1 × 107 photons/ﬂash.
Angular proﬁle Each LED has a unique angular proﬁle as seen in Figure 5.10. Although as many LEDs as possible will be measured, knowing

Normalized intensity

0.05

Jack's
a
b
c

0.04
0.03
0.02
0.01
0.003020

10 0
10Angle [deg]20

30

Figure 5.10: The default angular proﬁle “Jack’s”, and the angular proﬁle of otherthree LEDs, “a”, “b” and “c”, measured in Chiba. Although the measurement was
performed for both sides (angle 0◦ to 30◦ and 0◦ to −30◦ ), their average is shownsince the intensity is considered to be uniform over azimuth.

the true angular proﬁle of all of the LEDs is too time consuming.
In order to estimate the systematic error due to diﬀerences between thetrue angular proﬁle and an assumed one, the three angular proﬁles “a”, “b”,
“c” are tested assuming “Jack’s” is true.

5.3.4

Cable shadow

The D-Eggs will be deployed in the holes tied to a thick cable. If thecable is in the same direction ϕ as one of the four LEDs, the LED may not
be usable since light from the LED will be blocked by the cable. This eﬀect
is referred to as cable shadow. However, as mentioned in Section 3.1, theCHAPTER 5. SENSITIVITY TO THE HOLE ICE

48

D-Egg module also includes three cameras looking horizontally (Figure 5.11)
for calibration purposes [29]. It is expected that the cameras will be able
to determine the location of the cable. Thus, the cable shadow is included

Figure 5.11: Cameras in a D-Egg.

by creating test data sets where only three of the four LEDs are usable,
assuming the LED blocked by the cable is known from analyzing data fromthe cameras.

5.3.5⟨cos θ⟩As discussed in Section 5.2.2, the eﬀective scattering length is a mix ofthe geometrical scattering length λs and the average cosine of the scattering
angle ⟨cos θ⟩. In this study ⟨cos θ⟩ = 0.95 is used as default, however thetrue number is not known. The cases where the true ⟨cos θ⟩ is diﬀerent fromthe assumption are taken into account by generating test data with various
combinations of λs and ⟨cos θ⟩, but resulting in the same λe .

5.4Extraction of hole ice parameters

5.4.1

Analysis method

5.4.1.1

Likelihood construction

From the simulation, the NPE detected for both the forward and backward PMTs has been calculated over a large range of λs , D, r and ϕ.
A likelihood ﬁt test was performed in order to understand how precisely
the hole ice parameters can be estimated. To construct the PDF of R =nF /nB , the following assumptions are used:CHAPTER 5. SENSITIVITY TO THE HOLE ICE

49• NPE follows a Poisson distribution with the mean NPE determinedfrom simulations as a function of the LED intensity.
• The statistical uncertainty in the simulation is included by modifying the Poisson distribution using the weights w for each photon (seeEq. (5.5) and Eq. (5.6)). The probability of k photoelectrons being
detected for a given set of parameters Θ is written as:
( 2
)[ (
)]−1
µ2
( µ ) µ22 +1 (µ2µµ )k+ σ2 +1
σPeﬀ (k|Θ) =Γ k + 2 + 1 k! 1 + 2
Γ+1,(5.7)σ2σσσ2where µ = nF(B) =

F(B)
∑Nhit

wi F(B) is the number of photoelectrons
F(B)
∑Nhit
2
calculated from the simulation, and σ 2 = i=1
wi F(B) . µ and σ 2depend on Θ through w. Eq. (5.7) is adopted from [30].
i=1• The detector response represented by the charge resolution is characterized by a Gaussian distribution with a standard deviation of 20%.
Figure 5.12 shows a NPE distribution at each step. The Poisson distribution
is widened by Eq. (5.7) and the Gaussian distribution.

0.030

Poisson
Eff. Poisson
Eff. Poisson + Gaussian

0.025

PDF

0.020
0.015
0.010
0.005
0.0000

100

200

300
NPE

400

500

600

Figure 5.12: Example of a PDF of NPE. NPE sampled from a normal Poisson
distribution is shown as the blue histogram. The orange histogram shows theNPE distribution sampled from a modiﬁed Poisson distribution (Eq. (5.7)), andthe NPE is re-sampled from a Gaussian distribution with a standard deviation of
20% centered at the NPE, making the green histogram.

To perform a likelihood ﬁt, the likelihood L for test data x and a given
set of ﬂoating parameters Θ is constructed as:
L (x|Θ) =

4 N
evt
∏
∏
l=1 i=1( )pΘ l xi l ,(5.8)

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

50

where l is the LED number, i is the event number, and Nevt (= 100) is thenumber of events. xi l = log10 Ri l from the test data. Θ is a vector composedof the four hole ice parameters. pΘ l is the PDF of log10 RΘ l .
5.4.1.2

Test statistic

The log likelihood ratio is used as the test statistic:
L(Θ̂)
,
L (Θ)

(5.9)

Θ̂ = argmax L(Θ) .

(5.10)T S(Θ) = ln
whereΘWhen r, ϕ of Θ = (λe , D, r, ϕ) are treated as nuisance parameters,
T S(λe , D) = ln

L(Θ̂)

,

(5.11)(r̂, ϕ̂) = argmax L(λe , D, r, ϕ) .

(5.12)L(λe , D, r̂, ϕ̂)

where

(r,ϕ)

The test statistic distribution for each parameter Θ is generated by
performing a pseudo experiment 104 times (Figure 5.13).
The p-value for a test statistic T S(x|Θ) calculated for observed data x
is calculated as:
pvalue (Θ) = P(T S(Θ) > T S(x|Θ)) ,(5.13)and pvalue = 0.3173, 0.0455, 0.0027 correspond to the conﬁdence level (CL)of 1σ, 2σ, 3σ, respectively.
In the case where r and ϕ of Θ = (λe , D, r, ϕ) are treated as nuisanceparameters, the test statistic distribution for a (λe , D) depends on the true
value of (r, ϕ). At a (λe , D), the p-value is calculated for every (r, ϕ), andthe maximum is chosen as the p-value at the (λe , D) bin:()
pvalue (λe , D) = max P T S(λe , D, r, ϕ) > T S(x|(λe , D)) .
(5.14)(r,ϕ)

5.4.1.3

Test data

Test data are generated based on the assumptions described in Section 5.4.1.1 (Figure 5.14).

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

51

101
100

PDF

10-1
10-2
10-3
10-4 0

2

4

6

8

10

12

TS =ln(L̂/L)

Figure 5.13: Example of the test statistic distribution, when λe = 30 cm, D =20 cm, r = 10 cm, ϕ = 45◦ , and r and ϕ are treated as nuisance parameters. The
distribution depends on the parameters Θ, but most of the distributions have a
sharp peak at zero, followed by a gradual decrease.

Test data ( e30 cm, D20 cm, r10 cm, 30 deg)

PDF ( e30 cm, D20 cm, r10 cm, 30 deg)

PDF ( e50 cm, D20 cm, r10 cm, 30 deg)

2
02

1

0

1

0

1

0

1

0

log10R

1

2

3

1

2

3

1

2

3

1

2

3

PDF

2
02

log10R2
02

log10R2
02

log10R

Figure 5.14: Example of the PDF of R for ﬂashing LED1, 2, 3 and 4 from top
to bottom when λe = 30 cm, D = 20 cm, r = 10 cm, ϕ = 30◦ are shown with test
data of 100 events for this MC truth shown in blue, and the PDF of R for anotherparameter (λe = 50 cm, D = 20 cm, r = 10 cm, ϕ = 30◦ ) in orange.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

5.5

Results

5.5.1

Case study – Three scenarios

52

In this section, the results of likelihood ﬁt tests three true geometricalscenarios (Figure 5.15) are shown:
Scenario A (λe = 30 cm, D = 20 cm, r = 0)
Scenario B (λe = 30 cm, D = 20 cm, r = 10 cm, ϕ = 30◦ )Scenario C (λe = 30 cm, D = 50 cm, r = 10 cm, ϕ = 30◦ )Comparison of Scenario A with Scenario B can reveal diﬀerences between
cases where the position of D-Eggs is symmetric and asymmetric to the
bubble column. D = 20 cm was chosen because it is comparable to what
has been observed by the Swedish camera. However, it is hard to imagine
that D-Eggs will be placed just at the center of the bubble column, which
is why Scenario C was also chosen to be asymmetric. In Scenario C a large
bubble column was chosen because it is similar to the current hole ice model
used in IceCube, which considers that the optical properties are uniform in
the entire hole ice. In the current hole ice model λe = 50 cm is used. λe inthe bubble column should be shorter than in the outer region of the holeice, thus λe = 30 cm is commonly chosen in this study.
(b) Scenario B
D = 20 cm,
r = 10 cm, ϕ = 30◦(c) Scenario C
D = 50 cm,
r = 10 cm, ϕ = 30◦

30

30

20

20

20

10

10

10

0

y [cm]

30y [cm]y [cm](a) Scenario A
D = 20 cm,
r = 0, ϕ = 0◦

0

0

10

10

10

20

20

20

3030

3030

20

10

0
10
x [cm]

20

30

20

10

0
10
x [cm]

20

30

3030

20

10

0
10
x [cm]

20

30

Figure 5.15: True scenarios tested. The gray circle represents the bubble column,
and the dashed circle shows the size of the hole, where D-Eggs can locate inside.
The four stars represent the LEDs on the ﬂasher board shown as a black circle.
Their colors correspond to Figure 5.5(b).

5.5.2

A case when the geometrical information is available

Firstly, a likelihood ﬁt test was performed assuming the true values ofr, ϕ (rtrue , ϕtrue ) are known. This situation could be achieved by some independent measurement utilizing other calibration modules such as cameras

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

53

in the D-Eggs. For simplicity, no other systematic uncertainties except forthe detector response was considered.
Figure 5.16 shows the p-value for each scenario. The true hole ice parameters, the eﬀective scattering length and the bubble column diameter,are always covered by the 1σ conﬁdence region. In Scenario A, the best ﬁt
is found in the same bin as the MC truth, however, the conﬁdence region of
the eﬀective scattering length and the bubble column diameter distributes
as a curved band over a large range of the parameters because the degeneracy of the two parameters cannot be solved due to the symmetry of theposition of the D-Eggs to the bubble column. In Scenario B and C, the hole
ice parameters are found to be within the same bin as the MC truth at 3σ
CL.

5.5.3

A case when no external information is available

Secondly, a likelihood ﬁt test was performed for the case where the position of the D-Eggs in the hole (r, ϕ) is not known. Other conditions arestill the same as Section 5.5.2.
Figure 5.17 shows the p-value for each MC truth value. In all cases, thebest ﬁt values for λe and D are found in the 1σ conﬁdence region. The
conﬁdence region is larger than Figure 5.16 because of the indeﬁniteness ofthe nuisance parameters, (r, ϕ). If the situation will be similar to Scenario B
or Scenario C, the eﬀective scattering length and the bubble column diameterare determined within ±5 cm and ±1 cm, respectively, at 3σ CL even if noexternal information of the position of the D-Eggs is available.

5.5.4

Final result: all systematic uncertainties included

In the case where rtrue and ϕtrue are unknown, likelihood ﬁts were performed for test data generated from diﬀerent assumptions than those assumed in the ﬁts. Figure 5.18–5.21 show the expected largest impact fromthe systematic uncertainties in the brightness of the LEDs, the angular proﬁle of the LEDs, the cable shadow and ⟨cos θ⟩, respectively. The sparse
conﬁdence regions in some of them are due to the coarse binning of theparameters as well as the impact from the multiple tested scenarios. For
example, in Figure 5.20(b), the 3σ conﬁdence region is dominated by thecase where the light from LED3 or LED4 is obstructed by the main cable.
As these LEDs are inside or close to the bubble column in Scenario B, thelack of information from either of them results in the degeneracy between
λe , D and r, ϕ. If rtrue and ϕtrue are given, λe and D can be determinedwithin the MC truth bin.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

54(a) Scenario A

log10(P-value)

4.000
102
e [cm]

2.569
1.342

101

20

40
D [cm]

60

0.499
0.000

(b) Scenario B

log10(P-value)

4.000
102
e [cm]

2.569
1.342

101

20

40
D [cm]

60

0.499
0.000

(c) Scenario C

log10(P-value)

4.000
102
e [cm]

2.569
1.342

101

20

40
D [cm]

60

0.499
0.000

Figure 5.16: Results of likelihood ﬁt tests where rtrue , ϕtrue are known. The
shown − log10 pvalue values between 0.0 and 4.0 correspond to 1σ, 2σ and 3σ frombottom to top. P-value can be shown up to 0.0001 due to the number of pseudo
experiments done for generating the test statistic distributions. The MC truth ismarked with a white circle and the best ﬁt bin with a white star.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE55(a) Scenario A

log10(P-value)

4.000
102
e [cm]

2.569
1.342

101

20

40
D [cm]

60

0.499
0.000

(b) Scenario B

log10(P-value)

4.000
102
e [cm]

2.569
1.342

101

20

40
D [cm]

60

0.499
0.000

(c) Scenario C

log10(P-value)

4.000
102
e [cm]

2.569
1.342

101

20

40
D [cm]

60

0.499
0.000

Figure 5.17: Results of likelihood ﬁt tests where rtrue , ϕtrue are unknown. The
shown − log10 pvalue values between 0.0 and 4.0 correspond to 1σ, 2σ and 3σ frombottom to top. P-value shown is limited to 0.0001 by the number of pseudo experiments , 104 , performed for generating the test statistic distributions. The MC
truth is marked with a white circle and the best ﬁt bin with a white star.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE(b) Scenario B(c) Scenario C

101

20

40
D [cm]

60

102

2.569

1.342

1.342

0.499
0.000

0.499
0.000

101

20

40
D [cm]

60

4.000
log10(P-value)e [cm]

2.569

log10(P-value)

102

4.000

e [cm]

log10(P-value)

4.000

102

2.569

e [cm](a) Scenario A

56

1.342
101

20

40
D [cm]

60

0.499
0.000

Figure 5.18: Largest p-values for test data from LEDs with +30% of −30% ofbrightness. The MC truth is marked with a white circle.
(b) Scenario B(c) Scenario C

102

2.569

1.342
101

20

40
D [cm]

60

4.000
log10(P-value)e [cm]

2.569

log10(P-value)

102

4.000

e [cm]

log10(P-value)

4.000

102

2.569

e [cm](a) Scenario A

1.342

0.499
0.000

101

20

40
D [cm]

60

1.342

0.499
0.000

101

20

40
D [cm]

60

0.499
0.000

Figure 5.19: Largest p-values for test data from LEDs with a diﬀerent angular
proﬁle. The MC truth is marked with a white circle.
(b) Scenario B(c) Scenario C

102

2.569

1.342
101

20

40
D [cm]

60

4.000
log10(P-value)e [cm]

2.569

log10(P-value)

102

4.000

e [cm]

log10(P-value)

4.000

102

2.569

e [cm](a) Scenario A

1.342

0.499
0.000

101

20

40
D [cm]

60

1.342

0.499
0.000

101

20

40
D [cm]

60

0.499
0.000

Figure 5.20: Largest p-values for test data from three LEDs out of four. The MC
truth is marked with a white circle.
(b) Scenario B(c) Scenario C

101

20

40
D [cm]

60

102

2.569

1.342

1.342

0.499
0.000

0.499
0.000

101

20

40
D [cm]

60

4.000
log10(P-value)e [cm]

2.569

log10(P-value)

102

4.000

e [cm]

log10(P-value)

4.000

102

2.569

e [cm](a) Scenario A

1.342
101

20

40
D [cm]

60

0.499
0.000

Figure 5.21: Largest p-values for test data from ⟨cos θ⟩ from 0.7 to 0.9. The MC
truth is marked with a white circle.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

57

Figure 5.22 shows the ﬁnal result including the all systematic uncertainties shown above. The conﬁdence interval is calculated as a square root ofsum of squares of the changes in the conﬁdence intervals when each systematic uncertainty is ﬁxed to the extreme value in turn with the others
predictable from when no systematic uncertainty exists, as they are considered to be independent.
Figure 5.22(a) depicts Scenario A where the D-Eggs are aligned at thecenter of the hole. In this case the small bubble column with a short scattering length and the large bubble column with a long scattering length are
diﬃcult to be distinguished due to the geometrical symmetry. However, theregion where λe < 75 cm and 22 cm < D < 60 cm is excluded at 3σ CL.
In Scenario B, Figure 5.22(b) shows that the hole ice parameters are
estimated to be within λe < 200 cm and D < 46 cm at 3σ CL. The large
conﬁdence region is due to the systematic uncertainties in the position of
the D-Eggs and the cable shadow.
In Scenario C, Figure 5.22(c) describes the eﬀective scattering lengthis determined to be λe < 50 cm and the bubble column diameter 31 cm <D < 60 cm at 3σ CL. The cable shadowing the LED3 contributes to the
conﬁdence region around (λe = 10 cm, D = 32 cm). The conﬁdence region
primarily shows a band extending over a range of 15 cm < λe < 50cm and31 cm < D < 60 cm.

5.5.5

Discussion

The D-Egg’s ﬂashers have the potential to characterize the hole ice more
precisely than in current IceCube, though the accuracy depends on the actual hole ice properties. If the D-Eggs are aligned at the center of the
bubble column, the position of the D-Eggs is correctly determined to be at
the center, but a small bubble column with a short scattering length and alarge bubble column with a long scattering length are not distinguishable.
However, the bubble column boundary is expected to be determined by thecameras installed in the D-Eggs. If it succeeds, the range of possible eﬀective
scattering lengths will be restricted, breaking this degeneracy.
Given the case where at least one of the four LEDs are inside the bubble
column, the D-Egg’s ﬂashers can distinguish the small bubble column witha short scattering length and the large bubble column with a long scattering
length. The more LEDs located inside the bubble column, the more precisely
the eﬀective scattering length can be estimated.
In any case, external information on the bubble column diameter canplace another restriction on the range of possible eﬀective scattering lengths.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

58

3

e [cm]

102

2
1
101

20

40
D [cm]

log10(P-value)(a) Scenario A

60

3

e [cm]

102

2
1
101

20

40
D [cm]

log10(P-value)(b) Scenario B

60

3e [cm]

102

2
1
101

20

40
D [cm]

log10(P-value)(c) Scenario C

60

Figure 5.22: Results of likelihood ﬁt tests where rtrue , ϕtrue are unknown and thesystematic uncertainties are included. The MC truth is marked with a white circle.

CHAPTER 5. SENSITIVITY TO THE HOLE ICE

59

For example, in Scenario C, where the scattering length is only limited toa range shorter than 50 cm without any information on the bubble column
diameter, the eﬀective scattering length is limited to 20–40 cm if the cameras
can determine the bubble column diameter within ±10%.
Determining the hole ice parameters will be diﬃcult if the bubble column
is small and three or four LEDs are located outside the bubble column. In
this case, other external light sources are necessary, such as mDOM’s ﬂasher
LEDs and the POCAM [18] [31].
Furthermore, the POCAM has LEDs with diﬀerent wavelengths from 370
to 500 nm, which are useful for investigating the wavelength dependence ofthe Mie scattering in the bubble column. By performing the measurementwith D-Egg’s ﬂasher LEDs at all depths, the depth dependence of the opticalproperties of the hole ice will be able to be determined. Both wavelengthand depth dependence of the optical properties of the hole ice will further
improve neutrino reconstruction.

5.6

Conclusion

The D-Egg’s ﬂashers have the potential to characterize the hole ice more
precisely than in current IceCube, though the accuracy depends on the actual hole ice properties. If some of the LEDs are inside the bubble column,
the D-Egg’s ﬂashers can distinguish the small bubble column with a shortscattering length and the large bubble column with a long scattering length.
Precision can be further increased if more of the ﬂasher LEDs are locatedinside the bubble column.

CHAPTER 6. CONCLUSION

60

Chapter 6

Conclusion
The D-Egg will make use of the four downward-facing ﬂasher LEDs tocalibrate current IceCube models based on hole ice data collected in the
IceCube Upgrade. In this analysis the hole ice was parameterized by the effective scattering length λe and the bubble column diameter D. The precise
photon simulation and a maximum likelihood ﬁt for three scenarios were
performed to estimate how precisely the D-Egg’s hole ice calibration system
would determine the hole ice parameters.
The D-Egg’s ﬂashers have the potential to determine the hole ice parameters, but the accuracy depends on the actual hole ice properties. In
Scenario A, where the D-Eggs are at the center of the hole, the small bubble column with a short scattering length and the large bubble column witha long scattering length are diﬃcult to distinguish due to the geometricalsymmetry. However, the region where λe < 75 cm and 22 cm < D < 60 cm
is excluded at 3σ CL. In other cases, the D-Egg’s ﬂashers can estimate thehole ice parameters, within λe < 200 cm and D < 46 cm in Scenario B, andλe < 50 cm and 31 cm < D < 60 cm in Scenario C at 3σ CL.

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