Supernova Model Discrimination
with Hyper-Kamiokande
Jost Migenda

University of Sheﬃeld
Department of Physics & Astronomy

A thesis submitted in partial fulfilment of the requirements for the degree ofDoctor of Philosophy

November 2019

However big you think supernovae are, they’re bigger than that.
— Donald Spector [1]Supervisors: Dr. Susan L. CartwrightDr. Matthew S. MalekDeclaration
I, the author, confirm that the Thesis is my own work. I am aware of the University’s
Guidance on the Use of Unfair Means1 . This work has not been previously beenpresented for an award at this, or any other, university.

∗∗∗
Due to the nature of a large experiment like Hyper-Kamiokande, this research isbuilt on the contributions of hundreds of scientists. In the following, I will describe
the extent of my personal contributions.
Chapter 1 provides an overview over previous research on supernovae and neutrinos, summarising the work of many generations of scientists. The detector design
described in chapter 2 is the result of the combined work of the whole HyperKamiokande proto-collaboration. Both chapters do not constitute original researchof this thesis.
Chapter 3 describes a software toolchain for generating, simulating and reconstructing supernova neutrino interactions in Hyper-Kamiokande. While I havecontributed to all parts of this toolchain, my main contributions are the event generator sntools and the energy reconstruction. Both were largely developed by me,with some contributions by Liz Kneale and Owen Stone as part of undergraduate
research projects under my co-supervision.
The data analysis performed in chapter 4 constitutes original research performed
solely by me.
Finally, chapter 5 summarizes the results of this work and gives an outlook on
future research.

1 https://www.sheffield.ac.uk/ssid/unfair-meansiii

If I have seen further it is by standing on
the shoulders of giants.
Isaac Newton

Acknowledgements
First and foremost, I would like to thank my supervisors, Susan Cartwright andMatthew Malek.
The story of this PhD started in the spring of 2015, when I discovered the thesis
topic “Supernova Neutrinos in TITUS and Hyper-K” being advertised on the University of Sheffield’s website. The official application deadline had already passed, butsince the topic matched my interests so perfectly, I wrote an email to Susan anyway.
Without hesitation, she invited me to start a PhD in Sheffield. In the following years,
missing that application deadline has led to an unusual funding situation. However,Susan always went above and beyond to find the resources to allow me to attend
numerous conferences, workshops, collaboration meetings and summer schools
across three continents. Time and again, her incredibly sharp mind and attention
to detail have also helped me with issues ranging from physics to data analysis toproofreading this thesis.
Matthew is that legendary supervisor any PhD student can barely dare dreamof—a brilliant physicist and an equally wonderful human being, all in one person.
He has been my North Star during this research, always being available to provide
guidance and direction while, at the same time, giving me the freedom to find myown way. His intimate knowledge of the science involved in this research andfamiliarity with the scientists working on it have been invaluable resources for me.
At the same time, Matthew has fostered my outreach efforts, hobbled next to me on
the Big Walk, called me a gentleman2 , invited me to a late-night cup of tea in theAustin Room and has always been available when I wanted to chat about importantor not-so-important topics. His encouragement has been genuine and his criticism
fair and constructive (and more accurate than I wanted to admit at the time).
During the past four years, Marcus O’Flaherty has been almost like a brotherto me. He helped me find my feet when I first arrived, shared in the joys andtribulations of being a PhD student, accompanied me to my first conference andsummer school and, during my stay at Fermilab in August 2017, even let me stay in
his living room for over two weeks.
If Marcus is like an older brother, Liz Kneale is probably most akin to a younger
sister. When we first met in 2016, I was equal parts nervous and honoured toco-supervise her project work contributing to an early version of sntools. In the
2 and apologized afterwardsv

years since, I have seen her grow into an experienced neutrino physicist and spent
many lunch breaks with her discussing physics and life in general, which has been
incredibly enjoyable.
Completing the list of my academic siblings is Owen Stone. I started cosupervising him during a summer project in 2017 and was happy to see him return
to work with Matthew and me for several other projects since. I’m really excitedthat he has now started a PhD in our group and can’t wait to learn what he will
discover!
While I cannot list them all by name here, there are so many other members of
the neutrino group, the HEP group and the whole department who have created awonderful atmosphere that has truly allowed me to feel comfortable and do fantastic
work here. I’m also grateful to the staff in F10 (and elsewhere) without whom thegroup and the whole department couldn’t function.
Finally, writing the early parts of this thesis would have been much slower andmore frustrating if it hadn’t been for Connor Heapy’s help as part of the thesis
mentoring programme.

∗∗∗
Beyond Sheffield, I am grateful to the hundreds of members of the HyperKamiokande proto-collaboration around the world, without whom none of thiswork could exist. I particularly want to thank the leaders and fellow members of
the astrophysics and software working groups for many interesting discussions
and frequent feedback; Yano-san for patiently answering countless questions about
low-energy physics and the software tools; Francesca Di Lodovico for giving me
opportunities to contribute more than just my own research to the collaboration; andthe group at Kobe University for their hospitality during my visit in February/March
2017.
Starting in mid-2017, I also spent a few months working as part of the DUNE
collaboration. While this did not produce any tangible results, I am grateful tothe collaboration—particularly Kate Scholberg and the whole SNB/LE group—for
welcoming me with open arms and teaching me so much about LAr TPCs.
For giving me access to the supernova models used in this thesis and patiently
answering all my related questions, I am grateful to MacKenzie Warren, Nakazatosan, Totani-san, Adam Burrows, David Vartanyan and Irene Tamborra.
I would like to thank the organizers and participants of the various conferences,
workshops and summer schools I have had the pleasure to attend.
Georg Raffelt introduced me to supernova neutrinos during my Master’s thesis,
which led me to where I am today—even though neither of us could have seen thiscoming at the start. Thank you, Georg.

∗∗∗

vi

All of this work has been made so much easier by powerful tools that were oftena joy to use: online resources like InspireHEP, arXiv and NASA’s Astrophysics Data
System; software like Python, the MacTeX distribution, Keynote and BBEdit; and,of course, the operating system and trusty laptop on which all this software runs.
Thanks to the people who created all these tools.

∗∗∗
The past four years contained not only the work reflected in this thesis. They also
contained copious amounts of joy and sorrow, infinite jest and depths of despair,love and heartbreak and beauty and wonder and one thousand green-tinted photosof a rapper. One day, all these moments will be lost in time, like tears of a unicorn
lost in the rain. But today is not that day. Today, as I am writing these lines, all these
moments mean the world to me.
Thank you to my family: Angela. Thomas. Jakob. Uwe.
To Alex and to Lisa: We’ve known each other for over a decade now and I loveyou both dearly—in different ways yet equally much.
To Mel, for making me feel at home.
To my “cuddly friends”, both current and former.
To the CdE and all the wonderful people who make its events so special.
To Ashley, Izzy & Jess, Ida, Abbie and Jenna for being incredibly generous withyour time and advice and everything else.
To the whole LGBTSTEM community, particularly Beth and Alfredo and the manyothers who work tirelessly to build something wonderful.
To Héloïse, Catherine, Matt, Katherine, Morri, Burkhard & John and all the many,
many others who brightened up my days with open ears, deep conversations over a
cup of tea, heartfelt messages and—literal or figurative—rainbows.
To everyone who supported my outreach efforts—whether as organizers, as
speakers or simply by attending and getting excited about the universe.
To all those people I only know from afar, yet who make my life and work
beautiful with their writing or podcasts or music or videos.
Finally, to the many giants upon whose shoulders I stand.

vii

Abstract
Supernovae are among the most magnificent events in the observable universe.
They produce many of the chemical elements necessary for life to exist and theirremnants—neutron stars and black holes—are interesting astrophysical objects intheir own right. However, despite millennia of observations and almost a century
of astrophysical study, the explosion mechanism of supernovae is not yet wellunderstood.
Hyper-Kamiokande is a next-generation neutrino detector that will be able to observe the neutrino flux from the next galactic supernova in unprecedented detail. In
this thesis, I investigate how well such an observation would allow us to reconstruct
the explosion mechanism.
I develop a high-precision supernova event generator and use a detailed detector
simulation and event reconstruction to explore Hyper-Kamiokande’s response to
five supernova models simulated by different groups around the world. I showthat 300 neutrino events in Hyper-Kamiokande—corresponding to a supernova at a
distance of at least 60 kpc—are sufficient to distinguish between these models withhigh accuracy.
These findings indicate that, once the next galactic supernova happens, HyperKamiokande will be able to determine details of the supernova explosion mechanism.

ix

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Explosion Mechanism . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Summary of Previous Work . . . . . . . . . . . . . . . . . . . . . . . . .
2 The Hyper-Kamiokande Detector . . . . . . . . . . . . . . . . . . . . . . . .

2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 The Past: Kamiokande . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 The Present: Super-Kamiokande . . . . . . . . . . . . . . . . .
2.1.3 The Future: Hyper-Kamiokande . . . . . . . . . . . . . . . . .
2.2 Detector Design and Construction . . . . . . . . . . . . . . . . . . . . .
2.2.1 Location and Cavern . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Water Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Water Purification and Circulation System . . . . . . . . . . .
2.2.4 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Outer Detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.7 DAQ and Computing . . . . . . . . . . . . . . . . . . . . . . .
2.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Pre-Calibration of Photosensors . . . . . . . . . . . . . . . . .
2.3.2 Light Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Radioactive Sources . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Deployment System . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Radioactive Decays . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Muon-Induced Spallation . . . . . . . . . . . . . . . . . . . . .

1
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xi

Contents
3 A Software Toolchain for Supernova Neutrino Events in Hyper-Kamiokande 75

3.1 Supernova Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Totani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Nakazato . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Couch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Tamborra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.5 Vartanyan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 sntools: A Supernova Event Generator . . . . . . . . . . . . . . . . . . .
3.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Input Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Treatment of Neutrino Flavour Conversion . . . . . . . . . . .
3.2.4 Interaction Channels . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . .
3.4.3 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . .

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4 Supernova Model Discrimination . . . . . . . . . . . . . . . . . . . . . . . . 103

4.1
4.2
4.3
4.4

Generating Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Log-Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Distinguishing Different Models . . . . . . . . . . . . . . . . . . . . . . 108
4.4.1 N=100 Events Per Data Set . . . . . . . . . . . . . . . . . . . . 108
4.4.2 N=300 Events Per Data Set . . . . . . . . . . . . . . . . . . . . 111
4.5 Determining Progenitor Properties . . . . . . . . . . . . . . . . . . . . . 114
4.6 Bayesian Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.2.1 Progress in Supernova Simulations . . . . . . . . . . . . . . . . 122
5.2.2 Complementarity with Other Neutrino Detectors . . . . . . . 123
5.2.3 Beyond Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 126
A Neutrino Interaction Cross Sections . . . . . . . . . . . . . . . . . . . . . . 129

A.1 Inverse Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.2 Neutrino-Electron Scattering . . . . . . . . . . . . . . . . . . . . . . . . 131
B Derivation of Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . 135
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

xii

List of Figures
1.1 Solar neutrinos: The pp chain . . . . . . . . . . . . . . . . . . . . . . .
1.2 Solar neutrinos: The CNO cycle . . . . . . . . . . . . . . . . . . . . . .
1.3 The MSW effect in a simplified two-flavour picture . . . . . . . . . . .
1.4 Cross sections of main interaction channels of supernova neutrinos ina water Cherenkov detector . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Cross sections of main interaction channels of supernova neutrinos ina liquid scintillator detector . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Cross sections of main interaction channels of supernova neutrinos ina LAr TPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Six phases of the delayed explosion mechanism . . . . . . . . . . . . .
1.8 Luminosity and mean energy during three steps of neutrino emission
2.1
2.2
2.3
2.4
2.5
2.6
2.7

Schematic view of Super-Kamiokande . . . . . . . . . . . . . . . . . .
Schematic view of Hyper-Kamiokande . . . . . . . . . . . . . . . . . .
Schematic view of the outer edge of the water tank . . . . . . . . . . .
Water system design for Hyper-Kamiokande . . . . . . . . . . . . . .
Simulation of water replacement efficiency in Hyper-Kamiokande . .
Side view of the B&L PMT . . . . . . . . . . . . . . . . . . . . . . . . .
Quantum efficiency and single photon detection efficiency of B&L
PMT and Super-Kamiokande PMT . . . . . . . . . . . . . . . . . . . .
2.8 Transit time and charge for a single photoelectron in the B&L PMTand Super-Kamiokande PMT . . . . . . . . . . . . . . . . . . . . . . .
2.9 Front and side view of baseline design for protective cover . . . . . .
2.10 Drawing of the two-sided mPMT module . . . . . . . . . . . . . . . .
2.11 Schematic drawing of the wavelength shifting plate . . . . . . . . . .
2.12 Block diagram of the front-end electronics module forHyper-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 Block diagram of the front-end electronics inside an mPMT module .
2.14 Simplified block diagram of the DAQ system for Hyper-Kamiokande
2.15 Distribution of low-energy events in Super-Kamiokande duringphase IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Muon flux as a function of zenith and azimuth angle in Super- andHyper-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xiii

List of Figures
3.1
3.2
3.3
3.4
3.5
3.6
3.7

Overview over the software toolchain for Hyper-Kamiokande . . . . 75
Overview over the structure of sntools . . . . . . . . . . . . . . . . . . 83
Probability density P(tresidual ) used for vertex reconstruction inSuper-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Vertex resolution in Super-Kamiokande . . . . . . . . . . . . . . . . . 95
Distribution of angle between particle direction and the vector fromevent vertex to PMT location as a function of energy . . . . . . . . . . 97
Angular dependence of photocoverage correction inSuper-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Relation between Neff and reconstructed energy . . . . . . . . . . . . 101

4.1 Energy spectra for different interaction channels in Hyper-Kamiokande107
4.2 Distribution of ∆L for data sets generated from the Couch andNakazato models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 Distribution of ∆L for all pairs of supernova models: 100 events perdata set and normal mass ordering, comparison of 20 % and 40 %photocoverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4 Distribution of ∆L for all pairs of supernova models: 100 events perdata set and inverted mass ordering . . . . . . . . . . . . . . . . . . . 112
4.5 Distribution of ∆L for all pairs of supernova models: 300 events perdata set and normal mass ordering . . . . . . . . . . . . . . . . . . . . 113
4.6 Distribution of ∆L for all pairs of supernova models: 300 events perdata set and inverted mass ordering . . . . . . . . . . . . . . . . . . . 115
4.7 Luminosity and mean energy of νe , ν̄e and νx for progenitors withdifferent initial masses and luminosities . . . . . . . . . . . . . . . . . 116
4.8 Distribution of ∆L for all pairs of progenitors: 300 events per data set
and normal mass ordering . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.9 Distribution of ∆L for all pairs of progenitors: 300 events per data set
and inverted mass ordering . . . . . . . . . . . . . . . . . . . . . . . . 118

xiv

List of Tables
1.1 Overview of spectral types, their main properties and thecorresponding explosion mechanisms . . . . . . . . . . . . . . . . . . .

20

2.1 Comparison of Kamiokande, Super-Kamiokande andHyper-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Upper limits on radioactivity for photosensors in theHyper-Kamiokande inner detector . . . . . . . . . . . . . . . . . . . . .

70

3.1 Excitation energies and fitting parameters for charged-current
interactions on 16 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

39

4.1 Event numbers and corresponding distances for the supernova
models considered in this work . . . . . . . . . . . . . . . . . . . . . . . 104
4.2 Accuracy of model identification: 100 events per data set and normal
mass ordering, comparison of 20 % and 40 % photocoverage . . . . . . 110
4.3 Accuracy of model identification: 100 events per data set and inverted
mass ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.4 Accuracy of model identification: 300 events per data set and normal
mass ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.5 Accuracy of model identification: 300 events per data set and inverted
mass ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6 Accuracy of progenitor identification: 300 events per data set andnormal mass ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.7 Accuracy of progenitor identification: 300 events per data set andinverted mass ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.8 Interpretation of Bayes factor when comparing two models A and B . 119

xv

Remember when you were young
You shone like the sun
Shine on you crazy diamond
Now there’s a look in your eyes
Like black holes in the sky
Shine on you crazy diamond
Pink Floyd

Chapter 1
Introduction
A long time ago1 , in a galaxy far away2 the blue supergiant Sanduleak −69°202 [2]exploded, sending out ∼1058 neutrinos. This was a common occurrence throughout
the universe and would normally be unremarkable. This time, however, about twodozen of the resulting neutrinos were observed by humans—and that has made all
the difference.3
Supernovae, like SN1987A described above, are among the most energetic eventsin the universe—for a period of several days, a single star exploding in a supernova
shines as bright as a galaxy consisting of billions of stars. In a process calledsupernova nucleosynthesis, this explosion creates many of the chemical elementsthat are necessary for life as we know it to exist. It then expels them in an outgoingshock wave that produces instabilities in the surrounding interstellar gas and canincrease the local star formation rate, while also increasing the metallicity of that gas,
which affects the evolution of those newly-forming stars. The supernova remnant,meanwhile, forms a neutron star or a black hole, which are important subjects ofastrophysical research in their own right.
Understanding exactly how supernovae explode is therefore an important goalof astrophysics. However, in the electromagnetic spectrum we can only observe
what happens after the supernova shock wave reaches the surface of the progenitor
several minutes to hours after the start of the explosion. This electromagnetic signal
is largely decoupled from the processes that occur at the centre of the star and cannot
help us understand the explosion mechanism.
Investigations of the precise explosion mechanism have thus far relied on computer simulations. While these have progressed rapidly due to increases in available
computing power as well as improvements to simulation codes, they still suffer frommajor limitations. An ideal simulation would be fully three-dimensional and imple1 approximately 160 000 years
2 the Large Magellanic Cloud, a satellite galaxy of the Milky Way at a distance of approximately

160 000 lightyears
3 That difference, in this case, consists of more than 1600 papers written about those detected neutrinos.

These not only improved our understanding of supernovae themselves; they also let us set new
limits on properties of neutrinos as well as a wide range of hypothetical new elementary particles
and test the theory of relativity to an accuracy not accessible to lab-based experiments.

1

Chapter 1 Introduction
ment detailed flavour- and energy-dependent neutrino transport, all while including
effects of general relativity. However, these three features cannot be combined in asingle simulation on current supercomputers, so current simulations often artificially
impose rotational symmetry, effectively making them two-dimensional, and use
various approximations which may include simplified neutrino transport schemes
like the “ray-by-ray plus” method [3] and IDSA [4] or a modified gravitational
potential that attempts to include relativistic effects in an otherwise Newtonian
simulation [5]. The effects of these simplifications are not yet completely understoodand the resultant uncertainties often lead to physically meaningful differences thatcan even make the difference between a successful and a failed explosion. Overall,“results of different groups are still too far apart to lend ultimate credibility to any
one of them” [6].
The only way to settle this debate observationally is by detecting a high-statistics
neutrino signal from the next galactic supernova. Approximately 99 % of the energy
released in a supernova is in the form of neutrinos, which due to their weak interaction cross section are likely to travel through outer layers of the star unhindered,taking with them information about the processes happening at the centre of thesupernova right in the moment of explosion.
In this thesis, I investigate how well the Hyper-Kamiokande detector will beable to distinguish different supernova simulations based solely on their respective
neutrino signals. Using the same methods, observing an actual supernova in the
coming decades will let us determine which simulation most closely reproduces the
explosion mechanism inside a real supernova.
The remainder of this chapter describes the history and fundamentals of neutrino physics and supernova observations, as well as summarizing previous workon supernova neutrinos. Chapter 2 describes Hyper-Kamiokande and its history,
including the detector design and construction as well as calibration and sourcesof background that are relevant to supernova neutrino studies. The software toolchain for simulating and reconstructing supernova neutrino interactions in HyperKamiokande is introduced in chapter 3. Chapter 4 contains a detailed description
and the results of my analysis. Finally, chapter 5 concludes by summarizing themain findings of this thesis and providing an outlook on possibilities of extending
this work.

2

1.1 Neutrinos

1.1 Neutrinos
1.1.1 History
1.1.1.1 Theoretical Proposal

In the 1920s, it was already known that some nuclei undergo beta decay by transforming into a nucleus of a different chemical element and expelling an electron:A
A 0−
Z X → Z +1 X + e(+ν̄e )As this was thought to be a two-body decay, physicists at the time expected theelectrons to be monoenergetic due to conservation of energy and momentum. However, various measurements revealed a continuous spectrum whose upper endpoint
was the theoretically expected energy [7, 8]. Surprised by this, some physicists,
including Bohr [9], considered the possibility that energy may not be conserved at a
sub-atomic level—or that it may only be conserved “on average”.
In 1930, in a letter to Meitner, Pauli proposed an alternative solution—that another,thus far unobserved particle was produced in beta decay, which transports away
the missing energy and would thus lead to a continuous electron energy spectrum
while maintaining conservation of energy [10]. Pauli originally called this particle“neutron”, but when Chadwick in 1932 discovered the particle that is nowadays
known as the neutron [11], Pauli’s particle was renamed “neutrino”.4
While Pauli was originally hesitant to publish his proposal, word spread throughdiscussions at various conferences and in 1934, Fermi published a first theoreticaldescription of beta decay, including a discussion of how the shape of the electron
spectrum near the end point depends on the neutrino mass [14]. In the same year,
Bethe and Peierls published a first theoretical estimate of the neutrino interaction
cross section based on the known lifetime of beta decay nuclei, setting a limit ofσ < 10−44 cm2 for 2.3 MeV neutrinos [15]. Since such a particle would traverse∼1016 km of matter, they concluded “that there is no practically possible way ofobserving the neutrino.”
1.1.1.2 Experimental Detection

Over the following two decades, a wide range of experiments investigated beta
decays with increasing precision and restricted alternative explanations for thecontinuous beta decay spectrum, without finding direct evidence for the existenceof neutrinos [16, 17, 18, 19, 20].
4 This contraction of the Italian word “neutronino”—meaning “little neutron”—was first jokingly

suggested by Amaldi and got popularized by Fermi [12, 13].

3

Chapter 1 Introduction
After the second world war, in the wake of the Manhattan project, a group at
Los Alamos Scientific Laboratory worked on nuclear weapons testing. In 1951,
Reines and Cowan developed a plan to use such a nuclear test to look for neutrinos,
arguing that the intense yet brief burst would be advantageous in reducing possible
backgrounds. After presenting the planned experiment at an internal seminar thefollowing year, they were encouraged to use a nuclear fission reactor as a neutrino
source instead [21]. To reduce backgrounds, they relied on the spatial and temporalcoincidence of the signals from the positron and neutron emitted in the inverse beta
decay reaction (ν̄e + p → n + e+ ) in a liquid scintillator detector [22, 23]. While afirst experiment in 1953 at the Hanford nuclear reactor showed some evidence forthis process, results were not yet conclusive [24]. In 1956, an improved experimentat the Savannah River nuclear reactor confirmed the previous observations, finallyproviding direct proof for the existence of neutrinos [25, 26].
In the following two years, the parity and helicity of the neutrino were measured
by Wu [27] and Goldhaber [28] and their respective collaborators.
At that time, despite some hints from double beta decay experiments [29], it was
not yet clear whether neutrino and antineutrino were different particles. Direct
evidence was found by Davis, who exposed a tank containing carbon tetrachloride(CCl4 ) to antineutrinos from the Savannah River nuclear reactor to look for thereaction37
Cl + ν̄e → 37Ar + e−.
By 1959, Davis reached an upper limit on that cross section of 0.05 times the crosssection calculated for the equivalent neutrino reaction,
37

Cl + νe → 37Ar + e−,

thus showing a difference in the behaviour of neutrinos and antineutrinos [30, 31].
Similarly, it was not known at that time whether electron neutrinos and muon
neutrinos were different particles. This was experimentally determined in 1962
by producing a beam of muon neutrinos in pion decay, π ± → µ± + (νµ /ν̄µ ), andshowing that they produced muons, rather than electrons, in a nearby detector [32].
Following the discovery of the τ lepton in 1975 [33], the existence of a corresponding neutrino, ντ , was widely expected and experimental evidence was found in 2001
by the DONUT collaboration at Fermilab [34]. Measurements of the Z boson’s decay
width at LEP indicate that no other species of weakly interacting neutrinos with amass m < mZ /2 = 45.59 GeV/c2 exists [35, 36].
1.1.1.3 The Solar Neutrino Problem

For millennia, the Sun’s energy generation had been a mystery. Energy sources
known before the twentieth century, like chemical or gravitational energy, would

4

1.1 Neutrinos(pp) p + p ! 2 H + e+ + ⌫e

p + e + p ! 2 H + ⌫e<latexit sha1_base64="8etFVxGe+a4xjn/HsIgtIZGgdgw=">AAAB9HicbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QLGF20psMmZ1dZ3qDYcl3ePGgiFc/xpt/4+Rx0MSChqKqm+6uIJHCoOt+O7m19Y3Nrfx2YWd3b/+geHjUMHGqOdR5LGPdCpgBKRTUUaCEVqKBRYGEZjC8nfrNEWgjYvWA4wT8iPWVCAVnaCW/g/CEQZiVk+R80i2W3Io7A10l3oKUyAK1bvGr04t5GoFCLpkxbc9N0M+YRsElTAqd1EDC+JD1oW2pYhEYP5sdPaFnVunRMNa2FNKZ+nsiY5Ex4yiwnRHDgVn2puJ/XjvF8NrPhEpSBMXni8JUUozpNAHaExo4yrEljGthb6V8wDTjaHMq2BC85ZdXSeOi4rkV7/6yVL1ZxJEnJ+SUlIlHrkiV3JEaqRNOHskzeSVvzsh5cd6dj3lrzlnMHJM/cD5/ALrkkg4=</latexit>

99.6 %
H + p ! 3 He +2 · 10 5 %

85 %

3

He + 3 He ! 4 He + 2 p

15 %3<latexit sha1_base64="Xnw/YwFjFxARl76m/GTeVEMRBos=">AAACA3icbZDJSgNBEIZ74hbjFvWml8FEiJcwI0I8hnjxGMEskIyhp1OTNOlZ6K4RwzDgxVfx4kERr76EN9/GznLQxB8aPv6qoqt+NxJcoWV9G5mV1bX1jexmbmt7Z3cvv3/QVGEsGTRYKELZdqkCwQNoIEcB7UgC9V0BLXd0Nam37kEqHga3OI7A8ekg4B5nFLXVyx91ER7Q9ZJSsetTHGq6q6TFGpylvXzBKltTmctgz6FA5qr38l/dfshiHwJkgirVsa0InYRK5ExAmuvGCiLKRnQAHY0B9UE5yfSG1DzVTt/0QqlfgObU/T2RUF+pse/qzsmearE2Mf+rdWL0Lp2EB1GMELDZR14sTAzNSSBmn0tgKMYaKJNc72qyIZWUoY4tp0OwF09ehuZ52bbK9s1FoVqbx5Elx+SElIhNKqRKrkmdNAgjj+SZvJI348l4Md6Nj1lrxpjPHJI/Mj5/ACKelys=</latexit>

7

Li + p ! 2 4 He

(hep)<latexit sha1_base64="9gnit8vRf63XcHGMDWAAM1u00zM=">AAAB9XicbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QxDA76U2GzM4uM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dnIrq2vrG/nNwtb2zu5ecf+gYaJEc6jzSEa65TMDUiioo0AJrVgDC30JTX90PfWbD6CNiNQdjmPohmygRCA4QyvddxCe0A/S8hDi00mvWHIr7gx0mXgZKZEMtV7xq9OPeBKCQi6ZMW3PjbGbMo2CS5gUOomBmPERG0DbUsVCMN10dvWEnlilT4NI21JIZ+rviZSFxoxD33aGDIdm0ZuK/3ntBIPLbipUnCAoPl8UJJJiRKcR0L7QwFGOLWFcC3sr5UOmGUcbVMGG4C2+vEwaZxXPrXi356XqVRZHnhyRY1ImHrkgVXJDaqROONHkmbySN+fReXHenY95a87JZg7JHzifP3HuknU=</latexit>

0.13 %
7

Be + e ! 7 Li + ⌫e
7

He + p ! 4 He + e+ + ⌫e

He + 4 He ! 7 Be +99.87 %

(7 Be)<latexit sha1_base64="bxJOimgYTSmCVJd3jgSMT6Z/l8A=">AAAB9XicbVDLSgNBEJyNrxhfUY9eBoMQL2FXBD0GvXiMYB6QxDA76U2GzO4OM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dvpLCoOt+O7mV1bX1jfxmYWt7Z3evuH/QMHGiOdR5LGPd8pkBKSKoo0AJLaWBhb6Epj+6nvrNB9BGxNEdjhV0QzaIRCA4QyvddxCe0A/SsgJ1OukVS27FnYEuEy8jJZKh1it+dfoxT0KIkEtmTNtzFXZTplFwCZNCJzGgGB+xAbQtjVgIppvOrp7QE6v0aRBrWxHSmfp7ImWhMePQt50hw6FZ9Kbif147weCym4pIJQgRny8KEkkxptMIaF9o4CjHljCuhb2V8iHTjKMNqmBD8BZfXiaNs4rnVrzb81L1KosjT47IMSkTj1yQKrkhNVInnGjyTF7Jm/PovDjvzse8NedkM4fkD5zPH34ukn0=</latexit>

0.4 %
2

3

(pep)

8

Be + p ! 8 B +B ! 8 Be* + e+ + ⌫e8

(8 B)
<latexit sha1_base64="k0GMbgZsCWaQX7wyGSUM6zCMh0s=">AAACAnicbZDLSsNAFIYn9VbrLepK3ARboW5KIoJdlrpxWcFeoIllMp20QycXZk7EEoIbX8WNC0Xc+hTufBsnbRba+sPAx3/OYc753YgzCab5rRVWVtfWN4qbpa3tnd09ff+gI8NYENomIQ9Fz8WSchbQNjDgtBcJin2X0647ucrq3XsqJAuDW5hG1PHxKGAeIxiUNdCPbKAP4HpJtWL7GMaK7upppXmWDvSyWTNnMpbByqGMcrUG+pc9DEns0wAIx1L2LTMCJ8ECGOE0LdmxpBEmEzyifYUB9ql0ktkJqXGqnKHhhUK9AIyZ+3siwb6UU99VndmacrGWmf/V+jF4dSdhQRQDDcj8Iy/mBoRGlocxZIIS4FMFmAimdjXIGAtMQKVWUiFYiycvQ+e8Zpk16+ai3GjmcRTRMTpBVWShS9RA16iF2oigR/SMXtGb9qS9aO/ax7y1oOUzh+iPtM8fXJaWvQ==</latexit>

Be* ! 2 4 He

Figure 1.1: Reactions and branching ratios for the pp chain [40].
have given the Sun a life time of several thousand or several million years, whichappeared irreconcilable with geological evidence that suggested an age of billions ofyears.5
Only with the advent of nuclear physics in the early 1900s did it become possible
to solve this question. Eddington in 1920 was the first to suggest nuclear fusionas the source of energy production in stars [38] and in 1939, Bethe expanded upon
Eddington’s proposal by describing in detail the two participating reaction chains:
the pp chain (figure 1.1), which fuses four hydrogen nuclei into a single 4 He nucleus
directly, and the CNO cycle (figure 1.2), which uses a heavier nucleus as a catalyst
for the same fusion process [39]. In both reaction chains, part of the mass difference
between the four initial protons and the resulting 4 He nucleus is emitted as several
neutrinos with an energy at the MeV scale.

5 An account of the discussion between Kelvin and contemporary geologists is given in reference [37].

5Chapter 1 Introduction
12

15

13

C + p ! 13 N +N ! 13 C + e+ + ⌫e

13

N + p ! 12 C + 4 He

C + p ! 14 N +99.9 %
15

14

O ! 15 N + e+ + ⌫e

N + p ! 15 O +

0.1 %
15

N + p ! 16 O +17

16

O + p ! 17 F +17

O + p ! 14 N + 4 He

F ! 17 O + e+ + ⌫e

Figure 1.2: Reactions and branching ratios for the CNO cycle [40].
From an experimental point of view, the 8 B neutrinos from the reaction chain3

He + 4 He → 7 Be + γ
78Be + p → B
8

B → 8 Be* + e+ + νe

(1.1)
(1.2)
(1.3)

are a particularly interesting component of the solar neutrino flux due to their highenergy of up to 15 MeV. While some other components of the solar neutrino flux are
more abundant, their lower energy means that they are below the energy thresholdof many common detector materials. The flux of 8 B neutrinos was first thought to
be too small to be detected, since the cross section for 7 Be production (reaction (1.1))
was underestimated. After laboratory experiments found the cross section to be twoorders of magnitude larger than expected [41], Bahcall and Davis proposed to look
for the reaction
37
Cl + νe → 37Ar + e−
using a detector filled with 380 000 l of perchlorethylene, C2 Cl4 [42, 43]. This
proposal benefitted from an easily available detector material, the reaction’s low
threshold energy of 0.81 MeV and its enhanced cross section due to three excitedstates of 37Ar at energies of 1.4 MeV to 5.1 MeV [42].
The detector was built in the Homestake Gold Mine in South Dakota, with an
overburden of 1480 m—corresponding to 4400 metres of water equivalent (m. w. e.)—to reduce the background from cosmic ray muons. First results were published6

1.1 Neutrinos
in 1968 and found no evidence for solar neutrinos, setting an upper limit on the
product of flux and cross section of 3 SNU6 [44]. While this upper limit appeared to
be in conflict with an updated theoretical prediction of (7.5 ± 3.0) SNU, it seemed
likely at the time that this was caused by uncertainties in the solar model [45]. Overthe following decades, however, this conflict remainedas theoretical improvements
1.3of the solar model led to an updated value of 7.6+
−1.1 SNU [46], while the value

measured by the Homestake experiment was (2.56 ± 0.23) SNU [47].
Starting in the late 1980s, Kamiokande and, since 1996, Super-Kamiokande(see section 2.1) also searched for solar neutrinos. Due to their different detector technology, they were sensitive to the solar neutrino flux at higher energies
only, yet by the year 2000
they had found a similar deficit, observing a 8 B neu
+0.09
6trino flux of 2.40−0.08 · 10 cm−2 s−1 [48] compared to a theoretical prediction of


1.01
6
−2 −1 [46].
5.05+−0.81 · 10 cm s
In the 1990s, GALLEX [49] and its successor GNO [50] at Gran Sasso, as well as
the Soviet-American collaboration SAGE [51] at Baksan began using the reaction
71

Ga + νe → 71 Ge + e−

to look for solar neutrinos. With an energy threshold of about 0.2 MeV, much lower
than that of chlorine- or water-based detectors, this reaction is sensitive to pp and
7 Be neutrinos (see figure 1.1), which are dominant components of the solar neutrino
flux. Combined, these gallium experiments measured
a flux of (74.7 ± 5.0) SNU+9compared to a theoretical prediction of 128−7 SNU, confirming the deficit foundby other detectors [46].
This decades-long conflict between theoretical predictions and experimental measurements of the solar neutrino flux became known as the “solar neutrino problem”.
When first results by the Homestake experiment hinted at a conflict, various theoretical explanations were soon proposed. These included time-dependent variationsin the solar fusion rate which may not be observable in other channels due to thelarge time scale required for radiation to diffuse from the centre of the Sun to its
surface [52], neutrino decay [53], rotation of the solar core [54] or a central black holeinside the Sun [55]. Neutrino oscillations were originally considered an unlikely
explanation by many physicists [56].
After Kamiokande and Super-Kamiokande found evidence for neutrino oscillations in atmospheric neutrinos [57], the solar neutrino problem was ultimately laid
to rest by the Sudbury Neutrino Observatory (SNO) in 2002. The SNO detector,
located in one of the world’s deepest underground laboratories with an overburden of about 2000 m of rock (6000 m. w. e.), contains 1 kt of heavy water, D2 O, ina spherical acrylic vessel with a diameter of 12 m. This vessel is surrounded by a
6 A “solar neutrino unit” (SNU) is defined as one interaction per 1036 target atoms per second.

7

Chapter 1 Introduction
stainless steel support structure with a diameter of 17.8 m, which carries over 9000
inward-looking photomultiplier tubes and acts as an active shield. It is filled withlight water, H2 O, and placed inside a barrel-shaped cavern filled with light water,which acts as a passive shield [58]. Due to its unique detector material, SNO candetect solar neutrinos in three different interaction channels:
ν + e− → ν + e−

(ES)
−

(CC)

ν + D → p + n + ν.

(NC)νe + D → p + p + e

The elastic scattering (ES) channel, which was also used by Kamiokande and SuperKamiokande to detect solar neutrinos, is sensitive to all neutrino flavours but has alower sensitivity to νµ and ντ . The charged-current (CC) channel is sensitive onlyto νe , while the neutral-current (NC) channel is sensitive to all neutrino flavours
equally, allowing SNO to measure both the pure νe flux and the total flux of allneutrino flavours independently. While the measured ES event rate showed a
deficit compared to theoretical predictions, in line with Super-Kamiokande, the total
neutrino flux agreed with theoretical predictions, providing direct experimental
evidence for neutrino oscillations [59].

1.1.2 Neutrino Oscillations
1.1.2.1 In Vacuum

Mixing in the neutrino sector was first described in the context of neutrinoantineutrino oscillations in 1957 by Pontecorvo [60, 61] in analogy with neutralkaon mixing described by Gell-Mann and Pais shortly before [62]. Five years later7 ,Maki, Nakagawa and Sakata described mixing between the flavour eigenstates νeand νµ of weak interactions and the mass eigenstates ν1 and ν2 [63].8
Extending this model to three generations of neutrinos [67], the relationship
7 and within two weeks of the experimental observation that electron neutrinos and muon neutrinos

behave differently [32]
8 An obvious parallel exist to the quark sector, where eigenstates under strong and weak interaction

are not identical, leading to mixing between generations of quarks. This mixing was first describedin the case of two generations in 1963 by Cabibbo [64] and CP violation in kaon decays was
discovered experimentally shortly thereafter [65]. In 1973, Kobayashi and Maskawa showed that
this CP violation cannot be explained with two generations of quarks unless additional fields are
introduced, but arises naturally with three generations [66]; a prediction that was supported by thediscovery of the bottom quark in 1976.
Unlike the quark sector, however, where mixing angles are very small, two of the mixing angles
in the neutrino sector are large, with one being near-maximal. Whether this is coincidence or
caused by some as yet unknown physics beyond the standard model is subject to speculation.

8

1.1 Neutrinos
between flavour eigenstates and mass eigenstates is today written as
 
 
ν1
νe
νµ  = UPMNS ν2  ,
ντ
ν3

(1.4)

where UPMNS is called the Pontecorvo-Maki-Nakagawa-Sakata matrix or PMNS
matrix. For Dirac neutrinos, it is commonly parametrized in terms of three mixing
angles, θij , and a CP-violating phase δ in the form




1
0
0
c13
0 s13 e−iδ
c12 s12 01
0  −s12 c12 0
UPMNS = 0 c23 s23   0(1.5)
iδ
0 −s23 c23
0
0 1−s13 e 0c13c12 c13s12 c13s13 e−iδ= −s12 c23 − c12 s13 s23 eiδ c12 c23 − s12 s13 s23 eiδ
(1.6)
c13 s23  ,iδiδ
s12 s23 − c12 s13 c23 e−c12 s23 − s12 s13 c23 e
c13 c23

where sij = sin θij and cij = cos θij . If neutrinos are Majorana particles [68], thePMNS matrix contains two additional phases,
 iα
e 1 0 0Majorana
UPMNS = UPMNS  0 eiα2 0 ,
(1.7)
0
0 1

which do not affect flavour oscillations and are therefore usually omitted.
In this paradigm, neutrinos are created through the weak interaction in a flavour
eigenstate να , which is a superposition of three mass eigenstates. While travelling,if the three mass eigenstates are independent (i. e. if at least two of them havedifferent, non-zero masses), they can propagate independently such that at a latertime the combination of mass eigenstates does not correspond to the original flavour
eigenstate. Instead, as it propagates in vacuum, its state over time is described by∗|να (0, 0)i = Uα1|ν1 i∗|να (t, x )i = Uα1 |ν1 (t, x )i

∗
+Uα2
|ν2 i
∗
+Uα2 |ν2 (t, x )i

∗
+Uα3
|ν3 i
∗
+Uα3 |ν3 (t, x )i

= |να i6= |να i,

(1.8)
(1.9)

where |νk (t, x )i = e−i(Ek t− pk x) |νk i and Ek2 = p2 + m2k . When reaching the detector,
the neutrino is detected in a flavour eigenstate νβ , so using |νk i = ∑ β=e,µ,τ Uβk νβwe find∗|να (t, x )i = ∑ Uαk|νk (t, x )i

(1.10)k∗ −i ( Ek t− pk x )= ∑ Uαk
e
|νk i
k

=

∑

β=e,µ,τ

∑k∗ −i ( Ek t− pk x )
Uαk
e
Uβk

(1.11)!

νβ .

(1.12)

9

Chapter 1 Introduction
As a result, the probability of being detected in the flavour eigenstate νβ is
2

Pα→ β = ∑∗ −i ( Ek t− pk x )
Uαk
e
Uβk

.

(1.13)k

Since neutrino energies considered here are O(MeV) while neutrino masses are
O(eV), we can make the relativistic approximation t ≈ x = L, where L is the
distance between neutrino source and detector. Thus,
Ek t − pk x ≈ ( Ek − pk ) L =m2
Ek2 − p2k
L ≈ k L,Ek + pk
2E(1.14)and the transition probability becomesm2 L∗
exp −i k
Pα→ β = ∑ Uαk
2E
k

!

2

Uβk

∗
∗
= ∑ UαkUβk Uαj Uβj
exp −ik,j(1.15)∆m2kj L2E!

,

(1.16)

where ∆m2kj = m2k − m2j . The transition probability for antineutrinos can be found by
making the replacement U  U ∗ .
Neutrino oscillations are thus described by three mixing angles, θij , two independent mass differences between the three mass eigenstates, ∆m2ij , and a CP-violatingphase δ.
After early reactor and accelerator neutrino experiments showed no evidenceof neutrino oscillations due to their short baseline, first evidence came from observations of atmospheric neutrinos in Kamiokande and Super-Kamiokande. Atmospheric neutrinos are mainly produced when high-energy cosmic rays interactingwith nuclei in the Earth’s atmosphere produce charged pions which decay via
π ± →µ± + νµ (ν̄µ )µ± → e± + νe (ν̄e ) + ν̄µ (νµ ).

This should result in a constant 2:1 ratio of muon neutrinos to electron neutrinos,
almost independent of the cosmic ray flux model. In the late 1980s, Kamiokande
first found that the muon-to-electron ratio in atmospheric neutrino events wasmuch lower than expected [57]. Over time, it became clear that this deficit in muon
neutrinos varied with the azimuth angle, with downgoing events reproducing the
expected ratio, while upgoing events, which had travelled through the Earth on their
way to the detector, showed about half the expected number of muon neutrinos [69].

101.1 Neutrinos
Observations by Super-Kamiokande confirmed the Kamiokande data with muchhigher statistics, providing strong evidence for νµ → ντ oscillations in atmospheric
neutrinos [70].
These measurements allowed a first determination of the mixing angle θ23 and themass difference |∆m232 | [70], which are today usually determined from atmospheric
neutrinos or in long baseline experiments [71, 72, 73]. The second mixing angle,
θ12 , and the corresponding mass difference, ∆m221 , were first measured using solar
neutrinos by SNO [74] and shortly thereafter using reactor antineutrinos by KamLAND [75]. The third mixing angle, θ13 , is much smaller than the others and earlymeasurements remained compatible with zero. First hints of a non-zero value were
found by T2K [76], MINOS [77] and Double Chooz [78] and within a few months,
these hints were confirmed by Daya Bay [79] and RENO [80].
Today, the values of these mixing parameters have been measured to a highprecision and are given by [36]0.013
sin2 θ12 = 0.307+−0.012sin2 θ13 = 0.0212 ± 0.0008

0.025

0.417+
−0.028 (NO, if θ23 < π/4)0.597+0.024 (NO, if θ > π/4)
23−0.030sin2 θ23 =+0.033

0.421
(IO,
if
θ
23 < π/4)−0.0250.592+0.023 (IO, if θ > π/4)
23−0.030∆m221 = (7.53 ± 0.18) · 10−5 eV2((2.51 ± 0.05) · 10−3 eV2∆m232 =(−2.56 ± 0.04) · 10−3 eV2

(NO)
(IO).

Here, “NO” stands for normal ordering, where the mass eigenstates obey the relation
m1 < m2 < m3 , while “IO” stands for inverted ordering, i. e. m3 < m1 < m2 . The
value of the CP-violating phase δ is not yet known, though recent results by thelong baseline experiments T2K and NOvA show a slight preference for a value
near δ = 3π/2, with T2K excluding the CP-conserving values 0 and π at the 2σ
level [72, 73].
1.1.2.2 In Matter: The MSW Effect

The equations in the previous section describe neutrino oscillations while propagating in vacuum. In 1978, Wolfenstein pointed out that the presence of matter canaffect neutrino oscillations through coherent forward scattering. While neutralcurrent scattering produces a similar phase shift for all neutrino flavours and thus
has little practical effect, the presence of electrons in matter produces an additional

11

Chapter 1 Introduction
potential for νe through charged-current interactions, which is not present for otherflavours. Wolfenstein discussed the effects in a suggested long baseline experimentand on solar neutrinos, finding that this effect is not sufficient to solve the solar
neutrino problem [81].
Several years later, Mikheev and Smirnov showed that neutrinos propagating
through a medium with a smoothly varying electron density can experience a
resonance behaviour, where even a small mixing angle can lead to high transition
probabilities [82]. This effect is now called the Mikheev-Smirnov-Wolfenstein (MSW)
effect. While Mikheev and Smirnov already discussed implications of the MSW
effect for solar and supernova neutrinos, Bethe in the following year expanded on
their work by estimating neutrino oscillation parameters under the assumption that
this resonance explained the results of the Homestake solar neutrino experiment [83].
In the following, I will briefly sketch out the derivation of this resonance effect.
For simplicity, I assume a two-flavour scenario and ignore neutral-current scattering
as discussed above.
In vacuum, the Schrödinger equation for the neutrino mass eigenstates is     2
 
d ν1
E1 0
ν1
m1 0
ν1
i
=
∼
,
(1.17)
0 E2
ν2
0 m22
ν2
dt ν2
where the mass matrix in the final step is the only contribution that differs between
eigenstates. Using |νe i = cos θ |ν1 i + sin θ |ν2 i and νµ = − sin θ |ν1 i + cos θ |ν2 i aswell as the relations sin 2θ = 2 sin θ cos θ and cos 2θ = 1 − 2 sin2 θ = 2 cos2 θ − 1, themass matrix for the flavour eigenstates can be written asm2 + m22 1 0
m2 − m21 − cos 2θ sin 2θ
M= 1
+ 2
,
(1.18)
0 1
sin 2θ
cos 2θ
2
2
with off-diagonal elements, which were not present in equation (1.17), appearing
due to neutrino mixing.
Charged-current interactions of νe with electrons in the matter introduce anadditional√ term in the Hamiltonian which is equivalent to an effective potential
Veff = 2GF ne , where GF is the Fermi constant of weak interaction and ne is the electron density. Replacing E2 in the relation E2 = m2 + p2 with ( E − Veff )2 ≈ E2 − 2EVeffshows that this new term changes the effective mass of νe , adding a contribution of
1 0
2EVeff0 0
to the mass matrix in equation (1.18). Using ∆m = m22 − m21 , the eigenstates of themodified mass matrix are given by
q
1 2
1
∗2
2
mi = (m1 + m2 + 2EVeff ) ±(∆m cos 2θ − 2EVeff )2 + ∆2m sin2 2θ.
(1.19)
22
12

1.1 Neutrinos

m2

νe

m22

νμ

m12
ne
Figure 1.3: Impact of the presence of matter with electron density ne on the neutrino
eigenstates in a simplified two-flavour picture. Thin black lines show the effective
masses of the flavour eigenstates νe (diagonal) and νµ (horizontal), while thick bluelines show the evolution of the propagation eigenstates given in equation (1.19).
In figure 1.3, these mass eigenstates are plotted as a function of electron density.
When a νe is produced in a region with a high electron density, like the interior of
the Sun, it is in the mass eigenstate m2∗ . Assuming a smoothly varying density, it
stays in that eigenstate, propagating along the blue line and finally reaching thepure mass eigenstate ν2 as it exits the Sun, undergoing no vacuum oscillations as it
travels to Earth.
Similar to this simplified example, neutrinos produced in the dense region near
the centre of a supernova undergo this MSW effect as they travel through theouter layers of the star. Antineutrinos experience an analogous effect, with theelectron density being equivalent to a negative positron density. The resulting
fluxes Φi , which can be detected on Earth, are linear combinations of the original
fluxes produced inside the supernova, Φ0i . The resulting fluxes are described in
section 3.2.3.

1.1.3 Detection
Since the first detection of neutrinos, a wide range of different neutrino detection
techniques have been developed that employ different target materials, interaction
channels and readout techniques. As a result, an experimental collaboration canmake trade-offs between various detector properties—like its cost, size, resolution,energy range and sensitivity to different neutrino flavours—to develop a detector
design optimized for its specific physics goals.
13Chapter 1 Introduction
In this section, I will summarize detection techniques used by current or planned
detectors that are expected to play a major role in supernova neutrino physics in theforeseeable future. While a range of other detection techniques exist that may be ofhistoric, niche or novelty interest, these are beyond the scope of this brief overview.
1.1.3.1 Water Cherenkov Detectors

Water Cherenkov detectors use pure water as a target material. Supernova neutrinos
interacting through the processes displayed in figure 1.4 produce charged particles,
which receive a large portion of the neutrino energy and move at relativistic speeds.
If such a particle surpasses the speed of light in water, cH2 O ≈ cvacuum /1.3, it sends
out a cone of Cherenkov light which is then detected by photosensors in the detector.
Since water is an extremely cheap and common material that is easy to handle
and has excellent optical properties, this detection technique can be used to build
very large neutrino detectors with a relatively simple detector design. However,reliance on the Cherenkov effect means that particles below the Cherenkov thresholdcannot be detected and that the energy resolution is limited due to the low yield ofCherenkov photons.
Water Cherenkov detectors optimized for the energy range typical for supernova
neutrinos, like Super- and Hyper-Kamiokande, use an enclosed design, consistingof a human-made water tank—typically located underground to reduce cosmic
ray backgrounds—whose inside walls are covered with photosensors. Dependingon the fraction of the inside walls covered with photosensors and the efficiencyof these sensors, several Cherenkov photons per MeV energy will typically bedetected. Therefore, a simple trigger based on the number of hits above a threshold,which depends on the noise level of the photosensors, can be employed to identify
individual neutrino interactions.
On the other hand, neutrino telescopes like IceCube [85] and KM3NeT [86] are
optimized for high-energy astrophysical neutrinos and use an open design, where anaturally occurring body of water—like the antarctic ice or deep sea water—is instrumented with a sparse array of optical modules. With module separation ranging
from a few metres to over 100 metres, detector masses up to the Gton scale can be
instrumented, making this design suitable for detecting neutrinos with energies up
to several PeV, which have a much lower flux and produce particle showers thatcannot be contained in enclosed detectors like Hyper-Kamiokande. However, thesparse instrumentation means that neutrino telescopes are not sensitive to neutrinos
below the GeV scale and will usually detect at most one photon from each supernova
neutrino interaction in the instrumented volume. Any single neutrino interactionis therefore indistinguishable from noise and a supernova is only detectable as atemporary increase in the noise rate across the whole detector.

14

Cross-section (10

-38

cm2)

1.1 Neutrinos

102
IBDν e -eν e -eν x -eν x -eν e - 16O
ν e - 16O
16
NC O

10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7

10

20

30

40

50

60

70
80
90
100
Neutrino Energy (MeV)

Figure 1.4: Cross sections of main interaction channels of supernova neutrinos in awater Cherenkov detector. The main interaction channel is inverse beta decay (p +ν̄e → n + e+ ; solid black), which due to its low threshold energy of 1.8 MeV and highFigure3:upCrossfor relevant
processes
in water.
cross section
makes
about sections
90 % of detected
events. At
low energies,
a sizeable−−
contribution comes from elastic scattering on electrons (ν + e → ν + e ; red, withsolid, dashed and dotted lines for ν̄e , νe and νx , respectively), which provides theperformed mostto theprovidedcross
sectioncurve
to extrapolate
this up to 100 MeV. The fit
preciseinformationon thedirectionof incoming
neutrinos. Charged-current
16−+ νe →was
X +manuallye ; dashed fixed),
interactionson oxygen-16
nuclei point,of νe ( Ogreen) andwas excellent(save thelowest energywhichso ν̄theextrapolatione
16 O + ν̄ → X + e+ ; solid blue) have a high threshold energy of about 15 MeV and(eis likely quite valid.
11 MeV, respectively, and mainly contribute to the high energy tail. Figure from
SNOwGLoBES [84].

4.6Interactions with Lead

For lead, we include CC and NC cross-sections for both single and double neutron ejection
channels for: ⌫e +208 Pb ! e +208 Bi⇤ , ⌫x +208 Pb ! ⌫x +208 Pb⇤ , ⌫¯x +208 Pb ! ⌫¯x +208 Pb⇤ .
We use cross-sections from [19]. Lead cross-sections are plotted in Fig. 6. Uncertainties
on lead cross-sections are evaluated in [20].
155Detector Response Parameters

The smearing matrices provided are also in GLoBES format. The spectral distributions ofinteraction products and the detector response are handled simultaneously by this matrix:
each column of the matrix represents the detector response for a given monochromatic incom-

Chapter 1 Introduction
1.1.3.2 Liquid Scintillator

Liquid scintillator detectors like KamLAND [87], SNO+ [88] or, in the near future,
JUNO [89] use a design that is very similar to the enclosed water Cherenkov detectors described in the previous section. Instead of water, the target material inside thedetector is a scintillating material—usually one of several hydrocarbons, like linear
alkylbenzene—which may be doped with small amounts of wavelength shifting or
stabilizing agents to achieve the desired properties. Supernova neutrinos interacting
through the processes displayed in figure 1.5 produce charged particles that induce
emission of scintillation light as they move through the detector. The resulting
light yield is about two orders of magnitude higher than that of Cherenkov light,
depending on the composition of the medium.
This scintillation light enables liquid scintillator detectors to detect particles below
the Cherenkov threshold, which would remain undetected in water Cherenkov
detectors. Furthermore, since the energy resolution at low energies is limited by
Poisson fluctuations of the number of detected photons, the increased light yield ofscintillation light improves the energy resolution.
On the other hand, since scintillation light is emitted nearly isotropically, it drowns
out the directional information provided by Cherenkov light.9 Furthermore, compared to water the higher cost and lower attenuation length of liquid scintillators
limit the possible detector size.
In recent years, new water-based liquid scintillator (WbLS) materials have beendeveloped which consist of pure water with a small admixture of a liquid scintillator [91]. While the resulting material has a lower light yield than pure liquid
scintillators, it is still able to improve the energy resolution compared to a pure water
Cherenkov detector and it enables detection of sub-Cherenkov threshold particles.
At the same time, it largely eliminates the cost and light attenuation disadvantagesof liquid scintillators.
A concept for a WbLS neutrino detector—the Advanced Scintillator Detector
Concept, which has since been renamed THEIA—was presented in 2014 [92, 93]. A
large worldwide R&D programme consisting of several experimental collaborations
including SNO+, WATCHMAN/AIT, ANNIE and EGADS is currently ongoing.
Over the next years, these collaborations aim to develop and characterize the novel
technologies and components expected to be used for THEIA.

9 Scintillation light is slightly delayed compared to the Cherenkov light, so a separation based onemission time is in principle possible [90]. However, this requires sub-ns time resolution, which isbeyond the capabilities of the photosensors that are currently available in sufficient quantities (andat sufficiently low prices) to equip a large neutrino detector.

16

Cross-section (10

-38

cm2)

1.1 Neutrinos

102
IBDν e -eν e -eν x -eν x -eν e - 12C
ν e - 12C
NC 12C

10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7

10

20

30

40

50

60

70
80
90
100
Neutrino Energy (MeV)

Figure 1.5: Cross sections of main interaction channels of supernova neutrinos ina liquid scintillator detector. The main interaction channel is inverse beta decay(p + ν̄e → n + e+ ; solid black) due to its low threshold energy of 1.8 MeV and highFigureAt4:low
Crosssections
forcontribution
relevant processes
scintillator.
cross section.
energies,a sizeable
comes from inelastic
scattering−−
on electrons (ν + e → ν + e ; red, with solid, dashed and dotted lines for ν̄e ,νe and νx , respectively), while charged-current interactions on carbon nuclei of νe
12+
For some
smearing
information
was used; for others, the(12 Cof+ theνe →provided
X + e− ; dashedgreen)files,and ν̄publishede ( C + ν̄e → X + e ; solid blue) have
LBNE simulation
packagehasofbeen
estimates
maybehighratheroptimistic, as wehigh thresholdenergies
nearly used.
20 MeV Someand mainly
contributeto theenergytail.
Elastic
neutrino-proton
scattering,
which
can
be
detectedinliquidscintillator
tend to use optimistic smearing when little detailed information is available. Users may also
detectors with a sufficiently low energy threshold, is not included in this figure.
provide theirown smearing matrices and efficiency information. We will update smearing
Figure from SNOwGLoBES [84].

files as knowledge of expected detector responses improves.
Background is also handled: the user can provide a file of background as a function ofenergy to be smeared by the indicated detector response This is handled by creating a “fake”
interaction channel and accompanying smearing file. If a GLoBES-formatted backgroundfile labeled by the detector configuration is present in the backgrounds subdirectory, thebackground will be smeared and an additional output file created. The user
17 is responsible
for ensuring that the background events in the file correspond to the same time interval as
the signal.

5.1

Water Cherenkov

Currently, two water Cherenkov configurations are provided. The LBNE detector simulation
package, WCSim, was used to create the smearing and efficiency files for both of these.

Chapter 1 Introduction
1.1.3.3 Liquid Argon Time Projection Chamber

Liquid argon time projection chambers (LAr TPCs) employ a similar design to liquid
xenon TPCs which are now common in dark matter direct detection experiments.
Within a cryostat, a detector is filled with liquid argon as a detection material.
Neutrino interactions produce energetic particles, which lose energy through ionization of argon atoms along their tracks. Through an externally applied electric field,
the resulting free electrons are drifted to readout planes on one side of the detector
where they induce a signal on multiple layers of wires, enabling a 2D-reconstructionof each hit position along the track. Detectors also contain some photosensors to detect Cherenkov light and determine the time of interaction, which can be combinedwith the time delay of the drifting electrons to reconstruct the interaction in 3D.
LAr TPCs like ICARUS [94] or MicroBooNE [95] have been used for accelerator
neutrinos in the ∼GeV energy range in recent years, since their active calorimetry
enables a precise reconstruction of events. However, this technique has not yet beenused for the energy range required for supernova neutrino detection and a lot ofwork remains to precisely measure the interaction cross sections shown in figure 1.6,
optimize event reconstruction and characterize low-energy backgrounds including
those from radioactive argon isotopes.
Currently operating LAr TPCs are small compared to water Cherenkov detectors
and would only detect a small number of neutrinos from a galactic supernova. The
Deep Underground Neutrino Experiment (DUNE) [96], which is currently underconstruction, plans to build four detector modules with a fiducial mass of 10 kton
each. Due to the competitive size and the increased sensitivity to electron neutrinos,
this will provide interesting complementarity to other detector types.

1.2 Supernovae
1.2.1 History
The history of supernova observations goes back almost two millennia. The first
known observation of a supernova was reported in ancient China in the year 185 [97],while other well-known supernovae were observed by Chinese and Japanese astronomers in 105410 , Tycho Brahe in 1572 and Johannes Kepler in 1604.
The name supernova refers to the fact that these were originally thought to be
new stars (from Latin nova, meaning new). Only in 1934 was it suggested by Baadeand Zwicky that exactly the opposite might be true—that supernovae arise when
massive stars reach the end of their lifetimes and explode [98, 99, 100]. Around thesame time, a first systematic survey and better telescopes led to a rapid increase in
the number of observed supernovae [101]. A classification of supernovae based on
10 This supernova is the progenitor of the Crab Nebula.

18

Cross section (10

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cm2)

1.2 Supernovae

102

νe e
νe e
νx e
νx e
νe 40Arνe 40Ar

10
1

10-1

10-2
10-3
10-4
10-5
10-6
10-7

10

20

30

40

50

60
70
80
90 100
Neutrino Energy (MeV)

Figure 1.6: Cross sections of main interaction channels of supernova neutrinos ina LAr TPC. The main interaction channel is the charged-current interaction of νeon argon nuclei (40Ar + νe → X + e− ; dashed green). At low energies, a sizeable
contribution comes from elastic scattering on electrons (ν + e− → ν + e− ; red, withsolid, dashed and dotted lines for ν̄e , νe and νx , respectively), while charged-current
interactions of ν̄e on argon nuclei (40Ar + νe → X + e− ; solid blue) have a highthreshold energy of 16 MeV and mainly contribute to the high energy tail. Figure
from SNOwGLoBES [84].

19Chapter 1 Introduction
Spectral TypeIa

Spectral LinesSi

Explosion Mechanism
Light Curve
Neutrino Emission
Remnant

thermonuclear explosion
reproducible
minor
none

Ib, Ic and II
Ib: HeIc: No H, He or Si
II: H
core collapse
large variations
ca. 99 % of total energy
neutron star or black hole

Table 1.1: Overview of spectral types, their main properties and the corresponding
explosion mechanisms.
their spectral features and the time-dependence of their emission was first developedby Minkowski in 1941 and later extended by Zwicky [102, 101].
Today, supernovae are generally classified as type I if their spectra do not containhydrogen lines, or type II if they do. Type I is further subdivided into type Ia (if thespectrum contains silicon lines), type Ib (if it contains helium lines) or type Ic (if it
contains neither). Type II supernovae are subdivided based on the time evolutionof the supernova brightness into type IIP (if the lightcurve shows a plateau of
approximately constant brightness in the months after the explosion) or type IIL (ifthe brightness falls off linearly), as well as based on their spectra. However, a numberof supernovae have been discovered that do not neatly fit into this categorization
scheme, e. g. due to their untypical luminosity or time-dependent changes to theirspectra. For a recent review of such so-called “peculiar” supernovae, see [103].
This spectral classification, however, mainly reflects the properties of the progenitor star’s outer layers, like the size of its hydrogen envelope or its 56 Ni content [104].
Different spectral properties do not, generally, correspond to different explosion
mechanisms, as shown in table 1.1.
An explosion mechanism responsible for type Ia supernovae was suggested in1960 by Hoyle and Fowler [105], with Whelan and Iben proposing binary starsystems as progenitors [106]. According to this model, thermonuclear supernovae
originate in gravitationally bound systems of two stars, one of which is a whitedwarf consisting primarily of carbon and oxygen, while the other is a low mass starthat has entered its red giant phase. If both stars orbit each other at a sufficiently close
distance, the white dwarf will accrete matter from the envelope of its companion
until it reaches the Chandrasekhar mass limit of about 1.4 M . During accretion, thenuclear fuel in the white dwarf’s core heats up until a runaway fusion process starts,
which releases O(1051 ) erg within seconds. Most of this energy is released in theform of kinetic energy, ripping the white dwarf apart and expelling its companion
star.
20

1.2 Supernovae
While this mechanism is widely accepted, some recent supernova observations
appear to point towards a different progenitor model being responsible for at least
some type Ia supernovae. In that alternative model, two white dwarfs bound in abinary system merge to produce a supernova. A recent review of the observational
evidence can be found in reference [107], while computer simulations of theseprogenitor systems are reviewed in reference [108].
Independent of the progenitor model, type Ia supernovae create neutrinos mostly
through electron capture on free protons or heavier nuclei, i. e.
e− + ( A, Z ) → ( A, Z − 1) + νe .
Neutrinos do not greatly influence the explosion and are responsible for only asmall fraction of the total energy release. A type Ia supernova at a distance of lessthan about 1 kpc would be necessary to be able to detect neutrinos in current or
next-generation neutrino detectors [109, 110].
Supernovae with the spectral types Ib, Ic and II exhibit widely varying appearances, which are based on the properties of their progenitor. However, they are
generally thought to all explode through the same core-collapse mechanism. In
contrast to thermonuclear (or type Ia) supernovae, their progenitors are heavy stars
with a mass of more than about 8 M . Inside the core of such a star, temperaturesand densities are sufficiently high to go through all stages of nuclear fusion andfinally produce iron, which has the highest binding energy per nucleon such thatfurther nuclear fusion is energetically disfavoured. Once the mass of this iron coresurpasses the Chandrasekhar mass limit of about 1.4 M , it starts to collapse andthe core’s density rapidly increases until it surpasses nuclear density. At this point,
the equation of state of nuclear matter stiffens. Infalling matter now bounces off thecore and is reflected as an outgoing shock wave. When this shock wave is reheatedby neutrinos, the outer layers of the star are expelled, while the collapsed inner coreleaves a neutron star behind.11
Of the total explosion energy of such a core-collapse supernova, about 99 % orroughly 3 × 1053 erg is released in the form of neutrinos. These are produced in ornear the collapsing core of the star and traverse the outer layers of the star nearly
unhindered. Measuring properties of the neutrino flux therefore allows us to study
the interior of the supernova and the processes at work during the explosion.
In the remainder of this thesis, I will focus on core-collapse supernovae. The
closest visible supernova of this type since the invention of the telescope happened in
the Large Magellanic Cloud in 1987. This supernova, called SN1987A, is also the only
11 If the progenitor has a very large mass, the neutrino emission from the core collapse may not be

sufficient to reheat the shock wave and the star may instead collapse into a black hole without
producing a strong signal in the electromagnetic spectrum. These so called “failed” or “dim”
supernovae would produce a neutrino signal which first looks very similar to a regular supernova
but has a characteristic sharp cut-off.

21

Chapter 1 Introduction
supernova whose neutrino emission was observed by humankind. In the following
section, I will describe the current understanding of the core-collapse explosion
mechanism based on computer simulations and the observation of neutrinos from
SN1987A.

1.2.2 Explosion Mechanism
Today, over 50 000 supernovae or supernova candidates have been detected anddetailed lightcurves and spectra are available for several thousand of them according
to the Open Supernova Catalog [111, 112]. Furthermore, these numbers are expected
to grow rapidly in the near future, with the Large Synoptic Survey Telescope alone
expected to observe 3 × 105 core-collapse supernovae per year when it starts operations in the early 2020s [113, 114]. However, measurements in the electromagnetic
spectrum only allow observations of the surface layers of the supernova. Whilethese give detailed information on the composition of these outer layers and thus
the properties of the progenitor, they give little information about the mechanism
underlying the actual explosion, which takes place at the centre of the star several
minutes to hours before the resulting shock wave reaches the stellar surface and thesupernova becomes visible to telescopes.
Unlike electromagnetic radiation, neutrinos only interact weakly and are therefore
unlikely to experience scattering or be absorbed in outer layers of star. Neutrinos
are thus the only known channel that allows us to directly observe the processes
occurring near the centre of a star in the moment of explosion. On the other hand,the small cross sections of weak interactions mean that most neutrinos pass throughany detector unnoticed and only very large neutrino fluxes can be observed. This
limits the reach of current neutrino detectors to supernovae within the Milky Wayor its immediate cosmic neighbourhood, where the rate of core-collapse supernovae
is estimated to be about 2–3 per century [115].
Due to this severe scarcity of observational data, progress in understanding thecore-collapse explosion mechanism has come mostly from computer simulations.
Pioneering contributions to numerical models of supernovae were made by Colgate,
Grasberger & White [116, 117], Arnett [118] and Wilson [119, 120]. These early
simulations often imposed spherical symmetry to reduce the required computing
power, making them effectively one-dimensional. Optical observations of SN1987A
made it obvious that this assumption does not generally hold true in nature [121],
which increased the effort put into more complex simulations that only imposedrotational symmetry around one axis. Today, these two-dimensional simulations
are very common, while one-dimensional simulations are still used for parametricstudies that compare a wide range of models. Only in recent years has it becomecomputationally feasible to simulate three-dimensional models that include detailed
treatment of neutrino production and transport processes [122, 123].

22

1.2 Supernovae
The difficulty in simulating supernova explosions stems both from the huge
computing power required and the inherent complexity of the phenomenon itself:
Supernovae stand out from most other physical phenomena in that they involve all
known fundamental forces—gravity as well as the strong and electroweak force—and operate at extreme conditions, which often cannot be reproduced in laboratory
experiments. Simulating them also requires solving difficult and non-linear hydrodynamical equations and taking into account relativistic effects. The latter are
currently often treated as a modified potential in Newtonian gravity to simplify calculations, which might cause an error of tens of percent in some physical quantities
and lead to qualitatively different outcomes [124].
Computer simulations of supernovae have made remarkable progress in the last
decades, in part due to a dramatic increase in available computing resources and inpart due to an improved understanding of the neutrino physics and nuclear crosssections involved in the explosion of a core-collapse supernova. Thus, while current
simulations disagree on many points and “are still too far apart to lend ultimate
credibility to any one of them” [6], they have reached widespread agreement on thebasic explosion mechanism.
After Burbidge and others highlighted the gravitational instability of old massive
stars [125], Colgate and others proposed a solely hydrodynamical “bounce andshock” explosion mechanisms for core-collapse supernovae in 1961 [116], where theequation of state of the collapsing core stiffens after it reaches nuclear density andinfalling matter bounces off the now incompressible core resulting in an outgoingshock wave. Several years later, they studied the role of the high neutrinos fluxes
inside a supernova [117].
In the early 1980s, Wilson and Bethe [120, 126] described the delayed neutrinodriven explosion mechanism generally accepted today. This mechanism consists ofsix steps which are sketched in figure 1.7.
1. Initial phase: The progenitor of a core-collapse supernova is a star with a massof more than about 8 M , whose central region is sufficiently hot and dense to
produce iron through nuclear fusion. Since the iron cannot produce energy
through further nuclear fusion steps it forms an inner core, which is held up
5
by electron degeneracy pressure whose density dependence is initially P ∝ ρ 3 .
At the same time, hydrostatic equilibrium requires P ∝ GMρR−1 , which leads
1
to a mass-radius relationship for the iron core of R ∝ M− 3 . As silicon burning
continues to produce iron that accretes onto the core, the core shrinks dueto the increase in mass. Electrons occupy increasingly higher energy states
4
until they become relativistic and their equation of state changes to P ∝ ρ 3 .12
12 Analogous to the mass limit for white dwarf stars, this happens when the iron core reaches the

Chandrasekhar mass of about 1.4 M .

23

Chapter 1 Introduction
Initial Phase of Collapse(t ~ 0)RFe~ 3000

Neutrino Trapping(t ~ 0.1s, c ~10¹² g/cm³)

R [km]

δR [km]

RFe

νe
νe
νe

~ 100
Si

Si
νe

Fe, NiFe, Niνeνe0.5~ MCh M(r) [M ]

1.0

0.5
heavy nuclei

Si−burning shell

R [km]

δδ

RFeradius ofshockformation

Si−burning shell

Shock Propagation and νe Burst(t ~ 0.12s)

R [km]

Bounce and Shock Formation(t ~ 0.11s, c <∼ 2 o )M(r) [M ]Mhc 1.0

RFe
Rs ~ 100 km

νe

νe

Rν
νe
Si

~ 10
Fe, Niνe

0.5
nuclear matter

NiM(r) [M ]nucleiSi−burning shell

10 5

Neutrino Cooling and Neutrino−
Driven Wind (t ~ 10s)

νe,µ,τ ,νe,µ,τ

10 4

νe,µ,τ ,νe,µ,τ

Si

10 3

δ δ

Rs ~ 200

R [km]NiSip
R ν ~ 50

νe
νe

PNS

νe

1.0

Si−burning shellfree n, pνeFefree n,pM(r) [M ]Shock Stagnation and ν Heating,Explosion (t ~ 0.2s)

Rg ~ 100

νe
Si

νe

0.5
1.0
nuclear matter
nuclei( >∼ ο )R [km]

position ofshock
formationn

1.3
gain layer
cooling layer

νe,µ,τ ,νe,µ,τ

10

αr−process?

2

R ns~ 10
1.5 M(r) [M ]RνPNS 1.4

α, n
n, p

9

α,n, Be,C, seedHeO

νe,µ,τ ,νe,µ,τ

3 M(r) [M ]12Figure 1.7: Sketch of the six phases of the delayed explosion mechanism as describedin the text. In each panel, the upper section shows the dynamical processes, witharrows representing velocity vectors, while the lower section shows the nuclear
composition of the star. Figure from reference [127].
24

1.2 Supernovae
During this transition to the relativistic regime, the mass-radius relationshipbecomes steeper and the shrinking of the core accelerates until the mass-radiusrelationship of the iron core breaks down, indicating that there is no stableconfiguration. The core collapses. During this phase, some electrons get
captured by nuclei and the resulting neutrinos transport energy away from thecore, thus reducing the degeneracy pressure which counteracts the collapse.
2. ν trapping: After about 100 ms, the inner core reaches a density of about
1012 g/cm3 . At this density, the mean free path of neutrinos becomes smaller
than the radius of the inner core and they become trapped inside it.
3. Bounce and shock formation: After about 110 ms, the core has collapsed froma radius of about 3000 km to just tens of kilometres, with infalling matterreaching about 10 % of the speed of light. At this point, the density of theinner core surpasses nuclear density, reaching about 3 × 1014 g/cm3 , and its
equation of state stiffens. Infalling matter now hits a “wall” and is reflected,
resulting in an outgoing shock wave. Meanwhile, neutrinos are still trappedin the inner core due to its high density.
4. Shock propagation: After about 120 ms, the outgoing shock wave reaches thesurface of the iron core at a radius of about 100 km, dissociating the iron nuclei
into free nucleons along the way. Since the electron capture cross section onfree protons (e− + p → n + νe ) is much higher than on the larger, neutron-richnuclei, this leads to a sudden increase in the electron capture rate. The matter
density in the outer parts of the core is too low to trap the neutrinos, so a brief
νe burst is released.
5. Shock stagnation and ν heating: After about 200 ms, the shock wave stagnates
at a radius of about 100 km to 200 km, having used up most of its energy todissociate heavy nuclei into their constituent nucleons. Matter from outerlayers infalling onto the almost stationary shock front creates an accretion
shock, which powers neutrino emission. At this phase, convection sets in at
the accretion shock layer.
Meanwhile, the neutrinos that were trapped inside the inner core are starting
to diffuse out. While some escape the supernova immediately, others deposit
energy in the accretion shock layer mainly by neutrino capture on free nucleons, i. e. ν̄e + p → n + e+ and νe + n → p + e− . This heating increases thepressure in the region behind the shock front and reignites the shock wave.
6. ν cooling: During the following tens of seconds, the remnant of the core, aproto-neutron star (PNS), cools by diffusive neutrino transport. The outgoingshock wave takes several minutes or hours to reach the surface of the star,
where it will expel the matter in its outer shells and produce a signal that isvisible in the electromagnetic spectrum.
25

Chapter 1 Introduction

Figure 1.8: Luminosity (top) and mean energy (bottom) of νe (dashed blue line), ν̄e(solid black) and νx (dotted red) for a 20 M model [128]. The left panels show the
prompt νe burst and the following phase of shock stagnation, while the right panels
show the neutrino cooling phase.
Throughout this process, neutrino emission occurs in three distinct steps, which
are displayed in figure 1.8.
The first step is a prompt νe burst from electron capture during phase 4 above.
With a duration of roughly 10 ms, this is expected to give a very sharp and unmistakeable feature that consists of almost pure νe . Since this signal originates in theiron core, which collapses at a well-defined set of physical conditions, independentof the properties of the outer shells of the star, it is very similar across a wide rangeof simulations with different progenitors [129].
The second step has a duration of several 100 ms and corresponds to the shock
stagnation in phase 5 above. Neutrino emission during this phase is powered bymatter from outer layers accreting onto the shock front. Radial movement of theshock front therefore leads to changes in the accretion rate, such that hydrodynamical

26

1.2 Supernovae
features like the standing accretion shock instability could be observed as striking
sinusoidal features in the neutrino event rate [130, 131, 132, 133]. In this phase,the luminosities Lνe and Lν̄e are roughly equal (and higher than Lνx ) while theaverage energies are unequal (h Eνe i < h Eν̄e i ≈ h Eνx i), which contributes to thede-leptonization of the core. This energy difference is caused by the higher crosssection for νe in electron-rich matter, which means that νe leaving the star are, on
average, emitted at larger radii and thus lower temperatures.
The final step of neutrino emission corresponds to the ν cooling (phase 6) andhas a duration of some tens of seconds. During this time, the supernova remnant
cools through diffusive emission of neutrinos that became trapped in its core during
the earlier phases of the explosion. The composition of the neutrino flux at thisstage is governed by a number of different physical processes, including nucleonnucleon bremsstrahlung and neutrino-antineutrino pair annihilation [134, 135, 136,137], which lead to roughly equal luminosities of all neutrino species that fall off
exponentially with time, while the average energies remain unequal.

1.2.3 Open Questions
On February 23rd , 1987, three detectors around the world—Kamiokande [138, 139],
IMB [140] and Baksan [141]—detected a total of two dozen neutrinos from thesupernova SN1987A in the Large Magellanic Cloud. In the decades since, these
events have been analysed extremely closely and were used to set limits on neutrino
masses, charges and life times, as well as on a wide range of hypothetical particles
proposed by theorists13 . An overview over the information on particle physics
that was gained from SN1987A can be found in reference [142]. As the first and,for almost 30 years, only object outside of our solar system observed in a channel
outside of the electromagnetic spectrum, SN1987A also enabled tests of relativity
that were beyond the reach of lab-based experiments [143].
The neutrino events largely fell within the range of theoretical expectations, supporting the basics of the explosion mechanism described in the previous section [144].
The energy release in the gravitational collapse of a neutron star was expected to
be on the order of 2 × 1053 erg [145], predominantly in the form of neutrinos. This
turned out to be in good agreement with the observation of SN1987A. As expected,
the detectors observed a brief period with a high rate of neutrino interactions at thestart of the signal, followed by a period of much lower event rate with a duration of
about 10 s.
13 This is due to the fact that the neutrinos from SN1987A were observed over a duration of about

10 s. Any weakly-interacting new particle that would cool the core by transporting away energy
can therefore be produced only in limited quantities; otherwise, the core would cool down too
quickly and there would not be sufficient energy left to power the observed neutrino emission atlater times.

27

Chapter 1 Introduction
Some authors have pointed to irregularities in the neutrino signal from SN1987A
and used these as evidence for nonstandard physical phenomena. In addition to
the 7.3 s gap between the first 9 and the final 3 events observed in the Kamiokande
detector, this includes differences in the reconstructed flux spectra and angular
distributions between the Kamiokande and IMB detectors [146]. Due to the low
number of observed events, however, the alternative that these are simply artefacts
caused by statistical fluctuations cannot be excluded.
Another puzzle is caused by a cluster of 5 events observed by the LSD experiment
under Mt. Blanc almost 5 h earlier [147], at a time when none of the three otherneutrino detectors observed an excess of events above background. Some authors
have, however, argued that there is a coincidence between the cluster of events
observed by LSD and individual events in the other neutrino detectors as well as
possible events in two gravitational wave detectors [148, 149, 150]. It has also beenargued that the non-observation of the earlier burst in other detectors as well as
LSD’s non-observation of the burst observed by the three other detectors could
be explained by differences in the detector sizes and sensitivities as a function ofenergy [151]. To explain these observations, various multi-step supernova explosion
mechanisms [148, 152, 153] or exotic particle physics models [154] have been proposed; however, since these LSD-inspired models were invented ad hoc to accountfor the observations, they are widely viewed sceptically.
Even putting aside these puzzles, SN1987A clearly demonstrated that previous
computer simulations—most of which had imposed spherical symmetry—did notreflect realistic supernova explosions and that multidimensional effects needed tobe taken into account. Furthermore, the two dozen neutrinos detected were notsufficient to investigate details of the explosion mechanism. Many open questions
have therefore remained to this day.
First of all, the next observation of neutrinos from a galactic supernova would needto provide a higher-statistics signal that could provide incontrovertible evidence
to identify the supernova explosion mechanism and clear up the irregularities in
the SN1987A signal which are described above. Furthermore, if the basic explosion
mechanism described in section 1.2.2 is confirmed, a high-statistics neutrino signal
could be used to investigate details of the explosion mechanism where current
simulations give conflicting results.
One recent example for this is a hydrodynamic feature of the shock front called the“Standing Accretion Shock Instability” (SASI), which occurs during the shock stagnation phase shown in the fifth panel of figure 1.7. While this self-sustained oscillationof the shock front was observed in a number of two-dimensional simulations andcontributed to explosions there, it did not play a role in early three-dimensional
simulations, leading some authors to conclude that it had to be an artefact of therotational symmetry imposed in two-dimensional simulations [155]. While otherauthors have since found SASI oscillations in three-dimensional simulations [123],28

1.3 Summary of Previous Work
there is still no consensus. Some recent work suggests that the presence and importance of SASI may depend on the equation of state of nuclear material [156, 157], theshock radius [158] or rotation [159, 160], while other authors find that SASI is either
completely absent or negligible compared to the role of neutrino-driven convection
in a layer interior to the accretion shock [155, 161].
More generally, progenitors in computer simulations often do not explode on
their own but need to be triggered artificially. For example, the first successful
neutrino-driven explosion in a three-dimensional simulation was only achieved in2015 by the Garching group [162]. While this lack of explosions may simply be theeffect of imperfect modelling of the known physical processes, it could also be theresult of new physics—non-standard interactions of neutrinos or completely newparticles like axions or a dark sector [163, 164, 165, 166]—which are not included incurrent models.

1.3 Summary of Previous Work
After describing neutrino detection and supernova simulations in the earlier partsof this chapter, in this section I will broadly summarize ongoing work in these fields
and how it contributes to using supernova neutrinos to determine details of the
explosion mechanism. Astronomers and astrophysicists also perform extensive
research of supernovae that improves our understanding of stellar evolution andenables us to create increasingly detailed models of supernova progenitors. While
this work is extremely important, it is only indirectly connected to the neutrinosignal from a supernova and therefore beyond the scope of this overview.
Due to the severe lack of supernova neutrino observations, ongoing researchlargely depends on computer simulations. A number of different groups aroundthe world perform computer simulations of supernovae with progenitors that havea wide range of different masses, compositions, rotational velocities and otherproperties. Some of these simulations are very complex and aim to reproduce
a realistic supernova in the greatest possible amount of detail, which requires
huge amounts of computational resources and thus only allows the simulation ofindividual or very few progenitors. On the other end of the spectrum are very
simplified studies that usually impose rotational or even spherical symmetry anduse various approximations in neutrino transport and other physical parameters to
reduce the computational needs. While these simulations are less realistic, they allow
groups to perform a large number of simulations and study the effect of varying
parameters of the progenitor (like its mass or metallicity), numerical resolution orindividual approximations.
Various current and next-generation neutrino detection collaborations have determined the ability of their respective detectors to observe supernova neutrinos;

29

Chapter 1 Introduction
see e. g. references [89, 167, 168, 85, 96, 169]. These collaborations commonly use asmall number of supernova models as benchmarks to showcase the event counts
expected in their detector, its sensitivity to different interaction channels and ability
to distinguish supernova neutrinos from the dominant sources of background. In
the absence of any observations of supernova neutrinos, long-running experiments
can also use those analyses to set limits on the local supernova rate [170, 171].
Depending on the sensitivity of their detector, collaborations may also produce
more advanced analyses, such as the ability of a detector to detect pre-supernova
neutrinos [87] or to determine the direction of a supernova [172]. These analyses
often contain a very detailed treatment of detector efficiencies, reconstruction uncertainties and backgrounds. However, since they are restricted to a small numberof benchmark models, they are unable to investigate in detail the wide range offeatures displayed in modern computer simulations.
There are a number of publications, particularly by simulations groups or theorists, that focus on a specific aspect of the neutrino signal and try to determine how
well it could be detected in current or future detectors based on individual computer
simulations; for recent examples see e. g. references [131, 132, 133, 173, 174, 175, 176].
Partly for simplicity and partly due to a lack of access to or experience using
collaboration-internal tools and data, these authors often employ a simplified treatment of detector effects, like backgrounds and reconstruction uncertainties, or ofinteraction channels.
Of fundamental importance for comparing supernova neutrino observations tocomputer simulations is the ability to reconstruct the flux of emitted neutrinos fromthe detected events. The spectrum of emitted neutrinos in each flavour can be
described by a Gamma distribution [137, 177],
Eναf ( Eν ) =Γ ( α + 1)

α+1h Eν i α +1(α + 1) Eν
exp −,h Eν i(1.20)

where h Eν i is the mean energy of neutrinos and α is a shape parameter, with α = 2corresponding to a Maxwell-Boltzmann distribution and α > 2 corresponding
to a “pinched” spectrum. The neutrino flux at Earth is thus described by threeparameters: h Eν i, α and an overall normalization, which depends on the luminosityof the supernova and its distance.
Different groups recently showed that Hyper-Kamiokande will be able to reconstruct the time-integrated fluxes of ν̄e and νx to few percent precision, while thetime-integrated flux of νe can be determined to similar precision by exploiting thecomplementarity between Hyper-Kamiokande and DUNE [178, 179]. Since the flux
is time-dependent, however, it is important to determine how these flux parameterschange with time. This can in principle be done by simply splitting data into mul-30

1.3 Summary of Previous Worktiple time bins and reconstructing the spectrum in each time bin separately14 , thougha more advanced approach using a likelihood function can be employed—especially
if a relatively low number of events is observed—to reduce the information loss
inherent in binning [180].
A recent review of supernova neutrino detection and the lessons we can learn
about supernovae can be found in reference [181].
Despite this wide range of ongoing research, however, there is thus far no analysis showing how well we can discriminate between different computer models ofsupernovae in a realistic detector. This thesis is the first such analysis and includes
precision cross sections, subdominant interaction channels, a detailed detector simulation including reconstruction uncertainties and an unbinned likelihood analysis
that makes optimal use of the available time and energy information for all reconstructed events.

14 with an associated loss in precision due to the lower number of events in each time bin

31Things are easy when you’re big in Japan.
Alphaville

Chapter 2
The Hyper-Kamiokande Detector
Hyper-Kamiokande [169] is a next-generation ring imaging water Cherenkov detector that is currently in the planning stages and expected to start taking data in
2027. It is designed to be a general purpose detector contributing to various different
fields of particle and astrophysics.
In searches for proton decay, the large detector mass will enable it to explore
proton lifetimes of up to ∼1035 years in its most sensitive channel (p → e+ + π 0 ),and ∼1034 years in a range of other channels. Both represent roughly an order ofmagnitude improvement over previous limits set by Super-Kamiokande and would
cover large parts of the parameter space predicted by current theoretical models.
Hyper-Kamiokande will act as the far detector for a long baseline neutrino experiment, referred to as T2HK. Building upon the currently ongoing work of theT2K collaboration, this successor experiment will combine upgrades to the neutrino
beam and existing near detector that are already planned by the T2K collaboration
with a new intermediate water Cherenkov detector and a larger far detector, with
Hyper-Kamiokande replacing Super-Kamiokande. As a result, higher statistics
and reduced systematic uncertainties are expected to enable a determination of theneutrino mass ordering and a first measurement of δCP , as well as precision measurements of other oscillation parameters. Hyper-Kamiokande will also perform
detailed measurements of atmospheric neutrinos, which are the product of cosmic
rays interacting with nuclei in the Earth’s atmosphere. In addition to being sensitive
to the mass ordering and the octant of θ23 , this data set will help eliminate parameterdegeneracies in a joint analysis together with accelerator neutrinos.
For solar neutrinos, higher statistics will allow Hyper-Kamiokande to perform aprecise measurement of the day-night asymmetry caused by neutrinos traversing
the Earth’s matter potential before reaching Hyper-Kamiokande during the night.
While Super-Kamiokande has already measured this effect at 3σ, that measurement resulted in an unexpectedly small value of ∆m221 , producing a tension with
KamLAND measurements of reactor antineutrinos which Hyper-Kamiokande is expected to help clear up. Hyper-Kamiokande will also try to observe neutrinos fromthe 3 He + p fusion reaction inside the Sun, which have not yet been observed dueto the very low branching ratio of this reaction. Compared to other solar neutrino
species, these hep neutrinos have a higher energy and are expected to be produced33

Chapter 2 The Hyper-Kamiokande Detector
at larger distances from the centre of the Sun, making them an excellent tool totest the standard solar model. Finally, Hyper-Kamiokande will try to detect thetransition in neutrino oscillation probability between the region below ∼1 MeV,
where vacuum oscillations on the way to Earth dominate, and the region above∼10 MeV, where MSW oscillations in the Sun dominate.1 Various exotic models
like non-standard interactions [182], mass-varying neutrinos [183] or sterile neutrinos [184] predict modifications to the shape of this spectral upturn, which could betested by Hyper-Kamiokande.
If a supernova within our Milky Way happens during Hyper-Kamiokande’s
lifetime, we would observe 104 to 106 neutrino interactions and measure the precise
arrival time and energy of each event. Such a data set would not only enable adetailed investigation of the supernova explosion mechanism as described in thisthesis, but also provide valuable knowledge to many related areas of particle andastrophysics. Even in the absence of a galactic supernova, Hyper-Kamiokande could
perform a high statistics measurement of supernova relic neutrinos (SRN), with∼102 events expected within 10 years. This first determination of the SRN spectrum
would constrain parameters of theoretical models, such as the star formation ratein the universe as a function of redshift or the fraction of “failed” supernovae thatcollapse to a black hole without an optically visible explosion.
Finally, Hyper-Kamiokande will explore a wide range of rare or more speculative
topics including searches for an excess of GeV-scale neutrinos from the Sun or thecentre of the Milky Way, which might originate from annihilation of dark matter, or
high-energy neutrinos associated with astrophysical sources like solar flares, gamma
ray burst jets, new-born pulsars or colliding binary systems containing at least one
neutron star similar to the neutron star merger observed in gravitational waves andvarious electromagnetic wavelengths on 17 August 2017 [185].
This chapter begins by describing the history leading up to Hyper-Kamiokande,
including a brief discussion of its predecessor experiments, Kamiokande and SuperKamiokande. Section 2.2 describes the detector design and its components in detail.
Finally, sections 2.3 and 2.4 discuss detector calibration and sources of backgroundthat are relevant to the investigation of supernova neutrinos. By necessity, discussion of calibration and backgrounds will largely remain qualitative, since reliable
quantitative data will not be available until the detector is actually running.
Throughout, I will focus on the single tank planned to start construction in April
2020 in Japan. A proposed second Hyper-Kamiokande tank in South Korea [186]would likely be very similar to the one described here, though plans have not yet
progressed far enough to discuss them in detail. Other elements of the experiment,such as the beamline or near and intermediate detectors, are not related to theinvestigation of supernova neutrinos and will therefore not be discussed here.
1 See section 1.1.2 for an explanation of the MSW effect.

34

2.1 History

2.1 History
2.1.1 The Past: Kamiokande
The 1960s were a period of major changes across particle physics. In the lepton sector,
Glashow, Weinberg and Salam provided a unified description of electromagnetism
and weak interaction [187, 188, 189]. Around the same time, Gell-Mann and Zweig
proposed the quark model [190, 191] to categorize the rapidly growing “hadronzoo” found in experiments. By the early 1970s, the theory of strong interactions(known as quantum chromodynamics) was formulated [192, 193, 194], completing
the Standard Model (SM) of particle physics in its modern form.
While experimental particle physicists spent the next four decades detecting thematter particles and bosons predicted by the SM, theoretical physicists soon beganwork on so-called “Grand Unified Theories” (GUTs) that unified electroweak andstrong interaction, the first one being Georgi and Glashow’s SU(5) model [195]. In
many of these GUTs, instead of the baryon number, B, and the lepton number, L,
only their combination B–L was conserved. This allowed the proton—which, in
the Standard Model, was predicted to be stable—to decay via channels such as
p → e+ + π 0 and with predicted life times as low as 1030 years in some models,close to lower limits from contemporary experiments [196].
Encouraged by these predictions, several groups of physicists began work on
experiments to search for proton decay. These experiments consisted of a large tankof pure water—containing a large number of hydrogen nuclei, i. e. free protons—
whose inside walls were equipped with photosensors to detect the flash of light
expected from a decaying proton. One such experiment—known as IMB—wasbuilt in the U.S. by groups from Irvine, Michigan and Brookhaven, while a groupof Japanese physicists built a detector in the Kamioka mine in Japan’s Gifu region,
which they called the Kamioka Nucleon Decay Experiment or Kamiokande.
The Kamiokande detector [197] was a cylindrical tank with a diameter of 15.5 m
and a height of 16 m, containing 3 kt of water. It started operations in 1983 with afocus on looking for proton decay. Soon afterwards, it was pointed out that Kamiokande would be able to observe solar 8 B neutrinos if the low-energy backgrounds
were reduced sufficiently and beginning in 1985, the collaboration added an outerdetector and improved the electronics and water purification systems [198]. Following completion of this upgrade, in February 1987 Kamiokande-II observed a burstof 12 events caused by neutrinos from the supernova SN1987A [138, 139]. Together
with the 13 events observed by the IMB [140] and Baksan [141] detectors, thesemarked the beginning of extra-solar neutrino astronomy and remain the only supernova neutrinos observed to this day. In 2002, part of the Nobel Prize for Physics was
jointly awarded to Ray Davis Jr. and to the Kamiokande collaboration’s Masatoshi

35

Chapter 2 The Hyper-Kamiokande Detector
Koshiba for their “pioneering contributions to astrophysics, in particular for thedetection of cosmic neutrinos” [199].
Kamiokande also observed solar neutrinos, confirming the deficit observed by
the Homestake experiment [44], as well as atmospheric neutrinos. Notably, the ratioof muon-like to electron-like events in atmospheric neutrino interactions in Kamiokande deviated from theoretical expectations, hinting at neutrino oscillations2 [69].

2.1.2 The Present: Super-Kamiokande
By the end of the 1980s it became clear that Kamiokande, while very successful,
would soon be limited by its size and plans for a successor experiment called SuperKamiokande were made. Located in the same mine as its predecessor below 1000 mof rock shielding, corresponding to 2700 m. w. e., Super-Kamiokande [201] started
data-taking in April 1996 after 4.5 years of construction and commissioning. Similarin shape to Kamiokande, it is a cylindrical tank with a diameter of 39 m and a heightof 42 m, containing 50 kt of water. This total volume is divided by a stainless-steel
support structure into two optically separated regions: an inner detector (ID) region
with a diameter of 33.8 m and a height of 36.2 m and an outer detector (OD) region
with a width of approximately 2 m. See figure 2.1 for an overview.
The OD is sparsely instrumented by 1885 photomultiplier tubes (PMTs) with
20 cm diameter and wavelength shifting plates to increase light collection. It acts as
an active veto against incoming particles such as cosmic-ray muons and as a passive
shield against radioactivity from the surrounding rock.
The ID contains 32 kt of water, which is divided up for analysis purposes intoa central, fiducial volume of approximately 22.5 kt of water3 surrounded by anouter shell of 2 m width. That shell acts as a passive shield against radioactive
backgrounds, which mainly come from the PMT glass and enclosure or the stainlesssteel support structure.
The ID is densely instrumented with PMTs with 50 cm diameter, which are mounted on the support structure. Between April 1996 and June 2001, a period referred toas Super-Kamiokande-I, the ID was instrumented by 11 146 PMTs, effectively covering 40 % of its inner surface. When refilling the detector with water in November
2001 after being shut down for maintenance, an imploding PMT caused a chain
reaction that destroyed over half the PMTs in the detector. After fitting the PMTs
with pressure-resistant covers to avoid a reoccurrence, data-taking resumed with a
2 At the time, these observations were not yet fully accepted as evidence for neutrinos oscillations.

Instead, systematic errors due to misidentification of the observed particles were suggested as analternative explanation. To investigate this, an experiment with a scaled model of the Kamiokande
detector was performed in a charged particle beam at KEK, which confirmed the accuracy of
Kamiokande’s particle identification [200].
3 Depending on the background levels, a larger or smaller fiducial volume is used for some analyses.

362.1 History

S. Fukuda et al. / Nuclear Instruments and Methods in Physics Research A 501 (2003) 418–462

427

Fig. 6. A cross-section of the Super-Kamiokande detector.

Figure 2.1: Schematic view of Super-Kamiokande. Figure from reference [201].
high voltage ranging from 1700 to 2000 V. The
neck of each PMT was coated with a silver
reflector to block external light, although as noted,
light can enter through the back of the hemispherical portion of the PMT.
Fig. 11 shows a detail of the support structure
for the ID PMTs. All support structure components are stainless steel.
The basic unit for the ID PMTs is a ‘‘supermodule’’, a frame which supports a 3 ! 4 arrayof PMTs. Supermodule frames are 2.1 m inheight, 2.8 m in width and 0.55 m in thickness.
These frames are connected to each other inboth the vertical and horizontal directions. Thenthe whole support structure is connected to thebottom of the tank and to the top structure.
In addition to serving as rigid structural elements,
supermodules simplified the initial assembly of
the ID. Each supermodule was assembled on thetank floor and then hoisted into its final position.
Thus the ID is in effect tiled with supermodules.
During installation, ID PMTs were preassembled
in units of three for easy installation. Eachsupermodule has two OD PMTs attached on its
back side. The support structure for the bottom
PMTs is attached to the bottom of the 37
stainlesssteel tank by one vertical beam per supermodule
frame. The support structure for the top of
the tank is also used as the support structure forthe top PMTs.

Chapter 2 The Hyper-Kamiokande Detector
20 % photocoverage between December 2002 and October 2005, a period referred
to as Super-Kamiokande-II. Newly manufactured PMTs which restored the photocoverage to 40 % were added for the Super-Kamiokande-III period which started in
October 2006. For the Super-Kamiokande-IV period starting in September 2008, newfront-end electronics and a new data acquisition system were installed, while thephotocoverage stayed constant. Together with improvements to the water system,
calibration and analysis, this has allowed Super-Kamiokande-IV to observe electrons
with kinetic energies as low as 3.5 MeV [202]. Most recently, Super-Kamiokande
was shut down for maintenance in June 2018 to fix some water leaks and prepare
for the upcoming addition of gadolinium, which would strongly enhance its ability
to detect neutron captures and thus reduce backgrounds in a variety of analyses.
Super-Kamiokande confirmed the deficit of muon-like atmospheric neutrino
events observed in Kamiokande and was able to measure its dependence on theazimuth angle, providing strong evidence for neutrino oscillations. In 2015, theNobel Prize for Physics was jointly awarded to Takaaki Kajita (Super-Kamiokande)
and Arthur McDonald (SNO) for discovering neutrino oscillations [203]. Since
2010, Super-Kamiokande acts as the far detector of the T2K experiment [204], which
produces a beam of neutrinos at J-PARC in the city Tokai on the east coast of Japanand sends it over a distance of 295 km to Super-Kamiokande to measure neutrino
oscillation parameters.
Super-Kamiokande also performs precision measurements of the solar 8 B neutrino
flux [202], searches for nucleon decay channels, with lower limits on the proton
lifetime now surpassing 1034 years in the most sensitive channel [205], and a wide
range of other analyses.

2.1.3 The Future: Hyper-Kamiokande
Just a few years after Super-Kamiokande started taking data, the prospects of amegaton-scale successor were first being explored [206, 207]. A letter of intent
to build Hyper-Kamiokande was presented in 2011 which proposed to build two
horizontally segmented tanks with an egg-shaped cross section [208]. After several
years of ongoing R&D, a design report was published in 2016 [209] and mostrecently updated in 2018 [169]. The design report presented an optimized designthat returned to the cylindrical shape of its predecessors.
The collaboration has received seed funding from the Japanese Ministry of Education, Culture, Sports, Science and Technology in 2019 and expects to get fully
approved by 2020 [210]. Construction is scheduled to start in April 2020, withcommissioning and data taking expected by 2027.
Table 2.1 shows a comparison of Hyper-Kamiokande and its predecessors. The
design of Hyper-Kamiokande will be described in more detail in the following
section.

38

2.2 Detector Design and Construction

1000 m
2700 m. w. e.
16 m
15.6 mSuperKamiokande
1000 m
2700 m. w. e.
42 m
39 m

HyperKamiokande
650 m
1750 m. w. e.
60 m
74 m

4.5 kt3 kt
0.68 kt
20 %
948 (50 cm )
123 (50 cm )

50 kt
32.5 kt
22.5 kt
40 %11 129 (50 cm )1885 (20 cm )

258 kt216 kt187 kt40 %40 000 (50 cm )
6700 (20 cm )

4 ns

2 ns to 3 ns

1 ns

Kamiokande
Depthwater equivalent
HeightDiameterVolumetotal
inner
fiducial
ID Photocoverage
ID PMTsOD PMTs
Single-photon
detection efficiency
Single-photon
timing resolution

unknown

12 %

24 %

Table 2.1: Comparison of Kamiokande, Super-Kamiokande and Hyper-Kamiokande.
Note that this reflects Kamiokande-II and Super-Kamiokande-IV; some parameters
have been different during earlier phases.

2.2 Detector Design and Construction
Hyper-Kamiokande is a ring imaging water Cherenkov detector and relies on thebasic detection principle described in section 1.1.3. The detector will be built inside
a mountain to shield it against muons from cosmic ray interactions in the Earth’s
atmosphere. It consists of a cavern filled with ultra-pure water that is split by astainless steel structure into the outer detector, which is used as an active veto region,and the inner detector. This stainless steel structure also holds photodetectors forboth the outer and inner detector, which will detect light from particle interactionsin the detector. Signals from the photodetectors will be collected and digitized by
front-end electronics and then transferred to a data acquisition system, which combines information from all photosensors to identify and reconstruct events. Finally,reconstructed events will be stored by a multi-tiered computing infrastructure andused for physics analyses.
This section will describe these components of the detector in detail. It is basedon the November 2018 update to the Hyper-Kamiokande Design Report [169] and39

Chapter 2 The Hyper-Kamiokande Detector
reflects the status of the detector design at that time. At that time, R&D on many
components of the detector was still ongoing and final design decisions on thesecomponents had not yet been made. Throughout this section, where applicable, I
will therefore describe the baseline design of that component and briefly give an
overview over alternatives. While major changes are unlikely at this stage, the final
detector design may diverge in some aspects from the descriptions on the following
pages.

2.2.1 Location and Cavern
Hyper-Kamiokande will be built in the Tochibora mine of the Kamioka Mining
and Smelting Company, near the town Kamioka in Japan’s Gifu Prefecture. The
proposed location at geographic coordinates N 36°21.3300 E 137°18.8200 (using the
WGS 84 standard) is approximately 8 km south of Super-Kamiokande but lies atsame 2.5° off-axis angle from the J-PARC neutrino beamline. Located below thepeak of Mount Nijugo at an altitude of 514 m above sea level, Hyper-Kamiokande
will have an overburden of 650 m of rock (1750 m. w. e.).
The cavern design consists of a cylindrical (or “barrel”) section with a height of
62 m and a diameter of 76 m, which will house the detector volume4 , and a 16 m
high “dome” section on top of the cylinder, which will house detector infrastructuresuch as the data acquisition and calibration systems. A schematic drawing of thecavern and detector is shown in figure 2.2. The excavation work will also include
smaller caverns for the water circulation and purification systems as well as accesstunnels. Optimization of the cavern dimensions and the layout of the access tunnels
is still ongoing.5
To avoid fault lines and determine the rock quality, the collaboration has performed a geological survey of the mountain using pre-existing tunnels, some newly
drilled boreholes and seismic prospecting with acoustic waves. Using these results,
the location of Hyper-Kamiokande has been narrowed down to a candidate regionof approximately 200 m × 150 m which exhibits the best and most even rock quality.
A detailed survey of the geological conditions in this region is planned, which will
culminate in a precise cavern design including a pattern of pre-stressed anchorsnecessary to support the rock and ensure structural stability. Several possible rockquality distributions have been simulated and in all cases the cavern construction is
feasible with existing techniques.
4 This excavated volume is slightly larger than the detector volume to account for the water contain-

ment system described below.
5 In September 2019, the Hyper-Kamiokande proto-collaboration announced an updated detector

design with a diameter of 68 m and a water depth of 71 m. The total and fiducial volumes bothchanged by less than 1 %; the effect on the results described in this thesis, which still used theprevious design, will therefore be negligible.

402.2 Detector Design and Construction

Figure 2.2: Schematic view of the Hyper-Kamiokande detector. Figure from reference [169].

41

Chapter 2 The Hyper-Kamiokande Detector
The excavation will start by constructing “access tunnels”, which lead from themine entrance to the vicinity of the detector, and “approach tunnels”, which connect
the access tunnels to the water rooms and various levels of the main cavern. Oncethe tunnels are constructed, the cavern will be excavated starting with the dome andconcluding with the bottommost part of the barrel region.
An intermediate deposition site for excavated rock and a final disposal site wereidentified and the geological stability of the final disposal site was confirmed througha boring survey and several computer simulations. Both sites can be accessed via
existing roads, though some widening or re-routing of roads will be necessary toallow a large number of dump trucks to use them.

2.2.2 Water Tank
Once the cavern has been fully excavated, its surface will be treated with a layerof shotcrete, which will then be covered by a waterproof sheet to stop ultra-purewater from leaking out and to stop external sump water from entering the detector.
To ensure the stability of the cavern, a 50 cm thick layer of concrete is then added
which is reinforced with steel rods and lined on the inside with a 5 mm thick waterproof high-density polyethylene (HDPE) sheet. HDPE was chosen for its flexibility,
which allows it to cover cracks in the concrete wall without breaking, its low water
permeability and its high chemical resistance to both ultra-purified water and agadolinium sulfate solution. A schematic drawing of the outer edge of the watertank is shown in figure 2.3.
Magnetic fields perpendicular to a PMT’s direction reduce the collection efficiencyof large PMTs. For the B&L PMT described in section 2.2.4.1, the reduction wasmeasured to be 1 % at 100 mG, growing to 3 % at 180 mG. To counteract the effects ofthe geomagnetic field, which at the detector site is ( Bx , By , Bz ) = (−303, 0, −366) mG,
a combination of rectangular coils (in the y-z plane) and circular coils (in the x-yplane) will be embedded in the concrete layer. A preliminary design found that theresidual perpendicular magnetic field can be reduced to B⊥ < 100 mG for 97.8 % of
the ID PMTs, with only PMTs at the top and bottom edge of the detector experiencing
a higher residual B⊥ . Optimizations of the coil design are still ongoing.
Inside the water tank, a stainless-steel structure will separate the inner and outerdetector regions and support the PMTs and their covers (see sections 2.2.4 and 2.2.5)
as well as front-end electronics (see section 2.2.6). In Super-Kamiokande, the bottom
and barrel sections are a self-supported framework standing on the bottom of thetank. In Hyper-Kamiokande, due to the larger size of the detector, only the bottom
section will be free-standing on the bottom of the tank while the barrel and top
sections will be suspended from the ceiling of the cavern. This allows the frame tobe thinner and thus lighter and cheaper, since it is not at risk of buckling under its
own weight.

42

2.2 Detector Design and Construction!"#$%&%''()*+$$#

5"/6)7'/*#%879'/

:";$%/)$<7";"9'/!"#$%&%''(),'-.$#+.-$/$)01/1/2)344

Figure 2.3: Schematic view of the outer edge of the water tank. Figure from reference [169].
The strength of the frame is determined by the weight of the PMTs, covers andelectronics it has to support while the tank is empty. When determining the configuration of photosensors and covers, care must be taken to ensure that the buoyancyof the PMTs in water does not overcompensate for the weight of the structure. Otherwise, additional weights would need to be added to stop the structure from floating,which would require a stronger frame to support the additional weights when thetank is empty and thus increase the cost of the structure.
The inner and outer detector regions will be optically separated to allow the OD
to act as an active veto; however, the details of this are not yet fixed. In the simplest
case, as in Super-Kamiokande, this could be achieved with two layers of light-proof
sheets covering the inner and outer surfaces of the PMT support structure. However,43

Chapter 2 The Hyper-Kamiokande Detector
if Hyper-Kamiokande is to be loaded with gadolinium at some point, a hermetic
separation of the ID and OD may be desirable to ensure that the gadolinium remains
contained within the ID, which would simplify the water system and reduce costs.

2.2.3 Water Purification and Circulation System
All materials used in detector construction are extensively tested to avoid introducing sources of radioactivity or water-soluble impurities into the detector. Despite
these efforts however, radon emanating from materials in the tank, particularly the
glass of photosensors and the support structure, and from the rock surrounding thedetector is a major source of low-energy backgrounds. In addition, light scatteringand absorption due to impurities in the water are a major source of uncertainty inevent reconstruction. To reduce these effects, the water in the detector is constantly
recirculated and purified.
In Super-Kamiokande, after continuous improvements the water system is now
able to purify the water inside the detector to reach a water transparency of over
100 m and a radon concentration in the ID of less than 1 mBq/m3 . In HyperKamiokande, where the diagonal size of the detector increases to nearly 100 m,
a similar or better water quality will be required. To achieve this goal, the design of
the water system will be similar to that employed in Super-Kamiokande but scaled
up to account for the larger detector mass.
The system consists of two separate stages (see figure 2.4), one for initial fillingof the tank and one for ongoing recirculation of the water during operations. The
water to fill the detector will come from the storage well of the snow-melting systemof the nearby Kamioka town. During filling, 105 t/h of source water will be needed
to fill the detector with purified water at a rate of 78 t/h, with approximately half ayear needed to completely fill the detector. The water will be recirculated at a rateof 310 t/h, such that the total detector mass is recirculated approximately once permonth, at the same rate as in Super-Kamiokande.
In the first stage, the raw water is passed through a 10 µm filter to eliminate dust
and larger particles from the raw water, before going through reverse osmosis (RO)and additional filters (MB) to remove smaller particulates. A vacuum degasifier(VD) removes dissolved oxygen (which encourages growth of bacteria in the water)and radon from the water before the pre-cleaned water is fed into the second stageof the system.
In the second stage, water coming from the Hyper-Kamiokande tank is sterilizedwith UV light and filtered before going through a multi-stage process including RO,
further UV irradiation (UV TOC), a cartridge polisher (CP) that removes heavy ionsand more advanced filtration (MF, UF). The purified water is then cooled down in aheat exchanger (HE) to remove heat produced by photosensors and electronics in44

2.2 Detector Design and Construction
Rn/CO2/H2O/bacteria free air

Source water

MF

60t/d

pure water
buffer tankbuffer tankCP
UV TOC

10µ filter
1st RO
2nd RORO water Tank

Rejected water(drain)Rn/CO2/H2O/bacteria
free airMF
RO

RO
UV TOC

Collection
tank

CP
UF

UF

drain
cooling waterHE
MB
Vacuum Degasifiercooling water

VD
Rn/CO2/H2O/bacteria
free air

1µ Filter

pure water
buffer tankUVsterilizer
310t/h2nd stage
systemRn/CO2/H2O/bacteria free air

HK Tank
258,000m3

Figure 2.4: Water system design for Hyper-Kamiokande. See text for an explanationof the individual steps. Figure from reference [169].
the water as well as the water system itself. Finally, the cooled water is degasified ina VD and supplied back into the tank.
Radon-free air with a concentration of less than 1 mBq/m3 is used as a covergas for the Hyper-Kamiokande tank as well as for buffer tanks which are partof the water system. To produce enough radon-free air, the system employed inSuper-Kamiokande will be scaled up to the larger detector size.
To avoid radon from the surrounding rock entering the inner detector, there is
no water exchange between the inner and outer detector. Radioactive impurities
in the inner detector mostly originate from the photomultipliers and their support
structure. Controlling the water flow in the detector is essential to limit the spreadof these impurities in the inner detector and reduce their impact on the physics
performance of the detector. Computer simulations of the water flow (see figure 2.5)
show that supplying cold water at the bottom of the tank and draining water at the
top leads to laminar flow and ensures effective water replacement. Supplying cold
water at the top of the tank and draining water from the bottom would instead leadto convection in the tank, which leads to uniform water quality throughout the tank45

Chapter 2 The Hyper-Kamiokande Detector
10days20days10days20days30days(a) Supply to the bottom and drain from the top
30days

40days

40days(b) Supply to the top and drain from the bottom

Figure 2.5: Simulation of water replacement efficiency in Hyper-Kamiokande. The
tank is filled with old water (blue) at the start of the simulation and fresh water (red)is then supplied: (a) at the bottom of the tank while draining from the top; (b) at
the top of the tank while draining from the bottom. Supplying fresh water fromthe bottom leads to a higher replacement efficiency, displayed as a more reddish
colour, while supplying it from the top leads to large-scale convection in the tank
and a more uniform water quality. Figure from reference [169].
and decreases the efficiency of water replacement. These simulations agree withobservations in Super-Kamiokande.
Adding gadolinium to a water Cherenkov detector to detect neutron captures
and thus better identify events was originally suggested by Beacom and Vagins in2003 [211]. After extensive testing, gadolinium will be added to Super-Kamiokandein the near future [212] and is being explored as an option for Hyper-Kamiokande.
This would require changes to the water system to remove the gadolinium fromdrained water using molecular bandpass filters. Both components would then becleaned separately and recombined before supplying the water back into the tank.
The necessary technologies have been developed for Super-Kamiokande and use
a modular design, ensuring they can be scaled up for use in Hyper-Kamiokande.
Since gadolinium loading is not part of the Hyper-Kamiokande baseline design andmay instead be added in a later upgrade, I am not considering its benefits in thisthesis.

46

2.2 Detector Design and Construction

2.2.4 Inner Detector
The inner surface of the structure separating the inner and outer detector is divided
into 40 000 “cells” with a size of 70 cm × 70 cm, each of which can house either asingle 50 cm diameter PMT or a so-called multi-PMT module (mPMT) consisting ofan array of smaller PMTs with 8 cm diameter.
In the reference design, every cell houses one 50 cm PMT, resulting in 40 % of
the inner detector surface being light-sensitive. The newly developed PMT modeland two alternative designs that are currently under development are describedin sections 2.2.4.1 and 2.2.4.2, while covers to increase pressure-resistance of these
PMTs are described in section 2.2.4.3.
Alternative configurations, which employ half the number of 50 cm PMTs andaugment them with mPMTs or other modifications that increase light collection, arebriefly described in sections 2.2.4.4 and 2.2.4.5. Studies to determine the impact ofthese alternative designs on the performance of Hyper-Kamiokande are currently
ongoing.
2.2.4.1 B&L PMTs

A new 50 cm PMT model with a higher quantum efficiency and a box-and-line

ector Photosensors
167 isdynode (Hamamatsu R12860-HQE [213], hereafter referred to as the B&L PMT)

being developed for Hyper-Kamiokande. Figure 2.6 shows the B&L PMT in a side
PHOTOCATHODE

HEAT SHRINKABLE TUBE
with MASTIC

INPUT WINDOWWATER PROOF CABLE
.

5
R7

M

IN

115

82

508

42°

254

60

4

R5

SEALING PARTWATER PROOF CASE

ure of the HQE
210

190

2860 PMT.

690 1565

2018.6

Figure 2.6: Side view of the B&L PMT. Figure from reference [214].

FIG. 96. Side view of the HQE 50cm B&L R12860 PMT.

o 9.4mm diameter coaxial cables for the high voltage (RG-174/U, 8kV DC max) and47

C/U). The cable weight is 86.4g/m and its volume is 64.3cm3 /m. The outer sheath is

ck polyethylene with 1mm thickness. A dedicated connector, watertight up to 100m

has been developed for Hyper-K.
Ｐ
Ｇ
ＡＣＣ

R12860-R3600_カウントグラフ（Y軸）Quantum efficiency [%]40
High-QE R12860
35
Normal-QE R3600
30
25
20
15
10
5
0

300

350

400

450

500

550

600 650 700
Wavelength [nm]Relative single photon detection efficiency

Chapter 2 The Hyper-Kamiokande
Detector
各ポジションでのカウントをグラフ化（標準球のカウントを同じにした場合）

2+

High-QE box-and-line PMT(Hamamatsu R12860)
QE = 31% sample-

Box

Top View-

1
Super-K PMT average(Hamamatsu R3600, QE = 22%)

+

Line

Venetian
blind

+

-

+

Top View-

0 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90
Position angle [degree]

このデータのカウント値は入射光子数が一定になる様補正してあるが、QEとCEの固体差が含まれている。
R12860とR3600では、同一光子数を入射したと仮定した場合のカウント値に歴然と差があることが分かる。

Figure 2.7: Left: Quantum efficiency as a function of wavelength for six different
17
B&L PMTs (blue, solid) and a Super-Kamiokande PMT (black, dotted). Right:
Single photon detection efficiency as a function of photocathode position for a B&L
PMT (blue) and a Super-Kamiokande PMT (black, normalized to 1). Figure fromreference [169].
view. Compared to Hamamatsu’s R3600 model used in Super-Kamiokande, it offers
improvements to both detection performance and mechanical stability.
The total detection efficiency for a single photon was increased by a factor oftwo (see figure 2.7) by combining improvements to the quantum efficiency, which
now reaches 30 % at a wavelength of 390 nm, and the capture efficiency, which wasincreased from 73 % to 95 % in the central 46 cm diameter and is more uniform
near the edges of the detection area. The increased capture efficiency was reachedthrough changes to the glass curvature and the focusing electrode, as well as byusing the box-and-line dynode.
In the Venetian blind dynode used in the Super-Kamiokande PMTs, some photoelectrons would miss the first stage of the dynode, while the larger first stage
box-and-line has a much higher acceptance. In addition to the capture efficiency,
this also improves the time resolution to 4.1 ns at FWHM—approximately half thevalue of Super-Kamiokande PMTs—and the charge resolution to 35 % compared to
50 % in Super-Kamiokande PMTs (see figure 2.8).
The nominal gain of the B&L PMTs is 1 × 107 at 2000 V, though it can be adjusted
by changing the bias voltage in a range of 1500 V to 2200 V.
The charge response was measured to be linear within 5 % at up to 470 photoelectrons and the saturation threshold beyond which the nonlinear response cannot
be corrected for is higher than 2000 PE. This high dynamic range is sufficient toreconstruct events across Hyper-Kamiokande’s physics areas, covering the MeV tomulti-GeV range.
Along with the increased efficiency, the B&L PMTs have an increased dark noise
rate compared to the 4.2 kHz in Super-Kamiokande PMTs. For an earlier batch of48

50cm high-QE box&line PMT
50cm Super-K PMT-20 -15 -10

-5

0

5

10

15

20 25
Time [nsec]

Entries (a.u.)

Entries (a.u.)

2.2 Detector Design and Construction

50cm high-QE box&line PMT
50cm Super-K PMT

-1

0

1

2
3
Charge [photoelectron]

Figure 2.8: Distribution of the single photoelectron transit time (left) and charge(right) in the B&L PMT (blue, solid) and the Super-Kamiokande PMT (black, dotted).
Figure from reference [169].
B&L PMTs, a dark noise rate of 8.3 kHz was measured at a temperature of 15 ◦C after
a month-long stabilization period. By early 2019, improvements in the manufacturing process had reduced the dark rate to 6 kHz to 7 kHz. Further work to lower
the dark rate by eliminating radioactive impurities from the glass manufacturing
process is currently ongoing.
As part of the maintenance work in 2018, 136 B&L PMTs were added to SuperKamiokande to test them under real conditions and explore the long-term stabilityof gain and dark rate.
In addition to these sensitivity changes, the B&L PMTs includes mechanicalimprovements. The shape and thickness of the glass bulb were optimized forpressure resistance to ensure survival at the bottom of Hyper-Kamiokande below
approximately 60 m of water, corresponding to 0.6 MPa of pressure. Fifty sample
B&L PMTs were tested in water at pressures of up to 1.25 MPa and no damage wasfound. However, due to the large number of photosensors in Hyper-Kamiokande, it
is difficult to ensure that there is no glass failure and additional covers described in
section 2.2.4.3 will be employed to improve pressure resistance.
2.2.4.2 Alternative 50 cm Photosensors

In addition to the B&L PMTs, two alternative photosensors with a 50 cm diameterare currently under consideration for the inner detector.
The first alternative are micro-channel plate (MCP) PMTs, which were developed
for the JUNO experiment and are produced by North Night Vision Technology.
Their detection efficiency is comparable with that of the B&L PMTs and while thetime resolution of the GDB-6201 model used by JUNO was insufficient for Hyper-

49

Chapter 2 The Hyper-Kamiokande Detector
Kamiokande, a time resolution of 5.5 ns was achieved in a newly developed model.
At the moment, however, their high dark noise rate is an issue and further tests for
reducing it are ongoing.
Another alternative are the Hamamatsu R12850-HQE hybrid photodetectors(HPD), which use a bulb and photocathode that are almost identical to those of
the B&L PMT. Instead of multiplying photoelectrons on a metal dynode, however,they are accelerated and focussed on an avalanche diode by a high voltage of 8 kV.
The HPD offers an improved charge resolution of σ = 15 % for 1 PE, while its othercharacteristics are similar to the B&L PMT. At the moment, however, no capacities
for mass production of HPDs exist.
2.2.4.3 PMT Covers

Even with a range of pressure tests before installation in the tank, the risk of a PMT
glass failure cannot be fully eliminated. In November 2001 during refilling of SuperKamiokande, the pressure wave from an imploding PMT led to a chain reactionthat destroyed almost 7000 PMTs. To avoid a reoccurrence, Super-Kamiokande
afterwards added protective covers to all 50 cm PMTs, which consist of a transparent
front section allowing Cherenkov light from the inner detector to enter and a lighttight base section. Both components are assembled around the photosensor andconnected before being installed in the photosensor support structure inside thetank. For Hyper-Kamiokande, these covers are being redesigned to account for theincreased water depth in the detector.
The front section of the cover will be manufactured from acrylic and has a hemispherical shape with a flat flange around the edge to attach it securely to the base. In
the centre, its maximum height is 19 cm above the flange. The front section contains
small holes to allow water to flow past the photosensitive surface and to reducebuildup of radioactive material or biofilms. The optical properties of the acrylic aretested to ensure a transparency of at least 50 % for photons with 300 nm wavelengthand 90 % at 400 nm to 800 nm. A low reflectivity in water is also required to reducereflected photons that effectively increase the dark noise rate in other PMTs.
The base section is intended to be water- and light-tight to separate the innerdetector from the dead region between inner and outer detector and will also be
used to mount the photosensor assembly on the support structure. As a baseline,
a conical design made from stainless steel has been developed, which is shown infigure 2.9.
To ensure that the cover is able to withstand the implosion of a PMT, hydrostaticpressure tests at up to 1.5 MPa and a set of shock wave tests were performed. In theseshock wave tests, a 3 × 3 array of covered PMTs is placed under hydrostatic pressure
corresponding to 60 m or 80 m of water and the centre PMT is artificially imploded,
while pressure sensors and high-speed cameras observe the other PMTs. The cover50

2.2 Detector Design and Construction
FRONT VIEW

SIDE VIEW(Pitch Circle Diameter)

UV transparent acrylic cover

Cable hole

Photomultiplier tube

Stainless steel cover
Reinforcing ring

Unit : mm

Figure 2.9: Front and side view of the baseline design for the protective cover. Figure
from reference [169].
incurred no damage while reducing the pressure experienced by neighbouring PMTs
to less than 0.05 MPa, sufficient to prevent a chain reaction. During maintenancework in 2018, eight of these covers were installed in Super-Kamiokande to test themunder real conditions.
Two alternative designs for the base section are currently studied. The first uses apolyphenylene sulfide resin mixed with carbon fibre. While this would be lighter andcheaper to manufacture, an early version of this design failed hydrostatic pressure
tests at 0.6 MPa. Another design uses a stainless steel cover in a tubular shape insteadof the conical shape of the baseline design. While this design has passed hydrostaticpressure tests at 0.8 MPa and would be easier and cheaper to manufacture, it iscurrently significantly heavier than the baseline design. Improvements to bothalternative designs are currently under development. For the final detector design,
a mix of covers could be used at different depths to optimize the cost and weight
while ensuring pressure resistance.
2.2.4.4 Multi-PMT Optical Module

While the baseline design relies on 40 000 large-area photosensors with a 50 cm
diameter as described above, alternative designs are considered that employ 20 000of these large photosensors and supplement them with optical modules containing
multiple smaller 7.7 cm PMTs. These multi-PMT (mPMT) modules are based ona design by the KM3NeT collaboration [215], who are using modules comprising
31 smaller PMTs in a spherical glass pressure vessel for a neutrino detector in the
Mediterranean Sea.
For Hyper-Kamiokande, this design was initially adapted into a cylindrical module that combines photosensors for the inner and outer detector into one pres-51

Chapter 2 The Hyper-Kamiokande Detector

Figure 2.10: Drawing of the two-sided mPMT module described in the text. Figure
from reference [169].
sure module by placing a hemispherical section on each end (see figure 2.10). A
single-sided module containing only PMTs for the inner detector is currently underdevelopment. While the PMT arrangement and thus the physics sensitivities areunchanged compared to the two-sided module, the resulting design will be lighterand simpler to produce and install, thus reducing the cost.
The mPMT module consists of a cylindrical structure, which contains electronics
and a support structure holding the PMTs in place, The photosensitive surface ofeach PMT is surrounded by a conical reflector that increases the light collection
efficiency by 20 %. An acrylic window is placed in front of the PMTs and coupled tothem with optical gel.
Multiple 7.7 cm PMT models from different manufacturers are available that
fulfil the technical requirements for use in Hyper-Kamiokande. Prototype mPMT
modules have been constructed; however, the design of the electronics and thedetailed procedures for final assembly are still under development.
The main advantage of mPMTs over 50 cm photosensors is their higher granularity,
which may be particularly useful for reconstructing events close to the edge ofthe inner detector or for separating overlapping Cherenkov rings in proton decay
candidate events. Due to the hemispherical shape of the mPMT module, different
PMTs have different fields of view. This effect could be used to identify dark noisein PMTs facing away from the reconstructed event vertex, which would improve52

2.2 Detector Design and Construction
reconstruction particularly at low energies. The smaller PMTs may also be lesssensitive to external magnetic fields and offer a better timing resolution. However,
the total photosensitive area of an mPMT module is significantly smaller than thatof a 50 cm photosensor.
2.2.4.5 Light Collection

The photon detection efficiency of the 50 cm photosensors could be increased bycollecting photons that did not hit the photosensitive area directly.
Such a light collection system should have a high angular acceptance, which
ensures that events near the edge of the inner detector can still be reconstructedaccurately, and it should delay arrival times of the collected photons by no morethan 5 ns in order to not degrade the timing resolution of the photosensors. The
system should also minimize reflection of photons back into the inner detector andavoid introducing radioactive backgrounds or other impurities that decrease watertransparency.
Multiple designs for this light collection system have been suggested, includingreflective cones similar to those used in the mPMT modules, wavelength shifting
plates as used in the outer detector and Fresnel lenses mounted in front of thephotosensors. All these options are currently under investigation.

2.2.5 Outer Detector
The main function of the outer detector is distinguishing neutrino interactions in
the detector from external backgrounds. Incident cosmic ray muons, which area major background in Hyper-Kamiokande, can be identified due to spatial andtemporal coincidence of energy deposition in the outer and inner detector. The
outer detector also provides passive shielding against gamma rays or neutrons fromnatural radioactivity in the surrounding rock.
To serve as an active veto, the outer detector needs to detect the presence orabsence of a signal but does not need to provide precise reconstruction capabilities.
It is therefore equipped only with a sparse array of photodetectors.
In Super-Kamiokande [201], the outer detector is approximately 2 m wide andequipped with 1885 20 cm PMTs that provide a photocoverage of 1 %. The light collection is increased by approximately 50 % using wavelength shifting plates attachedto the PMTs which absorb UV light and re-emit photons in the visible spectrum,
better matching the spectral sensitivity of the PMTs. Inside the support structure separating the inner and outer detector, a dead zone of about 0.6 m provides additionalpassive shielding.
In Hyper-Kamiokande, the width of the outer detector is reduced to 1 m in thebarrel region, while remaining at 2 m at the top and bottom. The dead zone between

53

Chapter 2 The Hyper-Kamiokande Detector
inner and outer detector remains at 0.6 m and is limited by the depth of the covers
for the 50 cm photosensors. While this narrower outer detector increases the size ofthe fiducial volume, the background reduction capabilities must be equivalent tothose of Super-Kamiokande to enable the physics goals.
An outer detector design analogous to that of Super-Kamiokande has been considered, which would require 6700 20 cm PMTs to provide a 1 % photocoverage.
Due to the narrower outer detector in the barrel region, however, it is advantageous
to reduce the distance between PMTs and provide a more uniform coverage. The
baseline design for the Hyper-Kamiokande outer detector therefore uses 10 000 to
20 000 7.7 cm PMTs for a photocoverage of 0.21 to 0.42 % as well as wavelength
shifting plates to increase light collection. Performance studies to investigate theveto efficiency as a function of the number of PMTs are currently ongoing.
2.2.5.1 PMTs

The ET9302KB [216] and ET9320KFLB [217] models manufactured by Electron Tubes
have been studied for use in the outer detector. Both are 7.7 cm PMTs with a peak
quantum efficiency of about 30 % and a dark rate which, at 400 Hz, is about ten
times lower than for typical 20 cm PMTs. The gain of the ET9302KB (ET9320KFLB)
is 3 × 106 at 950 V (800 V) and the charge response is linear within a few percent up
to a light intensity of 1500 photoelectrons. The ET9302KB (ET9320KFLB) has a risetime of 7.5 ns (2.5 ns), both providing a timing resolution that is much better thanrequired for the active veto.
Compared to the 50 cm photosensors in the inner detector, the volume of outerdetector PMTs is much smaller while the distance between them is larger. In thecase of an implosion, the resulting pressure wave would thus be much smaller andthere is no risk of a chain reaction. As in Super-Kamiokande, no PMT covers are
therefore planned for the outer detector.
2.2.5.2 Light Collection

To increase the photosensitive surface, wavelength shifting plates (model Eljen EJ286) will be mounted around each PMT with light coupling achieved through close
contact between the plate and the side of the PMT’s hemispherical photocathode.
The plate absorbs UV light at 280 nm to 400 nm and re-emits approximately one
secondary photon for every absorbed photon. Figure 2.11 shows a conceptual
drawing of this process.
The secondary photon is emitted with a wavelength of 410 nm to 460 nm, where
the quantum efficiency of the PMT is near its peak, and at a random angle. The
refractive index of the WLS plate is 1.58 and the critical angle at a surface withwater is 57°, meaning that approximately 54 % of light is trapped inside the plate

54

184

ᶞ

III.7 OUTERDESIGN
2.2 Detector
DesignDETECTOR
and Construction

DIRECT
Collection
ᶕ
ᶕ

ᶕ
ᶕ

PMT

PMT

WLS

α
’

ᶕ

WLS
Reflective
Material

Photons
ABSORBED

FIG. 114. Sketch of the light collection using a WLS plate. A charged muon emits light by Cherenkov

Figure 2.11: Schematic drawing of the wavelength shifting plate. Figure fromradiation in[214].
the UV. This is absorbed inside the plate (yellow point), and reemitted as blue light in areference
random direction. By total internal reflection (right), and reflections at the edges of the plate (left), someof this light reaches the PMT indirectly, where it adds to any light that reaches the PMT directly.

due to total internal reflection. Very close to the PMT, almost half the trapped lightis emitted in the direction of the PMT. At larger distances r from the PMT, thisis inversely
proportional
to r,
thoughaddingthe issides
3339 geometricand can alsofactor
be reflected
at the edgesof the plate.
The
refractive
index reflectorsof the WLStoplate
1.58,
of the WLS plate can slow down this decrease.
3340
so the critical angle for total internal reflection is 39.3 for a surface with air, and 57.3 for a
Based on computer simulations and laboratory tests, adding a WLS plate with
3341
surfacewith water.
practical
createwould
an air gap
betweenthe collection
WLS plate inandthethedimensions
60 cmIt×is60notcmreallyaroundeachtoPMT
increaselight3342 outersurroundingwater
the large
area ofthan
the Hyper-K
OD, toso an
we effective
assume thephotocoverage
latter value of ⇡1raddetector
byovera factorof more3, leading
of
about
1
%.
3343
for the critical angle. The amount of light trapped in the plate is 54% (77%) for a water(air)While the primary goal of the outer detector is to identify muons entering the3344
surface. Near the PMT about half of this light travels towards the PMT, giving a maximum WLS
detector, tagging outgoing muons is desirable in the analysis of events from atmo3345
efficiencyor
of beam⇡25% (35%)
at shortThedistances.
For larger
distancesthe plate there
is a passing
geometric
spheric
neutrinos.
Cherenkov
lightfrom inoutgoing
muons
thethatouter
is largely
the outside wall of the tank,
3346 throughdependence
goesdetector
like 1/r ignoring
the emitted
reflectionstowards
at the edges.
away from the photosensors. By covering the outer wall with a sheet of highly
3347
Laboratory
teststheseof thephotons
WLS plates
been carried
Edinburgh
and usedto ordevelopreflective
Tyvek,
canhavebe collected
byout
theinouterdetector
PMTs
WLSa
3348 plates
model afterof theirproperties.
The 5
squarerectangular
usedthanfor thehaveresolution
dimensions
a delayof about
ns toand
10 ns,
which isplates
shorterthetests
timingrequiredfortheactiveveto.
3349
of 23 ⇥ 23 ⇥ 1.3 cm and 28 ⇥ 48 ⇥ 1.3 cm. For the Hyper-K OD we plan to use square plates of3350

48 ⇥ 48 ⇥ 1.3 cm. A curved circular hole is cut in the center of each of the plates, matching the

2.2.6 Electronics
3351

shape of the sides of the photocathode, as shown in Fig. 115 (left). This allows it to be coupledThe
tasks of thefront-end
electronics
are Theto provide
PMTs
insidethechosen
detector
3352
to a main3” ET9320KFLB
PMTwith a minimal
air gap.
dimensionsof thehole aresuchwith the high voltage necessary for regular operations and to collect and digitize
3353
that the base of the plate sits close to the measured lower edge of the sensitive area of the PMTtime and charge data for all detected hits. Where necessary, front-end electronics
3354
photocathode.
willthen buffer this data, before finally delivering it to the data acquisition systemdescribed
in section 2.2.7, which performs triggering and reconstruction.
3355
The studies are carried out inside a large light-tight dark box (Fig. 115(right)), and an LED
The electronics are designed to provide the ns-level timing precision that is neces3356
with toa wavelengthof 370nm
a light
source.
Thevery
light highfrom theLEDis guided
the box using
sary
reconstruct
eventsasandto deal
with
data
rates
from into
a combination
3357

a cladded optical fibre. The LED light is attenuated such that it provides a fast pulse matching a

55

Chapter 2 The Hyper-Kamiokande Detectorof the dark noise in each PMT, radioactive backgrounds in the detector and thepossibility of extremely high peak event rates in the case of a nearby SN.6
Since the planned lifetime of the detector is at least 20 years and many components
cannot be replaced while the detector is running, we also require a high reliability ofcomponents and have added redundancy in some key areas.
In Super-Kamiokande [201], every PMT is connected to a single cable which
provides it with the high voltage necessary to operate and transports away theanalog output signal. All cables lead to the dome on top of the detector, where four"electronics huts" (one per quadrant of the detector) contain high voltage power
supplies and electronics racks that digitize the signals from all PMTs. A “central
hut” in the dome combines the digitized signals from all quadrants and contains a
trigger system and control electronics. The readout electronics and trigger systemhave changed multiple times during the operation of Super-Kamiokande and are
beyond the scope of this thesis.
In Hyper-Kamiokande, such a design is not practical any more due to the increased
size of the detector and number of PMTs. The total weight of the cables would reachseveral hundred tons, which would require a stronger and more expensive support
frame, while the length of cables would need to be larger than 100 m for some PMTs,
which would degrade the quality of the analog signal.
Instead, front-end electronics modules mounted on the PMT support structure
will each have a power and data connection to the electronics huts located in thedome on top of the detector. Every module then provides high voltage power to
24 nearby PMTs and receives and digitizes the signal from those same PMTs before
transferring it to the data acquisition system located in the dome.
However, placing the electronics modules inside the water tank creates a new setof challenges. Modules need to be contained in a watertight and pressure-resistantcase and require watertight connectors for incoming and outgoing connections
to transfer power and data. In the current, preliminary design, the case will be
constructed mainly from stainless steel to ensure efficient heat exchange. Heating
the water in the inner detector too much would lead to convection, which decreases
the efficiency of the water purification system as discussed in section 2.2.3. Thiseffectively limits the power consumption of the front-end electronics module andneeds to be taken into account during development.
In this section, I will first describe the requirements and preliminary designs of
the electronics modules and its individual components for the baseline design of theinner detector, which uses exclusively 50 cm photosensors. For the outer detector
and for alternative inner detector designs that include mPMT modules, possible
6 If Hyper-Kamiokande were to observe the supernova explosion of Betelgeuse, a red supergiant witha distance of about 0.2 kpc from Earth, it is expected to observe a peak event rate of approximately
108 Hz.

56

4003

voltage for each of the other blocks, but the design of the LV block is rather simple and is not

4004

described in this document. All the blocks are enclosed in a watertight pressure-tolerant case. It

4005

is necessary to use water resistant connectors to the case for the optical communication fibres and4006

the metal power supply cables. It is also necessary to design water resistant connectors for the4007

signal and HV cables at the PMTs. Since the front-end electronics module is located under the4008

water and the surrounding water is degasified, the air inside the case, which encloses the electronics

4009

2.2 may
Detector
Design and Construction
blocks, may escape from the case and the pressure in the casedecrease.

F56+,<CG.A

5;)"4%&'<=>?@/A<BCA5;)"4%&'<BDA

7&548'9'75:$)+,
E.'F!

!&56'45$),5&-.'/0/)+1!0/)+1'45$),5&'
9'H+)65,8'I@J2%)%'3%$(&"$#!"#$%
2"#")"*+,'45$),5&!"#$%&'("#")"*+,!"#$%&'&!#()*+,

Figure 2.12: Block diagram of the front-end electronics module for Hyperof the front-end
electronics module.
Kamiokande. FIG.
See 142.
textBlockfordiagram
descriptionof individualcomponents. Figure fromreference [214].
modifications are described below. Development of the components and designof the interfaces and communication protocols between them is still ongoing andmany details are not yet determined. In some cases, multiple designs for a given
component exist; I will summarize those briefly.
2.2.6.1 Inner Detector

Figure 2.12 gives an overview over the components of the electronics module forthe inner detector, which are described in this section.
Power Supply

DC power is produced in the dome on top of the detector and provided toeach electronics module via a single cable. A voltage of 48 V is assumed here,
though this could be changed to 24 V or 12 V if a lower voltage is advantageous.
A low voltage power supply block (LV PS) provides power to other blocks inthe electronics module, while a separate high voltage (HV) system transforms

57

Chapter 2 The Hyper-Kamiokande Detector
this to the stable and low noise voltage required by the photosensors, whichis 1.5 kV to 2.5 kV for the 50 cm B&L PMTs and MCP PMTs or 8 kV for HPDs.
Power consumption for the HV system should be below 1 W per channel or
24 W per module.
Signal Digitizer

The signal digitizer digitizes the charge information from 24 PMTs and needs tobe able to handle a maximum data rate of 1 MHz per PMT. There are currently
two different designs for this component under development.
The first design combines a charge-to-time converter (QTC) with a time-todigital converter (TDC). Whenever the signal pulse height from the PMT
exceeds the threshold of 0.25 PE, the QTC integrates the charge in a predefinedtime window and outputs a single square shape pulse whose start time indicates the signal time and whose length is proportional to the integrated
input charge. The TDC, which is synchronized to an external reference clock
described below, then digitizes the time of the rising and falling edge. Since
the output signal of the QTC has a finite width, this system introduces a deadtime, which can be kept below 1 µs and therefore satisfies the requirementof a 1 MHz peak event rate. This design is similar to that used in SuperKamiokande since 2008. Based on over ten years of experience, this design has
been shown to be satisfy the requirements of Hyper-Kamiokande.
An alternative design would digitize the waveform directly and thus bedeadtime-free. This could be done either by using a Flash ADC (analogto-digital converter) with a sampling rate of at least 100 MHz or by a capacitor
array, which could reach extremely fast sampling rates of up to a few GHz.
Work on all these approaches is currently ongoing. Total power consumption
for the digitizer should be below 1 W per channel or 24 W per module.
Clock and Counter System

The goal of the clock system is to provide a detector-wide uniform timing
information with a long-term stability better than 2 × 10−11 and a phase change
across different parts of the detector, e. g. due to jitter or a reset of individualcomponents, of less than 100 ps.
A master clock generator located in the dome above the water tank uses anatomic clock and GPS signals as an external reference and provides a reference
clock, counter and control signal. These signals are sent via optical fibres to
distributor modules located in the dome and each distributor then distributes
this signal to 48 electronic modules in the water via individual optical fibres.
In the electronics module in the water tank, a clock and counter block with
two optical interfaces for increased fault tolerance receives these signals and58

2.2 Detector Design and Construction
distributes them to the signal digitizer and data handling blocks. It also
receives status information and number of hits from the digitizer and sends
them back to the distributor.
Data Handling and Digitizer Control

The data handling and digitizer control block receives data from the signal
digitizer and buffers it before sending it to the readout system. This requires atleast 8 GB of dedicated memory per module, to buffer all hits for up to several
minutes. The block also checks for errors in received data and could include
data compression to reduce memory usage.
Based on commands it receives from the readout system, it can initiate pedestal data taking or other calibration data taking. It also receives commands
to control other blocks, including slow control and high voltage, which itprocesses and then forwards accordingly.
This block may be integrated with the system control and network interface
into one module.
Slow Control

The slow control block monitors environmental conditions inside the electronics module using temperature and humidity sensors.
It also monitors voltages and currents of the low voltage and high voltage
systems and can control the current and voltage provided to each channel by
the HV system following commands from the digitizer control block.
System Control and Network Interface

The system control and network interface block provides communication
between other blocks in the module and the main electronics outside of thewater tank via multiple optical interfaces to ensure redundancy and fault tolerance. Data transfers are expected to use TCP/IP and support error detection
and correction, while control commands and monitoring are expected to use
UDP/IP.
2.2.6.2 Outer Detector

For the outer detector, front-end electronics are likely to be largely similar to thosefor the inner detector described above.
Since the 7.7 cm PMTs in the outer detector require a lower voltage of 600 V to1100 V and their use as a veto necessitates less precise charge and timing information,
the signal digitizer and HV system may be replaced with simpler and cheaper
designs. However, cost savings from mass production of uniform electronics forboth inner and outer detector may outweigh the advantages of simpler components.

59202 Chapter 2 The Hyper-Kamiokande
III.8
MULTIPLE PHOTOSENSOR MODULES
Detector

Figure 2.13: Block diagram of the front-end electronics inside an mPMT module.
Figurereference
FIG.from
129. Block
diagram [214].
of the mPMT mainboard for the FADC digitization option.

3687

3688
3689
3690
3691
3692

Modules
3. 2.2.6.3
The HV Multi-PMT
board

The mPMT modules contain individual front-end boards for every PMT and one
Each
PMT
needs peran appropriate
supplycollect 2.13.
the primary
photoelectric
main
board
module, voltage
as shown
intofigure
The mainboardemission
largelyoffulfils the
same
role
as
the
inner
detector
electronics
modules
for
the
inner
detector
the photocathode and the secondary multiplication of the dynodes. To produce a signal, the anodedescribedabove, combining power supply, digitization, clock and communication. Frontof the PMT has to be at a higher voltage with respect to the cathode. One can put the cathodeend boards located at the base of each individual PMT contain a Cockcroft-Walton
to ground and set the anode to a positive high voltage, or one can put the anode to ground andvoltage multiplier that generates the high voltage required by the PMT. Designs for
set thecathodeto a negativehighvoltage.
These twochoiceson.
have advantages and disadvantages.
theindividual
blocksarestill being
worked3693

The positive voltage supply has a lower dark count rate, and the cathode of the PMT is connected3694

to ground,
there isandno possibilityof glass discharges. On the other hand the pedestal shifts with
2.2.7soDAQ
Computing3695

the event rate, and it is not possible to use voltage multipliers to generate the power supply. To

3696

read out
the anode photosensors,
signal at high voltage
is necessary
to to
have
a decoupling
capacitor witha verysystem inindividual
thisit data
is sent
thedata acquisition
(DAQ)

3697

high theinsulation
voltageThesupplyhasof
a thehigherdark systemcount rate
the glass ofdata fromdometension.
aboveThe
thenegative
water tank.
goal
DAQ
is andto combine

After the front-end electronics located in the water read out and digitize data from3698

all PMTs,
identify
the detector
andthem
to storage
the PMTis connectedto theandhighreconstructvoltage supply,events
but thein
pedestaldoes no??tshiftwritewith the
event

3699

rate and the anode signal is read out relative to the ground.

for later analysis. This section will first discuss the basic design of the DAQ system
and its operations, before describing the separate operations mode designed for60

2.2 Detector Design and Construction

Readout
buffer unit

Readout
Front−end
Boards1

Buffering
Trigger info
building

2

Trigger
processing unit

3
4

Event builder
unit

To offline
5

Figure 2.14: Simplified block diagram of the DAQ system for Hyper-Kamiokande.
Figure from reference [169].
supernova bursts. Finally, the multi-tiered computing system used for data analysis
will be described briefly.
2.2.7.1 Design of the DAQ System

The basic design of the DAQ system is shown in figure 2.14. The system will
be implemented using the ToolDAQ framework [218], and consist of four main
components which are built using off-the-shelf server hardware.
Due to the high expected data rates, the system is designed to be modular andhighly parallelizable. The ToolDAQ framework uses messaging protocols, redundant connections and buffers along with dynamic service discovery to increase fault
tolerance by detecting and dynamically replacing unresponsive computing nodes.
Readout Buffer Units (RBU)

The DAQ system will contain approximately 70 RBUs that are connected to
the front-end electronics modules in the water via a gigabit network switch,allowing data to be rerouted to other RBUs if a failure occurs. Each RBU
is responsible for reading out the digitized signals from about 30 front-end
electronics modules in the water. It then buffers all data in active memory forabout 100 seconds and temporarily saves older data to hard drives for about
one hour.
During normal operations, RBUs additionally reduce data by eliminating all
PMT hits where the signal is below a threshold of 0.25 photoelectrons. This
reduced data in a given time window is then provided to trigger processing
and event building units upon request.
Trigger Processor Units (TPU)

Once all data is read out by the RBUs, the TPUs will analyse every time window
in the data for possible signals. To do this, the TPU requests the reduced data61

Chapter 2 The Hyper-Kamiokande Detector
for this time window from RBUs and then applies various trigger algorithms
to look for events.
The simplest trigger is the “NDigits” or “Simple Majority” trigger, whichapplies a sliding time window to the data and triggers if the number of eventsin that window surpasses a given threshold. This trigger will be able to identify
high-energy events but is not viable for low-energy events due to the highdark-noise rates of the PMTs. Instead, time windows that fail this NDigits
trigger get passed on to a more sophisticated trigger optimized for low-energy
events.
This “Vertex Reconstruction” trigger relies on the fact that a low-energy lepton
travels only a few centimetres in water before its energy falls below the Cherenkov threshold, so it is well approximated as a point source that emits all
Cherenkov photons at the same time and position. The trigger uses a uniformly spaced three-dimensional grid of test vertices in the detector. For eachvertex, it corrects the recorded hit times in all PMTs by the time-of-flight ofa Cherenkov photon originating at that vertex and then applies an NDigits
trigger to a shorter sliding time window of 20 ns. If the test vertex is close
to the true vertex of an event, this time-of-flight correction leads to a narrow
peak in the corrected arrival times, while dark noise hits remain randomly
distributed.
Furthermore, the TPUs will take into account external calibration triggers aswell as GPS timestamps sent from the J-PARC accelerator to help identify
events during beam spills.
Since all triggers are software-based, they can be updated if algorithmic improvements are available or increases in computing power enable a lower
threshold.
Event Builder Units (EBU)

Once a TPU has identified an event, the timestamps of that event are sent to an
EBU, which requests the data in that time window from the RBUs. The EBU
then identifies hits within the trigger time window that are associated withthe event and writes them to disk for permanent archival.
Brokers

A central broker is tasked with coordinating operations of the DAQ system.
To increase fault tolerance, two identical machines act as broker. The primary
one handles all tasks during normal operations, while the secondary keeps
track of all decisions of the primary and is ready to replace it at any time incase of a failure.
The broker distributes tasks to TPUs and EBUs. To reduce load, it does not62

2.2 Detector Design and Construction
transfer the data itself; instead, it tells a TPU or EBU which time window toanalyse and the TPU or EBU will then request the data for that time window
from the RBUs directly.
The broker handles failures of individual TPUs or EBUs by redistributing jobs
to other available units, while failures of individual RBUs are handled byreassigning front-end electronics modules to other RBUs.
2.2.7.2 Supernova Mode

The DAQ design also contains two dedicated supernova trigger machines thatexamine the event rate in each 1 ms time slice as well as in a sliding 20 s time
window.
If a significant increase in a 20 s window is detected, which could be the signal ofa distant supernova, all data from that time period is saved to long-term storage.
In the case of a galactic supernova, an increased event rate should be visible in a
1 ms time slice shortly after the start of the burst. In that case, an alert is sent out toall machines in the DAQ system to switch into a dedicated supernova operations
mode. While in this mode, RBUs will temporarily stop the processor-intensive
data reduction and stream all data to the EBUs for permanent storage as fast as the
network connections allow.
Buffer capacities and bandwidths throughout the DAQ system are designed to beable to handle a nearby supernova at a distance of 0.2 kpc with a peak event rate ofabout 108 Hz, corresponding to peak data rates of about 100 GB/s.
Like Super-Kamiokande, Hyper-Kamiokande is likely to participate in the SuperNova Early Warning System (SNEWS [219]) and would send out an alert to thatsystem in the case of a supernova trigger.
2.2.7.3 Computing

As common in modern high-energy physics experiments, Hyper-Kamiokande will
adopt a multi-tiered computing system based on the Worldwide LHC Computing
GRID. Kamioka, which hosts the Hyper-Kamiokande detector, as well as KEK, whichhosts the neutrino beamline and near detector, will be Tier-0 sites storing all raw
event data. Several Tier-1 sites hosted by major research facilities distributed aroundthe world will store all reduced data, while individual institutions participatingin the experiment will typically host Tier-2 sites that store subsets of the data as
required.
The Hyper-Kamiokande software will be made available via the Cern Virtual
Machine File System (CVMFS), a read-only file system optimized for software
distribution, to ensure that all users have access to the most recent versions.

63

Chapter 2 The Hyper-Kamiokande Detector

2.3 Calibration
In a sensitive detector like Hyper-Kamiokande, precise understanding of all components of the detector is essential to be able to properly identify and reconstruct events.
Gaining that understanding requires extensive commissioning before the start ofoperations, which includes comprehensive calibrations. Furthermore, variations
in water quality, defects, ageing of photosensors or a number of other effects leadto changes of the detector response over time which requires regular re-calibration
throughout the lifetime of the detector.
Super-Kamiokande has been running successfully for over 20 years and the collaboration has developed expertise in calibrating a large water Cherenkov detector.
The design of the Hyper-Kamiokande calibration system will therefore be based on
the techniques used in Super-Kamiokande, while adding improvements in crucial
areas. In particular, the increased detector volume compared to Super-Kamiokandemeans that calibration needs to be performed in more locations inside the detector,
which requires increased automation.
In this section, I will first discuss initial calibration of photosensors before installation in the detector. I will then discuss the various planned calibrations that will
be performed regularly during detector operations and that are essential for reconstructing low-energy events. At high energies, additional natural particle sources
like cosmic ray muons or π0 events can be used for calibration; however, these are
beyond the scope of this thesis. Finally, I will discuss the deployment infrastructure
for radioactive sources. Since results of calibration and comparison of data with MC
simulations will only be available once the detector is actually running, in this thesis
I will, by necessity, only give a qualitative overview over the calibration strategy.

2.3.1 Pre-Calibration of Photosensors
Before installation in the inner detector, all 50 cm photosensors will undergo brief,
automated tests to reject any defects and to confirm that properties like the gain anddark noise rate are within the expected ranges.
About 2 % of photosensors will undergo more extensive tests to measure thequantum efficiency and characterize the gain as function of high voltage. These tests
will take place in a dark room surrounded by coils that completely compensate thegeomagnetic fields. Photosensors calibrated like this will be installed uniformly
throughout the detector and used as a reference for calibrating the high voltage
settings of other sensors to ensure equal gain throughout the detector.
In addition, about 0.5 % of photosensors will undergo extensive tests to determine
the gain, quantum efficiency and timing performance as a function of the location
and angle of incident light, as well as the residual magnetic field. The performanceof the 50 cm B&L PMTs is known to depend significantly on these factors and this64

2.3 Calibration
detailed characterization is essential to account for photosensor performance inevent reconstruction.
All 7.7 cm PMTs used in the outer detector will undergo similar automated tests
to reject defects and check basic properties. In addition, once they are attached to
the wavelength-shifting plates, automated tests will check whether photon hits on
the plates are registered by the PMTs.
Since the outer detector is only used as an active veto and does not need toreconstruct Cherenkov rings, calibration requirements for it are less strict. Only
about 0.1 % of PMTs will undergo extensive tests which include measurementsof the gain and dark noise rate as a function of high voltage, of the charge andtiming resolution as well as of the spatial dependence of the quantum efficiency.
The smaller PMTs have a much lower sensitivity to residual magnetic fields, which
therefore does not need to be measured.
If mPMT modules are used in the inner detector, they will undergo a separate calibration procedure starting with tests of individuals PMTs similar to those describedabove. After those tests, fully assembled modules will undergo additional tests
to characterize the photon detection efficiency as a function of hit position. These
include effects of the reflectors around each PMT and changes to the reflectivity due
to the pressure vessel.

2.3.2 Light Sources
The Hyper-Kamiokande calibration system will use a commercially available Xenon
lamp located in the dome above the tank, which is connected via an optical fibre
to an acrylic ball containing 2000 ppm of MgO as a diffuser to ensure uniform
light emission in all directions. This diffuser ball is then lowered into the centre ofdetector to produce uniform illumination of all photosensors in the inner detector.
Using the 2 % of photosensors that underwent more extensive pre-calibration as areference, this will be used during initial detector commissioning to tune the highvoltage settings for every individual photosensor and equalize the detector response.
During data taking, the Xenon lamp can be used to monitor uniformity of response
throughout the detector and correct for long-term drift of individual PMTs.
Hyper-Kamiokande will include an integrated light injection system that will be
used to regularly monitor the optical properties of the water like scattering andabsorption as well as their spatial dependence in both the inner and outer detector.
It will also be used to monitor photosensor timing, drift of gain over time andmulti-photon response.
The light injection system uses light sources in the dome on top of the tank, which
could be LEDs or similar sources capable of producing light pulses of approximately
1 ns length in several different wavelengths in the range from 320 nm to 500 nm.
This light source is connected via optical fibres to a number of permanently installed

65

Chapter 2 The Hyper-Kamiokande Detector
light injection points which are located on the support structure in gaps between
photosensors for the inner detector and in the detector wall for the outer detector.
Light could be injected into the detector by a collimator, which produces a narrowangle beam illuminating only a small number of PMTs, by a naked fibre, which
produces a light cone with approximately a 12° opening angle, or by a diffusor
which produces a wide-angle beam to illuminate a high number of PMTs.
For the inner detector, a system combining all three injection approaches has been
designed and was deployed for tests in Super-Kamiokande in the summer of 2018.
The combination of all three approaches creates a versatile system that allows a wide
range of calibration schemes and cross checks.
The outer detector has a width of 1 m to 2 m, so a narrow beam would only reachindividual PMTs. To limit the number of injection points required, the calibration
strategy for the outer detector will therefore rely solely on the diffuser. This issufficient to fulfil the less stringent calibration requirements for an active veto that
does not need to precisely reconstruct events.

2.3.3 Radioactive Sources
Three different radioactive sources are planned to be used for calibration in HyperKamiokande.
A nickel-californium source consists of a Cf source surrounded by a sphere ofhigh-density polyethylene containing NiO2 powder. 252 Cf produces neutrons which
are thermalized and then captured on 58 Ni. When the resulting excited state of 59 Ni
decays, it releases gamma rays with a total energy of approximately 9 MeV. Thiscan act as a uniform, stable source of low-intensity Cherenkov light to measure
the gain and single photoelectron charge distribution of photosensors. Since thesignal contains a background component coming mainly from neutron capture onhydrogen, this source cannot be used to calibrate the absolute energy scale.
An americium-beryllium source uses α decays of 241Am to induce an (α, n) capture
reaction on 9 Be. The resulting excited state of 12 C then decays emitting a 4.44 MeV γ,
while the free neutron gets captured on hydrogen nuclei on a timescale of several µs,
resulting in a 2.2 MeV γ emission. The coincidence of the 12 C deexcitation signal andthe neutron capture signal will be used to determine the neutron capture detection
efficiency of Hyper-Kamiokande. If gadolinium is added to the detector, about half
the neutrons would get captured on gadolinium, producing several photon with a
total energy of about 8 MeV. In that case, this calibration source could be used todetermine the relative capture rates on Gd and H as well as the combined neutron
detection efficiency.
The third calibration source uses a commercial deuterium-tritium generator to
produce 14.2 MeV neutrons in the water. This is above the 11 MeV threshold to
produce 16 N from 16 O nuclei in the water via a (n, p) reaction. 16 N decays with a half66

2.3 Calibration
life of 7.13 s producing both an electron with β endpoint of 4.3 MeV and a 6.1 MeV γ
in the dominant decay branch. This calibration will be repeated at multiple vertices
within detector to calibrate the energy scale as a function of position and direction.
If a LINAC cannot be used to calibrate Hyper-Kamiokande, this source will also
be used to calibrate the collection efficiency of photosensors and to fix the absoluteenergy scale.

2.3.4 LINAC
The Super-Kamiokande calibration system contains a LINAC that delivers a lowintensity beam of single electrons with a well-defined energy of around 6 MeV
or 13 MeV to calibrate the absolute energy scale at low energies. The beam istransported into the dome and deployed into the water using a guide tube thatallows injecting electrons into the tank at varying depth. For Hyper-Kamiokande, toachieve the physics goals in full, it is required to reduce the energy scale uncertainty
to below 0.3 % and the energy resolution uncertainty to 2 % across the whole fiducial
volume, which can only be achieved with a LINAC.
While the design of the LINAC system for Hyper-Kamiokande is not yet completed, two main improvements are currently under consideration. A commerciallyavailable LINAC model could be used that produces electrons with a wider range
of energies of 4 MeV to 20 MeV. At the bottom end of the guide tube, a magnet
system could be installed to vary the electron direction in the tank and probe thedependence of energy scale on the particle direction, which is one of the major
uncertainties in Super-Kamiokande.

2.3.5 Deployment System
Due to the large detector volume, calibrating Hyper-Kamiokande requires deploying sources in a large number of different positions throughout the detector tounderstand the position and direction dependence of reconstruction. To reduce themanual labour required and the detector downtime associated with calibration, asource deployment system needs to be designed.
For Hyper-Kamiokande, the deployment system is designed to allow vertical
deployment through calibration ports located along two perpendicular axes acrossthe detector, exploiting cylindrical symmetry to achieve a full three-dimensional
calibration.
Different types of calibration ports will be provided. Regular ports will havea diameter of approximately 22 cm and be located in gaps between neighbouring
photosensors. They will typically be located at a distance of 3 m from each other,which is reduced to 0.5 m near the edges of the inner detector to achieve precise
calibration near the edge of the fiducial volume and reduce systematic uncertainties.

67

Chapter 2 The Hyper-Kamiokande Detector
Regular size ports will be used both for deployment of sources and for the LINAC,
though the LINAC may have higher loading requirements due to the more complicated transport and deployment system. These ports will also be available in theouter detector. Near the centre of the detector, one oversized port with a diameter ofat least 75 cm will be provided for deployment of larger sources, which may require
removal of one photosensor.
A prototype of the automatic source deployment system for radioactive sources
designed for Hyper-Kamiokande was installed in Super-Kamiokande during 2018
for testing.

2.4 Backgrounds
Supernova burst neutrinos are observed in the energy range of 5 MeV to almost
100 MeV. At the upper end, this overlaps with the low end of the energy range ofatmospheric neutrinos, while at intermediate energies of about 20 MeV to 40 MeV,
supernova relic neutrinos are another main signal that Hyper-Kamiokande will try
to observe. Below about 20 MeV, Hyper-Kamiokande will observe solar neutrinos,
as well as a small number of reactor antineutrinos near its lower energy threshold.
However, the event rate of each of these conflicting signals is between less than
one and up to about one hundred events per day, with zero or at most one event
expected during the 10 s to 20 s duration of a supernova burst. These are therefore
negligible as background sources.
The main sources of background in the energy range relevant for supernova burst
neutrinos are radioactive decays in the detector with energies below 5 MeV andspallation events induced by cosmic ray muons, which can reach energies of up
to 20 MeV. Since these backgrounds cover the full energy range of solar neutrinos,
which are a major area of physics in both Super- and Hyper-Kamiokande, they havebeen investigated in great detail and are well understood. The Super-Kamiokande
collaboration has been able to reduce these backgrounds significantly, which hasenabled them to routinely detect and perform precision measurements with solar
neutrinos down to a kinetic energy of 3.49 MeV in recent analyses [202]. In thissection, I will discuss these backgrounds in Hyper-Kamiokande and approaches toeliminate them as far as possible.
Since the flux of supernova burst neutrinos is several orders of magnitude higher
than that of solar neutrinos, with about 104 to 106 events expected in a 10 s to
20 s time window, applying the background reduction techniques developed forsolar neutrino analyses would guarantee an effectively background-free signal. As
discussed in section 2.2.7, the DAQ system for Hyper-Kamiokande is designed tosave a complete, unreduced data set to permanent storage if a supernova burst
is detected. After a burst, it will therefore be possible to developed optimized

682.4 Backgrounds
triggering and background reduction algorithms and apply them to the data. It
will likely be possible to relax some of the cuts used in solar neutrino analyses and,for example, to increase the size of the fiducial volume, which has the potential tosignificantly increase the number of observed events.
Due to the advanced triggering algorithms described in section 2.2.7, dark noise ofphotosensors does not produce background events above 5 MeV and will therefore
not be considered as a background source here. Its effects on energy reconstruction
will be discussed in section 3.4.3.

2.4.1 Radioactive Decays
In Super-Kamiokande, radioactive decays in the detector are the dominant background at the lowest energies and effectively preclude Super-Kamiokande fromdetecting solar neutrino events with an energy below 3.49 MeV [202].
Measurements in Super-Kamiokande found that the decay chain of 222 Rn is thelargest component of this background, while decay products of 220 Rn give only aminor contribution. Many daughter isotopes of 222 Rn have an energy that is too low
to produce Cherenkov light and the biggest exception is beta decay of 214 Bi, which
has a Q-value of 3.27 MeV.
There are three main sources introducing radon into the Hyper-Kamiokande
detector.
The first source is air inside the mine, which contains radon emanating fromthe surrounding rock. Measurements with a new radon monitoring system [220]showed that the radon level in the Tochibora mine, where Hyper-Kamiokande will
be built, is about 1200 Bq/m3 , which is comparable to that in the Mozumi mine near
the Super-Kamiokande detector. Like in Super-Kamiokande, a fresh air system will
be installed for Hyper-Kamiokande, which pumps outside air into the experimental
area to keep the radon level in the dome below about 100 Bq/m3 .
Another source of radon is the rock surrounding the detector itself. Traces ofradon will be able to penetrate the surface of the tank and enter the detector. A firstestimate of the radon levels that will be introduced in this way indicates that theconcentration in the outer detector will be O(10) mBq/m3 , similar to that observedin the Super-Kamiokande outer detector. This is achieved to a large part by lining
the cavern with a 5 mm thick layer of HDPE which has a low radon permeability.
To achieve a more reliable estimate of the radon levels that can be achieved, theHyper-Kamiokande collaboration is testing the radon permeability of HDPE sheets
in water. First results found the permeation to be less than 5 × 10−7 cm2 /s, while
high-sensitivity measurements are still ongoing.
From experience in Super-Kamiokande, we know that the radon concentration in
the outer detector has little influence on the concentration in the inner detector as

69

Chapter 2 The Hyper-Kamiokande Detector
Radioactive Source
U decay chain
Th decay chain
40 K
Rn emanation

Requirement≤ 3 Bq per PMT≤ 1 Bq per PMT≤ 10 Bq per PMT≤ 3 mBq/m3

Table 2.2: Upper limits on radioactivity for photosensors in the Hyper-Kamiokande
inner detector. Values from reference [214].
long as there is no water exchange between both. In Hyper-Kamiokande, the innerdetector will be completely separated from the outer detector.
The main source of radon in the inner detector is therefore expected to be impurities in the glass used in photosensors. Requirements defined by the collaborationfor 50 cm PMTs are listed in table 2.2. We are currently in the process of determining
the origin of radioactive impurities in prototype PMTs and aim to improve theproduction process to reduce these impurities.
In addition to photosensors, all other materials that are planned to be used insidethe detector—including photosensor covers, the support structure, sheets separating
the inner and outer detector, cables, electronics modules and components of mPMT
modules—will undergo screening in an effort to reduce radioactive backgrounds
through appropriate choice of raw materials or changes to production processes.
As long as water flow in the detector is well-controlled, radioactive elements
emanating from photosensors or other detector components will remain near theedges of the inner detector so that any background events are concentrated in that
region. Removing all events that are reconstructed to be outside of the fiducial
volume, i. e. less than 1.5 m away from the walls of the ID, therefore dramaticallyreduces these backgrounds. For solar neutrino analyses in Super-Kamiokande, inthe energy range below 5 MeV the collaboration uses a much stricter fiducial volume
cut shown in figure 2.15. That stricter cut eliminates all events with a distance ofless than about 5 m from the wall of the inner detector or less than about 10 m fromthe bottom of the inner detector, since radioactive backgrounds are largest in thoseparts of the detector.
In the current Super-Kamiokande solar neutrino analysis, a number of additional
cuts are used, which are based on the spatial and temporal distribution of observed
hits [202]. While changes in detector geometry would likely require modifications
to these cuts, they could, in principle, be used for background reduction in HyperKamiokande as well.

70

2.4 Backgrounds
3.5-4.0 MeV

4.0-4.5 MeV

4.5-5.0 MeV

Figure 2.15: Distribution of low-energy events in the Super-Kamiokande detector
during phase IV. Black lines indicate the reduced fiducial volume at the respectiveenergies, while the fiducial volume above 5 MeV is the whole area, corresponding to22.5 kt. Colours show the event rate per day and bin, while r and z correspond to thehorizontal and vertical axis of the detector, respectively. Figure from reference [169].

2.4.2 Muon-Induced Spallation
Cosmic ray muons entering the detector can produce unstable isotopes via theinteraction µ +16 O → µ + X or via capture on 16 O to produce 16 N. The resulting
nuclei will then decay by emitting beta or gamma particles with an energy of up
to about 20 MeV, making them an important background for neutrino detection atthese energies.
The flux and average energy of cosmic ray muons in the Tochibora mine, whereHyper-Kamiokande will be located, was simulated with the muon simulation code
MUSIC [221] using a topological map with 5 m mesh resolution and assuming arock density of about 2.7 g/cm3 . Figure 2.16 shows the directional dependence ofthe simulated muon flux in Super- and Hyper-Kamiokande as well as the measured
muon flux in Super-Kamiokande, which shows good agreement with the simulation.
The expected muon flux in Hyper-Kamiokande is Jµ = 7.55 × 10−7 cm−2 s−1 withan average energy of h Eµ i = 203 GeV, compared to Jµ = 1.54 × 10−7 cm−2 s−1
and h Eµ i = 258 GeV in Super-Kamiokande. The higher overburden of SuperKamiokande leads to a lower total flux than in Hyper-Kamiokande and has arelatively stronger shielding effect for low-energy muons, which leads to an increasein the average energy of observed muons. Thus, while the muon flux in HyperKamiokande is increased by a factor of five, the average spallation yield per muon
calculated with the FLUKA code [222] is reduced by about 20 % due to the lower
muon energy so that the total rate of spallation events per unit volume is about fourtimes as high as in Super-Kamiokande.
The rate of downward-going muons is about 2 Hz in Super-Kamiokande [223]and will increase to about 50 Hz in Hyper-Kamiokande due to the lower overburden
and larger detector size. In Super-Kamiokande, the yield of unstable isotopes

71

Muon Flux (cm-2 s-1)

Chapter 2 The Hyper-Kamiokande Detector

× 10-6
2
Data
MC
1.5
1
0.5
0
0

Muon Flux (cm-2 s-1 rad-1)

Hyper-K

Super-K
0.2

0.4

0.6

0.8

× 10-7
2.5
Data
2
MC

1
cosθ

Hyper-K

1.5
1Super-K

0.5
0
0

100

200

300
φ (deg)Figure 2.16: Muon flux as a function of zenith angle θ (top) and azimuth angle φ(bottom). Red lines show the result of simulation with MUSIC in Super- and HyperKamiokande, while blue lines show the measured fluxes in Super-Kamiokande.
Figure from reference [169].

72

2.4 Backgroundswith decay energies of more than 3.5 MeV for a single muon was calculated to be
5 × 10−6 g−1 cm2 [224]. Assuming the density of water in the detector to be 1 g/cm3
and a track length of 32.2 m (corresponding to the height of the fiducial volume), thisgives about 0.016 spallation events per muon. In Hyper-Kamiokande, a 20 % lower
spallation yield per unit length combined with a 1.6 times taller fiducial volume
yields about 0.02 spallation events per muon, As a result, the rate of spallation eventsin Hyper-Kamiokande is expected to be approximately 1 Hz.
Since the half-life of spallation products is between several milliseconds and a few
seconds, these events can in principle be identified through spatial and temporalcoincidence with cosmic ray muons that pass through the detector. The first modern
search for supernova relic neutrinos with Super-Kamiokande employed a two-stepprocess to reduce spallation backgrounds [225, 226], starting with a time correlation
cut which removed all events within 0.15 s after a muon event. Remaining eventswere then subject to a likelihood function cut. In addition to the time delay after themuon event, this took into account the distance between the reconstructed event
vertex and the preceding muon track as well as the residual charge Qres , which was
defined as the detected charge (measured in photoelectrons) that is above the typicalionization loss of 2300 PE per metre track length. A large and positive value of Qres
indicates energy loss through showers, which could produce spallation products.
This likelihood cut reduces the spallation background by an order of magnitude
while introducing a detector dead time of about 20 %.
A later analysis discovered that spallation events are correlated with peaks inthe energy loss rate dE/dx along the muon track, which can be used for improved
background rejection [227]. In a range of papers over the following years, Li and
Beacom provided a theoretical description of spallation processes, which put thisempirical observation onto a theoretical foundation, and suggested a number ofsignificant improvements to muon reconstruction and spallation cuts [224, 228, 229].
While the lower overburden and increased rate of downward-going muons inHyper-Kamiokande will require some modifications to these cuts, it is clear thatthe spallation event rate can be reduced to much less than 1 Hz, which enables aneffectively background-free observation of supernova burst neutrinos.

73True heroism is minutes, hours, weeks,
year upon year of the quiet, precise,
judicious exercise of probity andcare—with no one there to see or cheer.
David Foster Wallace

Chapter 3
A Software Toolchain for Supernova
Neutrino Events in Hyper-Kamiokande
In addition to the detector described in the previous chapter, the Hyper-Kamiokande
collaboration is developing a software toolchain for generating and simulating
events as well as reconstructing simulated or observed events to enable physics
analyses. A schematic overview of this toolchain is given in figure 3.1.
In this chapter, I will describe the toolchain insofar as it applies to supernova burst
neutrinos. It starts with neutrino fluxes as a function of neutrino flavour, time andenergy that are produced by computer simulations of supernovae. Section 3.1 describes the supernova models I use in this thesis. I then use a custom software called
sntools, introduced in section 3.2, to generate neutrino interactions in the detector
volume from these neutrino fluxes. Section 3.3 describes the detector simulation
software, WCSim, which simulates propagation of particles and Cherenkov light in!
Physics
Modelssntools
NEUT
etc.

WCSim

Event
Generators

Detector
Simulation
Event
Reconstruction

BONSAI
FiTQunetc.

furtheranalysis

observed events

Figure 3.1: Overview over the software toolchain for Hyper-Kamiokande. Software
used for supernova burst neutrinos is highlighted in bold.

75

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
the detector and applies detector effects, including digitization and triggering. The
output of this detector simulation should be equivalent to the output of the DAQ
system once Hyper-Kamiokande is operational and observes actual neutrino interactions. Finally, reconstruction of the vertex, direction and energy of each simulated
event is described in section 3.4. Further analysis of the simulated data sets, whichbuilds on the results of the event reconstruction, is described in chapter 4.

3.1 Supernova Models
In this thesis, I use five supernova models that are developed and run by externalgroups not affiliated with the Hyper-Kamiokande proto-collaboration. These models
are simulated with custom software suites that typically combine a hydrodynamics
solver and a neutrino interaction code. The hydrodynamics code simulates selfinteractions of matter by solving the differential equations for conservation of mass,
momentum and energy in the system. The neutrino interaction code implements
transport of neutrinos and their interactions with the background matter.
In these simulations, it is typically assumed that temperatures inside the supernova are too low to produce µ and τ leptons.1 As a result the emitted fluxes of νeand ν̄e differ significantly from each other and from those of heavy lepton flavour
neutrinos, while the differences between νµ , ντ and their respective antineutrinos
are assumed to be negligible. It is therefore common to label the different neutrino
species as νe , ν̄e and νx .2
These simulations are then performed on supercomputers using a numerical gridwith model-dependent resolution. After post-processing, the output of these models
is generally provided in the form of text files describing the neutrino flux at theouter edge of the simulation volume—i. e. before traversing the outer layers of thestar—as a function of neutrino species, time and energy.
To truly understand the explosion mechanism, high-fidelity three-dimensionalmodels are required that solve the magnetohydrodynamical equations in highspatial resolution and full general relativity, while taking into account complex
microphysics of the equation of state for nuclear matter and accurate energy- andflavour-dependent neutrino transport. Current simulations are still severely limitedby the available computing power and thus unable to simultaneously include allthese effects to the highest possible accuracy. Furthermore, even the most sophisticated simulations available today require millions of node-hours on modern
1 A recent study indicated that this assumption may not be realistic and that µ production near thecentre of the supernova can facilitate explosions in some models [230]. However, such effects are
not yet taken into account in most recent simulations, including the ones used in this thesis.
2 Throughout this thesis, I will use ν to refer to any one of the four heavy lepton flavours. Note thatx
this is not handled uniformly in literature and some authors use νx to refer to the sum of all four
flavours instead.

76

3.1 Supernova Models
supercomputers and may take weeks or months to run, so that only a small numberof models can be simulated at the highest possible levels of precision.
It is thus impossible to perform such sophisticated simulations for a large numberof possible progenitors, which span a wide range of masses, metallicities, rotational
velocities and magnetic fields, all of which may have a significant quantitative andqualitative impact on the outcome of the simulation (for recent studies of theseparameters, see e. g. references [128, 231, 232, 233, 234, 235, 236]). Additionally, inbinary systems, interactions with a companion star may affect stellar evolution andthus the fate of a star [237].
One-dimensional (i. e. spherically symmetric), computationally much less expensive models are therefore necessary to explore this wide range of progenitors andstudy the population of supernovae. However, they face a major problem: The
core-collapse supernova explosion mechanism is fundamentally multi-dimensional
and imposing spherical symmetry suppresses explosions in many simulations. Several different methods may be used to artificially initiate explosions. Two early
approaches, which neglected neutrino contributions to the explosion mechanism
and were mainly used for studying nucleosynthesis yields in the ejecta, are the“piston”, where an outgoing shock wave was artificially started within the stellar
core, or the “thermal bomb”, where matter in the stellar core is artificially heated tocause an expanding shock wave [238]. More recently introduced approaches for triggering explosions (see e. g. references [239, 240, 232]) include more realistic neutrino
physics but are still sensitive to the choice of free parameters, which may be chosensuch that the outcome reproduces observations or results of more sophisticatedsimulations.
A comparison of six different modern simulation codes that simulated an identical
20 M progenitor with largely identical input physics showed good qualitative
agreement in spherical symmetry. Differing treatments of hydrodynamics or neutrino transport caused O(10) % differences in the neutrino luminosity and meanenergy, as well as the event rate expected in a neutrino detector such as SuperKamiokande [241]. When comparing simulations between different publications,however, there may be significantly stronger disagreement since simulations may
also differ in aspects of input physics—such as the equation of state for nuclear
matter or the set of included neutrino interactions—that were intentionally kept
identical in the above comparison.
In this thesis, I use five different models: a one-dimensional model that is primarily of historic interest, two one-dimensional models from recent parametric studies
and two more complex multi-dimensional models. These simulations were performed by different groups using different simulation codes that implement different
approximations. They are intended to represent the much wider range of available
models.

77

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande

3.1.1 Totani
This model [180], which is also referred to as the “Livermore model” or “Wilson
model” in literature, was published in 1997 and is one of a small number of models
that include the late-time evolution of the neutrino emission. While it is now dated
and has been surpassed by more accurate models, it is still used for comparisons withliterature in some recent publications, for example by the Super-Kamiokande [172]and DUNE [96] collaborations. I include it here since it is used as a baseline modelin the Hyper-Kamiokande Design Report [169].
It uses a 20 M progenitor, which was modelled to resemble the progenitor of
SN1987A, and a simulation code developed by Wilson and Mayle [242, 243]. Neutrino transport is modelled by the flux-limited diffusion approximation with 20
logarithmically spaced energy groups up to 322.5 MeV. The simulation is onedimensional and was performed from start of collapse to 18 s after the core bounce.
Neutrino data for this model was provided in the Totani format described below
in section 3.2.2. Spacing of time steps was 0.2 ms during the neutronization burst(for νe only), 10 ms to 25 ms during the first 250 ms and 100 ms to 1000 ms at latertimes.

3.1.2 Nakazato
This family of models [128] offers a modern successor to the Totani model describedabove. It was used by the Super-Kamiokande collaboration for designing theirreal-time supernova burst monitor [172] as well as by the Hyper-Kamiokande
collaboration in their design report [169].
It contains simulations of multiple progenitors with a range of initial masses(Minit = 13 M , 20 M , 30 M and 50 M ), each with solar metallicity (Z = 0.02)
and a lower metallicity of Z = 0.004, which is typical for supernova progenitors in
the Small Magellanic Cloud.3 In this work, I focus on the 20 M progenitor withsolar metallicity. Additionally, I will use several other progenitors for comparison insection 4.5.
The one-dimensional simulation was performed from start of collapse to 20 s after
core bounce in two stages. Both stages used the Shen equation of state [246], thesame set of neutrino interactions [247] and 20 variably spaced energy groups up to
300 MeV.
The first part of the simulation starts with the collapse of the stellar core and ends
at 550 ms, while the outer layers of the core are accreting onto a standing shock front.
This part is simulated with a general relativistic neutrino-radiation-hydrodynamics
3 The metallicity of the Large Magellanic Cloud, where the progenitor of SN1987A was located, isabout half the solar metallicity [244, 245].

78

3.1 Supernova Models(νRHD) code that solves the differential equations for hydrodynamics and neutrinotransport simultaneously [247].
The second stage of the simulation starts at an arbitrarily chosen shock revival
time of trevive = 100 ms, 200 ms or 300 ms and ends at 20 s after the core bounce.
Using the result of the νRHD simulation as an initial condition, the proto-neutronstar cooling (PNSC) is then simulated in general relativity by solving the hydrostatic
equations and using a multi-group flux-limited diffusion scheme to model neutrinotransport. Since the amount of matter falling back onto the proto-neutron star after
the revival of the shock-wave is small, effects of accretion are not simulated.
Combining these two simulation stages allows performing a more detailed andcomputationally expensive simulation for the accretion phase, where dynamics ofthe shock front are essential, while still determining the evolution of the supernova
out to late times using a simpler simulation. However, the physical differences
between both stages lead to a discontinuity in the resulting neutrino flux.
During the νRHD stage, neutrino emission is dominated by the accretion shock
resulting from outer layers of the stellar core falling onto the outgoing shock wave.
Most one-dimensional simulations, including the one described here, do not successfully produce a supernova explosion except when artificially triggered, since
the lack of multi-dimensional effects leads to an unrealistically high mass accretion
rate. Therefore, the neutrino emission during this phase is likely overestimated. On
the other hand, during the PNSC stage, neutrino emission from the accretion onto
the revived shock front and the proto-neutron star is completely ignored, which
underestimates the emission particularly shortly after the shock revival.
The authors recommend interpolating between these stages using an exponentialfunction, such that the flux Fνi of each neutrino species is given byFνi ( E, t) = f (t) FννRHD( E, t) + (1 − f (t)) FνPNSC( E, t),iiwhere
f (t) =

(

1,
exp



+tshift )− t−(treviveτdecayt ≤ trevive + tshift, trevive + tshift < t

(3.1)

(3.2)

is an interpolating function, tshift = 50 ms is a time shift necessary to avoid discontinuous effects during the switch from the νRHD to the PSNC stage andτdecay = 30 ms is a decay time scale.
Unfortunately, while this approach eliminates the discontinuity it introduces
an exponential drop-off in the luminosity and mean energy across all neutrino
species at trevive + tshift , which would make it easy to identify this model. Since thisthesis focusses on the early part of the neutrino signal, I will use the fluxes fromthe νRHD phase only and not use this interpolation. Insofar as this overestimates
the neutrino luminosity by a constant factor, that will not affect the results of the79

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
analysis in chapter 4 since that analysis assumes an unknown supernova distanceand normalizes the differential event rates to a fixed total number of events.
If the overestimation of the neutrino luminosity is time-dependent, the size of thiseffect depends on the shock revival time, which is not known. For the purposes ofthis thesis, I assume that this effect is negligible. This is similar to assuming a shock
revival time larger than about 500 ms, which does not appear improbable.4 For theprogenitor comparison in section 4.5, this effect will largely cancel out under theconservative assumption that shock revival times are similar across progenitors. If
the shock revival time varies significantly between progenitors, that would increase
the difference in their neutrino emission and thus increase the identification accuracy
above the results shown in this thesis.
Neutrino data for this model was provided in the Nakazato format described
below in section 3.2.2 with sub-ms spacing of time steps.

3.1.3 CouchThis family of models [232, 248] introduces a new approach for including effectsof convection and turbulence in a one-dimensional simulation, which the authors
call STIR (Supernova Turbulence In Reduced-dimensionality). In this approach, theeffective strength of convection depends on one tuneable parameter, αΛ . The authors
find that a value of 0.8 to 0.9 best reproduces the results from a three-dimensional
simulation of the same progenitor [158]. In the following, I therefore use resultsfrom the simulation with αΛ = 0.8.
The model family contains 138 solar-metallicity progenitors with masses from
9 M to 120 M . Here, I use results from the simulation of a 20 M progenitor. This
progenitor was originally described in reference [249].
The simulation was implemented in the FLASH simulation framework [250,251] using a newly-implemented hydrodynamics solver with a modified effective
potential to approximate effects of general relativity [5, 252] and the SFHo equationof state [253].
Neutrino transport is simulated using a so-called “M1” transport scheme [254, 252]
with 12 logarithmically spaced energy groups up to 250 MeV. Starting at 5 ms postbounce, effects of inelastic neutrino-electron scattering are turned off to reducethe computational power required. While this has little impact on the supernova
dynamics, it may result in an increased mean energy for νx [252].
Neutrino data for this model was provided in the Gamma format described below
in section 3.2.2 in time steps of approximately 0.5 ms.
4 While the paper by Nakazato et al.

only considered revival times up to 300 ms [128], different
simulations of the same progenitor often produce large variations in explosion time; see e. g. table 1of [232].

80

3.1 Supernova Models

3.1.4 Tamborra
This model [123, 255] is a pioneering three-dimensional supernova simulation withsophisticated neutrino transport. It reported significant effects of the standing
accretion shock instability (SASI) [130], large-scale sloshing motions of the shock
front that may compete with neutrino-driven convection in facilitating explosions in
multi-dimensional simulations and are fundamentally multi-dimensional and thus
not observable in one-dimensional simulations of identical progenitors.
I use results from simulations of a 27 M progenitor from reference [256]. To seed
the growth of hydrodynamic instabilities, random density perturbations of 0.1 %were manually introduced at the start of the simulation.
The simulation was performed using the P ROMETHEUS -V ERTEX code consistingof the P ROMETHEUS [257] code, a hydrodynamics solver which implements thepiecewise-parabolic method [258], and the neutrino transport code V ERTEX [259],
which uses the “ray-by-ray-plus” approach for velocity- and energy-dependentneutrino transport [3]. In this approximation, the neutrino moments equations fordifferent angular bins (“radial rays”) decouple and can be solved independently.
It assumes that neutrino fluxes are symmetric around the radial direction, while
including non-radial neutrino advection and pressure terms.
The simulation employs a sophisticated set of neutrino interaction rates describedin reference [124]. It uses the Lattimer and Swesty equation of state with compressibility K = 220 MeV [260] and an effective potential to account for general relativistic
corrections to Newtonian gravity [5].
In multi-dimensional simulations, the neutrino signal inherently depends on the
direction of the observer relative to the progenitor and extensive post-processing isnecessary to determine the directionality dependence of the neutrino signal. Here, I
use the fluxes in the “violet” observer direction identified in reference [255], which
exhibits a particularly large amplitude of the SASI oscillations in the luminosity andmean energy of neutrinos.
Neutrino data for this model was provided in the Gamma format described below
in section 3.2.2 in time steps of approximately 0.5 ms.

3.1.5 Vartanyan
This model is a very recent two-dimensional simulation with high-precision neutrino
radiation hydrodynamics. It is similar to the simulations presented in references [261,262] but used a different equation of state and grid resolution, which caused somephysical and numerical differences. As a result, while the luminosity and meanenergy are qualitatively very similar to those described in reference [262], exact
values may differ by several percent.

81

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
I use results of a simulation of a 9 M progenitor with solar metallicity fromreference [231].
This two-dimensional simulation was performed using the neutrino-radiationhydrodynamics code F ORNAX [263], which combines a radiation hydrodynamics
solver using a generalized variant of the piecewise-parabolic method [258] withneutrino transport using the “M1” scheme [264, 265], similar to that used in the
Couch model. It used 20 logarithmically spaced energy groups with energies up to
300 MeV for νe and up to 100 MeV for ν̄e and νx . The detailed set of neutrino-matterinteractions employed are summarized in reference [266]. The simulation used
the SFHo equation of state [253] and an effective potential to account for generalrelativistic corrections to Newtonian gravity [5].
Neutrino data for this model was provided in the Princeton format described
below in section 3.2.2 in time steps of 1 ms.

3.2 sntools: A Supernova Event Generator
sntools [267] is a Monte Carlo (MC) event generator for supernova neutrino interactions in water Cherenkov detectors. Based on detailed time- and energy-dependentneutrino fluxes provided by the supernova models described in the previous section, it generates interactions within the detector for the dominant and the mostimportant subdominant interaction channels, before writing them to event files thatcan be used as an input for the full detector simulation described in section 3.3.
While a similar event generator was already developed by the Super-Kamiokande
collaboration [172], that code is proprietary and not currently available to nonmembers. Furthermore, it would have likely required extensive modifications forcompatibility with the new detector simulation for Hyper-Kamiokande and to use
more recent cross-section calculations and different input formats.
The SNOwGLoBES software [84] is widely used to compute event rates andenergy distributions for supernova burst neutrinos in various different detectors.
While it is an excellent tool for preliminary studies or quick comparisons of different
detector configurations, it uses simplified approximations for detector effects likeenergy resolution or threshold and does not take into account time-dependence of
input fluxes. It is an event rate calculator—not an event generator—and is by its
own admission “not intended to replace full detector simulations” [84].
Finally, a number of other event generators like NEUT [268] or GENIE [269] exist.
However, these are focussed on atmospheric or accelerator neutrinos which typicallyhave much higher energies than supernova burst neutrinos and may therefore be
incomplete or inaccurate at these low energies. They would require extensive
modifications to be used for here.
Since none of these existing codes are suitable for the purposes of this thesis, I82

3.2 sntools: A Supernova Event Generator
have developed a completely new event generator called sntools. In this section,
I will start by describing its overall design. I will then discuss the supported
input formats, its treatment of neutrino flavour conversion and the implemented
interaction channels.

3.2.1 Design
Input

!

sntools
genevts.py…

Output!

channel.py

Input Formats

Interaction Channels

Figure 3.2: Overview over the structure of sntools. See text for a detailed description.
An overview over the structure of sntools is given in figure 3.2. sntools is written
in Python, making it easy to read and extend the code, and designed to be extensible
and accurate. It makes use of the scipy and numpy libraries [270, 271], which
implement many numerical calculations in Fortran for performance reasons, and I
have tuned some performance-critical parts of sntools for increased performance.
On a current desktop computer, sntools needs O(10) min to generate events for a
supernova at the fiducial distance of 10 kpc in Hyper-Kamiokande.
The main user interface is provided by the file genevts.py. It requires an input
file containing neutrino fluxes from the supernova, while other, optional arguments
include the format of the input file (see section 3.2.2), the neutrino mass ordering(see section 3.2.3), the distance to the supernova5 and the interaction channels
to consider (see section 3.2.4). A full list of possible arguments can be found by
executing python genevts.py -h.
After parsing the arguments, events are generated separately for each combinationof interaction channel and input species by calling code in the file channel.py.
The code first calculates the total number of events expected in each 1 ms bin, which
5 which can be selected using the --distance<value> command line argument, where the value

is in kpc

83

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
is given by
N (t) =xd Φ(t, Eν ) d σ( Eν , Ee )dEe dEν ,
dEν
dEe

(3.3)

where Φ(t, Eν ) is the neutrino flux and σ( Eν , Ee ) is the cross section of the current
interaction channel. It then picks the actual number of events to generate withinthat time bin from a Poisson distribution with expectation value N (t). Finally,
it generates events by rejection sampling from the energy spectrum of neutrino
interactions at that time and the distribution of outgoing particle directions.
The event generation code relies on a plug-in architecture to support various
different input formats and interaction channels. Input format plug-ins provide
functions that read in the data from an input file and return the number luminosity
as a function of time and energy. Interaction channel plug-ins specify properties of
the interaction channel, like the number of targets per water molecule or the neutrino
species that undergo this interaction, and provide functions to calculate quantities
like the differential cross section dσ( Eν , Ee )/dEe or the kinematically allowed energy
range. This modular design makes sntools easily extensible, with roughly 100 lines
of code required to add a new input format or interaction channel.
Finally, genevts.py collects the events generated in all interaction channels
and writes them to a text file, which can be used as an input file for a full detector
simulation.

3.2.2 Input Formats
sntools supports multiple different input formats for the neutrino fluxes from asimulation, which can be selected using the --format <value> command line
argument. This section will briefly describe each format and the processing steps
necessary to calculate the spectral number luminosity.
All formats contain separate information on the three species νe , ν̄e and νx . I will,
however, omit the reference to each species in the following for simplicity.
3.2.2.1 Totani Format

The files provided by Totani contain, for each time step tn , the total number ofneutrinos emitted until that time, which makes it possible to calculate the number
Nn of neutrinos emitted since the previous time step.
For 20 energy bins Ek per time step, a quantity Xk is provided, which is proportional to the number of neutrinos emitted during that time step and in that energy
bin. I divide this by the width of each energy bin to get
spec

Xk

84

=

Xk
,
Ek+1 − Ek(3.4)

3.2 sntools: A Supernova Event Generator
which is proportional to the spectral number emission during that time step.
spec
Integrating Xk over all energy bins and dividing it by that integral gives the
spectral number emission during that time step normalized to 1, Xknorm . The spectral
number luminosity at time tn and energy Ek is given byd NL(tn , Ek )Nn=
· Xknorm .
dEt n − t n −1

(3.5)

Finally, a linear interpolation in time and log cubic spline interpolation in energy areused to determine the spectral number luminosity at an arbitrary time and energy.
This approach closely follows that used in code provided by Totani. I haveconfirmed that there is excellent agreement of the calculated fluxes between Totani’s
code and sntools, with differences of at most a few per mille due to slight differencesin the numerical interpolation algorithms used.
3.2.2.2 Nakazato Format

Files in this format contain, for 20 energy bins Ek during each time step tn , thequantities ∆Nk (tn )/∆Ek and ∆Lk (tn )/∆Ek , which reflect the number luminosity andluminosity at those energies, respectively. For each energy bin, I calculate the meanenergy within that bin, which is given by

h Ek i =∆Lk (tn )∆Ek∆Nk (tn )
∆Ek

,

(3.6)

and set the differential neutrino number flux at that energy to ∆Nk (tn )/∆Ek . Finally,a linear interpolation in time and cubic spline interpolation in energy are used
to determine the spectral number luminosity at an arbitrary time and energy, as
recommended by Nakazato6 .
3.2.2.3 Gamma Format

Files in this format contain, for each time step tn , the luminosity L, mean energyh Eν i and mean squared energy h Eν2 i of neutrinos. To reconstruct the spectrum from
this, I assume that the neutrino spectrum is described by a normalized Gamma
distribution [137, 177] given byEναf ( Eν ) =Γ ( α + 1)



α+1
A

 α +1(α + 1) Eν
exp −
.
A

(3.7)

6 private communication, April 7, 201885

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
In this formula, A is an energy scale, while α determines the shape of the distribution:
α = 2 corresponds to a Maxwell-Boltzmann distribution, while α > 2 corresponds toa “pinched” spectrum, which is more typical for neutrino spectra from supernovae.
The first two energy moments of the distribution are

h Eν i =Z∞

dEν Eν f ( Eν ) = A

h Eν2 i =Z∞

dEν Eν2 f ( Eν ) =

(3.8)

0

0

α+2 2
A ,
α+1

(3.9)

and therefore,h Eν2 i − 2h Eν i2.
(3.10)h Eν i2 − h Eν2 i
Thus, the shape of the spectral number luminosity is uniquely determined by themean energy h Eν i and the mean squared energy h Eν2 i, while the normalization isprovided by L/h Eν i. To determine the spectral number luminosity at arbitrary times,
each of the three parameters is interpolated separately before calculating the spectral
number luminosity using the interpolated values.
α=3.2.2.4 Princeton Format

Files in this format contain, for each time step tn , the spectral luminosity dL/dE
for√ 20 logarithmically spaced energy bins Ek . I divide this by the central energy
Ek Ek+1 of the respective bin to get the spectral number luminosity at that energy.
Finally, a linear interpolation in time and cubic interpolation in energy are used todetermine the spectral number luminosity at an arbitrary time and energy.
This follows the procedure described in reference [262]. It is similar to that used
for the Nakazato format described above, though with a different definition of thebin energy.

3.2.3 Treatment of Neutrino Flavour Conversion
sntools implements three different mass ordering scenarios that can be selected byusing the --ordering <value> command line argument.7
The first scenario, noosc, assumes that neutrino oscillations do not take placesuch that the flux of a neutrino species νi observed by a detector on Earth, Φνi , isidentical to the fluxes originating within the supernova, Φ0νi .8
7 The alias --hierarchy<value> also exists.

8 For simplicity, throughout this section I omit the geometrical factor

distance d of the supernova.

86

1
which depends on the
4πd2

3.2 sntools: A Supernova Event Generator
The other two scenarios, normal and inverted, assume that adiabatic flavour
conversion happens via the MSW effect since neutrinos traverse a smoothly varying
density profile while exiting the star. The resulting observed fluxes are linear
combinations of the initial fluxes, which, for normal mass ordering, are given
by [272]Φνe = sin2 θ13 · Φ0νe + cos2 θ13 · Φ0νxΦν̄e = cos2 θ12 cos2 θ13 · Φ0ν̄e + (1 − cos2 θ12 cos2 θ13 ) · Φ0ν̄x

2Φνx = cos2 θ13 · Φ0νe + (1 + sin2 θ13 ) · Φ0νx

(3.11)

2Φν̄x = (1 − cos2 θ12 cos2 θ13 ) · Φ0ν̄e + (1 + cos2 θ12 cos2 θ13 ) · Φ0ν̄x ,while for inverted ordering, they areΦνe = sin2 θ12 cos2 θ13 · Φ0νe + (1 − sin2 θ12 cos2 θ13 ) · Φ0νxΦν̄e = sin2 θ13 · Φ0ν̄e + cos2 θ13 · Φ0ν̄x

2Φνx = (1 − sin2 θ12 cos2 θ13 ) · Φ0νe + (1 + sin2 θ12 cos2 θ13 ) · Φ0νx

(3.12)

2Φν̄x = cos2 θ13 · Φ0ν̄e + (1 + sin2 θ13 ) · Φ0ν̄x .

In both cases, the factor of 2 in the last two equations accounts for the fact that I
combine the fluxes of νµ and ντ , as well as those of the corresponding antineutrinos,
into νx as well as ν̄x , respectively. These equations assume purely adiabatic transition(corresponding to PH = 0 in [272, 273]) as explained below.
In cases where the detected flux is a mixture of original fluxes of different species,
sntools generates events for each original species separately with the appropriate
weighting factor applied. For example, when generating inverse beta decay eventsin the normal ordering, sntools will generate events first using the input flux Φν̄e =cos2 θ12 cos2 θ13 · Φ0ν̄e and then using the input flux Φν̄e = (1 − cos2 θ12 cos2 θ13 ) · Φ0ν̄x ,before finally combining both sets of events into one output file.
Several other effects may induce additional time- and energy-dependent flavour
conversion. These effects, together with a brief explanation of why they are notcurrently implemented in sntools, are discussed in the following.
After the accretion phase, the revived shock front travels outwards and passes
through the layer within the star where the adiabatic flavour conversion describedabove takes place. This causes a sudden change in the matter and electron density
and can severely impact the flavour conversion processes [274]. Since this occurs
after the shock wave is revived, it mainly affects the late-time part of the supernova
neutrino signal9 and would almost certainly not impact the analysis in chapter 4.
Furthermore, this effect is highly dependent on the the density structure of each
9 For the Totani model, this effect is expected to become relevant more than 1 s after core-bounce [273].

87Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
individual progenitor and cannot be taken into account by sntools. Instead, whereappropriate, groups performing supernova simulations will need to include thiseffect in their codes and publish neutrino flux data that takes it into account.
Near the centre of the supernova, the high neutrino density could induce a
matter effect that causes self-induced flavour conversion [275, 276]. These collective
effects—and their observable consequences, which could include energy-dependent
flavour conversion (so called “spectral splits”)—are the subject of intense theoretical
study [277, 278, 279, 280, 281], though no clear picture has yet emerged of how theseeffects will manifest in a given supernova. See reference [282] for a recent review.
Flavour conversion may also be suppressed in dense matter [283, 284]. As a result,the consequences in a realistic supernova are currently not well understood and may
depend on the progenitor [285]. They can therefore not be taken into account by
sntools. Once theoretical understanding has improved, it may be more appropriate
to include these effects in individual supernova simulations and publish neutrino
flux data that takes this into account.
Finally, depending on the location of the supernova relative to the detector, theneutrino detector may be “shadowed” by the Earth. For a detector in Kamioka, theshadowing probability for a galactic supernova is 56 % [286]. As neutrinos traverse
the Earth’s matter potential before detection, they can undergo energy-dependent
flavour transitions which are, in principle, detectable in Hyper-Kamiokande [287].
Since the presence and amplitude of this shadowing effect depends on the locationof the progenitor within the Milky Way as well as, due to the Earth’s rotation, on
the time of day that the neutrinos arrive on Earth, I will not consider it in this thesis.
However, Hyper-Kamiokande will be able to measure the position of a galactic
supernova to within a few degrees uncertainty. That would allow us to theoreticallycalculate the influence of this shadowing effect, if present, which could then becompared to the observed energy-dependent variations in the signal to set limits on
non-standard interactions and reduce the uncertainty introduced by the shadowing
effect.

3.2.4 Interaction Channels
sntools supports multiple different interaction channels described in this section. Bydefault, it will generate events across all supported channels, but it can be restricted
to a single channel by using the --channel <value> command line argument,
where <value> can be one of ibd, es, o16e or o16eb.
In water Cherenkov detectors like Hyper-Kamiokande, the dominant interaction
channel for supernova neutrinos is inverse beta decay, which makes up about 90 %of events. Another important interaction channel is elastic scattering on electrons,
which makes up only a few per cent of events but provides precise information on
the direction of the supernova. The cross sections for both interactions have been
calculated to a high level of precision.
883.2 sntools: A Supernova Event Generator
Another important subdominant channel are charged-current interactions of νeand ν̄e on 16 O nuclei. While this channel suffers from large theoretical uncertainties,
it is very sensitive to the high-energy tail of supernova neutrino fluxes, so that the
number of events in this channel can vary greatly between models.
Consistent with recent work on the Super-Kamiokande supernova burst monitor [172] and with the Hyper-Kamiokande Design Report [169], I have not included
additional subdominant interaction channels like neutral-current interactions on
16 O nuclei or neutral- and charged-current interactions on heavier oxygen isotopes.
Due to their low event rates, these channels would have a relatively small influenceon the observed event spectra, while introducing additional uncertainties since
their cross sections are not well known. Furthermore, their contributions would
be mainly at low or medium energies, where inverse beta decay dominates, while
their contributions at high energies would be much smaller than that of the chargedcurrent 16 O channel. As a result, these channels have a very minor dependence on
the supernova model and would contribute little to the analysis presented in thisthesis.
Neutral-current scattering on free protons, which may be an important detection
channel in scintillator detectors, cannot be detected by Hyper-Kamiokande since theoutgoing proton is below the Cherenkov threshold in water [288].
3.2.4.1 Inverse Beta Decay

In Hyper-Kamiokande, inverse beta decay (IBD; ν̄e + p → n + e+ ) is the dominantinteraction channel for supernova neutrinos due to its relatively high cross section
and low energy threshold of Eνthr ≈ 1.8 MeV, as well as the large number of free
protons in the detector. The observed energy of IBD events is closely related to theneutrino energy, making this an excellent channel to reconstruct the ν̄e spectrum.
In sntools, I have implemented IBD using the full tree-level cross section calculated
in reference [289] and including radiative corrections based on the approximationfrom reference [290].10 The calculation of the cross section is summarized in appendix A. Due to uncertainties in experimental measurements of input parameters,
the overall uncertainty is estimated to be 0.4 % at low energies and reaches about
2 % at Eν = 100 MeV, which is the upper end of the energy range of supernova
neutrinos.

10 That calculation uses the limit me → 0. This approximation is accurate to better than 0.1 % above
Ee = 1 MeV and the effect in Hyper-Kamiokande, whose energy threshold is much higher than
1 MeV, is completely negligible.

89

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
3.2.4.2 Neutrino-Electron Scattering

In Hyper-Kamiokande, elastic neutrino-electron scattering (ν + e− → ν + e− ) is a
subdominant interaction channel due to its low cross section, which is only partiallycompensated by the large number of electrons in the detector which is 5 (10) times
bigger than the number of free protons (16 O nuclei). Elastic scattering events makeup only a few per cent of all events but their angular distribution is strongly peaked
into a forward direction, pointing away from the supernova. They can therefore
be used to determine the direction of a supernova at the fiducial distance of 10 kpc
with an accuracy of 3° to 5° in Super-Kamiokande [172] or about 1° in HyperKamiokande [169].
Elastic scattering is the only interaction channel considered here which is sensitive
to all neutrino flavours. However, the cross section of νe and ν̄e , which can interact
through both neutral and charged currents, is higher than that of νx and ν̄x , which
can interact only through neutral currents.
In sntools, I have implemented elastic scattering using the tree-level cross sections
from standard electroweak theory calculated by ’t Hooft [291] and including oneloop electroweak and QCD corrections as well as QED radiative corrections ascalculated in reference [292]. The calculation of the cross section is summarized inappendix A. Similar to the calculation of the IBD cross section above, the uncertainty
due to experimental measurements of some input parameters is on a per mille level.
3.2.4.3 Charged-Current Interactions on 16 O

In Hyper-Kamiokande, charged-current interactions of νe and ν̄e on 16 O nuclei,
νe +16 O → e− + X
16+ν̄e + O → e + X,

(3.13)(3.14)

are a subdominant interaction channel.11 Due to the high energy threshold of bothinteractions of approximately 15 MeV and 11 MeV, respectively, as well as the steepenergy-dependence of the cross sections, the number of events in each channel is avery sensitive probe of the high-energy tail of the supernova neutrino flux. It mayvary by more than two orders of magnitude depending on the supernova models
and oscillation scenario, making up anywhere from < 1 % to over 10 % of all events
observed in Hyper-Kamiokande.
In sntools, I have implemented a recent approximation of the cross section for bothinteraction channels [293], which is based on a new shell model calculation [294].
An earlier calculation used the continuum random phase approximation (CRPA)
and tabulated the resulting total cross sections, instead of partial cross sections for
11 Charged-current interactions of other neutrino species do not occur, since the energy of supernova

neutrinos is too small to produce muons or τ leptons.

90

3.2 sntools: A Supernova Event Generator
reaction
16 O(νe , e− ) X

16 O(ν̄e , e+ ) X

group g
1
2
3
4
1
2
3
4

Eg (MeV)
15.21
22.47
25.51
29.35
11.23
18.50
21.54
25.38

ag
-40.008-39.305-39.655-39.166-40.656-40.026-40.060-39.862

bg
4.918
4.343
5.263
3.947
4.528
4.177
3.743
3.636

cg
1.036
0.961
1.236
0.901
0.887
0.895
0.565
0.846

Table 3.1: Excitation energies and fitting parameters for charged-current interactions
on 16 O. Values from reference [293].
each excitation energy [295]. A fit based on those results therefore only considered asimplified scenario where all final nuclear states shared the energy of the groundstate [296]. This significantly overestimated the energy spectrum of the emitted e± .
The modern calculation selected 42 different nuclear states and calculated theirrespective partial cross sections. To simplify the evaluation of the cross section, theauthors of reference [293] divide these states into four groups such that the total
cross section is4σ( Eν ) = ∑ σg ( Eν ),(3.15)

g =1

where the partial cross sections for each group, σg , are given by the expression
log10



σg ( Eν )cm2

= ag + bg Λ( Eν ) + cg [Λ( Eν )]2
"

 #

Eg 1/4Eν 1/4
Λ( Eν ) = log10
−
.
MeV
MeV

(3.16)(3.17)The excitation energies Eg and fit parameters ag , bg and cg of each group of states
are shown in table 3.1.
This fit matches the cross sections calculated from the full set of nuclear states towithin a few per cent at neutrino energies of up to 100 MeV. For a typical supernova
neutrino flux, the difference in the resulting event spectra when using the fourgroups instead of all 42 nuclear states is also very small.

91

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande

3.3 Detector Simulation
To simulate events in Hyper-Kamiokande, we use WCSim [297], a package forsimulating water Cherenkov detectors that is based on the physics simulation
framework G EANT 4 [298] and the data analysis framework ROOT [299].
It was originally developed by the Long Baseline Neutrino Experiment collaboration12 and is now used primarily by the Hyper-Kamiokande collaboration, where
it will replace the G EANT 3-based SKD ET S IM software which is currently used forSuper-Kamiokande.
As an input, WCSim takes text files in the N UANCE format (see references [301,302]), which contain the particle species (e+ or e− ) as well as the initial energy,
position and direction for each event. Based on physics lists included in G EANT 4,
WCSim then simulates the propagation of each primary particle through the detector,
including production of secondary particles like Cherenkov photons and theirrespective propagation. WCSim registers when photons hit photosensors aroundthe edge of the detector and applies the quantum and collection efficiency. It canalso simulate dark noise or after-pulsing in the photosensors and digitization of thesignal.
Currently, WCSim also includes simple triggers that decide which data is written
to the output file. In the future, triggering will be performed by a specialized
framework as part of the DAQ system described in section 2.2.7. However, thisframework was still in the very early stages of development when the analysis in
this thesis was performed.

3.4 Event Reconstruction
After simulating the detector response to supernova neutrino events, this section
describes how the digitized photosensor signals are used to reconstruct the event.
In contrast to the previous parts of this chapter, which are concerned only withsimulated events, the reconstruction methods described in this section apply equally
to simulated events and—once Hyper-Kamiokande is operating—actual observed
events. As far as possible, the same code will be used for both simulated andobserved events in order to avoid duplication of effort and reduce discrepancies andsystematic errors between MC and observations.
Despite this, there are some inherent differences between simulations and actual
data taking. These include, for example, the occurrence of technical issues (like12 The LBNE collaboration initially considered several different designs for their far detector, including

one based on water Cherenkov technology [300]. They have since decided to use a different design
based on a liquid argon time projection chamber and became the Deep Underground Neutrino
Experiment (DUNE) collaboration. See also section 5.2.2.3.

92

3.4 Event Reconstruction
defects in individual photosensors or electronics modules), variations in the noise
rate of individual photosensors or time-dependent changes to the water quality.
These often require additional steps in data processing that are not necessary for
simulated data. An extensive programme of calibrations discussed in section 2.3 isunder development to understand and—wherever possible—correct for these detector effects. Throughout this section, I will discuss these issues where appropriate
and describe how they are handled in the simulations.
Due to the wide energy range of events in Hyper-Kamiokande, several different reconstruction algorithms are used which are optimized for specific energy
ranges or event topologies. For low-energy events up to about 100 MeV, the SuperKamiokande collaboration has developed the BONSAI (Branch Optimization Navigating Successive Annealing Interactions) code for phase II of the experiment, which
was later optimized for the higher density of PMTs in Super-Kamiokande-III [303].
For Hyper-Kamiokande, we will continue using BONSAI with minor modifications
to work with the new simulation software (WCSim) and re-tuning for the newphotosensors and detector size.
BONSAI’s method for reconstructing the vertex of an event is described in section 3.4.1 and the method for reconstructing the direction of the outgoing particle isdescribed in section 3.4.2. A separate script then uses these results to reconstruct theparticle’s energy as described in section 3.4.3.

3.4.1 Vertex Reconstruction
Supernova neutrino interactions typically produce electrons and positrons withenergies of a few tens of MeV. At these energies, the typical track length of e±
in water is at most a few cm. Since they are required to be above the Cherenkov
threshold, i. e. v > cvacuum /nwater ≈ 22 cm/ns to be detected in Hyper-Kamiokande,
this track length corresponds to a travel time of less than 1 ns. This travel time issmaller than the time resolution of the photosensors and small compared to thetotal detector size. We therefore ignore the track length and assume a point-likeinteraction for the purposes of reconstructing the event vertex.
In Super-Kamiokande-I, vertex reconstruction relied on a grid of test vertices
spaced at about 4 m distance throughout the detector [223]. The reconstruction
software would calculate an ad-hoc goodness for each test vertex and then repeat
the procedure with a finer grid spacing around the vertex from the previous test
grid that gave the highest goodness.
Due to the lower photocoverage of Super-Kamiokande-II, the reconstruction
performance of the previous approach deteriorated significantly at low energies anda new vertex reconstruction code named BONSAI was developed [304].
Instead of using a fixed grid, BONSAI generates test vertices by selecting tuplesof four PMT hits and calculating the event vertex which would reduce the timing

93

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
1

10–1

10–2

10–3

10–4

0

50

100

150

200

250
tresidual [ns]Figure 3.3: Probability density P(tresidual ) used for vertex reconstruction in SuperKamiokande. The width of the peak around tresidual = 0 depends on the timing
resolution of PMTs, while the additional peaks at 30 ns and 100 ns are caused byafter-pulsing in the PMTs. Figure from reference [305].
residuals of all four hits to zero. This improves reconstruction performance andsimultaneously reduces the risk of getting stuck in a local maximum that is at a large
distance from the global maximum. After identifying these test vertices, BONSAI
performs a maximum likelihood fit over all Nhit PMT hits in the event, which isdefined as
Nhit

L ( x0 , t0 ) = ∑ log P(tresidual ),(3.18)

i =1

where ( x0 , t0 ) is the test vertex and P(tresidual ) is a probability density function which
is determined through calibration. The function used in Super-Kamiokande-IV isshown in figure 3.3. It depends on the time-of-flight-corrected timing residual,
which is defined as tresidual = ti − t0 − ttof , where ti is the time of the i-th PMT hit
and ttof = | xi − x0 |/cwater is the light travel time between the test vertex and the
PMT location xi .
The resulting vertex resolution achieved across different phases of SuperKamiokande is shown in figure 3.4. At 22 cm/ns, this corresponds to a few ns,
which is comparable in magnitude to the time resolution of PMTs. Overall, the event
time can be reconstructed with an uncertainty of a few ns, which is much smaller
than the ms-scale time resolution of neutrino fluxes provided by most supernova

94

Vertex Resolution (cm)

3.4 Event Reconstruction

250
200
150
100
50
0

5

7.5
10
12.5
15
True Electron Energy (MeV)

Figure 3.4: Vertex resolution in Super-Kamiokande-I (dotted blue line), -II (dashdotted green), -III (dashed red) and -IV (solid black) as a function of the true electronenergy. While the resolution in phase II is worse due to the lower photocoverage,
the improvement in phases III and IV compared to phase I is due to the improved
vertex reconstruction described in the text. Figure from reference [202].
simulations (see section 3.1).13 For all practical purposes, Hyper-Kamiokande’s
event time reconstruction is thus perfect.

3.4.2 Direction Reconstruction
Electrons and positrons travelling through water emit Cherenkov light in a conewith an angle
1
cos θCh =(3.20)nβ
13 Due to their finite mass, neutrinos travel slightly slower than the speed of light in vacuum, withthe exact speed depending on the neutrino energy. The resulting time-of-flight difference between
high- and low-energy neutrinos from a galactic supernova is [131] m 2  30MeV 2  D v,(3.19)∆t = 0.57ms
eV
E
10kpc
implying that sub-ms features in the neutrino flux may get washed out on the way to Earth.

95

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
relative to the particle’s direction. Since the index of refraction in water is n ≈ 1.34
and β = v/c ≈ 1 for electrons and positrons with an energy of Ee  me , that angle
is θCh ≈ 42°.
By combining this knowledge with the reconstructed vertex, BONSAI is able
to reconstruct the direction of individual particles. To reduce the contribution ofdark noise and scattered photons, it considers only the N20 hits whose time-of-flightcorrected hit time is within 20 ns of the reconstructed event time. It then maximizes
the likelihood function [305]N20

L(d) = ∑ log ( f (cos θi , Ee )) ×icos θiinc.
a(θiinc )(3.21)

Here, f (cos θi , Ee ), is the expected distribution of the angle between the direction
d of the particle and the vector pointing from the reconstructed vertex to the locationof the hit PMT. While the maximum of this distribution is approximately at cos 42° ≈
0.75 as discussed above, an energy-dependent spread in the opening angle occurs
due to multiple Coulomb scattering of the particle in water. The exact shape of this
distribution is determined from MC simulations; the one used in Super-KamiokandeIV is shown in figure 3.5.
The second term in that likelihood function depends on the angle of incidence
onto the PMT, θiinc , which is defined in the same way as θ in figure 3.6. a(θiinc ) is
determined by the shape of the PMT and the acrylic cover. In Super-Kamiokande,
the expression used since phase II isa(θiinc ) = 0.205 + 0.524 cos θiinc + 0.390 cos2 θiinc − 0.132 cos3 θiinc .

(3.22)

3.4.3 Energy Reconstruction
Based on the reconstructed event vertex, it is now possible to reconstruct the energyof the detected particle from the amount of Cherenkov light it produced. To dothis, I have developed a ROOT script [307] that implements the algorithm used inSuper-Kamiokande [306]. The algorithm itself and changes due to the different
detector are described in this section.
We first calculate the light travel time from the reconstructed event vertex to eachhit photosensor to determine the time-of-flight-corrected times of each hit in theevent. Assuming a sufficiently accurate position reconstruction, Cherenkov photons
should now form a narrow peak around the event time, while the dark noise hits
will remain randomly distributed. We then search for the 50 ns interval with thehighest number of time-of-flight-corrected hit times and refer to the number of hitsas N50 .
Broadly speaking, a higher N50 indicates a higher-energy particle; however, at agiven particle energy N50 has a significant position dependence due to geometric and96

cos theta

3.4 Event Reconstruction

1

1

0.8

0.9

0.6

0.8

0.4

0.7

0.2

0.6

0

0.5

-0.2

0.4

-0.4

0.3

-0.6

0.2

-0.8

0.1

-1

4

6

8

10

12

14

16

kinetic electron energy(MeV)
Figure 3.5: Distribution of angle between particle direction and the vector from event
vertex to PMT location as a function of energy. At lower energies, multiple Coulomb
the particle
whichleads to a function
wider angularspread.
Thescattering
energydeflects
dependence
ofmorethe strongly,
angularlikelihoodusedin the direction
Figure from reference [306].

gure 4.3:
construction [99].

detector effects. To correct for this, we estimate the effective number of Cherenkov
photons
sent out
the detectedwhich
is given
by hit PMT which observes moreconsidered. In order
to bycorrect
the particle,
fractionof thei−th correction
than a single photon,
factor is definedN50  the occupancy correction is used.The
NPMT
1
ri
1
N
=
(
X
+
ε
−
ε
)
×
×
×
exp
×
.
(3.23)eff∑ i tail dark Nalive S(θi , φi )
as
λeff
QEi
i
! log[1/(1−xi )]xi <1,Each term in equation 3.23 is discussedxin a separate
subsection
below.
iX=(4.3.2)i
Neff is a position-independent quantity
that
can
be
used
to
estimatethe energy of
3.0
xi = 1,the detected particle. The relation between both quantities is described in the final
subsection below.

where xi is the fraction of the hit PMT in a 3 × 3 patch around the i−th hit PMT.
2. Late hits (εtail ): Some of the emitted Cherenkov photons can be scattered or reflectedduring traveling in the water. Such photons are not detected within the 50 nsec timing
window. In order to correct these late signals, the late hits should be added for thecorrection. The correction factor is defined as
97
N100 − N50 − Nalive × Rdark × 50 nsec,
(4.3.3)N50
where N100 is the maximum number of the hits in a 100 nsec timing window, Nalive is thenumber of the functioning PMTs and Rdark is the average of the dark rate. The dark rateis measured for each run and it varies in time as shown in Figure 4.4.
εtail =

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande
3.4.3.1 Occupancy Correction

For the purposes of this section, we assume that each photosensor was hit by at mostone photon.14 That assumption may not be true for high-energy events or events
that are close to and pointing towards the wall such that the Cherenkov cone did
not have the opportunity to spread out.
To correct for this, we take advantage of the fact that if a photosensor detected
more than one photon, it is very likely that its neighbouring photosensors have also
detected photons. We define xi as the fraction of photosensors within a 3 × 3 gridaround the original photosensor that registered a hit within that same time-of-flightcorrected 50 ns window.15 The corrected number of hits in the i-th photosensor isthen given by
if xi = 01
− ln(1− xi )(3.24)Xi =if xi < 1xi
3
if xi = 1.

This correction term is derived from a Poisson distribution by assuming thatthe 3 × 3 photosensors receive the same expected number of photons. For thedetector configuration with 20 % photocoverage, the distance between neighbouring
photosensors is increased and this assumption starts to break down—particularly
for high-energy events that occur close to the wall. In that configuration, I therefore
use a modified occupancy correction given by Ximod = Xi1.4 , where the value 1.4
in the exponent was calibrated using Monte Carlo simulations to reproduce anapproximately linear relation between true particle energy and reconstructed Neff .16
3.4.3.2 Late Hit Correction

Scattering in the water means that the time-of-flight correction underestimates thepath length travelled by some Cherenkov photons before arriving at the photosensor.
As a result, their corrected arrival time may be outside of the 50 ns window.
14 This reflects the poor charge resolution of the PMTs used in Super-Kamiokande (see figure 2.8),

which meant that their 1 PE and 2 PE peaks are not well separated. The B&L PMTs developed forHyper-Kamiokande (see section 2.2.4.1) have an improved charge resolution which may in the
future be used instead of or in addition to this occupancy correction. However, since the B&L
PMTs are still under development, trying to include this within this thesis would be premature.
15 Photosensors at the top or bottom edge of the barrel have five neighbours instead of eight, which I
take into account. For photosensors located at the edge of the top or bottom plane of the detector,
there may be between three and seven neighbours within the plane. Since this depends on theexact layout of photosensors, it is not yet determined and I will omit this correction here. Due tothe small number of affected photosensors, the effect of this is negligible.
16 An alternative approach would be to consider only the four closest neighbouring photosensors
instead of all eight. While this would salvage the assumption of equal illumination, it would leadto a lower dynamic range and decrease reconstruction accuracy in that way.

98

3.4 Event Reconstruction
To account for these scattered photons, we define N100 analogous to N50 anddetermine the fraction of delayed hits by calculating
ε tail =N100 − N50 − Nalive · Rdark · 50 ns,
N50(3.25)

where Nalive is the number of working photosensors and Rdark is their dark noiserate.
3.4.3.3 Dark Noise Correction

To substract dark noise events, we determine the fraction of dark noise events
expected within that 50 ns window by calculating
ε dark =Nalive · Rdark · 50 ns.
N50(3.26)

3.4.3.4 Dead Photosensor Correction

Despite testing before installation, some photosensors will break during the lifetimeof the detector. Out of the total number of photosensors, NPMT , only a smaller
number (Nalive ) of photosensors may be working correctly at any point in time. To
correct for this, the formula for Neff contains the factor NPMT /Nalive .
However, such defects do not affect the simulations performed here and as aresult, I assume Nalive = NPMT here.
3.4.3.5 Photocoverage Correction

The effective photocoverage S(θi , φi ) depends on the angle at which the incoming
photon hits the detector wall. For small θi , the effective photocoverage is equal to thenominal photocoverage, i. e. either 40 % or 20 %. At large θi , the protruding PMTs
shadow parts of the detector wall so that the effective photocoverage increases.
The exact shape of S(θi , φi ) is determined via Monte Carlo simulation of thedetector and depends on the exact arrangement of photosensors as well as the shapeof the photosensors and acrylic covers. In Super-Kamiokande IV, the shape shown infigure 3.6 is used. Since the final design of those components for Hyper-Kamiokande
is not yet fixed, in this thesis I use a simplified angular dependence with ten bins in
θi and I omit the dependence on φi . This qualitatively reproduces the more precise
angular bins used in Super-Kamiokande and changes Neff by O(1 %).

99

Chapter 3 A Software Toolchain for Supernova Neutrino Events inHyper-Kamiokande

FigureThe definitionof the angles(θi , φi ) for the correction.
i−th hit PMT.
Right:The ofeﬀective
Figure4.5:
3.6:Left:
Angulardependenceof photocoverage
Left:
Sketchinner
PMTcoverage correction
factor ofS(θ,as φa ifunction(θ, φ) of[99].
wall photo-cathodeof detector, showing
the definition
θi φ)
and
. Right: ofShape
S(θi , φi ) usedby the Super-Kamiokande collaboration. Figures from references [308, 305].
energy extracted by LINAC calibration data and MC simulation. In the case of Neﬀ < 189.8(∼ 25 MeV), the following function is used

3.4.3.6 Water Transparency Correction

4!

Erec =
Absorption losses in the water scaleasai (Neﬀ )i ,i=0

(4.3.5)

where a0 = 0.82, a1 = 0.13, a2 = −1.11 × 10−4r,i a3 = 1.25 × 10−6 and a4 = −3.42 × 10−9,
(3.27)
exp
respectively. Since above 25 MeV, the proportionality
λeff is better than that below ∼ 25 MeV, thefirst order polynomial fit is used as,

where λeff is the water transparency and ri is the distance between the event vertex= 25.00 + 0.138(N(4.3.6)eﬀ − 189.8).
and the position of the i-thErec
photosensor.
In Super-Kamiokande,
the water transparency
over time
but isis typically100
m positrons[202]. Innot
thisforthesis,
assumeThisvaries
reconstruction
methodapplied to above
electrons
andmuonsIand
pions.afixed water transparency of 100 m for simulations in WCSim as well as for energy
reconstruction.
3.4.3.7 Quantum Efficiency Correction

The quantum efficiency QEi of photosensors in the detector can differ due to individual variations or if different types of photosensors are used, e. g. due todefective photosensors being replaced with modern ones during upgrades of SuperKamiokande. This variation is accounted for by dividing by the quantum efficiencyof each individual photosensor.
In the simulations performed here, the quantum efficiency of all PMTs is identical.
As a result, QEi becomes a constant that I absorb into the relation between Neff andthe reconstructed energy described below.

54

100

3.4 Event Reconstruction
3.4.3.8 Determination of Particle Energy

After including all corrections described above to calculate Neff , I use MC simulationsof mono-energetic electrons to determine the relation between Neff and the particle
energy, as shown in figure 3.7.
While this relation is expected to be approximately linear, the Super-Kamiokande
collaboration has found a slightly non-linear relation at low energies and uses afourth-order polynomial fit in that region [306]. In my calibration, using a higher
order polynomial has not produced a noticeably improved fit for the 40 % photocoverage configuration. For the 20 % photocoverage configuration, a quadratic function
has produced an improved fit. In addition, as discussed earlier I use the modified
occupancy correction Xi1.4 for that configuration, which affects the relation between
energy and Neff at high energies.
As a result, in this thesis I use the relations(
0.02360Neff + 0.082 if Neff < 1320
Ereco =
(3.28)
0.02524Neff − 2.081 if Neff ≥ 1320
for the detector configuration with 40 % photocoverage and(2 + 0.0215N + 0.429
2.55 × 10−6 Neff
if Neff < 701
eff
Ereco =−
62
1.148 × 10 Neff + 0.02032Neff + 1.94 if Neff ≥ 701(3.29)

3000

3000

2500

2500

2000

2000
N_eff

N_eff

for the detector configuration with 20 % photocoverage. However, given the various approximations discussed throughout section 3.4.3, this relation needs to berecalibrated once the detector design has been finalized.

1500

1500

1000

1000

500

500

0
0

10

20

30
energy [MeV]

40

50

60

0
0

10

20

30
energy [MeV]

40

50

60

Figure 3.7: Relation between Neff and Ereco for 40 % photocoverage (left) and 20 %photocoverage (right). Marks give MC results while the solid line is the fit describedin the text.

101All supernova models are different,
but some are more different than others.
George Orwell

Chapter 4
Supernova Model Discrimination
While the fundamental explosion mechanism of core-collapse supernovae is believed
to be understood thanks to a combination of computer simulations and observations of the neutrino burst from SN1987A, details of the explosion mechanism still
remain unclear. Even for identical progenitors, different simulations—which use
various different approximations due to computing power limitations—give quantitatively [241] and, in some cases, qualitatively [252] different results. It is therefore
essential to use the next galactic supernova—which may well be a once-in-a-lifetime
opportunity—to compare model predictions with observations and figure out whichmodel best represents reality.
Among current and planned neutrino detectors, Hyper-Kamiokande is uniquein its ability to detect both a high number of neutrinos from a galactic supernova—
about an order of magnitude higher than detectors like Super-Kamiokande, DUNEor JUNO—and provide precise energy information for every single event, whereas
IceCube would only be able to determine the average neutrino energy. The goal ofthis thesis is to develop a method of distinguishing between different supernova
models that makes optimal use of Hyper-Kamiokande’s capabilities.
After laying the groundwork in previous chapters by introducing HyperKamiokande and the software toolchain for simulating and reconstructing supernova neutrino events, this chapter describes my analysis and its results. I start insection 4.1 by describing how the data sets used for this analysis were generated,
simulated and reconstructed. Section 4.2 discusses the cuts applied to reconstructed
events. In section 4.3, I derive the log-likelihood function used, before showing
results of a comparison of five different supernova models in section 4.4. I give one
example of a more targeted study by showing how this same method can be used to
distinguish between closely related simulations in section 4.5. Finally, section 4.6
discusses how the analysis of an observed supernova neutrino burst will differ fromthe one presented here.
Throughout this chapter I will assume that the distance to the supernova—andthus the normalization of the neutrino flux—is completely unknown. If additional
distance information is available—e. g. because an optical counterpart is identified—
this could in principle be used to further distinguish between different supernova
models as described in section 5.2.3.

103

Chapter 4 Supernova Model Discrimination
Model
TotaniNakazato
Couch
Vartanyan
Tamborra

N10 kpc
19 716
17 97827 53910 37225 021d100
140 kpc
134 kpc
166 kpc
102 kpc
158 kpc

d300
81 kpc77 kpc96 kpc59 kpc91 kpcTable 4.1: Number of events expected during the time interval of 20 ms to 520 ms fora supernova at the fiducial distance of 10 kpc (N10 kpc ) and the distances at which
100 or 300 events are expected (d100 and d300 , respectively) for the five supernova
models considered in this work.

4.1 Generating Data Sets
I have used the event generator sntools (described in section 3.2) to generate data
sets of 100 and 300 events from the five supernova models described in section 3.1
and for both normal and inverted mass ordering. For every combination of theseparameters, I have generated 1000 data sets in order to estimate how well HyperKamiokande is able to identify the true model despite the random fluctuations in
the observed events.
Since the main goal of this thesis was a broad model comparison demonstrating
the reach of Hyper-Kamiokande, the two sizes of data sets were chosen to represent
supernovae at distances that mark the upper end of the expected spatial distributionof observable supernovae. As table 4.1 shows, 300 events correspond to a distanceof 59 kpc or more for all supernova models considered here, which includes thewhole Milky Way and many of its satellite galaxies, including the Large and Small
Magellanic Clouds at distances of 50 kpc [309] and 61 kpc [310], respectively.
A closer supernova—particularly one within the Milky Way, i. e. at distances ofless than 20 kpc—would of course result in a higher number of events and thus
improve our ability to distinguish different models. This will be particularly interesting for future, more targeted studies and I will give one example of such a study
in section 4.5.
Throughout this chapter, I consider only the time interval from 20 ms to 520 ms
after the core bounce. This time interval contains the shock stagnation and accretion
phase (described in section 1.2.2), which contains clear signatures of the explosion
mechanism and exhibits the largest differences between models. The earlier [129] (νeburst) and later1 (cooling) phases of neutrino emission are much better understood
1 see e. g.

reference [311], which also shows that the neutrino signal from the cooling phase caninstead be used to determine properties of the resulting neutron star104

4.2 Data Reductionand exhibit only minor variations between models, making them less relevant
for the analysis presented here. Furthermore, due to the limited computing time
available, many simulations—including the Couch, Vartanyan and Tamborra models
used here—focus on the accretion phase and don’t include the full cooling phase.
Accordingly, by considering only this 500 ms time interval I am able to include awider range of models.
These events are then simulated in the detector simulation software WCSim (seesection 3.3). As discussed in section 2.2.4, the exact photosensor configuration of
the detector has not yet been decided upon. Here, I will initially consider two
configurations. The first is the reference configuration described in the design
report [169]. It consists of approximately 40 000 box-and-line PMTs, resulting in aphotocoverage of 40 %. The other is a minimal configuration, which uses half thenumber of B&L PMTs to achieve a 20 % photocoverage.2 Results for the smaller data
set size (100 events), shown in section 4.4, demonstrate that there is no significant
difference between both configurations in this analysis. For the larger data set size(300 events), I have therefore focussed on the minimal configuration, which requires
significantly less computing resources to simulate and reconstruct events.
The position, direction and energy of the outgoing lepton were then reconstructedusing hk-BONSAI and the energy reconstruction script described in section 3.4.

4.2 Data Reduction
After reconstruction, I apply two cuts to all reconstructed events: an energy cut,which removes all events with a reconstructed energy less than 5 MeV, and a fiducial
volume cut, which removes all events whose reconstructed vertex is less than 1.5 m
away from the top, bottom or side walls of the inner detector.
These cuts are intended to eliminate low-energy background from accidental
coincidences of dark noise as well as radioactive decays in the detector. Analogous
cuts are also used for the solar neutrino analysis in Super-Kamiokande [202]. While
several more advanced cuts used in that analysis cannot currently be applied tothe analysis presented here,3 the more stringent energy cut together with the muchhigher event rate (102 Hz to 103 Hz for the distant supernova bursts considered here,
compared to about 10−4 Hz for solar neutrinos in Super-Kamiokande) result in an
2 This configuration is not being considered by the Hyper-Kamiokande collaboration. The alternative

configurations that are under consideration would augment this minimal configuration with several
thousand multi-PMT modules. I use this minimal configuration only as the most conservative
estimate since the exact number of mPMT modules is not yet known.
3 Note that the Super-Kamiokande analysis includes events with energies as low as 3.49 MeV within areduced fiducial volume and instead uses several more advanced cuts to cut remaining background
events. Since these cuts rely on comparison of Monte Carlo simulations with observed data, theycannot be applied to Hyper-Kamiokande at this time.

105

Chapter 4 Supernova Model Discrimination
effectively background-free data set. Other backgrounds, including muon-induced
spallation events or atmospheric neutrinos, occur at a much lower rate and are thus
negligible during the single 500 ms time interval considered here.
Once Hyper-Kamiokande is operating and the low-energy backgrounds are characterized in detail, it will likely be possible to develop more targeted cuts that allow
us to include more low-energy events and extend the fiducial volume while remaining effectively background-free. For the purposes of the current analysis, however, I
have decided to err on the side of more conservative results, which are unaffectedby variations in background levels, instead of presenting more optimistic results,
which are dependent on uncertain assumptions regarding background levels.
Furthermore, I do not take into account the effects of other cuts that will occasionally occur during detector operations—e. g. due to calibration runs or hardware
issues.
The fiducial volume cut described above removes about 13 % of all events in the
inner detector. The effect of the energy cut depends on the energy spectrum of theinitial neutrino flux and therefore on the supernova model and the mass ordering.
As an example, figure 4.1 shows the energy spectra in different interaction channels
for the Totani model. Due to the strong energy-dependence of the cross sections,
three of the four interaction channels produce almost no events at 5 MeV or below.
Only elastic νe-scattering—a subdominant channel which contributes about 5 % of
all events—has a significant contribution at energies below 5 MeV. Overall, outof the initial 100 or 300 events per data set more than 80 % typically remain after
applying these cuts.

4.3 Log-Likelihood Function
After the cuts described above, I apply a log-likelihood function to the reconstructed
times and energies of the remaining events in each data set to determine how wellthat data set matches each of the supernova models.
This log-likelihood function is similar to one that was originally derived foranalysis of SN1987A taking into account only the main interaction channel, inverse
beta decay [312]. However, the function used here includes all interaction channels.
It is derived in appendix B and given byNobs

L = ln L = ∑ ln Ni ,

(4.1)

i =1

where the index i runs over the Nobs events remaining in the data set and Ni is
the number of events predicted by a given supernova model in an infinitesimallysmall bin around the reconstructed time and energy of event i, summed over all
interaction channels.

106events/0.22Mt/MeV

4.3 Log-Likelihood Function

–

10

νe+p

3

ν+e

10

-

νe+16O2–

νe+16O

10

1

0

10

20

30

40

50

60

visible energy (MeV)
Figure 4.1: Energy spectra of events from a supernova neutrino burst in HyperKamiokande assuming the Totani model and a fiducial distance of 10 kpc. Different
colours stand for inverse beta decay (black), νe-scattering (red), νe +16 O CC (purple)and ν̄e +16 O CC (light blue), while solid, dashed and dotted lines correspond tono oscillation, normal ordering and inverted ordering, respectively. Figure fromreference [169].
By using infinitesimally small bins in time and energy, this likelihood function
makes optimal use of all available information. In contrast, using a binned chisquared test to compare observation with models requires a sufficiently large numberof events per bin to be accurate. Especially in the case of a distant supernova, where
only hundreds or thousands of events may be observed in Hyper-Kamiokande,
two-dimensional binning in time and energy would only be possible in very coarse
bins, which would lose a lot of the available information.
The absolute numerical values of this likelihood function depend on the bin size
chosen and are therefore not physically meaningful. However, when calculating
likelihood ratios for different models (i. e. differences in the log-likelihood, ∆L =L A − L B ), this dependence cancels out and the ratio describes whether model A or B
is more likely to produce a given data set. In the following sections, I will therefore
exclusively use likelihood ratios to compare different models.
As an example, figure 4.2 shows a comparison of the Couch and Nakazato models.

107

Chapter 4 Supernova Model Discrimination

Figure 4.2: Histograms showing the distribution of ∆L = LCouch − LNakazato for thedata sets generated from the Couch model (black) and from the Nakazato model(red), for 100 events per data set and normal mass ordering.
For most data sets generated from the Couch (Nakazato) model, ∆L = LCouch −LNakazato is positive (negative), indicating that this method is generally able toidentify the true model. However, the overlap of both histograms indicates thatmisidentification sometimes occurs because of random fluctuations in the data sets.
The accuracy of this method will be evaluated below.

4.4 Distinguishing Different Models
4.4.1 N=100 Events Per Data Set
4.4.1.1 Normal Mass Ordering

Figure 4.3 shows pairwise comparisons of the five different models described in
section 3.1 for both 20 and 40 % photocoverage. Similar to the Couch/Nakazato
comparison highlighted in figure 4.2, the model pairs generally show clear separation with only minor overlap around ∆L = 0. The largest overlap is seen between
the Couch and Tamborra models, indicating that these models are most similar andhardest to distinguish.

108

4.4 Distinguishing Different Models

Figure 4.3: Top: Histograms showing the distribution of ∆L = Lblack − Lred for all
pairs of supernova models considered here, for 100 events per data set, normal massordering and 20 % photocoverage. The purple vertical line in each panel indicates∆L = 0. Bottom: As above, but for 40 % photocoverage.
109

Chapter 4 Supernova Model Discrimination
True Model
Couch
Nakazato
Tamborra
Totani
Vartanyan

Couch
795
33
84
4
0

Nakazato
57
961
0
0
1

Tamborra
122
3
853
16
17

Totani
12
1
33
979
3

Vartanyan
14
2
30
1
979

True Model
Couch
Nakazato
Tamborra
Totani
Vartanyan

Couch
768
41
65
2
1

Nakazato
32
951
0
0
0

Tamborra
174
5
867
11
10

Totani
11
0
34
985
2

Vartanyan
15
3
34
2
987

Table 4.2: Top: Accuracy with which the true model can be identified, for 100 events
per data set, normal mass ordering and 20 % photocoverage. Shows how many of
the 1000 data sets generated for a given model (left column) were identified as eachof the five models. Correctly identified models are highlighted. Bottom: As above,
but for 40 % photocoverage.
This can be seen more clearly in table 4.2, which compares all five supernova
models simultaneously by determining which of them produces the highest likelihood for a given data set. For each model, the respective row indicates how many
data sets (out of the 1000 that were generated) were identified as which model.
For example, in the 20 % (40 %) photocoverage scenario 853 (867) Tamborra data
sets were identified correctly, while 84 (65) were misidentified as corresponding to
the Couch model. For the Couch model, almost 80 % of data sets were identified
correctly in both photocoverage scenarios, with most of the remaining data sets
being misidentified as the Tamborra model. Finally, the three other models are
identified correctly in over 95 % of all cases.
Both figure 4.3 and table 4.2 indicate that differences between both photocoverage scenarios are within the range expected due to random fluctuations. Thisis consistent with expectations: Even for the 20 % photocoverage configuration,
event times are reconstructed in Hyper-Kamiokande with an uncertainty of a few
ns, while changes in the supernova neutrino fluxes take place on the scale of several
ms. Thus, any incremental improvements to time reconstruction offered by a higher
photocoverage do not affect the likelihood. The improved energy reconstruction
could, in principle, have an impact. However, the energy dependence of the event
rate is relatively shallow across most of the energy range (see e. g. figure 4.1). Even110

4.4 Distinguishing Different Models
for the 20 % photocoverage configuration, the energy reconstruction uncertainty is
sufficiently small that it has only a minor impact on the likelihood.4 Additionally,
this impact may partially cancel itself out as the reconstructed energy is equally
likely to be too low or too high.
In the future, improvements to vertex and energy reconstruction offered by ahigher photocoverage may allow us to relax the cuts described in section 4.2 beyond
what may be possible with a lower photocoverage. This would allow us to include
more events which could improve the accuracy of model discrimination. At thispoint, however, it is not possible to determine the quantitative effect this might have.
Since there is no significant difference between the two photocoverage scenarios in
the current analysis, in the interest of clarity I will only show results for the 20 %photocoverage configuration in the following sections.
4.4.1.2 Inverted Mass Ordering

Figure 4.4 and table 4.3 show results for the inverted mass ordering. In this scenario,
the largest overlap is observed between the Tamborra and Vartanyan models, withan 85–90 % chance of identifying those data sets correctly and a chance of just over
10 % of confusing these models for one another. As for the normal mass ordering,the other three models are identified correctly in over 95 % of all cases.

4.4.2 N=300 Events Per Data Set
When considering larger data sets, the effect of random fluctuations between individual data sets will decrease. As a result, the accuracy of model identification is
expected to increase significantly.
4.4.2.1 Normal Mass Ordering

Figure 4.5 shows the pairwise model comparisons for 300 events per data set andnormal mass ordering. Compared to figure 4.3, the separation of models is clearly
improved, consistent with expectations. As a result, table 4.4 shows that the Couchand Tamborra models—which are most likely to be confused for each other innormal mass ordering—are now identified correctly with about 98 % accuracy andthe probability of misidentifying one for the other is just 1.6 %. The other threemodels are identified correctly with almost 100 % accuracy.

4 In contrast, if a background component has a very steep energy cut-off, incrementally improved

energy resolution can lead to a significant improvement, e. g. when distinguishing solar 8 B
neutrinos from hep neutrinos [169].

111

Chapter 4 Supernova Model Discrimination

Figure 4.4: Histograms showing the distribution of ∆L = Lblack − Lred for all pairsof supernova models considered here, for 100 events per data set, inverted massordering and 20 % photocoverage. The purple vertical line in each panel indicates∆L = 0.

True Model
Couch
Nakazato
Tamborra
Totani
Vartanyan

Couch
960
8
0
3
0

Nakazato
35
992
1
0
2

Tamborra
4
0
858
20
105

Totani
1
0
21
977
1

Vartanyan
0
0
120
0
892

Table 4.3: Accuracy with which the true model can be identified, for 100 events perdata set, inverted mass ordering and 20 % photocoverage. Shows how many of the1000 data sets generated for a given model (left column) were identified as each of
the five models. Correctly identified models are highlighted.

112

4.4 Distinguishing Different Models

Figure 4.5: Histograms showing the distribution of ∆L = Lblack − Lred for all pairsof supernova models considered here, for 300 events per data set, normal massordering and 20 % photocoverage. The purple vertical line in each panel indicates∆L = 0.

True Model
Couch
Nakazato
Tamborra
Totani
Vartanyan

Couch
982
1
16
0
0

Nakazato
2
999
0
0
0

Tamborra
16
0
980
0
0

Totani
0
0
2
1000
0

Vartanyan
0
0
2
0
1000

Table 4.4: Accuracy with which the true model can be identified, for 300 events perdata set, normal mass ordering and 20 % photocoverage. Shows how many of the1000 data sets generated for a given model (left column) were identified as each of
the five models. Correctly identified models are highlighted.

113

Chapter 4 Supernova Model Discrimination
4.4.2.2 Inverted Mass Ordering

Figure 4.6 shows the pairwise model comparisons for 300 events per data set andinverted mass ordering. Compared to figure 4.4, the separation of models is clearly
improved, consistent with expectations. As a result, table 4.5 shows that the Tamborra and Vartanyan models—which are most likely to be confused for each otherin inverted mass ordering—are now identified correctly with over 97 % accuracy.
The other three models are identified correctly with almost 100 % accuracy.

4.5 Determining Progenitor Properties
In the previous section, I have compared supernova models simulated by different
groups using different codes and employing different approximations that lead toquantitatively and sometimes qualitatively very different outcomes. Such a comparison is important as long as details of the explosion mechanism are not understood,
since it would help determine which model best reproduces the observed signaturesof the explosion mechanism.
However, Hyper-Kamiokande is expected to start data taking in 2027 and, due
to the low galactic supernova rate, it may be decades beyond that before it firstdetects a high-statistics supernova neutrino burst. If computer models have started
to converge by then—or if details of the explosion mechanism are confirmed as
discussed above—it is of great interest to the field to determine what more detailed
information can be extracted from the neutrino signal. In particular, one important question is whether the neutrino signal can help us figure out details of theprogenitor.
It was previously shown that some carefully chosen properties of the supernova
neutrino signal may be used to determine the core compactness of the progenitor
star [313] or the mass and radius of the resulting proto-neutron star [311]. In contrast,
the approach described in the previous sections is a fully general method that can,in principle, be used to determine any parameter that affects the neutrino fluxes
emitted by a supernova. As an example, in this section I will consider the mass andmetallicity of progenitors.
I use fluxes provided by Nakazato et al. [128], who simulated a range of progenitors with different masses and metallicities using the same code. Unlike above, alldifferences in the neutrino fluxes therefore correspond to differences in the progenitors. Details of these simulations are provided in section 3.1.2. In addition to the
20 M progenitor with solar metallicity (described as the “Nakazato” model in theprevious section), I use 13 M and 30 M progenitors with solar metallicity and a
20 M progenitor with lower metallicity. Below, progenitors are labelled “Nxxy0”,

114

4.5 Determining Progenitor Properties

Figure 4.6: Histograms showing the distribution of ∆L = Lblack − Lred for all pairsof supernova models considered here, for 300 events per data set, inverted massordering and 20 % photocoverage. The purple vertical line in each panel indicates∆L = 0.

True Model
Couch
Nakazato
Tamborra
Totani
Vartanyan

Couch
999
0
0
0
0

Nakazato
1
1000
0
0
0

Tamborra
0
0
974
0
8

Totani
0
0
1
1000
0

Vartanyan
0
0
25
0
992

Table 4.5: Accuracy with which the true model can be identified, for 300 events perdata set, inverted mass ordering and 20 % photocoverage. Shows how many of the1000 data sets generated for a given model (left column) were identified as each of
the five models. Correctly identified models are highlighted.

115

Chapter 4 Supernova Model Discrimination

Figure 4.7: Luminosity (top) and mean energy (bottom) of νe (left), ν̄e (centre) andνx (right) as a function of time for the N1300 (dash-dotted green line), N2000 (solid
black), N2010 (dashed blue) and N3000 (dotted red) progenitor.
where xx corresponds to the mass in M and y is either 0 (for solar metallicity,
Z = 0.02) or 1 (for the lower metallicity, Z = 0.004).5
Figure 4.7 shows the luminosity and mean energy of neutrino fluxes predictedby these simulations. Since the predicted fluxes for all progenitors are very similar,
separation is difficult and I will only show results for the larger data set size of
300 events. Apart from this, I have followed the same procedure described in theprevious sections.
Figure 4.8 shows a pairwise comparison of all four progenitors for normal massordering. I find that the N3000 progenitor is clearly distinct from the other progenitors, whereas all other pairs show some overlap near ∆L = 0, indicating a risk of
misidentification. Accordingly, table 4.6 shows that all data sets generated from theN3000 progenitor are identified correctly, while the accuracy is between 85 and 95 %for the three other progenitors.
Results for inverted mass ordering are shown in figure 4.9 and table 4.7. They arevery similar, with N3000 clearly distinct while N1300, N2000 and N2010 are all at
risk of being mistaken for each other with an identification accuracy of about 85 %.
Overall, while determining progenitor properties is more difficult than the model
discrimination discussed in the previous section, these results show that it is clearly
5 This follows the convention adopted by the authors for the published flux files. See asphwww.ph.

noda.tus.ac.jp/snn/index.html.

116

4.5 Determining Progenitor Properties

Figure 4.8: Histograms showing the distribution of ∆L = Lblack − Lred for all pairsof progenitors considered here, for 300 events per data set, normal mass orderingand 20 % photocoverage. The purple vertical line in each panel indicates ∆L = 0.

True Progenitor
N1300
N2000
N2010
N3000

N1300
878
17
74
0

N2000
61
944
75
0

N2010
61
39
850
0

N3000
0
0
1
1000

Table 4.6: Accuracy with which the true progenitor can be identified, for 300 events
per data set, normal mass ordering and 20 % photocoverage. Shows how many of
the 1000 data sets generated for a given progenitor (left column) were identified aseach of the four progenitors. Correctly identified progenitors are highlighted.

117

Chapter 4 Supernova Model Discrimination

Figure 4.9: Histograms showing the distribution of ∆L = Lblack − Lred for all pairsof progenitors considered here, for 300 events per data set, inverted mass orderingand 20 % photocoverage. The purple vertical line in each panel indicates ∆L = 0.

True Progenitor
N1300
N2000
N2010
N3000

N1300
866
64
53
0

N2000
78
848
88
0

N2010
56
88
859
0

N3000
0
0
0
1000

Table 4.7: Accuracy with which the true progenitor can be identified, for 300 events
per data set, inverted mass ordering and 20 % photocoverage. Shows how many of
the 1000 data sets generated for a given progenitor (left column) were identified aseach of the four progenitors. Correctly identified progenitors are highlighted.

118

4.6 Bayesian Interpretationln BAB
0 to 1
1 to 33 to 5>5BAB
1 to 33 to 20
20 to 150
> 150

Evidence for model A over model B
Negligible
Positive
StrongVery strong

Table 4.8: Interpretation of Bayes factor when comparing two models A and B.
Adapted from [315].
within the capabilities of Hyper-Kamiokande. In fact, progenitor discrimination
with 300 events per data set shows a similar accuracy to model discrimination with
100 events per data set. This suggests that 3 to 10 times higher statistics may besufficient to determine progenitor properties with a high accuracy. Based on table 4.1,
this would correspond to a supernova at distances larger than about 20 kpc, which
encompasses the whole Milky Way.

4.6 Bayesian Interpretation
Throughout this chapter, I have answered the following question: Assuming model
X describes the actual neutrino fluxes from a supernova, how likely are we tocorrectly identify X when comparing it with a range of other, different models?
This lets us identify which models are more or less similar to each other and assess
Hyper-Kamiokande’s model discrimination capabilities. However, the results are
sensitive to adding other models to the comparison which are similar to the truemodel. Furthermore, this does not reflect the scenario we will face in the future when
we observe a single supernova neutrino burst and do not know the true model.
Thus, another question of interest is: Assuming that we observe a supernova
neutrino burst that is best described by model X, how confident are we that we
can exclude some alternative model Y? To answer this, we need to consider theinterpretation of the likelihood ratio.
In a Bayesian interpretation [314], the ratio of likelihoods for two models A and B
is equal to the Bayes factor Bij and equivalently, the difference in log-likelihoods is∆L = ln Bij . If there is no a priori reason to prefer one model over the other, this canbe used to exclude disfavoured models beyond a certain threshold.
A suggested interpretation of Bayes factors is listed in table 4.8.6 Looking at the
pairwise model comparison in figure 4.2, we see that this interpretation matches
our intuition: The range from ∆L = −5 to 5 contains almost the complete overlap
6 Note that I show B here, whereas the original paper lists 2B due to its similarity with the moreij
ij
familiar ∆χ2 values. [315, 316]

119Chapter 4 Supernova Model Discrimination
between both histograms, where misidentification of data sets may occur, indicatingthat requiring ∆L ≥ −5 is unlikely to wrongly exclude the true model. At the sametime, a significant fraction of data sets based on the wrong model are excluded by thiscriterion. Once we observe an actual supernova neutrino burst, this criterion would
therefore allow us to narrow down the list of supernova models or progenitors thatare compatible with the observed signal.

120

A real Galactic supernova cannot,
unfortunately, be guaranteed on thetimescale of a PhD studentship . . .
Susan Cartwright

Chapter 5Conclusions and Outlook
5.1 Conclusions
The observation of neutrinos from SN1987A was a breakthrough for neutrino astronomy and dramatically improved our understanding of supernovae. However, due
to the small number of observed events, many questions still remain today and theneutrino community is desperate to prepare for the next galactic supernova. As partof those preparations, in this thesis I have investigated the ability of the planned
Hyper-Kamiokande detector to extract information from a supernova neutrino burst.
I showed that its large volume and ability to reconstruct individual events give it anexcellent ability to discriminate between different supernova models and deduce
details of the supernova explosion mechanism.
As part of this thesis, I have developed a complete toolchain for generating,simulating and reconstructing supernova neutrinos in Hyper-Kamiokande, which is
described in chapter 3.
In particular, I have developed sntools—a high-precision event generator for
supernova neutrino burst observation with water Cherenkov detectors. In addition
to inverse beta decay—the main interaction channel, and often the only channel considered in the literature—sntools includes three subdominant interaction channels.
It implements precise, modern cross sections for all channels as well as a precise
treatment of neutrino oscillations via the MSW effect. sntools supports multiple
input formats for neutrino fluxes and is designed to be modular and extensible to
make it easy to add other supernova models.
I have also developed the first energy reconstruction for Hyper-Kamiokande. It
follows an approach pioneered by the Super-Kamiokande collaboration with somealterations in response to the modified detector design. While this reconstruction iscurrently at an early stage and will require further adjustments once the detector
design is finalized, it is already satisfactory for the analysis described here and I
have demonstrated that further improvements would not affect the results.
To demonstrate the capabilities of Hyper-Kamiokande and this software toolchain,
I have derived an improved likelihood function that supports multiple interaction
channels. It makes optimal use of event-by-event timing and energy information

121

Chapter 5 Conclusions and Outlook
available in Hyper-Kamiokande to determine how well the neutrino fluxes predictedby a supernova model describe the observed events. I have applied this likelihood
function to a set of five supernova models representing the wide variety of models
developed by different groups around the world. I have found that by observing
just 100 to 300 events, Hyper-Kamiokande will be able to distinguish these models
with high accuracy. This event count corresponds to supernovae at distances of atleast 59 kpc, which includes the whole Milky Way and many of its satellite galaxies,
including the Large and Small Magellanic Clouds. When an actual supernova neutrino burst is observed in the future, this model discrimination capability will allow
us to determine which model best reproduces the supernova explosion mechanism
realized in nature.
The method developed in this thesis is very general and can in principle be used
to determine any parameter of a supernova that influences its neutrino emission.
As an example of a more targeted analysis, I have performed a comparison ofdifferent progenitors simulated with the same code. The results demonstrate thatby observing at least 300 events, Hyper-Kamiokande may be able to distinguishbetween progenitors with different masses or metallicities.

5.2 Outlook
Science is a team effort—and this is especially true in astroparticle physics. Individual people or experiments may make important contributions but sustained
progress is possible only through cooperation of groups from all different countries
and subfields. While this thesis focused on the contributions of Hyper-Kamiokande,
I now want to take a step back and give an overview over other approaches that canbe used in conjunction with Hyper-Kamiokande to study supernovae.

5.2.1 Progress in Supernova Simulations
Current supernova simulations are severely limited by the available computing
power. In response, two complementary approaches are possible: On one hand,running large cohorts of simpler, one-dimensional simulations makes it possible
to extensively study the effect of individual factors—like progenitor properties
or simulation parameters—on the outcome of simulations. On the other hand,
performing a small number of increasingly realistic, multidimensional simulations
enables the study of details of the supernova explosion mechanism.
In the coming years, both approaches are likely to see steady progress from a
combination of increases in computing power, improvements to simulation codes
and theoretical progress in input physics. The ultimate goal however—a highresolution, fully three-dimensional simulation in General Relativity with exact122

5.2 Outlook
treatment of neutrino transport and a complete set of precision microphysics—
remains elusive and convergence of different models is therefore unlikely.
In the absence of such convergence, direct comparisons of different simulation
codes are essential for estimating the uncertainty of simulation outcomes. Recently, an extensive comparison of six simulation codes showed that, when using an
identical set of basic input physics, the codes exhibit good qualitative and quantitative agreement [241]. Future work extending such comparisons to more advanced
setups—including multiple dimensions and more advanced input physics—would
be particularly valuable.
Furthermore, it may be interesting to apply the analysis pipeline developed inthis thesis to the outputs of such a model comparison and determine whether the inherent differences between simulation codes are large enough to be detectable. This
would be particularly useful if the progenitor of a galactic supernova is identified
by telescopes, giving us independent information on the progenitor.

5.2.2 Complementarity with Other Neutrino Detectors
While Hyper-Kamiokande offers a unique combination of large detection volume
and ability to precisely reconstruct individual events, other neutrino detectors may
be more sensitive to different parts of the neutrino signal. Below, important current
or future neutrino detectors that offer such complementarity to Hyper-Kamiokande
are briefly described.
5.2.2.1 Super-Kamiokande

Apart from its smaller size, Super-Kamiokande is very similar to Hyper-Kamiokande.
Since small differences in energy resolution have a negligible effect of the resultspresented in this thesis, they should approximately be equally valid for SuperKamiokande. Since Super-Kamiokande’s fiducial√
volume is 8.4 times smaller, 300
observed events corresponds to a distance that is 8.4 ≈ 2.9 smaller than listed intable 4.1, i. e. at least 20 kpc, depending on the model. Therefore, Super-Kamiokande
is likely to have accurate model discrimination capabilities for a supernova anywhere
within the Milky Way. However, since backgrounds and energy reconstruction inSuper-Kamiokande are well understood, the collaboration would be able to perform
a more precise analysis than presented here, which may improve results further.
During the second half of 2018, extensive work took place to prepare SuperKamiokande for the addition of gadolinium [212]. Gadolinium has a high neutroncapture cross section and, upon capturing the neutron, emits a gamma cascade with
about 8 MeV energy. This will enable Super-Kamiokande to efficiently tag neutrons,
allowing it to distinguish between interaction channels that produce neutrons—
such as inverse beta decay and some 16 O charged-current interactions—and other123

Chapter 5 Conclusions and Outlook
interaction channels on an event-by-event basis. This would help to identify analmost pure sample of elastic scattering events, which would enable a more accurate
determination of the direction of the supernova and a more precise measurementof the initial νe burst. In the future, experiences gained from adding gadolinium toSuper-Kamiokande may be used in an upgrade to Hyper-Kamiokande.
5.2.2.2 Second Hyper-Kamiokande Detector in Korea

Plans to build a second Hyper-Kamiokande detector in South Korea were publishedin a white paper in 2018 [186]. While the primary motivation is significant improvements to neutrino oscillation measurements, supernova burst observations wouldof course benefit from the increased detection volume. Furthermore, since a galactic
supernova would likely be a once-in-a-lifetime event, the redundancy offered by asecond detector would dramatically reduce the risk of missing the observation due
to detector downtime e. g. during maintenance work.
Depending on position of the supernova, comparing the fluxes observed by both
detectors may also allow for a direct observation of Earth matter effects [286, 186].
In that case, the similar design of both detectors would cancel out some systematic
uncertainties that would make such a comparison between other detectors much
more difficult.
5.2.2.3 DUNEDUNE [96] is a liquid argon time projection chamber that is currently under construction with a first 10 kt detector module expected to begin operations shortly
before Hyper-Kamiokande. After construction of three additional modules expected
over the following years, it may observe over 3000 events for a supernova at 10 kpc
distance. Since its main interaction channel is νe charged-current interaction on 40Ar,
DUNE will observe a large sample of almost pure νe interactions, which makes ithighly complementary to Hyper-Kamiokande.
5.2.2.4 JUNO

JUNO [89] is a 20 kt liquid scintillator detector that is currently under construction,with completion expected in 2021. In the case of a supernova at 10 kpc distance, it isexpected to observe about 5000 inverse beta decay events. Its low energy thresholdenabled by the liquid scintillator technology and a high photocoverage will allow it
to observe elastic neutrino-proton scattering. This channel is sensitive to neutrinos
and antineutrinos of all flavours. If proton quenching in the liquid scintillator is wellunderstood, this channel would therefore enable a measurement of the full neutrino124

5.2 Outlook
flux which will be important to understand flavour conversions and the total energy
emitted by the supernova in neutrinos.
5.2.2.5 THEIA

THEIA [93], previously known as the Advanced Scintillator Detector Concept [92],is a concept for a future neutrino detector employing water-based liquid scintillator
as a detector material. It would be comparable in size to or larger than SuperKamiokande, combining the large volume of water Cherenkov detectors with the
sub-Cherenkov threshold sensitivity and excellent energy resolution of liquid scintillator detectors. In addition to observing a high-statistics sample of supernova
neutrinos, THEIA could tag inverse beta decay events via neutron capture—similar
to a gadolinium-loaded Super-Kamiokande, but with higher efficiency—which
would give the benefits explained above.
5.2.2.6 IceCube and KM3NeTBoth IceCube [85] and KM3NeT [86] are water Cherenkov detectors whose large
volume and sparse instrumentation are optimized for high-energy neutrinos at
the GeV-scale and above. At the energies typical for supernova burst neutrinos,
both would likely detect just one photon per neutrino interaction, making any
individual event indistinguishable from noise. As a result, both detectors could
detect a supernova neutrino burst because of a sudden and temporary increase of the“noise” rate across the whole detector, but unlike Hyper-Kamiokande and the otherneutrino detectors described above, they would not be able to reconstruct individual
events. As a result, they will not deliver the event-by-event energy information usedin this thesis, offering at best a measurement of the average anergy of all neutrinosin the burst by observing the rate of coincidences of multiple photosensors.
Furthermore, while Hyper-Kamiokande would make an effectively backgroundfree detection of supernova burst neutrinos, IceCube and KM3NeT have a significant
background coming from dark noise of photosensors and radioactive impurities inthe detector material. Due to their higher event rate, however, the signal-to-noise
ratio in measuring the event rate may still be larger than that of Hyper-Kamiokande
for a sufficiently close supernova.
5.2.2.7 Others

The HALO experiment [317] detects neutrinos via neutral-current scattering on leadnuclei, while upcoming xenon-based dark matter detectors [318, 319] could detectsupernova neutrinos via coherent elastic neutrino-nucleus scattering (CEνNS). Bothinteraction channels are sensitive to all neutrino flavours, making these detectors

125Chapter 5 Conclusions and Outlook
complementary to Hyper-Kamiokande and many of the detectors listed above. However, due to their relatively small sizes, at most a few hundred events are expectedin these detectors for a supernova at 10 kpc distance, limiting their contribution.
Furthermore, a number of other, smaller neutrino detectors exist that use thesame detector technologies as some of the future experiments described above.
The advantages and disadvantages of the respective detector technology discussed
above apply equally to them. However, due to their smaller size their contribution
may be statistics-limited and I have not highlighted them here individually.

5.2.3 Beyond Neutrinos
Neutrinos are a particularly interesting channel for observing supernova, since they
allow a direct observation of the stellar core at the moment of explosion.
Gravitational waves similarly allow for a direct observation of the explosion
and are sensitive to the asymmetric component of the explosion. After multiple
successful detection runs of both LIGO detectors [320] and the Virgo detector [321]in the past years, the KAGRA detector [322, 323] is expected to join the currently
ongoing detection run in late 2019 [324]. Like the neutrino signal, the gravitational
wave signal from a supernova has large uncertainties and is highly model-dependent.
However, a galactic supernova burst would likely be within the detection range ofthese detectors [324].
Finally, observations across the electromagnetic spectrum become possible oncethe shock wave of the supernova reaches the surface of the star. The initial signal iscalled the shock breakout and takes place after the initial explosion with a delay of
about one minute for very compact Wolf-Rayet stars, one hour for blue supergiants
or one day for red supergiants [325]. Afterwards, follow-up observations acrossmultiple wavelengths may be possible for months. While these observations are notdirectly connected to the explosion mechanism, they offer a wealth of information.
For example, the spectra give information on the abundance of light elements inthe outer layers of the star which lets us identify the type of progenitor, while thelight curves of some supernovae give information on the amount of 56 Ni produced
through nuclear burning in the wake of the shock wave [326].
To realize the full potential of multi-messenger astronomy, we need to draw allthese different methods of observing the supernova together and combine theminto a coherent picture. While the phenomenology of supernovae is so broad that
it would not be feasible to exhaustively discuss potential combinations of theseobservation channels here, a few remarks are in order.
If an optical counterpart to a galactic supernova is observed—which is not certain,
due to either dust extinction in the galactic plane or the unknown fraction of “failed”
supernovae which collapse into a black hole before the shock wave is revived—it
would likely be possible to identify the progenitor. This may make it possible to126

5.2 Outlook
significantly narrow down the range of possible progenitor properties and thus therange of supernova simulations that would need to be compared using the method
described in this thesis.
Furthermore, observing an optical counterpart would enable a distance measurement. If the uncertainty in the measured distance is on the order of 10 % or smaller,
this may further help distinguish different models, since different models often
predict clear differences in the total number of events at a fixed distance. In thatcase, the total likelihood would become

Ltotal = P( Nobs , X ) · Lfixed N ,(5.1)

where Lfixed N is the likelihood derived in section 4.3 and P( Nobs , X ) is the Poisson
probability of observing Nobs events when X events were predicted by a given
model based on the observed distance.
Without an optical counterpart, it would still be possible to estimate the distanceby using the size of the neutronization burst as a standard candle [129]. However,even with Hyper-Kamiokande or DUNE, this method would be likely be able todetermine the distance only to an uncertainty of a few tens of per cent.1 Considering
the range of models shown in table 4.1, this would likely be of little help in trying todistinguish between models except in extreme cases.
Finally, coordination between all observers is essential to be able to exploit thefull potential of the next galactic supernova. For this purpose, the supernova early
warning system (SNEWS) was formed in 1999 [219, 327]. Its main goal is to alert
astronomers if multiple neutrino detectors around the world observe a coincident
neutrino burst, enabling them to observe the light curve of the supernova as quickly
as possible. After an initial test phase, SNEWS has been operating in automatic
mode since 2005 but has not sent out a supernova alert.
Not yet.

1 While reference [129] claims an accuracy of 5–10 %, this assumes a megaton water Cherenkov

detector with gadolinium loading enabling a 90 % neutron tagging efficiency to identify inverse
beta decay events. Such a detector will, unfortunately, not exist in the foreseeable future.

127

Appendix A
Neutrino Interaction Cross Sections
A.1 Inverse Beta Decay
In this thesis, I use the inverse beta decay cross section derived in reference [289].
Here, I will briefly summarize the equations necessary to calculate that cross section.
I start by defining the constants∆ = mn − m p ≈ 1.293 MeV
m p + mn
≈ 938.9 MeV
M=
2
MV = 0.71 GeV(A.3)

M A = 1.03 GeV

(A.4)

(A.1)
(A.2)

and the quantitiess = m2p + 2m p Eν(A.5)

s − u = 2m p ( Eν + Ee ) − m2et = m2n − m2p − 2m p ( Eν − Ee )f1 = 

t
1 − 4.706 4M
2

2
t
1 − 4M
1 − Mt2
2

(A.7)
(A.8)

V

f2 = 

3.706

2
t
1 − 4M
1 − Mt22

g1 = 

1 − Mt2

g2 =

(A.6)

(A.9)

V

−1.27

2M2 g

A

1
.
2
mπ − t2(A.10)(A.11)

129

Appendix A Neutrino Interaction Cross Sections
The differential cross section is then given by" 1.5 !#m
GF2 cos2 θC
dσ
α
3
me
p
=
M2 × 1 +6 + log
+ 1.2
,
2
dEe
4πm p Eν
π
2
2Ee
Ee

(A.12)

where the first part is the tree-level cross section and the term in square brackets
corresponds to radiative corrections at one-loop level [290]. The matrix element
M2 is given by
M2 = A − (s − u) B + (s − u)2 C,(A.13)
where A, B and C depend on the transferred 4-momentum t = q2 < 0 as describedby the expressionsA= 4m2e tg22
t − m2e4 f 12 4M2 + t + m2e + 4g12 −4M2 + t + m2e +
16
M2

 2


t
2
2
2
2
+ f2
+ 4t + 4me + 8 f 1 f 2 2t + me + 16me g1 g2
M2




f 22
∆2
2
−
4M2 + t − m2e + 4g12 4M2 − t + m2e
4 f1 + t 2
16
M
#


4m2e g22 t − m2e22++ 8 f 1 f 2 2t − me + 16me g1 g2
M2− 2m2e M∆g1 ( f 1 + f 2 )m2 ∆ f 22 + f 1 f 2 + 2g1 g2
B = tg1 ( f 1 + f 2 ) + e
4M
C=



f 12 + g12
t f 22−.
4
16M2(A.14)(A.15)(A.16)The kinematically allowed range of positron energies E1 ≤ Ee ≤ E2 as a functionof neutrino energy Eν is given by
E1,2 = Eν − δ −130
1 CM  CM
Eν
Ee ± pCM,
e
mp(A.17)

A.2 Neutrino-Electron Scattering
where δ and the center-of-mass energies and momenta are given byδ=

m2n − m2p − m2e2m ps − m2p√
2 s
s − m2n + m2e√
EeCM =2 srhihis − ( m n − m e )2 s − ( m n + m e )2
√
pCM
=
.
e
2 s
EνCM =(A.18)(A.19)(A.20)(A.21)

I have also implemented the angular distribution of outgoing positrons,
dσ/d cos θ derived by reference [289] in sntools. However, since the angular distribution of events was not used in this analysis, I will not include that equation
here.

A.2 Neutrino-Electron Scattering
In this thesis, I use the cross section derived in reference [292] for neutrino-electron
scattering. Here, I will briefly summarize the equations necessary to calculate thatcross section.
I start by defining the quantities
T = Ee − meql = Ee2 − m2e

l
Ee
T
z=
Eν
ρNC = 1.0126
r
1 + 2mex=TEeEe + l
f0 =
ln
−1
l
me
β=

(A.22)(A.23)(A.24)(A.25)(A.26)(A.27)(A.28)

131

Appendix A Neutrino Interaction Cross Sections
and the functions
1
I (T ) =6
L( x ) =

Zx



0





1
1
x+1
2
+ (3 − x ) x ln
−1
3
2
x−1

(A.29)

ln |1 − t|dt.
t

(A.30)For νe -electron scattering,κ ( T ) = 0.9791 + 0.0097 · I ( T )12
g L ( T ) = ρNC− κ ( T ) sin θW − 1
2gR ( T ) = −ρNC κ ( T ) sin2 θW ,(A.31)(A.32)(A.33)

while for νx -electron scattering,κ ( T ) = 0.9970 + 0.00037 · I ( T )1− κ ( T ) sin2 θW
g L ( T ) = ρNC
2gR ( T ) = −ρNC κ ( T ) sin2 θW .

(A.34)(A.35)(A.36)For antineutrino-electron scattering, κ remains unchanged while g L and gR areswapped.
The cross section, including QCD and electroweak loop corrections, is then givenbyhid σ 2GF2 me 2α=g L ( T ) 1 + f − (z)(A.37)
dEe
π
π
i
h
α
+ g2R ( T )(1 − z)2 1 + f + (z)
π
i
me h
α
− gR ( T ) g L ( T ) z 1 + f ± (z) .
EνπThe terms proportional to α/π describe QED corrections to the cross section due tovirtual and real photons. Instead of the exact expressions given in reference [328], I
use the following simplified expressions which are typically accurate to much better132

A.2 Neutrino-Electron Scatteringthan 1 % [292].



5
ln z
f − (z) = f 0−− ln(1 − z) −(A.38)2121ln2 (1 − z)
11 z
+ [ L(z) − L( β)] −−+ln(1 − z)
2
2
12 2


 

1
2Eν
31 ln z11z
z2
+ z ln z + ln
−
+
β−
+
2
me
18
12
12
24




me
ln z 2 z2 ln z + 1 − z
f + (z) = f 0 2 ln 1 − z −− ln(1 − z) −− −Ee + l232(1 − z )2no1−ln2 (1 − z) + β [ L(1 − z) − ln z ln(1 − z)]
2



1−z
1
ln(1 − z) z2
ln
z
+
2z
−
+
(1 − z )2 2
3
2
 2

1
z
z(1 − 2z)z (1 − z )−L (1 − z ) −ln z −(1 − z )2 2
3
6


β
115 − 109z−
ln z + (1 − z)2
12(1 − z)
6(A.39)

me(A.40)
f ± (z) = 2 f 0 ln 1 − z −Ee + lme
2 ln 1 − z −Ee + l

The energy Ee of the scattered electron depends on the neutrino energy Eν andthe angle θ between the initial neutrino direction and the final electron direction. It
is given by
2me Eν2 cos2 θ.
(A.41)
Ee = me +(me + Eν )2 − Eν2 cos2 θ

133Appendix B
Derivation of Likelihood Function
In this appendix, I derive the likelihood function used for the analysis in chapter 4.
It is based on the likelihood function derived by Loredo and Lamb to analyse eventsfrom SN1987A [312], but I extend it to account for multiple interaction channels.
I start by considering bins in time and observed energy, where the bin size ∆t · ∆E
is arbitrary as long as the expected number of events per bin,Ni = ∑ Niα =αd2 N α ( Ei , ti )
∆E∆t,
dEdt

(B.1)

is much smaller than 1 for all bins i. Here, N α ( E, t) is the observed event rate
predicted by a supernova model in the interaction channel α as a function of timeand energy.
Assuming a Poisson distribution, the probability of observing no events in a single
α = exp − N α .
interaction channel α in a bin around time ti and energy Ei is P0,ii
When considering multiple interaction channels, the probability of observing noevents is simply the product of the probabilities of observing no events in every
single interaction channel, i. e.
αP0,i = ∏ P0,i
= ∏ exp (− Niα )αα!

= exp − ∑ Niα(B.2)= exp (− Ni ) .

(B.3)

α

The probability of observing exactly one event in the interaction channel α is
α = N α exp − N α , so the total probability of observing exactly one event is
P1,ii
i
P1,i = ∑
α

=∑
α

α
P1,i
· ∏ P0,i
β

"

β6=α

!

Niα exp (− Niα ) ·

(B.4)

∏ exp

β6=α



β
− Ni



#

(B.5)

135

Appendix B Derivation of Likelihood Function"= ∑ Niα · ∏ exp
α

β



β
− Ni

= P0,i · ∑ Niα = P0,i · Ni .



#

(B.6)
(B.7)

α

The bin size was chosen such that the probability of observing more than one
event in a bin is negligible.
The likelihood of observing exactly Nobs events in a certain set of bins—which I
refer to as B here—is then given by

L = ∏ P1,i · ∏ P0,i
i ∈B

(B.8)

i∈
/B

= ∏ ( P0,i · Ni ) · ∏ P0,i

(B.9)

= ∏ Ni · ∏ P0,i

(B.10)

i ∈B

i ∈B

i∈
/B

i

where the products over i ∈/ B include all bins that do not contain an event.
For simplicity, I consider the log-likelihood L = ln L. Using ln( a · b) = ln( a) +ln(b), the log-likelihood function is
L = ∑ ln Ni + ∑ ln P0,i ,i ∈B(B.11)iwhere the second term simplifies to∑ ln P0,i = ∑ ln [exp (− Ni )] = − ∑ Ni ,ii

(B.12)iwhich is the number of events predicted by the model. Since I assume in thisthesis that the distance to the supernova is unknown, I have normalized all models
so as to reproduce the observed number of events. This term is therefore modelindependent and since I only consider likelihood ratios1 of different models A and B,∆L = L A − L B , it cancels out. The final likelihood function I use is thus given by
L = ∑ ln Ni .

(B.13)i ∈B

1 Note that the exact values of this log-likelihood function are not physically meaningful since they

depend on the arbitrary choice of bin size. In the likelihood ratio, this dependence cancels out; theratio thus is a meaningful measure of which model is more likely to produce the observed events.

136

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