FY2022
Master’s Thesis

Evaluation of Supernova Model Discrimination andPointing Accuracy with SK-Gd(SK-Gd における超新星爆発モデルの区別と方向決定精度の評価)
Yuri Kashiwagi
Depertment of Physics
Graduate School of Science, University of Tokyo
Student ID: 35-216030
Supervisor: Prof. Sekiya, Hiroyuki
2023/1/6

Abstract
Super-Kamiokande (SK) detector has a vital role in detecting supernova neutrinos, determining thedirection of the supernova, and issuing an alarm to astronomical observatories for multi-messenger
observation of supernovae. For accurate pointing of supernova, it is essential to extract as manyelastic scattering (𝜈 + e− → 𝜈 + e− ) events which have the direction information of the supernova as
possible by identifying the inverse beta decay (IBD) events (𝜈¯e + p → e+ + n) without the direction
information. For identifying IBD events in SK, the coincidence between the prompt signal frome+ and the delayed signal from gamma rays emitted by neutron capture is used. To take advantageof the improved neutron detection eﬃciency by gadolinium loading into SK’s water in 2020 and
2022 (SK-Gd project), the modiﬁcation of the supernova direction determination algorithm has
been necessitated.
Supernova neutrino detection at SK also helps astrophysicists to elucidate the explosion mechanism. However, supernova neutrinos have not been detected since the last supernova neutrino
detection in 1987. To understand SK’s response to supernovae in advance and evaluate pointing
accuracy and the model discrimination in SK-Gd, it is crucial to simulate supernova bursts using
supernova models. The purpose of this thesis is to systematically understand the SK’s response
and pointing accuracy since the start of SK-Gd. In this thesis, I developed the method of data
format uniﬁcation of supernova models, which enables the comparison of SK’s responses andpointing accuracy among models for the ﬁrst time. I systematically studied SK’s responses tosimulated supernova bursts at a distance of 10 kpc and pointing accuracy for six supernova models
considering neutrino oscillations. SK’s responses vary in models, reﬂecting the diﬀerence inthe time and energy structures characteristic of models as well as the composition of neutrino
ﬂavors and the eﬀect of neutrino oscillation. These diﬀerences indicate that the supernova model
discrimination using SK’s response is possible. I derived the pointing accuracy for the six models
considering neutrino oscillation and found it varies in models from 3◦ to 7◦ . The SK-Gd aims todetermine a galactic supernova direction with 3◦ accuracy. I conﬁrmed that SK-Gd achieves thisgoal in Wilson model but not in other models with less neutrino ﬂuxes.

Abstract2

This thesis is organized as follows. Chapter 1 describes the physics of neutrinos and supernovae, including the standard scenario of a supernova explosion. Chapter 2 explains theSuper-Kamiokande detector, SK-Gd experiment, determination of supernova direction, and pointing accuracy, as well as the Monte Carlo simulations for supernova neutrino detection. Chapter 3
summarizes the six supernova models used in this thesis and describes the method of data format
uniﬁcation to compare SK’s response among models. Chapter 4 reports the diﬀerence in SK’s
responses and pointing accuracy among the six models for supernova at 10 kpc with the consideration of neutrino oscillation. Chapter 5 gives the conclusion and describes prospects. Appendix A
lists the ﬁgures of diﬀerence in SK’s response to a supernova at 10 kpc among models that are notincluded in Chapter 4.

3

Acknowledgement
First, I would like to express my sincere gratitude to my supervisor, Prof. Hiroyuki Sekiya, forrespecting my wishes to study the diﬀerence in SK’s response to simulated supernova bursts using
supernova models. Throughout the two years of my master’s course, I have been encouraged byhis excellent and patient guidance and his words of tackling problems one by one when I face lotsof troubles in my work.
I am also particularly grateful to Prof. Yusuke Koshio for taking the time to explain SK MC
simulations in detail, especially when I knew nothing about supernova study in SK, along withhis dedication to developing SK MC for supernova simulation. I would like to show my special
appreciation to Dr. Guillaume Pronost for always helping me in processing SNWATCH and forhis kind clariﬁcations on so many questions I asked about my analysis, as well as his dedication todeveloping SNWATCH. I would also like to express my appreciation to Prof. Masayuki Nakahata
for his constructive suggestions in meetings, especially for studying the threshold dependence ofpointing accuracy. I am also grateful to Dr. Motoyasu Ikeda for giving me comments and advice on
my study in meetings. I could never achieve the results in this work without Fumi Nakanishi-san’s
dedicated work in modifying SKSNSim and her great help with my analysis.
I would like to acknowledge with appreciation the crucial role of Prof. Ken’ichiro Nakazato
who developed “Nakazato format” data and guided me in making supernova models in other data
formats to “Nakazato format.” I am deeply grateful to Jost Migenda-san for answering manyquestions about model discrimination using the log-likelihood method.
I would like to oﬀer my special thanks to Yuki Nakano-san, Kei Ieki-san, and Shota Izumiyamasan for giving me helpful feedback on my JPS presentation practice. Special thanks to Masayuki
Harada-san, Tomoaki Tada-san and Seiya Sakai-san for giving me suggestions for my research.
I give special gratitude to Yuki Kanemura-san, Shintaro Miki-san, Hiroki Kochi-san, and Yoshino
Kaminaga-san for supporting and encouraging me in my research and life in Kamioka. I am deeply
thankful to my colleague Ryota Kaneshima-san who helped me improve my awkward coding in
C++ and ROOT. I would also thank another colleague, Shunsuke Yoshida-san, for giving me a

Acknowledgement

4

brilliant idea to realize what I would like to do in programming. I am also grateful to anothercolleague Kotaro Shimizu-san for always taking care of every colleague and helping me with
ROOT usage. I am also thankful to another colleague Takuya Tomiya-san for giving me the way tothink logically to ﬁgure out the cause when I was overwhelmed when a program stopped working
properly. I also thank the other colleague Hayato Shiba-san for checking my calculation of neutrino
oscillation. I will never forget all the memorable moments I shared with them over the two years.
I owe my comfortable and healthy life in Kamioka to every Kamioka staﬀ who provided mewith delicious and nutritionally balanced meals and a clean living environment.
Finally, I would like to express my wholehearted thanks to my family for always supportingme ﬁnancially and mentally. My progress at night after moving back to my dormitory room inautumn was encouraged by my sister, who connected with me via zoom almost every night to work
together.

iContents

Acknowledgement

3

Chapter 1

Neutrinos and Supernovae

1

Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.1

Neutrino Oscillation in Vacuum . . . . . . . . . . . . . . . . . . .

2

1.1.2

Matter Eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.1.3

Oscillation Parameters and Unsettled Problem . . . . . . . . . . .

5Classiﬁcation of neutrinos by neutrino sources . . . . . . . . . . . . . . .

8

1.2.1

Atmospheric neutrinos . . . . . . . . . . . . . . . . . . . . . . .

9

1.2.2

Solar neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.2.3

Reactor neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.2.4

Accelerator neutrinos . . . . . . . . . . . . . . . . . . . . . . . .

14

1.2.5

Supernova burst neutrinos . . . . . . . . . . . . . . . . . . . . . .

15

1.2.6

Diﬀuse supernova neutrino background . . . . . . . . . . . . . .

15

Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

1.3.1

Categories of Suprenova . . . . . . . . . . . . . . . . . . . . . .

16

1.3.2

Scenario of Core-Collapse Supernova Burst . . . . . . . . . . . .

19

1.3.3

Supernova Neutrino Observed Before . . . . . . . . . . . . . . .

24

1.3.4

Nearby Supernova Candidates . . . . . . . . . . . . . . . . . . .

25

1.1

1.2

1.3

Chapter 2

2.1

Supernova Neutrino Detection with Super-Kamiokande Detector

27

Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2.1.1

ID, OD and Detector Geometry . . . . . . . . . . . . . . . . . . .

28

2.1.2

20-inch Photo Multiplier Tube . . . . . . . . . . . . . . . . . . .

29

2.1.3

Geomagnetic compensation coils . . . . . . . . . . . . . . . . . .

32

2.1.4

Water Puriﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . .

32

Contents

ii
2.1.5

Air Puriﬁcation System . . . . . . . . . . . . . . . . . . . . . . .

33

2.2

Cherenkov Light Detection Principle . . . . . . . . . . . . . . . . . . . .

34

2.3

Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

2.3.1

PMT Signal Readout with QBEE . . . . . . . . . . . . . . . . . .

36

2.3.2

DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

2.3.3

Software Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

SK-Gd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

2.4.1

SK-Gd Experiment Overview . . . . . . . . . . . . . . . . . . . .

38

2.4.2

Water Puriﬁcation System for SK-Gd . . . . . . . . . . . . . . . .

40

Supernova Neutrino Detection with SK-Gd . . . . . . . . . . . . . . . . .

43

2.5.1

Supernova Neutrino Interaction in SK-Gd . . . . . . . . . . . . .

43

2.5.2

Real-time Supernova Monitoring System SNWATCH . . . . . . .

45

2.5.3

Low Energy Event Reconstruction in SK . . . . . . . . . . . . . .

45

2.5.4

Event Selection and Neutron Tagging in SNWATCH . . . . . . .

48

2.5.5

Determination of the Supernova Direction . . . . . . . . . . . . .

51

2.5.6

Pointing Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . .

53

2.5.7

Alert Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Supernova Burst Neutrino Simulations in SK-Gd . . . . . . . . . . . . . .

54

2.6.1

SKSNSim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

2.6.2

SKG4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

2.6.3

mccomb_sn . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

2.4

2.5

2.6

Chapter 3

3.1

3.2

Summary of Supernova Models

58

Supernova Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

3.1.1

Wilson model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

3.1.2

Nakazato model . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

3.1.3

Mori model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

3.1.4

Hüdelpohl model . . . . . . . . . . . . . . . . . . . . . . . . . .

64

3.1.5

Fischer model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

3.1.6

Tamborra model . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Data Format Uniﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.2.1

Linear Interpolation and Extrapolation . . . . . . . . . . . . . . .

67

3.2.2

Diﬀerential Number Flux Calculation . . . . . . . . . . . . . . .

68

3.2.3

Diﬀerential Number Luminosity Calculation . . . . . . . . . . . .

69

3.2.4

Normalization for Reproducing Original Luminosity . . . . . . . .

69

Contents
Chapter 4

4.1

4.2

iii
Detector Response and Pointing Accuracy

70

Energy Threshold Dependence of Pointing Accuracy . . . . . . . . . . . .

70

4.1.1

Event Selection in SNWATCH . . . . . . . . . . . . . . . . . . .

72

4.1.2

ES Eﬃciency and Ineﬃciency . . . . . . . . . . . . . . . . . . .

73

4.1.3

ES purity and Contamination to ES . . . . . . . . . . . . . . . . .

74

4.1.4

Energy Threshold in SNWATCH . . . . . . . . . . . . . . . . . .

76

Detector Response for Supernova at 10kpc . . . . . . . . . . . . . . . . .

76

4.2.1

Average Number of Generated Events in SK by SKSNSim . . . .

76

4.2.2

Average Number of Reconstructed Events in SK . . . . . . . . . .

79

4.2.3

Oscillation-Dependent Diﬀerence in SK’s Response . . . . . . . .

80

4.2.4

Detection of Neutronization Burst . . . . . . . . . . . . . . . . .

97

4.2.5

Diﬀerence in Models in NMO case . . . . . . . . . . . . . . . . .

99

4.3

Pointing Accuracy for Supernova at 10 kpc . . . . . . . . . . . . . . . . . 110

4.4

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Chapter 5Conclusion

114

Appendix A

Diﬀerence in SK Response among Models

116

A.1

A.2

References

Diﬀerence in Models in No Oscillation case . . . . . . . . . . . . . . . . 117
A.1.1

Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

A.1.2

Energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

A.1.3

Angular Distribution . . . . . . . . . . . . . . . . . . . . . . . . 126

Diﬀerence in Models in IMO case . . . . . . . . . . . . . . . . . . . . . . 129
A.2.1

Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.2.2

Energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

A.2.3

Angular Distribution . . . . . . . . . . . . . . . . . . . . . . . . 138
140

1

Chapter 1
Neutrinos and Supernovae
Neutrinos are of interest for both particle physics and astrophysics. This chapter describes generalproperties of neutrinos and physics of supernovae in terms of the important observational targetsof Super-Kamiokande detector.

1.1 Neutrinos
Neutrinos are neutral, spin-half particles which are categorized into leptons in the Standard
Model. Among the four fundamental forces, neutrinos participate only in weak interaction andgravitational interaction. However, neutrino masses are extremely small that it is very diﬃcult
to detect gravitational interaction with other matter. In the Standard Model, neutrinos have beentreated as mass-less particles. However, it is conﬁrmed that neutrinos have masses by the discoveryof the atmospheric neutrino oscillation in Super-Kamiokande detector in 1998 (see Section 1.1.1).
Neutrinos have three species called ﬂavors: electron neutrino 𝜈e , muon neutrino 𝜈 𝜇 , and tau
neutrino 𝜈 𝜏 . For each ﬂavor, antineutrino ( 𝜈¯e , 𝜈¯ 𝜇 , 𝜈¯ 𝜏 ) exists. The existence of neutrino wastheoretically introduced by Pauli in 1930. Experimental discovery started from 𝜈¯e in 1958, 𝜈 𝜇 in
1962, and 𝜈 𝜏 in 2000.
Mass Eigenstates and Weak Eigenstates
It is considered that there are two types of eigenstates for neutrinos: mass eigenstates |𝜈𝑖 i(𝑖 = 1, 2, 3) and weak eigenstates (ﬂavor eigenstates) |𝜈 𝛼 i (𝛼 = 𝑒, 𝜇, 𝜏). A neutrino is generated
via weak interaction as a weak eigenstate. During the propagation the neutrino behaves as asuperposition of three mass eigenstates. The moment it interacts with other particle, its statebehaves a single weak eigenstate again. Mass eigenstates and weak engenstates are related by a

Chapter 1 Neutrinos and Supernovae

2

3×3 unitary matrix called Pontecorvo–Maki–Nakagawa–Sakata (PMNS)-matrix [1], as:
𝑈𝑒1
𝜈e
©
ª ©
­ 𝜈 𝜇 ® = ­ 𝑈 𝜇1
« 𝜈 𝜏 ¬ « 𝑈 𝜏1

𝜈1
𝑈𝑒3
ª
ª©
𝑈 𝜇3 ® ­ 𝜈2 ® .
𝑈 𝜏3 ¬ « 𝜈3 ¬

𝑈𝑒2
𝑈 𝜇2
𝑈 𝜏2

(1.1)

The PMNS-matrix is written using three real parameters called mixing angles 𝜃 12 , 𝜃 13 , 𝜃 23 and asingle phase called CP-Phase 𝛿𝐶 𝑃 , as:
𝑈𝑒1©
­ 𝑈 𝜇1« 𝑈 𝜏1

𝑈𝑒2
𝑈 𝜇2
𝑈 𝜏2

𝑈𝑒3
1
ª ©
𝑈 𝜇3 ® = ­ 0
𝑈 𝜏3 ¬ « 0

0
𝑐 23
−𝑠23

0
𝑐 13
ª©
𝑠23 ® ­
0𝑐 23 ¬ « −𝑠13 𝑒 𝑖 𝛿𝐶 𝑃

𝑐 12 𝑐 13©
= ­ −𝑠12 𝑐 23 − 𝑐 12 𝑠23 𝑠13 𝑒 𝑖 𝛿𝑖𝛿« 𝑠12 𝑠23 − 𝑐 12 𝑐 23 𝑠13 𝑒

010

𝑠13 𝑒 −𝑖 𝛿𝐶 𝑃
𝑐 12
ª©
0
® ­ −𝑠12𝑐 13¬« 0

𝑠12 𝑐 13𝑐 12 𝑐 23 − 𝑠12 𝑠23 𝑠13 𝑒 𝑖 𝛿−𝑐 12 𝑠23 − 𝑠12 𝑐 23 𝑠13 𝑒 𝑖 𝛿

𝑠12
𝑐 12
0

0
ª
0 ®
1 ¬
(1.2)

𝑠13 𝑒 −𝑖 𝛿ª𝑠23 𝑐 13 ® (1.3)
𝑐 23 𝑐 13 ¬where 𝑐 𝑖 𝑗 ≡ cos 𝜃 𝑖 𝑗 and 𝑠𝑖 𝑗 ≡ sin 𝜃 𝑖 𝑗 .

1.1.1 Neutrino Oscillation in Vacuum
Neutrino oscillation is a phenomenon that the probability of a neutrino’s being a speciﬁc ﬂavor
oscillates with time during its propagation. As a result, the observed ﬂavor can be diﬀerent fromwhat it was at the produced point. If neutrinos are mass-less, the mass eigenstates coincide withthe weak eigenstates, thus neutrino oscillation does not occur. Therefore, observation of neutrino
oscillation guarantees non-zero neutrino masses. The ﬁrst discovery of neutrino oscillation wasmade in 1998 at Super-Kamiokande detector [2].
Oscillartion Probabilities
The aim of this section is to derive neutrino oscillation probability in vacuum. Neutrino
oscillation in a matter is discussed later. Consider a neutrino produced as a ﬂavor eigenstate |𝜈 𝛼 i
at time 𝑡 = 0. From Eq. (1.1), the mass eigenstate of this neutrino state is written as:Õ
𝑈 𝛼𝑖 |𝜈𝑖 i|𝜈 𝛼 (𝑡 = 0)i =

(1.4)

𝑖

After the propagation of time 𝑡, the state becomes:Õ|𝜈(𝑡)i =𝑈 𝛼𝑖 𝑒 −𝑖𝐸𝑖 𝑡 |𝜈𝑖 i
𝑖

(1.5)

Chapter 1 Neutrinos and Supernovae
where 𝐸 𝑖 =q3

𝑝 2𝑖 + 𝑚 𝑖2 is the neutrino energy with the momentum 𝑝 𝑖 and the mass 𝑚 𝑖 . The

probability of observing ﬂavor eigenstate |𝜈 𝛽 i at time 𝑡 is:𝑃(𝜈 𝛼 → 𝜈 𝛽 ) = |h𝜈 𝛽 |𝜈(𝑡)i| 2 = |

Õ
𝑖

∗ 2
𝑈 𝛼𝑖 𝑒 −𝑖𝐸𝑖 𝑡 𝑈𝛽𝑖
| =

ÕÕ
𝑖

𝑗

∗
𝑈 𝛼𝑖 𝑈𝛽 𝑗 𝑈𝛽𝑖
𝑈 ∗𝛼 𝑗 𝑒 −𝑖 (𝐸𝑖 −𝐸 𝑗 )𝑡 . (1.6)

By considering the neutrino is relativistic i.e., 𝑝 𝑖  𝑚 𝑖 , the energy is approximately written as:
𝐸𝑖 =

q

𝑚 𝑖2
2
2
𝑝𝑖 + 𝑚𝑖 ' 𝑝𝑖 +
.
2𝑝 𝑖

(1.7)

Since it can be assumed that 𝐸 𝑖 ' 𝐸 𝑗 = 𝑝 𝑖 ,𝐸𝑖 − 𝐸 𝑗 '𝑚 𝑖2 − 𝑚 2𝑗2𝐸≡

Δ𝑚 𝑖2𝑗(1.8)

2𝐸

Because neutrinos propagate almost at the velocity of light, it can be assumed that 𝑡 ∼ 𝐿 (𝐿: traveling distance) in natural units. Hence, Eq. (1.6) becomes:!
ÕÕ−𝑖Δ𝑚 𝑖2𝑗 𝐿∗
𝑈 𝛼𝑖 𝑈𝛽 𝑗 𝑈𝛽𝑖
𝑈 ∗𝛼 𝑗 exp
𝑃(𝜈 𝛼 → 𝜈 𝛽 ) =2𝐸𝑖𝑗= 𝛿 𝛼𝛽 − 4

Õ
𝑖> 𝑗

∗
Re(U 𝛼i U𝛽j U𝛽i
U ∗𝛼j ) sin2Δm2ij L
4E

−2

Õ

∗
Im(U 𝛼i U𝛽j U𝛽i
U ∗𝛼j ) sin2i>jΔm2ij L
2E
(1.9)

Note that the transition probability for switching ﬂavors 𝛼 ↔ 𝛽 in Eq. (1.9) can be obtained by∗ 𝑈 ∗ ) ∗ . Also,
reversing the sign of the second summation because 𝑈𝛽𝑖 𝑈 𝛼 𝑗 𝑈 ∗𝛼𝑖 𝑈𝛽∗ 𝑗 = (𝑈 𝛼𝑖 𝑈𝛽 𝑗 𝑈𝛽𝑖
𝛼𝑗for antineutrino ﬂavor conversion 𝜈 𝛼 → 𝜈 𝛽 , the sign before the second summation is inverted.
2 = Δ𝑚 2 + Δ𝑚 2 , neutrino oscillation is described by six parameters: the three mixing
Since Δ𝑚 31
32
21
2 , Δ𝑚 2 , and a single CP-phase 𝛿angles 𝜃 12 , 𝜃 13 , 𝜃 23 , the two squared-mass diﬀerences Δ𝑚 21
𝐶 𝑃 . As
32

Eq. (1.9) suggests, the ﬂavor conversion probability oscillates if 𝑚 𝑖 ≠ 𝑚 𝑗 . Oscillation probabilities
depend on squared-mass diﬀerence Δ𝑚 𝑖2𝑗 , neutrino energy 𝐸, and traveling distance 𝐿.
Neutrino Oscillation of Two Flavors
It is helpful to understand the main features of neutrino oscillation between just two ﬂavors. For
the two ﬂavors’ case, we can use:

 
𝜈𝛼
cos 𝜃
=
𝜈𝛽
− sin 𝜃

sin 𝜃
cos 𝜃



𝜈1
𝜈2


(1.10)

Chapter 1 Neutrinos and Supernovae

4

instead of Eq. (1.1), with a mixing angle 𝜃. By following the discussion above, oscillation
probabilities for two ﬂavors can be expressed as:22
2 Δm L sin 2𝜃 sin
4E 2𝑃(𝜈 𝛼 → 𝜈 𝛽 ) =
Δm L

2

 1 − sin 2𝜃 sin24E

(𝛼 ≠ 𝛽)(1.11)(𝛼 = 𝛽)where Δ𝑚 2 ≡ 𝑚 22 − 𝑚 12 . We can see that the ﬂavor conversion probability depends on Δ𝑚 2 𝐿/𝐸
and the amplitude of the oscillation is determined by the mixing angle.
Neutrino Oscillation of Three Flavors
The oscillation probabilities for three ﬂavor case can be obtained by a steady calculation of
Eq. (1.9) using Eq. (1.3), but they are very complex. Assuming one possible scenario of neutrino
2  Δ𝑚 2 ≈ Δ𝑚 2 (see Section 1.1.3) gives the following expression as themass ordering Δ𝑚 21
31
32

three ﬂavor oscillation probabilities for the speciﬁc channels:
Δm232 L
Δm232 L= sin2 2𝜃 13 sin2 𝜃 23 sin2
4E
4E
2 L
2 L
Δm
Δm
32
32
2
2
2
2
2
2
𝑃(𝜈e → 𝜈 𝜏 ) = 4|𝑈33 | |𝑈13 | sin= sin 2𝜃 13 cos 𝜃 23 sin
4E
4E
2Δm32 L
Δm232 L222
2
42
𝑃(𝜈 𝜇 → 𝜈 𝜏 ) = 4|𝑈33 | |𝑈23 | sin= sin 2𝜃 23 cos 𝜃 13 sin.
4E
4E
𝑃(𝜈e → 𝜈 𝜇 ) = 4|𝑈13 | 2 |𝑈23 | 2 sin2

(1.12)(1.13)(1.14)

1.1.2 Matter Eﬀect
Neutrino oscillation in a matter is modiﬁed compared to that in vacuum due to the scatteringwith electrons, protons and neutrons that constitute the matter. Since neutral current reactions
occur regardless of neutrino ﬂavors, only the modiﬁcation on the eﬀective potential of 𝜈e due
to charged current reactions aﬀects neutrino oscillation. The eﬀective potential of each neutrino
ﬂavor propagating through a neutral matter is:𝑉𝜈𝑒 = 𝑉𝐶𝐶 + 𝑉𝑁 𝐶 , 𝑉𝜈𝜇 = 𝑉𝜈𝜏 = 𝑉𝑁 𝐶 .

(1.15)√
Here, 𝑉𝐶𝐶 = ± 2𝐺 𝐹 𝑁𝑒 is the potential of charged current reaction and 𝑉𝑁 𝐶 = ∓ √1 𝐺 𝐹 𝑁 𝑛 ,2with the electron (neutron) number density in the matter 𝑁𝑒 (𝑁 𝑛 ) and the Fermi coupling constant
𝐺 𝐹 . Under this condition, neutrino oscillation probability in a matter is written by replacing

Chapter 1 Neutrinos and Supernovae

5

sin2 2𝜃, Δ𝑚 2 of Eq. (1.11) with:sin2 2𝜃
!2
√
2
2𝐺
𝑁
𝐸
𝐹
𝑒
sin2 2𝜃 + ±− cos 2𝜃
Δ𝑚 2
v
u
!2
t
√
2 2𝐺 𝐹 𝑁𝑒 𝐸
22
2
Δ𝑚 Matter = Δm
sin 2𝜃 + ±− cos 2𝜃 ,Δ𝑚 2
sin2 2𝜃 Matter =(1.16)(1.17)

respectively. As it is seen from Eq. (1.17), the oscillation probability resonates when the condition√
2 2𝐺 𝐹 𝑁𝑒 𝐸±
− cos 2𝜃 = 0
Δ𝑚 2(1.18)(positive sign for neutrino, and negative sign for anti-neutrino) is satisﬁed. This condition is called
Mikheyev–Smirnov–Wolfenstein (MSW) condition. The sign of Δ𝑚 2 determines whether thisresonance condition is satisﬁed in neutrinos or antineutrinos (see Section 1.2.1).

1.1.3 Oscillation Parameters and Unsettled Problem
As mentioned in Section 1.1.1, neutrino energy 𝐸 and traveling distance 𝐿 determine in which
ﬂavor dominant oscillation occurs. Making use of this, oscillation parameters have been mea2 have been mainly measured from solar neutrino
sured using several neutrino sources. 𝜃 12 , Δ𝑚 21

observation (see Section 1.2.2), 𝜃 13 measurements are from reactor neutrino observation (see2 ,𝛿Section 1.2.3), and 𝜃 23 , Δ𝑚 32
𝐶 𝑃 measurements are from atmospheric neutrinos and accelerator

neutrinos (see Section 1.2.1 and Section 1.2.4, respectively) . Recent measurements of oscillation
parameters are summarized in table Table 1.1.
Table 1.1: Oscillation parameters [3].

Measurements
Parameters

Normal Mass Ordering

Inverted Mass Ordering

sin2 𝜃 12

0.307+0.013−0.0130.307+0.013−0.013sin2 𝜃 13(2.20 ± 0.07) × 10−2

(2.20 ± 0.07) × 10−2

2 [10−5 eV2 ]Δ𝑚 21

7.53+0.18−0.18

7.53+0.18−0.18

sin2 𝜃 23

2 [10−3 eV2 ]Δ𝑚 32

𝛿𝐶 𝑃 [rad]0.546+0.021−0.0212.453+0.033−0.033
1.36+0.20𝜋−0.16

0.539+0.022−0.022−2.536+0.034−0.034
1.36+0.20𝜋−0.16Regarding oscillation parameters, the following three topics remain unsettled;

Chapter 1 Neutrinos and Supernovae

6

Mass Ordering
2 is measured to be positive, there are two possible ordering for the
Since the sign of Δ𝑚 21

neutrino masses: whether 𝑚 3 is heavier or lighter than 𝑚 1 and 𝑚 2 , as shown in Fig. 1.1. The
former scenario, i.e., 𝑚 1 < 𝑚 2  𝑚 3 , is referred to as Normal Mass Ordering; NMO, and thelatter scenario i.e., 𝑚 3 < 𝑚 1 < 𝑚 2 is referred to as Inverted Mass Ordering; IMO. There
are two methods for the mass ordering determination: observation of the resonant oscillation inmatter (see Section 1.1.2) and the direct measurements of absolute neutrino masses. Recent global
analysis prefers NMO for 2.7𝜎 [4]. Since the sign of Δ𝑚 2 cannot be determined from Eq. (1.11),
the absolute neutrino mass is not measurable from neutrino oscillation observation. Instead, thekinematics of single-𝛽 decay or electron capture is utilized for direct 𝜈e mass measurement. Fromthe high-precision measurement of tritium 𝛽 decay, the upper limit of 𝜈e mass has been measured
to be 0.8 eV · c−2 (90% CL) [5].

Fig. 1.1: Neutrino Mass Ordering. 𝑚 1 < 𝑚 2  𝑚 3 is called Normal Mass Ordering (NMO),
𝑚 3  𝑚 1 < 𝑚 2 is called Inverted Mass Ordering (IMO).

CP-Phase
In order to explain the matter-antimatter asymmetry observed in our universe, at least CP
symmetry needs to be violated. CP violation itself is conﬁrmed in the quark sector, which is
insuﬃcient to explain the observed matter-antimatter asymmetry. If 𝛿𝐶 𝑃 ≠ 0, 𝜋, the PMNSmatrix is no longer a real matrix, suggesting the possibility of CP violation in the lepton sector.
Therefore, 𝛿𝐶 𝑃 measurement is a key to settling this. Its role is mainly played by the observationof 𝜈 𝜇 → 𝜈e and 𝜈 𝜇 → 𝜈 e oscillation in accelerator neutrinos. However, 𝛿𝐶 𝑃 measurement still
has large uncertainty as shown in Table 1.1. Fig. 1.2 shows 𝜒2 ﬁtting results from long baseline
experiments and a global analysis [6]. The NMO case (left panel) still shows a preference for
CP-conserving phase 𝛿𝐶 𝑃 = 𝜋. For the IMO case (right panel), 𝛿𝐶 𝑃 ≈ 1.5𝜋 is favored. The otherChapter 1 Neutrinos and Supernovae

7

CP-conserving phase 𝛿𝐶 𝑃 = 0 is disfavored for both orderings.

Fig. 1.2: Δ𝜒2 proﬁle of 𝛿𝐶 𝑃 for NMO (left panel) and IMO (right panel) [6]. The red, blue, black, and green
lines represent NOvA data, T2K data, all long-baseline data, and global ﬁt data, respectively.

Octant Degeneracy
Since atmospheric and accelerator neutrino oscillation experiments are mainly sensitive tosin2 𝜃 23 , the value of 𝜃 23 degenerates. Whether 𝜃 23 is larger or smaller than 𝜋/4 (i.e., whether
sin2 𝜃 23 > 0.5 or sin2 𝜃 23 < 0.5) remain unknown, which is called octant degeneracy. However,this degeneracy is slightly resolved in the atmospheric oscillation experiments due to the mattereﬀect inside the Earth. Fig. 1.3 shows the result of 𝜒2 ﬁtting of 𝜃 23 of a global analysis [6].

Fig. 1.3: Δ𝜒2 proﬁle of 𝜃 23 [6]. NMO and IMO are represented by blue and magenta, respectively.

Chapter 1 Neutrinos and Supernovae

8

1.2 Classiﬁcation of neutrinos by neutrino sources
Neutrinos are emitted from various sources. Fig. 1.4 shows measured and expected ﬂuxes of natural and artiﬁcial neutrinos other than accelerator neutrino [7]. Among them, SK’s observationaltargets are (1) atmospheric neutrinos, (2) solar neutrinos, (3) reactor neutrinos, (4) accelerator
neutrinos, (5) supernova burst neutrinos, and (6) supernova relic neutrinos. This section gives
an introduction to each neutrino source, including the production mechanism, produced ﬂavor,
typical energy range, and the related physics and experiments.

Fig. 1.4: Expected and measured neutrino ﬂuxes and energy from various sources [7]. Each neutrino source isindicated in the ﬁgure. "Cosmological 𝜈" means cosmological neutrino background (C𝜈B). "Terrestrial anti𝜈", also referred to as geoneutrinos, are produced from the decay of long-lived natural radioactive isotopes
such as 238 U, 232 Th and 40 K inside the Earth. "Background from old supernovae" corresponds to Supernova
Relic Neutrinos (Diﬀuse Supernova Neutrino Background) in Section 1.2.6. "𝜈 from AGN" means neutrinos
from Active Galactic Nuclei. "Cosmogenic 𝜈" are neutrinos generated through the interaction between
ultrahigh-energy cosmic rays and cosmological photons. Other neutrino sources are explained in the text.

Chapter 1 Neutrinos and Supernovae

9

1.2.1 Atmospheric neutrinos
Atmospheric neutrinos are generated by the decay of hadrons that are produced by the interaction
between cosmic rays (mainly protons) and the Earth’s atmosphere. The predominant channel ofhadron decay is the pion decay and the succeeding muon decay:
𝜋 + → 𝜇+ + 𝜈 𝜇 ,𝜇+ → e+ + 𝜈e + 𝜈 𝜇(1.19)

𝜋 − → 𝜇− + 𝜈 𝜇 ,

𝜇− → 𝑒 − + 𝜈 e + 𝜈 𝜇 .

(1.20)

Kaon’s two-body decay channels:
K+ → 𝜇 + + 𝜈 𝜇−−

K → 𝜇 + 𝜈𝜇(1.21)(1.22)and three-body decay channel:
KL → 𝜋 + + e + + 𝜈 eorKL → 𝜋 − + e− + 𝜈 e(1.23)

are also responsible for atmospheric neutrino generation. The energy of atmospheric neutrinos
spans a wide range from ∼100 MeV to ∼100 TeV as shown in Fig. 1.4.
Atmospheric Neutrino Experiments
Super-Kamiokande is now a representative experiment for atmospheric neutrino observation. As
shown in Section 1.1.1, oscillation probabilities depend on Δ𝑚 2 𝐸/𝐿. Since atmospheric neutrinos
are produced at any longitude and latitude of the Earth’s atmosphere, the traveling distance is
diﬀerent between "downward-going" neutrinos generated above Super-Kamiokande and "upwardgoing" neutrinos coming from the other side of the Earth. Thus, upward-going neutrinos canoscillate to change their ﬂavor when they are detected at Super-Kamiokande detector. In the
1990s, when the possibility of neutrino oscillation was not widely accepted, Super-Kamiokandeobserved this as 𝜈 𝜇 deﬁcit due to 𝜈 𝜇 → 𝜈 𝜏 oscillation at 6.2𝜎, demonstrating the evidenceof atmospheric neutrino oscillation [2]. Fig. 1.5 shows expected and observed zenith angle
distributions of 𝜈e and 𝜈 𝜇 at Super-Kamiokande I-IV [3]. The bottom left and bottom middle cyan
histograms, representing the expected number of neutrinos without oscillation, peak at cos 𝜃 𝑧 ∼ 0
because for this direction hadrons and resulting muons travel longer and are more likely to decay
by Eq. (1.19)-Eq. (1.23) than cos 𝜃 𝑧 ± 1 direction. It is clear from the bottom middle panel that the
number of upward-going 𝜈 𝜇 is about half of that of down-going 𝜈 𝜇 .
Fig. 1.6 shows expected oscillation probability for neutrino and antineutrino with neutrinoenergy and cos 𝜃 𝑧 assuming NMO [8]. The similar ripple pattern seen in both panels in ≲ 10 GeV
2 𝐿/4𝐸, whose amplitude is proportional to sin2 𝜃 .
region corresponds to the oscillation with Δ𝑚 32
23

Chapter 1 Neutrinos and Supernovae

10

Fig. 1.5: Zenith angle distributions of atmospheric neutrino events at Super-Kamiokande I-IV [3]. Fully
contained 𝑒-like and 𝜇-like events with visible energy below 1.33 GeV (sub-GeV) and above 1.33 GeV(multi-GeV), as well as upward stopping muon samples and upward through going muon samples are shown.
Partially contained (PC) events are combined with muti-GeV 𝜇-like events (bottom middle panel). The
black cross represents Super-Kamiokande I-IV’s data corresponding to 328 kton-years of exposure. The
cyan histograms represent Monte-Carlo simulation assuming no neutrino oscillation. The red histograms are
the best-ﬁt expectations for neutrino oscillations. cos 𝜃 𝑧 = −1 corresponds to upward-going neutrinos, andcos 𝜃 𝑧 = 1 corresponds to downqard-going neutrinos.

Thus, atmospheric neutrino oscillation measurements are sensitive to 𝜃 23 octant. The discontinuity
around cos 𝜃 𝑧 ∼ −0.85 in the left panel originates from neutrinos penetrating both the mantle andthe high-density region near the center of the Earth (outer core). The pattern in cos 𝜃 𝑧 ≲ −0.85(namely upward going) and 2-10 GeV region of 𝜈 𝜇 → 𝜈e transition correspond to the resonanceoscillation due to matter eﬀect, which is not seen in 𝜈 𝜇 → 𝜈 e transition. If IMO is assumed, thefeatures appear in 𝜈 𝜇 → 𝜈 e plot instead. In other words, the resonance condition is satisﬁed inneutrinos (antineutrinos) under the assumption of NMO (IMO). Therefore, measuring the mattereﬀect of neutrinos and antineutrinos in this energy region is a key to determining the neutrino’s
mass ordering. The ordering aﬀects the number of events of each interaction observed in SK (seeSection 2.6.1).

Chapter 1 Neutrinos and Supernovae(a) 𝑃 (𝜈𝜇 → 𝜈e )11(b) 𝑃 ( 𝜈¯ 𝜇 → 𝜈¯e )Fig. 1.6: Oscillation probabilities assuming NMO [8]: (a) 𝜈 𝜇 → 𝜈e oscillation. (b) 𝜈 𝜇 → 𝜈 e oscillation.
The horizontal and vertical axis represents neutrino energy and cosine of zenith angle 𝜃 𝑧 , with up-going
2 =neutrinos of cos 𝜃 𝑧 = 1 and down-going neutrinos of cos 𝜃 𝑧 = −1. Here, oscillation parameters of Δ𝑚 32
2.5 × 10−3 eV2 , sin2 𝜃 23 = 0.5, sin2 𝜃 13 = 0.0219 and 𝛿𝐶 𝑃 = 0 are assumed. Distorted pattern due to mattereﬀects inside the Earth is seen in 2-10 GeV for (a) but does not appear in (b).

1.2.2 Solar neutrinos
Solar neutrinos are created in the nuclear fusion in the very dense (∼150 g/cm3 ) and hightemperature (∼ 1.5 × 107 K) environment at the center of the Sun. Only electron neutrinos 𝜈e
are emitted as solar neutrinos. There are two nuclear fusion processes illustrated in Fig. 1.7: ppchain reaction and CNO cycle. The pp-chain reactions are a series of nuclear fusion processes ofprotons, and the CNO cycle is a hydrogen burning process involving carbon, nitrogen, and oxygenas catalysts. While the former accounts for 98.4% of the energy produced by the Sun, the latter is
responsible for 1.6%. Note that for stars heavier than the Sun (with core temperature ≳ 1.8×107 K),
the CNO cycle can be the primary source of energy production. Fig. 1.8 shows the expected
spectrum of solar neutrino ﬂuxes.
Table 1.2 summarizes pp-chain neutrinos. It can be seen that the typical energy range of solar
neutrinos is 0.1-20 MeV. Note that pep neutrinos and 7 Be neutrinos are mono-energetic because
they are produced in two-body decay. The other solar neutrinos are produced by three-body decay
and thus they are not mono-energetic.

Chapter 1 Neutrinos and Supernovae

12(a) pp-chain(b) CNO cycle

Fig. 1.7: Schematic picture of nuclear reactions in the Sun: (a) pp-chain reaction and (b) CNO cycle. The
reaction formula for each label is speciﬁed in Table 1.2. The eﬀective lifetime for each starting nuclide isalso labeled in panel (b). Thicker arrows in panel (b) indicate faster transmutation [9].

Table 1.2: Summary of solar neutrinos produced in the pp-chain reactions.

Label

pp
pep
7 Be

Chain

pp-I
(pp-I)
pp-II

Fraction[%]* Notation in Nuclear Reaction

89.9
0.22
7.2

Notation in Particle Reaction

1 H( 𝑝, e+ 𝜈 ) 2 H
e
2 H( 𝑝, 𝛾) 3 He𝑝 + 𝑝 → e+ + 𝜈e +2 H

3 He( 3 He, 2𝑝) 4 He

23 He→ 2𝑝+4 He

1 H( 𝑝𝑒 − , 𝜈 ) 2 He

𝑝 + 𝑒 − + 𝑝 → 𝜈 e +2 H

3 He(𝛼, 𝛾) 7 Be

3 He+𝛼 → 𝛾+7 Be

7 Be(𝑒 − , 𝜈 ) 7 Lie
7 Li( 𝑝, 𝛼) 4 He

7 Be+𝑒 − → 𝜈 +7 Lie
7 Li+𝑝 → 𝛼+4 He

7 Be( 𝑝, 𝛾) 8 B

7 Be+𝑝 → 𝛾+8 B

2 H+𝑝 → 𝛾+3 He

8B

pp-III

7.8 × 10−3

8 B(e+ 𝜈 ) 8 Be∗e
8 Be∗ (𝛼) 4 He

8 B→ e+ + 𝜈 +8 Be∗e
8 Be∗ → 24 He

hep-

3 × 10−5

3 He( 𝑝, e+ 𝜈 ) 4 Hee

3 He+𝑝 → e+ + 𝜈 +4 Hee* Fraction of each pp-chain neutrino in the entire solar neutrino produced in the Sun.

Chapter 1 Neutrinos and Supernovae

13

Fig. 1.8: Expected spectrum of solar neutrino ﬂuxes from diﬀerent nuclear processes [9]. Note that neutrino
ﬂuxes originated from electron capture (labeled "ec" in the ﬁgure) are plotted in cm−2 s−1 .

Solar Neutrino Problem and Solar Neutrino Experiments
Solar neutrino measurements such as Homestake experiment in the 1970s and Kamiokande
detector in the late 1980s reported less number of solar neutrinos than expected in the standard
solar model. The discrepancy between the observed and the expected, referred to as the solar
neutrino problem, had been puzzled physicists for many years. In 1985, the theory of matter eﬀect
in neutrino oscillation (see Section 1.1.2) was proposed [10] that could explain this discrepancy.
After about 15 years since then, the combination of the results from the solar neutrino measurement
at Super-Kamiokande detector in 2000 and at Sudbury Neutrino Observatory (SNO) in 2002
demonstrated neutrino oscillation as the reason for the solar neutrino problem.
Currently, solar neutrino observation with Super-Kamiokande aims to measure more precise
2 to conﬁrm of matter eﬀect on solar
values for the solar oscillation parameters 𝜃 12 and Δ𝑚 21

neutrinos passing through the Sun and the Earth, etc. Other solar neutrino experiments are SAGE
(1989-) [11], GALLEX/GNO (1998-2003) [12], Borexino (2007-2021) [13], and KamLAND(2002-) [14].

1.2.3 Reactor neutrinos
Reactor neutrinos are anti-electron neutrinos resulting from the 𝛽-decay (n → e− + p + 𝜈 e )of ﬁssion products of 235 U, 238 U, 239 Pu, and 241 Pu. The energy range of these neutrinos is ∼110 MeV. As it can be seen from Fig. 1.4, reactor neutrinos can be the background for detecting

Chapter 1 Neutrinos and Supernovae

14

diﬀuse supernova neutrino background (see Section 1.2.6).
Reactor neutrino experiments observe the disappearance of 𝜈 e due to neutrino oscillation.
For example, KamLAND experiment demonstrated the evidence of neutrino oscillation by themeasurement of the energy spectrum of 𝜈¯e from reactors in Japan [15], and Daya Bay (20112020) [16], RENO (2011-) [17], and Double Chooz experiments (2011-2017) measured 𝜃 13 [18,19].

1.2.4 Accelerator neutrinos
Accelerators are another artiﬁcial neutrino source with the capability of controlling neutrinoenergy. Neutrino oscillation measurements with accelerator neutrinos have been performed incollaboration with Cherenkov detectors or calorimetric tracking detectors as long-baseline experiments. The accelerator generates a neutrino beam with a speciﬁc energy for each experiment.
To make a neutrino beam, hadrons (mainly pions) created by hitting a proton beam to carbon
target decay in the same way as Eq. (1.19)-Eq. (1.23) are utilized. Therefore, the ﬂavors at the
production are 𝜈e , 𝜈 𝜇 , 𝜈 e and 𝜈 𝜇 . An electromagnetic ﬁeld is applied to charged hadrons to alignthe neutrino beam before decaying into neutrinos. Then, neutrino oscillation from the accelerator
to the detector is observed.
Long-baseline experiments
The ﬁrst long-baseline experiment was K2K (KEK to Kamioka) experiment, performed with thecollaboration of KEK 12 GeV Proton Synchrotron complex (KEK-PS) and Super-Kamiokande over
1999-2004. SK observed 𝜈 𝜇 disappearance due to 𝜈 𝜇 → 𝜈 𝜏 oscillation during the 250 km travel
underground from KEK, demonstrating the capability of accelerator-based neutrino oscillation
measurement. K2K is now succeeded to T2K (Tokai to Kamioka, 2010-) [20] with the new highintensity beam in Japan Proton Accelerator Research Complex (J-PARC). Recent results from T2K
experiment suggests non-zero 𝛿𝐶 𝑃 value by excluding 𝛿𝐶 𝑃 = 0, 𝜋 at 90% conﬁdence level [21].
Other accelerator-based oscillation experiments are MINOS (2005-2012), OPERA (CERN to
Gran Sasso, 2008-2012) and NOvA (2014-) [22, 23]. For the next generation experiments, HyperKamiokande (HK) [24] and Deep Underground Neutrino Experiment (DUNE) [25] are underconstruction.

Chapter 1 Neutrinos and Supernovae

15

1.2.5 Supernova burst neutrinos
Supernova neutrinos are emitted when heavy stars with 𝑀 ≳ 8𝑀 explode at the end of theirlives. The dying star releases 99% of the explosion energy in the form of neutrinos within about
10 seconds before the radiation of electromagnetic waves. During the explosion process, neutrinosof all ﬂavors are emitted (see Section 1.3.2 for more detail). The typical energy range of supernova
burst neutrinos is 1-100 MeV.
The observational importance of supernova neutrinos is that they hardly interact with matter
until detected at the terrestrial detector. Thus the information from the star remains intact.
Moreover, supernova neutrino detection has another vital role: identifying supernova position
before it becomes observable with electromagnetic radiation. In 1987, Kamiokande, IMB, andBaksan detected supernova burst neutrinos, on the occurrence of SN1987A, for the ﬁrst time in
the world [26] (a more detailed description is given in Section 1.3.3). SN1987A was ﬁrst observed
optically, and then the experts searched the neutrinos from it.

1.2.6 Diﬀuse supernova neutrino background
Whereas supernova neutrino detection is only once in 1987 so far, there should exist neutrinos
that were produced by all the supernovae that occurred from the birth of the universe until thepresent. In fact, there are ∼ 1017 stars in the whole universe, and 0.3% of them are estimatedto have masses larger than 8𝑀 , with their lives ended by core-collapse supernova explosions.
These unobserved neutrinos are called Supernova Relic Neutrinos (SRN) or Diﬀuse Supernova
Neutrino Background (DSNB). Flavors and the energy range at their production are the same assupernova burst neutrinos. A possible observational window is open to ∼10-25 MeV because
reactor neutrinos and atmospheric neutrinos are dominant below 15 MeV and above ∼ 25 MeV as
shown in Fig. 1.9 [27].
DSNB can be a probe for star formation history and for searching heavy elements (i.e., elements
other than hydrogen and helium) that are only provided through supernova explosions.

1.3 Supernovae
A Supernova burst is an explosion phenomenon at the end of the evolution of heavy stars withemissions of electromagnetic waves at every wavelength, neutrinos, and gravitational waves. As
described in Section 1.2.5, observation of supernova burst neutrinos with Super-Kamiokande isessential for the following two reasons: (1) neutrinos coming from supernovae are intact andcarry essential information to elucidate the mechanism of explosion, (2) Super-Kamiokande is theChapter 1 Neutrinos and Supernovae

16

Fig. 1.9: Expected DSNB signal and the background (reactor 𝜈¯e and charged current events by atmospheric
neutrinos) by inverse beta-decay search [27].

only detector capable of identifying the position of the exploding star by itself, broadcasting suchinformation to astronomical observation network for a full timescale optical observation.
This section is organized as follows; the categories of supernovae and their overview are
explained in Section 1.3.1. A detailed mechanism of core-collapse supernova burst as an importantneutrino source is described in Section 1.3.2. Examples of supernovae observed before, especiallyfor the ﬁrst and only supernova neutrino detection SN1987A, are described in Section 1.3.3.
Finally, in Section 1.3.4, neighboring supernova candidates are introduced.

1.3.1 Categories of Suprenova
There are two classiﬁcations of supernovae: one based on spectroscopic observations and theother based on the physical process of the explosion. The former characterizes supernovae by
optical spectra and optical light curves as shown in Table 1.3. Type I supernova does not havehydrogen spectral line, which are observed in Type II. The upper case represents the feature in thelight curve, whereas the lower case just after the upper case represents the feature in the spectrum.
The typical shape of the optical light curve for each type is illustrated in Fig. 1.10.
This classiﬁcation reﬂects the physical state of the outer stellar layers seen by optical observations

Chapter 1 Neutrinos and Supernovae

17

Table 1.3: Observational classiﬁcation of supernovae.

Spectroscopic

Spectral feature

Type I

Type II

with He?

Light curve feature

with H?

with Si?

Ia

no

yes

Ib

no

no

yes

Ic

no

no

no

IIP

yes

plateauIIL

yesmonotone decreasingIIn

yes (narrow emission lines)

classiﬁcation

Fig. 1.10: Optical light curve for each spectral supernova type [28]. The horizontal and vertical axes representdays passed from the maximum light observation and magnitude in the blue band, respectively.

and does not necessarily correspond to the physical process of the explosion. Type Ib, Ic, and II
are classiﬁed as core-collapse supernovae and are distinguished from Type Ia in the categorization
based on the explosion process.
Type Ia Supernovae
Runaway nuclear reactions trigger Type Ia supernovae. In a binary system, a constituent whitedwarf grows its mass by accretion from or binary star merger with the other constituent star. Whenthe mass reaches Chandrasekhar mass (∼ 1.4𝑀 ), nuclear reactions start to run away, and theChapter 1 Neutrinos and Supernovae

18

white dwarf explodes. The runaway occurs because the shape of a white dwarf is supported by thedegeneracy pressure of electrons. Normal stars maintain their shape by the pressure of hot gas,
so when the temperature rises due to nuclear fusion, the pressure also increases, causing the star
to expand. Therefore, nuclear reactions are suppressed in these stars due to the negative feedbackon the temperature increase. In white dwarfs, however, the degeneracy pressure is independent of
temperature. Hence, once nuclear fusion occurs, the star does not expand, and the temperature
continues to rise, which triggers positive feedback that leads to further fusion, resulting in runaway
nuclear reactions. Type Ia supernovae are believed to occur in binary systems composed of two
white dwarfs or a white dwarf and a red giant [29]. Type Ia supernovae neither emit neutrinosnor
leave any compact celestial bodies such as neutron stars and black holes.
Core-collapse Supernovae
Type Ib, Ic and II supernovae are categorized as core-collapse supernovae because the corecollapse of the stellar cores triggers their explosions. Since nuclear fusion reactions in the centerof a star synthesize elements in the order of lightest to heaviest, the star has a concentric sphericalshell structure with a hydrogen layer on the outermost surface and a helium layer on the innersurface. Once an iron core is formed in the innermost part of a massive star with a mass ofmore than 10 𝑀 , no further fusion reactions can occur, and the degenerate pressure of electrons
supports the star. In the stellar core which becomes hot and dense due to the weight of the staritself, electron capture (see Eq. (1.25)) and the photodisintegration of iron (see Eq. (1.26)) induce
core collapse. The resulting shock wave propagates outward and blows away the star’s outer layers.
The outer layers’ expansion and the bright glow due to materials being heated by the shock areobserved as optical burst. As shown in Table 1.3, if the burst occurs before the hydrogen layer isremoved, it is considered to be observed as a Type II supernova. The explosion after the blowoutof the hydrogen layer is observed as a Type Ib supernova. If the helium layer is also blown oﬀ andthen explodes, it is a Type Ic supernova. The loss of outer layers of a star is believed to originate
from very active mass ejection observed in high mass stars and mass exchange between binarystars [30].
A core-collapse supernova emits diﬀerent types of neutrinos at each stage and leaves a neutronstar or a black hole after its burst. More detailed explosion mechanisms and supernova neutrino
emission are given in Section 1.3.2.
Electron-Capture Supernovae
The supernovae in which gravitational collapse is caused solely by electron capture are called
electron-capture supernovae. A low-mass star with 8-10𝑀 develops a stellar core made of oxygen

Chapter 1 Neutrinos and Supernovae

19

and neon (and magnesium), called O-Ne-Mg core or ONe core, at the ﬁnal stage of its evolution.
When the core grows to Chandrasekhar mass, a rapid electron capture on magnesium and neon
begins, leading to core collapse. Since the evolution after the core collapse is similar to the caseof an iron core, electron-capture supernovae are classiﬁed into a subcategory of core-collapse
supernovae. It is estimated that electron-capture supernovae account for at most 30% of all
core-collapse supernovae [31].
Pair-Instabillity Supernovae
Very massive stars with 100-300 𝑀 can initiate core collapse with electron-positron annihilation
2𝛾 → e− + e+ .

(1.24)

These supernovae are called pair-instability supernovae. When nuclear synthesis in the centerof very massive stars proceeds to oxygen, the density and the temperature reach 𝜌 ≲ 106 g/cm3
and 𝑇 ≳ 109 K, respectively [30]. In such a high-temperature, high-density environment, somephotons gain their energy to the rest energy of an electron 𝑚 𝑒 = 0.511, and electron-positron pairs
are created according to Eq. (1.24). As a result, the number of photons that support the pressure of
the star decreases, and the core contracts gravitationally. The gravitational energy released in thisphase produces further electron-positron pairs, which causes positive feedback on the gravitational
contraction and makes the core unstable. This is called pair creation instability. The temperaturerise due to gravitational contraction also increases the oxygen burning rate, raising the temperatureand producing explosive oxygen combustion. The heat energy generated in this process increases
the pressure, which causes the star to expand rapidly and explode, breaking apart the entire star.
As seen from the explosion process, no neutrinos are ejected in pair-instability supernovae.

1.3.2 Scenario of Core-Collapse Supernova Burst
This sub-section describes a standard scenario of a core-collapse supernova burst of a massive
star with an iron core. Fig. 1.11 illustrates the evolution of a core-collapse supernova burst from the
beginning of the core-collapse to the proto-neutron star cooling phase. For each stage of evolution,
typical timescale and neutrino emission processes that carry 99% of the released gravitationalenergy away are explained.
Pre-supernova
Massive stars nearing the end of their lives are referred to as pre-supernova stars. These stars
comprise concentric shells of diﬀerent nuclei resulting from nucleosynthesis from the light nucleus

Chapter 1 Neutrinos and Supernovae

20

Fig. 1.11: Schematic picture of evolutionary phases of core-collapse supernova burst, from the onset ofcore-collapse to proto-neutron star cooling [32]. Each panel displays the dynamical condition in its upper
half and the nuclear composition and processes in its lower half. The straight arrows in the upper half ofeach panel represent velocity vectors. 𝜚 𝑐 and 𝜚 𝑜 represent the density at which neutrino trapping occurs
and nuclear matter saturation density, respectively. The horizontal axis provides mass information in unit of
𝑀 . 𝑀Ch is the Chandrasekhar mass and 𝑀hc means homologous inner core mass. The vertical axis gives
corresponding radius information in units of km. 𝑅Fe , 𝑅s , 𝑅g , 𝑅ns and 𝑅 𝜈 stand for iron core radius, shock
wave radius, gain radius, neutron star radius, and neutrinosphere radius, respectively. Here, neutrino heating
is assumed for the shock revival mechanism.

Chapter 1 Neutrinos and Supernovae

21

to the heavy nucleus at the core. Most exterior shell is made up of hydrogen. Inner shells arecomposed of heavier nuclei from outside inward: helium shell, carbon and oxygen (C+O) shell,a mixture of oxygen, neon and magnesium (O+Ne+Mg) shell, silicon shell (indicated by thearrow in Fig. 1.11 upper left panel), and ﬁnally iron core is at the center. Table 1.4 shows how
nuclear burning proceeds in a pre-supernova. During this nuclear burning phase, neutrino andantineutrino pairs of all ﬂavors are emitted and work as a cooling system. These neutrinos arecalled pre-supernova neutrinos. The silicon burning phase, the ﬁnal nuclear burning phase thatlasts only about a day, brings a dramatic increase in neutrino luminosity and average neutrinoenergy.

Table 1.4: Summary of nuclear burning [33, 34].
Fuel
1H
4 He
12 C
20 Ne
16 O
28 Si

Temperature[K]1 × 107
2 × 108
5 × 108
8 × 108
3 × 109
8 × 109* For 25𝑀

Reactions
1 H →4 He
4 He →12 C, 16 O
12 C →20 Ne, 24 Mg
20 Ne →16 O, 24 Mg
16 O →28 Si
28 Si →56 Fe, 56Ni

Composition
1 H, 4 He
4 He
12 C, 16 O
16 O, 20 Ne, 24 Mg
16 O, 24 Mg, 28 Si
28 Si, 32 S

Burning time* Cooling process
7 × 106 years𝛾, 𝜈
5
5 × 10 years𝛾
600 years
𝜈
1 year𝜈
180 days
𝜈
1 day
𝜈

.

Core Collapse
Further nuclear fusion to heavier nuclei than silicon is impossible because iron has the maximum
binding energy per nucleon. Thus, the iron core grows its mass to the Chandrasekhar mass
𝑀Ch ∼ 1.44 𝑀 . At this point, the stability by dynamical equilibrium so far kept between
gravitation and pressure (mainly supported by the degenerate pressure of relativistic electrons) islost by the following two processes, which is the initiation of gravitational core collapse (Fig. 1.11
upper left panel).
The ﬁrst process is electron capture with 𝜈e emission:p + e− → n + 𝜈e .

(1.25)

This process consumes electrons, the primary supporters of stellar pressure against gravitation.
Hence the adiabatic index 𝛾 falls below the critical value of 4/3 and becomes dynamically unstable.
In general, electron capture processes do not occur naturally. However, since the Fermi energyof electrons increases with density, there is suﬃcient energy in the high-density environment ofcollapsing core to start electron captures. Once electron capture starts, it continues due to thepositive feedback of electrons gaining energy from the increased density by the compression from

Chapter 1 Neutrinos and Supernovae

22

the previous electron capture. Note that this electron capture is suppressed at some density pointdue to neutrino trapping (see the next process).
The second process is the photodisintegration of iron:56

Fe → 134 He + 4n − 124.4MeV.

(1.26)

This reaction is caused because heavy nuclei, such as iron, try to become light nuclei, such as
helium, in a high-temperature, high-entropy environment. Photo-disintegration is an endothermic
reaction. Though the dying stellar core is supported mainly by the degenerate pressure of electronsat zero temperature as mentioned above, there is a small contribution from the pressure due toﬁnite temperature. Therefore, the stellar core also loses its stability due to photodisintegration
temperature deprivation.
The collapsing core comprises two parts: the inner core (homologous core) that shrinks with
subsonic velocity and the outer core that contract with supersonic speed. The components of eachcore continue falling to the center with respective velocity until the central density reaches thenuclear density (∼ 3 × 1014 g/cm3 ). The typical timescale of core collapse is ∼10-100 ms.
Neutrino Trapping
The mean free path of a neutrino before the collapse is larger than the core radius, enablingthem to escape from the core. However, the density rise as the progress of gravitational collapse
increases the cross section of neutrino reactions, resulting in the decrease of the mean free pathto the inner core radius [30]. This phenomenon is essentially a conﬁnement of neutrino inside a"neutrinosphere" with an optical depth of 2/3. Thus it is called neutrino trapping (described in the
red region in Fig. 1.11 upper right panel). Neutrino trapping typically occurs at ∼ 100 ms after
the collapse. Once neutrino trapping occurs, neutronization due to electron capture Eq. (1.25)
is suppressed. As a result, neutrino density increases, and the inverse reaction of Eq. (1.25)
i.e., n + 𝜈e → p + e− begins, and n + 𝜈e ↔ p + e− reaches equilibrium (called beta equilibrium).
Reactions from then on proceed adiabatically.
Core Bounce and Shock Wave Outbreak
When the central density exceeds the nuclear density, the adiabatic index far below the criticalvalue rapidly increases to recover the dynamical stability, and the inner core inﬂates. This dynamicchange is called “core bounce.” Since the outer core shrinks supersonically, a shock wave is formedat the boundary of the inner and outer cores. The bounce and shock wave outbreak occur at ∼110
ms after the collapse, as shown in Fig. 1.11 middle left panel.

Chapter 1 Neutrinos and Supernovae

23

Shock Propagation and Neutronization Burst
The shock wave propagates outward, breaking nuclei of the outer core matter into nucleon pieces
and losing its energy by photo-disintegration like Eq. (1.26). The outer core matter obtains energy
from the shock wave and departs outward. In the downstream of the shock, nucleons as productsof photo-disintegration experience rapid electron capture, and 𝜈e are produced. These neutrinos
cannot escape until the shock wave reaches the radius of the neutrinosphere. In other words, 𝜈esuddenly can escape when the shock passes through the surface of the neutrinosphere (illustrated
in Fig. 1.11 middle right panel). This is observed as a dramatic increase of 𝜈e luminosity to1053 erg·−1 within a few miliseconds. It is referred to as a neutronization burst because electron
capture is a neutronization of matter.
Neutronization burst detection is vital in neutrino mass estimate and neutrino oscillation measurement. Finite neutrino mass makes their velocity depend on energy, which makes the arrival
time to the detector diﬀerent. Therefore, neutrino mass can be estimated if the rise time of neutronization burst is enough shorter than the arrival time diﬀerence. For all that, neutrino oscillation
can cause a drop in 𝜈e luminosity at neutronization burst.
Stagnation and Revival of Shock Wave
As mentioned above, the shock wave loses its energy during the propagation due to photodisintegration. This is the stagnation of the shock wave. At this stage, the outer core matter nolonger obtains outgoing velocity from the passage of the stalled shock wave. The optical explosion
occurs when this shock wave regains energy by some mechanism and penetrates the outer core
and the outer stellar layers to reach the photosphere near the stellar surface. Since the shock
revival mechanism is unknown, several scenarios are proposed. Neutrino heating (indicated in
the bottom left panel of Fig. 1.11) is one of the most promising. Other possible mechanisms arehydrodynamical instability such as convection (e.g., [35]) and standing-accretion-shock instability(SASI, e.g., [36]), acoustic oscillation (e.g., [37]), and magnetic ﬁeld (e.g., Kuroda+21[38]).
The neutrino heating hypothesis as a shock revival mechanism is that the energy carried out
by the neutrino emission in the proto-neutron star (PNS) cooling phase (described in the next
subsection) partially contributes to reviving the stalled shock wave. As illustrated in the bottom
left panel of Fig. 1.11, the region between the shock and the proto-neutron star (red and brown
regions) is rich in nucleons produced by photo-disintegration of nuclei in the outer core. These
nucleons absorb neutrinos through the following reaction:
𝜈e + n → p + e−

(1.27)

𝜈¯e + p → n + e+ .

(1.28)

Chapter 1 Neutrinos and Supernovae

24

These absorptions by nucleons heat the matter, whereas the neutrino emission around the neutrinosphere cools the matter by the inverse reactions of Eq. (1.27) and Eq. (1.28). The radius atwhich neither heating nor cooling occurs is the gain radius 𝑅𝑔 . The gain layer (the red region) is
between the shock and 𝑅𝑔 .
Proto-Neutron Star Cooling
A proto-neutron star (PNS) is formed at the center of the collapsed supernova. Unlike a neutronstar, a proto-neutron star is abundant in protons and electrons. The process of a proto-neutronstar becoming a neutron star by emitting neutrinos and shrinking is referred to as proto-neutronstar cooling. The proto-neutron star’s temperature decreases in this phase, and neutronization
proceeds. The proto-neutron star (PNS) is cooled in ∼10 s [30]. As illustrated in the bottom
two panels of Fig. 1.11, neutrinos and antineutrinos of all ﬂavors are produced via the following
reactions as well as electron capture in Eq. (1.25):
Positron capture :n + e+ → p + 𝜈 e

Neurtino emission by nucleus(1.29)

𝐴 + e− → 𝐴 0 + 𝜈e

Neutrino pair generation by electron − positron pair0

Nucleon − nucleon bremsstrahlung :Plasmon decay :(1.30)−+

e + e → 𝜈𝑖 + 𝜈 𝑖
0

N + N → N + N + 𝜈𝑖 + 𝜈 𝑖

𝛾 ∗ → 𝜈𝑖 + 𝜈 𝑖 .

(1.31)(1.32)(1.33)

Through these neutrino emissions, the gravitational energy stored in the proto-neutron star as
internal energy is carried out. The following neutrino scatterings and neutrino-neutrino reactions
also occur :Neurtino scattering by nucleon

𝜈+𝑁 →𝜈+𝑁

Neurtino coherent scattering by nucleus

𝜈+𝐴→𝜈+𝐴

Neutrino scattering by electron/positron :Neutrino scattering by neutrino :𝜈( 𝜈)¯ + e± → 𝜈( 𝜈)¯ + e±(1.34)(1.35)(1.36)

𝜈𝑖 ( 𝜈¯𝑖 ) + 𝜈𝑖0 ( 𝜈¯𝑖0 ) → 𝜈𝑖 ( 𝜈¯𝑖 ) + 𝜈𝑖0 ( 𝜈¯𝑖0 )(1.37)

𝜈𝑖 + 𝜈¯𝑖 → 𝜈𝑖0 + 𝜈¯𝑖0 .

(1.38)

Neutrino pair generation by neutrino pair :1.3.3 Supernova Neutrino Observed Before
Before the acquisition of instruments to detect supernova neutrinos, humans have witnessed atleast seven supernovae so far. The oldest documented supernova in human history dates back to
185 A.D. and was recorded by Chinese astronomers [39]. Surprisingly, three supernovae in the
11th and 12th centuries, identiﬁed as SN1006, SN1054, and SN1181, were recorded in a single
document in Japan [40].

Chapter 1 Neutrinos and Supernovae

25

SN1987A
Progress in physics and technological developments for experimental equipment enabled astrophysicists and astronomers to observe supernovae with a multi-messenger approach, including
neutrinos. The observable supernova with the naked eye occurred only once on 23 February 1987
(JST), for the ﬁrst time in about 400 years since the last galactic supernova SN1604 occurred.
This important supernova is labeled as SN1987A (A means it is the ﬁrst supernova observed in
the year. SN1987A is not a galactic supernova: it is found in Large Magellanic Cloud locatedoutside the Milky Way galaxy, 50 kpc away from the Earth. Kamiokande, the former generationof the Super-Kamiokande, recorded eleven neutrinos over 13 seconds [41]. This is the ﬁrst andonly example of supernova burst neutrinos recorded in human history.
Irvine-Michigan-Brookhaven water Cherenkov detector for the proton decay search also detected
eight neutrinos [42]. The progenitor of SN1987A is identiﬁed as a blue supergiant with 𝑀 ∼20𝑀 [34].
While one core-collapse supernova occurs somewhere in the universe in a second on average,
the observed rate for core-collapse supernovae in one galaxy is expected to be several times in one
century [30]. Regarding neutrino astronomy, we are waiting for the next core-collapse supernova
in the Milky Way galaxy or nearby universe detectable on Super-Kamiokande and other neutrino
detectors.

1.3.4 Nearby Supernova Candidates
Fig. 1.12 shows the map of nearby core-collapse supernova candidates. The average angulardistance between a candidate and its nearest neighbor, i.e., minimum separation, is 10.4◦ [43].
Therefore, the angular resolution of ' 10◦ is required to discriminate these supernova progenitorswith a neutrino detector.

Chapter 1 Neutrinos and Supernovae

26

Fig. 1.12: Positions of core-collapse supernova candidates within 1 kpc of the Earth illustrated in equatorial
coordinate system [43]. Each label shows the star’s name, mass, and distance. The spectral type of each staris indicated by color.

27

Chapter 2
Supernova Neutrino Detection with SuperKamiokande Detector
The Super-Kamiokande detector (hereafter SK) is the world’s largest water Cherenkov detector
aiming at the observation of neutrinos from various sources, proton decay, and even dark matter.
In 2020 and 2022, 13 ktons and 26 ktons of gadolinium sulfate octahydrate are dissolved in thedetector water respectively, to enhance the detector sensitivity to DSNB. This chapter describes the
SK detector in detail and gives an introduction to SK-Gd in terms of supernova neutrino detection.

2.1 Detector Overview
Super-Kamiokande detector is a large water Cherenkov detector located 1000 m under the peakof Mt. Ikenoyama in Kamioka Town, Hida City, Gifu Prefecture. Fig. 2.1 shows the overview ofthe detector and related facilities with the sketch of Mt. Ikenoyama in the bottom right section. The
detector itself is a cylindrical water tank 39.3 m in diameter and 41.4 m high with ∼13,000 photomultiplier tubes (PMTs). The tank had been ﬁlled with ∼ 50,000 tons of ultra-pure water until
July 2020. Note that gadolinium sulfate is loaded into the water since July 2020 as described in
Section 2.4. The tank is a two-layered optical structure: inner detector (ID) with inward-facing
PMTs and outer detector (OD) with outward-facing PMTs. Their details are shown in Section
2.1.1. The underground depth of the detector reduces the amount of cosmic ray muons incident
on the detector which causes backgrounds for the observation.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

28

Fig. 2.1: Overview of the Super-Kamiokande Detector and related facilities [44]. A cylindrical stainless-steel
water tank 39.3 m in diameter and 41.4 m in height is located 1000 m underground in Mt. Ikenoyama. The
tank is optically double-layered structured: inner detector (ID) with inward-facing 11,129 PMTs and outerdetector (OD) with outward-facing 1885 PMTs. The tank roof is equipped with detector-related facilities
such as Electronics Huts and LINAC beamline.

2.1.1 ID, OD and Detector Geometry
The ID is a cylindrical shape, 33.8 m in diameter and 36.2 m in height with a volume of
32.5k m3 . A total of 11,129 inward-mounted 20-inch PMTs in the ID, covering ∼ 40% of the ID
surface area, detect Cherenkov light from charged particles. The OD is surrounding the ID, withan average thickness of about 2.6 m on top and bottom, and 2.7 m on the side wall (called “barrel”),
with a volume of 17.5k m3 . The OD PMTs are mounted outward in the OD for distinguishing
the backgrounds due to neutrons and gamma rays originating from the surrounding rocks and forshielding the cosmic ray muons.
The ID and the OD are separated by stainless-steel structures called super modules. The border
between the ID and the OD locates at 2-2.5 m inside the tank walls on all sides. Fig. 2.2 (a)shows how the ID PMTs and the OD PMTs are mounted on the super modules. The ID side of
the super modules is covered with opaque black sheets made of polyethylene terephthalate so that
only the photocathode of each 20-inch PMT is exposed in order to prevent reﬂection within the ID
and light leakage from the OD side. On the other hand, for the enhancement of light collection
eﬃciency in the OD, white reﬂective material Type 1073B Tyvek covers the OD side so that only
the photocathode of each 8-inch PMT is exposed.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

29

Fig. 2.2 (b) illustrates the deﬁnition of detector coordinate. The coordinate origin 𝑂 is at thecenter of the tank, with 𝑥 and 𝑦 axes in a horizontal plane and a vertical 𝑧 axis. Cylindricalpcoordinates with 𝑟 = 𝑥 2 + 𝑦 2 , the zenith angle 𝜃 (0 ≤ 𝜃 ≤ 𝜋) and the azimuth angle 𝜙(0 ≤ 𝜙 ≤ 2𝜋) are also used to express the location of the vertex (the originating point ofCherenkov light).

Fig. 2.2: (a) Super Modules separating the ID and the OD and supporting the PMTs [44]. Black sheets andwhite reﬂective material cover the ID side and the OD side, respectively, so that only the photosensitive areaof each PMT is exposed. (b) Detector coordinate.

2.1.2 20-inch Photo Multiplier Tube
As the ID PMTs, Hamamatsu Type R3600 hemispherical PMTs are used. One PMT is 20-inch(∼50 cm) in diameter, weighs 13 kg, and can withstand pressures up to 6 kg · cm−2 .
Fig. 2.3 shows the conﬁguration of a 20-inch PMT. The photocathode material is bialkali (SbK-Cs) which is sensitive to visible light regions. Fig. 2.4 shows the quantum eﬃciency of atypical photocathode as a function of wavelength. The actual sensitive wavelength range and peak
quantum eﬃciency of a photocathode depend on the production year, but typically, it is sensitive tothe wavelength region of 280-660 nm, with a peak quantum eﬃciency of 21% at 360-400 nm. The
dynode structure is “venetian blind” type. The collection eﬃciency for photoelectrons (hereafterp.e.) surpasses 70%. The distribution of 1 p.e. pulse height is shown in Fig. 2.5. The pulse
height drop at ∼100 ADC count corresponds to 0.25 p.e., which is used as the “hit” threshold inChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector30

SK trigger system. The dark noise rate at this threshold has ﬂuctuated between 6-8 kHz in recent
years. The photon multiplication factor (i.e., the gain) of the ID PMTs is set to ∼ 107 in a supply
high voltage range of 1700-2000 V.

Fig. 2.3: Schematic picture of 20-inch PMT [44].

Fig. 2.4:[44].]Quantum eﬃciency of a photocathode as a function of wavelength [nm] [44].
Generally, PMTs with larger diameters have worse time resolution because the transit time
spread of photoelectrons increases by where photons hit the photocathode. For SK PMTs, thisdrawback is overcome by the enlargement of the dynode area, and the transit time spread of an ID

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

31Fig. 2.5: Pulse height distribution for one photoelectron [44].

PMT for 1 photoelectron is 2.2 ns as described in Fig. 2.6.

Fig. 2.6: Transit time spread at one photoelectron signal, tested using a typical PMT with 410 nm wavelength
light [44].

Anti-implosion coverSince the interior of a PMT is a vacuum, the PMT glass break causes implosion. In 2001,
a serious accident occurred in which the shock wave from an implosion of one PMT caused achain of neighboring PMTs to implode, resulting in the damage of about half of the PMTs. In
order to prevent the recurrence of chain implosion, the photocathode of each PMT is protected

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

32

with an acrylic cover with a light transmittance of 95%. The rest of the PMT is covered withﬁber-reinforced plastics (FRP).

2.1.3 Geomagnetic compensation coils
The average geomagnetic ﬁeld at the detector site is about 450 mG with ∼ 45◦ inclination relative
to the horizon. This could bias timing in PMTs and trajectories of photoelectrons during theircollection to dynode. To cancel this out, Helmholtz coils are arranged horizontally and verticallyaround the inner tank surfaces as shown in Fig. 2.7. These geomagnetic compensation coils reduce
the average magnetic ﬁeld in SK to about 50 mG [44].

Fig. 2.7: Geomagnetic compensation coils surrounding the inner surface of the SK tank [45]. The table on
the right lists the electric current value in each coil labeled A through G.

2.1.4 Water Puriﬁcation
An enormous volume of high-quality ultra-pure water is essential for the SK experiment. SK
manufactures its ultra-pure water from the groundwater in Kamioka mine. Dust and bacteria
contained in the groundwater lead to superﬂuous scattering and absorption of Cherenkov lightand their radioactivity causes serious background in neutrino detection. The gravest backgroundcomes from the radioactivity of dissolved radon gas. 222 Rn whose decay product 214 Bi produces
an electron with a Q-value of 3.26 MeV by beta decay has a serious impact on neutrino observation
in low energy regions (which is the target of solar neutrino). It is also important to maintain theChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

33

water temperature stable and low. PMTs to which high voltage is constantly applied are thermal
sources inside the tank. The high water temperature encourages bacteria propagation and the riseof PMTs’ dark noise due to thermal electron emission. In addition, the consequent temperature
non-uniformity causes water convection, which leads to the diﬀusion of 222 Rn in water, resulting
in the increase of the background. In order to eliminate these contaminations as much as possible
and to control water temperature, SK established a water puriﬁcation system.
The puriﬁed water is supplied to the tank through inlets at the bottom. At this injection, thewater temperature is kept cooler than the ambiance. This enables the gradual temperature gradientof the water from the bottom to the top of the tank, localizing the remaining radon impurities inthe bottom, which prevents them from spreading. The temperature diﬀerence between the top andthe bottom of the tank is kept at less than 0.2◦ C [46]. The water is drained through outlets at the
top of the tank. 222 Rn concentration of the supply water is ∼ 1.7 mBq·m−3 . The water system for
the SK-Gd phase is described in Section 2.4.2.

2.1.5 Air Puriﬁcation System
It is also necessary to purify the air in the detector. As 222 Rn gas is emanated from the mine rock,
222 Rn concentration of the air in the mine is 100-1000 Bq·m−3 , which is 10-1000 times higher

than that outside the mine. To reduce 222 Rn concentration of the mine air, SK established the air
puriﬁcation system (Rn free air generator) shown in Fig. 2.8. The system puriﬁes the mine air andsupplies it to the SK tank (to the space between the water surface and the tank roof). Another roleof this system is to keep the pressure inside the tank at +0.3 kPa higher than the pressure outside
the tank, which prevents outside air from entering the tank and also tank collapse due to negative
pressure. The conﬁguration and the process of making Rn-reduced air are described below.

Fig. 2.8: Schematic illustration of the air puriﬁcation system (Rn-reduced air generator). See the text for a
detailed explanation.

(1) Compressor: For compressing air to 0.5-0.65 MPa.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

34(2) Air Filters
For eliminating dust. The air passes three types of ﬁlters in the descending order of theﬁneness; 0.3 𝜇m, 0.1 𝜇m, and 0.01 𝜇m.
(3) Air Driers: For removing moisture and carbon dioxide.
(4) Carbon columns
For making 222 Rn in the air adsorbed onto activated charcoal (8 m3 in total).
(5) Cooled charcoal
For making 222 Rn in the air adsorbed onto activated charcoal which is cooled at −60 ◦ Cwith higher adsorption eﬃciency [47].

2.2 Cherenkov Light Detection Principle
Cherenkov radiation is a phenomenon that a charged particle passing through matter witha velocity faster than the light velocity 𝑐 within matter emits conular light. SK detects thisCherenkov light with ID PMTs to reconstruct the vertices, trajectories, energies, and momentumof particles as illustrated in Fig. 2.9.

Fig. 2.9: Cherenkov ring observation at SK.

Within time 𝑡, a charged particle with velocity 𝑣 passing through matter with a refractive index
𝑛 travels a distance of 𝛽𝑡 (in natural units: 𝑐 = 1), where 𝛽 = 𝑣/𝑐. Within the same time, lighttravels in matter a distance of 𝑡/𝑛. Therefore, Cherenkov radiation occurs when𝛽𝑡 >𝑡
⇔ 𝛽𝑛 > 1𝑛(2.1)

is satisﬁed. The threshold energy that meets Eq. (2.1) 𝐸 𝑡 ℎ depends on the mass of the charged
particle:

𝑛𝑚 0
𝐸𝑡 ℎ = √𝑛2 − 1(2.2)

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

35

where 𝑚 0 represents the invariant mass of the particle. Table 2.1 lists 𝐸 𝑡 ℎ for typical charged
particles observed at SK.
Table 2.1: Threshold energy 𝐸 𝑡 ℎ for some particles observed at SK.

charged particle

mass[MeV]

𝐸 𝑡 ℎ [𝑀𝑒𝑉]

e+ /e−

0.511

0.77

𝜇+ /𝜇−

10.5.66

158.73𝜋 + /𝜋 −139.57209.68The angle between the particle track and Cherenkov light is referred to as Cherenkov angle 𝜃 C .
It is expressed as:cos 𝜃 C =

𝑡/𝑛
1
=
.
𝛽𝑡
𝑛𝛽

(2.3)

For pure water (𝑛 ∼ 1.34), Cherenkov angle for an electron is 𝜃 C ∼ 42◦ . Note that the refractive
index of the water with 0.033% gadolinium concentration can be considered the same as that ofpure water.
The rest of this section discusses the expected number of Cherenkov photons detected for SK’ssensitive wavelength region ∼ 300-600 nm. The number of Cherenkov photons emitted from aparticle with a charge of 1𝑒 at a traveling distance of d𝑥 is given as:
d2 𝑁
2𝜋𝛼
1
= 2 (1 − 2 2 )
d𝑥d𝜆
𝜆
𝑛 𝛽

(2.4)

where 𝛼 ' 1/137 is the ﬁne structure constant and 𝜆 stands for the wavelength of the light emitted.
By integrating Eq. (2.4) over the wavelength range of 300-600 nm and the total traveling distance
1 cm, for example, the number of Cherenkov photons is calculated as:∫ 600nm ∫ 1cm
1
2𝜋𝛼
1 − 2 2 d𝑥d𝜆 ∼ 340.
𝑁=
𝜆2
𝑛 𝛽
300nm
0cm

(2.5)

A charged particle keeps Cherenkov radiation until its energy becomes less than the thresholdenergy 𝐸 𝑡 ℎ mentioned earlier. Note that gamma rays without any charge can be also detectedby observing Compton scattered electrons and Cherenkov light emitted by pair-created electrons/positrons.

2.3 Data Acquisition System
All the PMT signals are read by a front-end electronics called QBEE (QTC Based Electronics
with Ethernet). Among them, only the signals that satisﬁed some conditions of the number ofChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

36

PMT hits (explained in Section 2.3.3) are recorded as events. SK has adopted this data acquisition
system since 2008 [48].

2.3.1 PMT Signal Readout with QBEE
The primary role of QBEE is to compute the amount of charge and timing of each PMT hit fromall the received signals and to preserve them. One QBEE board consists of QTC (charge to time
converter), TDC (time to digital converter), and two types of FPGAs (Field Programmable Gate
Arrays) as shown in Fig. 2.10. Each role is described below.

Fig. 2.10: Picture of a QBEE board [48]. The input PMT signals are processed with QTC, TDC, and DSM(the ﬁrst type of FPGA), and then stored in SIC (the second type of FPGA). One QBEE board has eight
QTCs and four DSMs. Each QTC receives signals from three PMTs. One DSM processes data from six input
channels. Network interface card issues a request to send the stored data to SIC and output it.

(1) QTC
QTC integrates the charge of the received PMT signal when the signal amplitude reaches
the value corresponding to 0.25 p.e., and output pulse whose width is proportional to theintegrated charge. The pulse rise time corresponds to the PMT hit timing. The integration
time window is 400 ns. Three measurement ranges (small, medium, and large) cover thewide dynamic range of the PMT signal from 0.2 pC up to 2500 pC [48]. Note that it takes
900 ns for a QTC to process one PMT signal.
(2) TDC
TDC measures the width of the output pulse from QTC by computing the time diﬀerenceChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

37

between the leading and falling edges and digitizes the data.
(3) FPGA
One QBEE board has two types of FPGAs, DSM (Data Sort Mapping) and SIC (System
Interface Control). DSM receives and processes the timing and charge information per one
PMT hit and input channel information. SIC stores the output of DSM in Fast-In Fast-Out(FIFO) memory.

2.3.2 DAQ
Fig. 2.11 shows the whole picture of the data acquisition (DAQ) system for SK since 2008 [48].
24 PMTs are connected to one QBEE board, and about 550 QBEE boards send the data to about
20 front-end PCs as TCP packets. One front-end PC processes data from about 30 QBEE boards
and sends them to 10 Merger PCs. Merger PCs merge all the data and apply software trigger (seeSection 2.3.3) to select and classify events. The selected events are sent to an Organizer PC and
are written on oﬄine disks.

Fig. 2.11: Block diagram of the data acquisition system for SK [48]. See the text for a detailed explanation.

2.3.3 Software Trigger
The trigger of the DAQ adopts a software trigger for event categorization issued if the numberof PMT hits within 200 ns time window (𝑁200 ) exceeds any of the thresholds listed in Table 2.2.
There are four types of software triggers according to the threshold of 𝑁200 : SLE (Super Low
Energy), LE (Low Energy), HE (High Energy), and SHE (Super High Energy). AFT (After)Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

38

trigger has the same threshold of 𝑁200 but has a diﬀerent time window (explained in the following
paragraph).
Once a trigger is issued, the designated time window opens to record all the signals within therange for searching related events of the triggered event. As shown in Table 2.2, the width of thetime windows for the SLE is set shorter (1.5 𝜇s) than that for the other triggers, in order to reduce
the amount of data. This is because the high rate of radioactive background is observed in theenergy region where the SLE triggers are issued. AFT trigger is a special trigger issued only when
the SHE trigger is issued. Its time window starts at the end of the SHE trigger’s time window,
which is how it got the name “after”. AFT trigger is for detecting neutron capture event candidates
related to the SHE-triggered event. The width of the AFT trigger time window is set to 500 𝜇s inorder to cover the time constant of neutron capture ∼ 200 𝜇s for pure water and ∼ 60 𝜇s for waterwith 0.03% gadolinium concentration.

Table 2.2: Summary of software trigger types, thresholds, time windows forrecording the signals when the trigger is issued (𝑡 = 0) to search the related
events, and frequencies of the trigger issue. AFT trigger is issued only when
the SHE trigger is issued, in order to search neutron capture event candidates
associated with the triggered event.

Trigger TypeThreshold of 𝑁200

Time Window[𝜇s]Frequency

SHE

60-5 → 35

∼3 Hz

HE

52

-5 → 35∼30 HzLE

49-5 → 35∼80 HzSLE

34 (typical)*-0.5 → 1∼14 kHz

AFT

60

35 → 535∼3 Hz* SLE threshold is changed ﬂexibly depending on the trigger frequency.

2.4 SK-Gd
2.4.1 SK-Gd Experiment Overview
SK-Gd is a new phase of SK operation that uses ultra-pure gadolinium sulfate octahydrate(Gd2 (SO4 )3 · 8H2 O) solution instead of ultra-pure water. The SK-Gd experiment aims to enhance
SK’s neutron detection eﬃciency to increase the sensitivity to DSNB and improve pointing
accuracy for a nearby supernova. The original idea of Gd loading to SK water is proposedby Beacom and Vagins (2004) [27]. Gadolinium (hereafter Gd) loading to SK water enables thisChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

39

for the following reason.
A thermal neutron in pure water is captured by a proton with a time constant 200 𝜇s and emits
2.2 MeV gamma rays. The PMT hits resulting from the gamma rays (∼ 7 PMT hits) can be utilized
to detect neutrons. In this energy region, however, it is hard to diﬀerentiate these 2.2 MeV gamma
rays from other background events such as cosmic ray muon spallation and radioactive radon decay.
The estimated detection eﬃciency of neutron capture by proton is only 26% [49]. The drawbacksof neutron capture on proton are its small cross section (0.33 barn as shown in Table 2.3), theemission of low energy gamma rays (2.2 MeV), and the large time constant (∼ 200 𝜇s). Loading
Gd to SK can ideally overcome these obstacles. First, the isotopes of Gd have large neutron capture
cross sections, 155 Gd and 157 Gd, in particular, have more than 100 thousand times larger crosssections than that of a proton (1 H), which is shown in Table 2.3. Second, 8 MeV gamma rays intotal are emitted in neutron capture on Gd. Finally, the time constant of neutron capture becomesshorter (116 𝜇s for 0.1% Gd concentration and 60 𝜇s for 0.03% Gd concentration). Therefore, evena small amount of Gd enhances SK’s neutron detection eﬃciency. Fig. 2.12 shows the neutron
capture eﬃciency as a function of Gd concentration in water by mass. It can be seen that 0.1% Gd
concentration brings about a neutron capture rate of 90%.
Table 2.3: Natural abundance and thermal neutron capture cross section for isotopes relevant to SK-Gd [50].

IsotopeNatural abundance [%]Neutroncapturecross section [barn]
152 Gd0.20

740

154 Gd2.18

85.8

155 Gd

14.80

61100

156 Gd

20.47

1.81

157 Gd15.65

254000158 Gd

24.84

2.22

160 Gd

21.86

1.42

1H

99.99

0.33

16 O

99.76

0.0002

32 S

94.85

0.53

The Gd loading to SK has been performed twice so far using the water puriﬁcation system
for SK-Gd described in Section 2.4.2. The ﬁrst Gd loading from July to August 2020 realized
0.011% Gd concentration (equivalent to 0.021% Gd2 (SO4 )3 concentration by mass). The second

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

40

Fig. 2.12: Neutron capture eﬃciency as a function of Gd concentration in water by mass [51].

Gd loading from May to July 2022 was conducted to raise the concentration to 0.033 %, resulting
in a 75% neutron capture rate [50]. Note that Gd itself is insoluble in water, so we dissolved
Gd2 (SO4 )3 · 8H2 O instead. Since commercially available “high purity” Gd2 (SO4 )3 · 8H2 O has
an unignorable amount of radioactive impurities for SK-Gd’s physics goals, an extremely pureGd2 (SO4 )3 · 8H2 O in which radioactive contaminants are reduced about four orders of magnitude
has been developed [50].
The physics goals of SK-Gd are (1) Detection of DSNB, (2) Galactic Supernova neutrino
detection, (3) Reduction in the background for proton decay search, reactor neutrinos, and solar
neutrino observation, (4) Discrimination between neutrinos and anti-neutrinos for any neutrino
sources including atmospheric neutrinos and J-PARC neutrino beam (T2K).

2.4.2 Water Puriﬁcation System for SK-Gd
SK-Gd needs a sophisticated water puriﬁcation system capable of removing impurities (dust,
bacteria, and ions) in the same way as described in Section 2.1.4 while at the same time preserving
Gd3+ and SO2−
4 in solution. To realize this, a new water puriﬁcation system has been developed asshown in Fig. 2.13 [50]. The new system is composed of three subsystems explained below.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

41

Fig. 2.13: Schematic illustration of SK-Gd water system [50]. See the text for a detailed description.

Gd Dissolving System
In a designated time, the Gd dissolving system automatically dissolves a speciﬁc amount of
Gd2 (SO4 )3 · 8H2 O powder. Only what needs to be done manually is to put Gd2 (SO4 )3 · 8H2 O
powder into the weighing hopper three times a day. The amount of dissolved powder was always
monitored and recorded by the system and checked by Gd-loading shifters.
(1) Weighing hopper: For measuring Gd2 (SO4 )3 · 8H2 O amount.
(2) Circle feeder: For feeding the adjusted amount of Gd2 (SO4 )3 · 8H2 O powder to be dissolved.
(3) Solvent tank: For storing returned water from the SK tank, to be used for dissolving.
(4) Shear blender and Dissolving tank:
For blending the powder from the circle feeder with the returned water from the solventtank.
(5) Solution tank: For storing the Gd2 (SO4 )3 · 8H2 O solution product.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

42

Pretreatment System
The pretreatment system is used for the solution from the dissolving system. This systemremoves impurities other than Gd3+ and SO2−
4 in solution, as well as sterilizing bacteria.
(1) 1 𝜇m Filter:
For removing both dust larger than 1 𝜇m and radioactive substances adhered to the dust.
(2) UV total organic carbon reduction lamp (TOC lamp):
For oxidative degrading of organic compounds in the Gd2 (SO4 )3 · 8H2 O solution by irradiating ultraviolet rays (184.9 nm). UV irradiation (253.7 nm) is also conducted here tosterilize bacteria.
(3) Acidic Cation Exchange Resin (C-Ex resin):
For removing positively charged impurities, especially radium ions. This resin contains
Gd3+ to prevent loss of dissolved Gd3+ .
(4) Basic Anion Exchange Resin (A-Ex resin):
For getting rid of negatively charged impurities, especially uranyl complex formed by
2−
uranium in solution. This resin contains SO2−
4 to prevent loss of dissolved SO4 .

(5) UV sterilizer: For killing bacteria in the water by irradiating ultraviolet rays (253.7 nm).
(6) Mechanical Filter: For removing particles larger than 0.2 𝜇m (0.1 𝜇m) in 2020 (2022).
Re-circulation System
The re-circulation system works as the main water puriﬁcation of the SK tank. It has two
circulation lines with each ﬂow rate at 60 m3 /hour. That enables continuous circulation even when
one line is under maintenance. The conﬁguration is the same as that of pretreatment system,
but the heat exchanger (HE) is added after TOC lamp, and the Mechanical ﬁlter is replaced with
Ultraﬁltration modules (UF).
(1) Return water ﬁlter: For removing impurities larger than 1 𝜇m from SK return water.
(2) 1st buﬀer tank:
For receiving Gd2 (SO4 )3 · 8H2 O solution from the pretreatment system, SK return water,
and the rejected water from the UF modules (explained later). Also, for dividing water into
two parallel circulation lines.
(3) TOC lamp: Same as aforementioned.
(4) Heat exchangers (HEs): For controlling the water temperature at ∼ 13◦ C.
(5) C-Ex resin: Same as aforementioned.
(6) A-Ex resin:
Same as aforementioned, other than the volume is twice that of (5) C-Ex resin.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

43(7) 1 𝜇m Filter: Same as aforementioned.
(8) UV sterilizer: Same as aforementioned.
(9) Ultraﬁltration modules (UF): For ﬁnal ﬁltrating to remove ﬁne particles.
(10) 2nd buﬀer tank: For merging the water from two circulation lines.
(11) Temperature Control Units: For controlling with the precision of 0.01◦ C.
(12) Membrane Degasﬁer (MD)For getting rid of gas in the water, especially intended to remove remaining 222 Rn gas.

2.5 Supernova Neutrino Detection with SK-Gd
At the occurrence of a galactic supernova, SK is expected to observe a burst of neutrinos in avery short time. The vital role of SK is to detect this burst of supernova neutrinos, identify the
direction of the supernova, and issue a warning to astronomical observatories immediately before
the optical burst. This section describes how SK-Gd identiﬁes a supernova direction from thedetection of supernova neutrinos in SK-Gd water and issues an alert, as well as the oﬄine analysis
for supernova simulations in SK-Gd using supernova models.

2.5.1 Supernova Neutrino Interaction in SK-Gd
Through the four types of neutrino interactions, supernova neutrinos are observed in water
Cherenkov detectors. Relevant cross sections as a function of energy are shown in Fig. 2.14.
Inverse beta decay (hereafter IBD) represented with𝜈 e + p → e+ + n(2.6)

dominates the energy region below 30 MeV, accounting for about 90 % of supernova neutrino events
in SK. The resulting positron is emitted in an isotropic manner, which means IBD interactions do
not have directional information of supernova. As many IBD as possible, identiﬁcation of IBD isimportant to improve the accuracy in pointing a supernova, for which neutron capture is utilized
as mentioned in Section 2.4.1.
The second neutrino interaction is elastic scattering (hereafter ES) represented with
𝜈 + e → 𝜈 + e.

(2.7)

ES accounts for about 5 % of supernova neutrino events in SK. Since ES interaction is a forward
scattering, it carries the information of the supernova direction.
The third neutrino reaction is oxygen charged current interactions (hereafter oxygen CCChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

44

100
10 1

Scholberg, K., Albert, J. B., & Vasel, J. (2021).
SNOwGLoBES: SuperNova Observatories with GLoBES.
Astrophysics Source Code Library, ascl-2109.

Cross section (10 38 cm2 )

10 2

IBD

e

10 3

e

16 O CC

16 O CC

16 O NC

10 4
10 5

e ES

e ES

10 6
10 70

x ES

x ES

10 20 30 40 50 60 70 80 90 100
Neutrino energy (MeV)

Fig. 2.14: Cross sections of neutrino interactions in SK as a function of neutrino energy [52]. The solid red
represents IBD, and the green lines represent ES with a neutrino ﬂavor: 𝜈e (dashed), 𝜈¯e (solid), 𝜈 𝑥 (dotted),and 𝜈¯ 𝑥 (dot-dashed). The dashed blue and solid blue lines stand for oxygen CC reactions of 𝜈e and 𝜈 e ,respectively. The dot-dashed cyan line indicates oxygen NC reactions.

interactions) represented with𝜈e +16 O → e− +16 F(2.8)

𝜈 e +16 O → e+ +16 N.

(2.9)

Their cross section exceeds that of ES at ∼ 20 MeV (Fig. 2.14). The electron/positron emission has
a backward anisotropy. Oxygen CC interactions sometimes are accompanied by neutron capture
because the resulting excited nucleus sometimes emits gamma rays and one or two neutron(s).
About 30 % of oxygen CC interactions are accompanied by neutron capture.
Finally, oxygen neutral current interactions (hereafter oxygen NC interactions) represented

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

45

with
𝜈 +16 O → 𝜈 +16 O∗(2.10)

16

O∗ →15 N + p + 𝛾(2.11)

16

O∗ →15 O + n + 𝛾(2.12)

also have a larger cross section than ES in the energy region above ∼ 20 MeV as shown in Fig. 2.14.
The emission of gamma rays is isotropic. The typical energy range of the emitted gamma rays
is 5-9 MeV. The reaction Eq. (2.12) is accompanied by neutron capture. These neutron captures
might be misidentiﬁed as IBD delayed events in analysis.

2.5.2 Real-time Supernova Monitoring System SNWATCH
SK has a real-time supernova monitoring system called SNWATCH [53]. Fig. 2.15 illustrates
the ﬂow of SNWATCH. The SK data gathered by the DAQ system and sent to the event builder are
separated into ∼ 1 minutes segment and stored in a “sub-run” ﬁle. Each sub-run ﬁle is sent to boththe oﬄine process and SNWATCH (described in Section 2.3). SNWATCH continuously performs
data conversion to the oﬄine data formats (reformat process), reconstruction of neutrino eventswith speciﬁc selection criteria (described in Section 2.5.4), and judgment on whether the events
are supernova-like events or not (see Abe et al. (2016)[53] for details). If the events are judged assupernova-like events, SNWATCH issues a prompt supernova warning called a “golden” alarm,
identiﬁes the supernova direction (explained in Section 2.5.5), and broadcasts an announcementof the supernova pointing with its accuracy (see Section 2.5.6) to some astronomical networks(described in Section 2.5.7) for the optical burst observation from its onset.

2.5.3 Low Energy Event Reconstruction in SK
The data of PMT hit timing and PMT charge of each event from the DAQ system are reformatted
to actual seconds and photoelectron count units, before being reconstructed to obtain the event
vertex (the originating point of Cherenkov light) and the event direction. In low energy region, aﬁtter called BONSAI [54] is applied to each event for reconstruction using only PMT hit timing
and pattern information (i.e., charge information is not used), as follows.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

Fig. 2.15: Block diagram of SNWATCH [53].

46

See the text for details.

Event Vertex Reconstruction
PMT hit timing information is ﬁtted by a maximum likelihood ﬁtting program called BONSAI [54] to reconstruct the vertex position. The likelihood function is deﬁned as
L ( 𝑥®, 𝑡 0 ) ≡𝑁hitÕ

log(𝑃(𝑡 − 𝑡tof − 𝑡0 ))(2.13)

𝑖=1

where 𝑥® is the position of the testing vertex and 𝑃(𝑡 − 𝑡tof − 𝑡0 ) is the probability density functionof the timing residual of each PMT hit 𝑡 − 𝑡tof − 𝑡 0 for 1 p.e. signal. Here, 𝑡 is the hit timing, 𝑡 tof is
the time of ﬂight from the vertex position to the hit PMT, and 𝑡 0 is the time of the interaction. The
testing vertex position is determined by grid search.
Event Direction Reconstruction
PMT hit pattern information is used to reconstruct the event direction. Cherenkov angle 𝜃 C ofan e± event is ideally 42◦ as mentioned in Section 2.2. Still, in reality, the Cherenkov ring patternis blurred due to some factors like scattering and reﬂection in SK water. The event direction 𝑑® isestimated by maximum likelihood estimation so that the likelihood:® ≡𝐿 ( 𝑑)𝑁20Õ
𝑖=1log [ 𝑓dir (cos 𝜃 dir,𝑖 , 𝐸)] 𝑖 ×cos 𝜃 𝑖𝑎(𝜃 𝑖 )

(2.14)

is maximized. Here, 𝑁20 is the number of PMT hits in the 20 ns time window around 𝑡 − 𝑡 tof − 𝑡0 .
𝑓dir (cos 𝜃 dir,𝑖 , 𝐸) is the expected distribution function of energy 𝐸 and the opening angle 𝜃 dir,𝑖 ,Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

47

the angle between 𝑑® and the direction from the event vertex to 𝑖-th PMT. 𝑓dir (cos 𝜃 dir,𝑖 , 𝐸) is
determined by Monte Carlo simulation in SK. cos 𝜃 𝑖 /𝑎(𝜃 𝑖 ) is the correction term for the eﬀect of𝜃 𝑖 , the photon’s incident angle to 𝑖-th PMT weighted by the PMT acceptance function 𝑎(𝜃 𝑖 ). The
deﬁnition of 𝜃 dir,𝑖 and 𝜃 𝑖 is shown in Fig. 2.16.

Fig. 2.16: Deﬁnition of 𝜃 dir,𝑖 and 𝜃 𝑖 .

The direction 𝑑® search starts from the initial direction 𝑑®initial :𝑑®initial =

𝑁20
Õ

𝑣®𝑖

(2.15)

𝑖=1

and the best-ﬁt direction is determined.
Energy Reconstruction
Since the number of Cherenkov photons produced by an event is proportional to the energy ofcharged particles involved in the event, it is reasonable to use PMT charge information for reconstructing the energy of an event. However, in the low energy region, the number of photoelectrons
in a hit PMT is only one. Therefore, information on the number of PMT hits is used instead.
The number of PMT hit 𝑁hit depends on the event vertex position, the event direction, waterparameters, and the conditions of PMTs. For this reason, the eﬀective number of PMT hits 𝑁eﬀ isused. It is deﬁned as [55]
𝑁eﬀ =

𝑁50 
Õ
𝑖=1




𝑟𝑖
1
𝑆(0, 0)𝑁all(𝑋𝑖 − 𝜖dark + 𝜖tail ) ×
× exp
×
×
𝑁alive 𝑆(𝜃 𝑖 , 𝜙𝑖 )𝜆eﬀ
𝑄𝐸 𝑖 (𝑡)(2.16)

where 𝑁50 is the number of PMT hits in the 50 ns time window. 𝑋𝑖 represents the eﬀect of multiple
photoelectrons in a PMT hit. The event with multiple photoelectrons in a PMT hit is caused if theevent is near the tank wall and Cherenkov ring is oriented to the wall. To correct this inﬂuence, 𝑋𝑖

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector
is deﬁned as − log(1 − 𝛼𝑖 )
𝛼𝑖
𝑋𝑖 ≡

 3.0


(𝛼𝑖 < 1)(𝛼𝑖 = 1)48

(2.17)

where 𝛼𝑖 is the ratio of the number of PMT hits over the number of PMTs surrounding 𝑖-th PMT.
𝜖 dark is the correction term for the dark noise and is given by:
𝜖 dark =𝑁alive × 𝑅dark × 50 ns
𝑁50(2.18)

where 𝑁alive is the number of properly-working PMTs, and 𝑅dark is the dark noise rate in the unitof hits/ns. 𝜖tail is the correction term for scattering and reﬂection of Cherenkov lights and is givenby:
𝜖 tail =𝑁100 − 𝑁50 − 𝑁alive × 𝑅dark × 50 ns
𝑁50(2.19)

where 𝑁100 represents the maximum number of PMT hits in the 100 ns time window. 𝑁all /𝑁aliveis the correction term for bad PMTs where 𝑁all is the total number of PMTs. 𝑆(0, 0)/𝑆(𝜃 𝑖 , 𝜙𝑖 )is the correction term for photocathode coverage, where 𝑆(𝜃 𝑖 , 𝜙𝑖 ) is the eﬀective photocathodearea of the 𝑖-th PMT, 𝜃 𝑖 is the incident angle to the 𝑖-th PMT, and 𝜙𝑖 is the azimuth angle.
exp(𝑟 𝑖 /𝜆eﬀ ) is the correction term for the attenuation of Cherenkov light by the water, where 𝜆eﬀ
represents the measured water transparency and 𝑟 𝑖 is the distance between the 𝑖-th PMT position
and the reconstructed vertex position. Finally, 𝑄𝐸 𝑖 (𝑡) is the quantum eﬃciency of 𝑖-th PMT which
depends on the production year.
The actual event’s energy can be converted from 𝑁eﬀ value obtained by Eq. (2.16) using acalibration function deﬁned by the LINAC calibration.

2.5.4 Event Selection and Neutron Tagging in SNWATCH
In SNWATCH, the reconstructed events are selected and divided into two: IBD prompt event
candidates and IBD delayed event (i.e., neutron capture) candidates. Next, pairs of IBD prompt
events and IBD delayed events with speciﬁc time and spatial diﬀerences are tagged as IBD events(neutron tagging). The tagged IBD events are ﬂagged in supernova direction determination(described in Section 2.5.5). Fig. 2.18 illustrates these event selections and the neutron tagging
algorithm in SNWATCH. Each process and its selection criteria are described below.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector(a) Deﬁnition of (𝜃𝑖 , 𝜙𝑖 )49(b) 𝑆 ( 𝜃 , 𝜙)Fig. 2.17: (a) Deﬁnition of (𝜃 𝑖 , 𝜙𝑖 ) [55]. (b) Correction term 𝑆(𝜃, 𝜙) for eﬀective photocathode area of the𝑖-th PMT [55].

Selection of Prompt Event Candidates
Reconstructed events that satisfy the following criteria are selected as IBD prompt event candidates:• reconstructed e− /e+ energy ≥ 7 MeV• inside the ﬁducial volume (FV)
• PMT hit timing goodness ≥ 0.4• noise ratio ≤ 0.4• total charge ≤ 1000 p.e.
As deﬁned here, the energy threshold of SNWATCH is 7MeV. The ﬁducial volume (FV) for SK
is the region 2 m inside the detector’s inner wall. It is set for analysis to eliminate the low energy
background events due to radioactive impurities contained in PMTs and their housing observed
more frequently in the volume close to the detector wall than in the region away from the wall.
The total ﬁducial volume is 22.5k m3 . The goodness is the parameter that indicates how good thevertex ﬁtter (BONSAI) applied to the event is (Section 2.5.3). Goodness for PMT hit timing iscalled bsgood. The reconstructed events with bsgood < 0.4 are removed as background events. The
noise ratio 𝑅noise is deﬁned as 𝑅noise = 𝑁noise /𝑁total , where 𝑁noise represents the number of PMT
hits with 0.5 p.e. or less and 𝑁total is the total number of PMT hits of the event. The reconstructed
events with 𝑅noise > 0.4 are rejected as noise events. The total charge is the total amount ofChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

50

Fig. 2.18: Schematic illustration of the prompt event selection, the delayed event selection, and the neutron
tagging used in SNWATCH. First, events that satisfy the selection criteria described in Section 2.5.4 (alsowritten in the red balloon) are selected as IBD prompt event candidates. The energy threshold for selecting
prompt event candidates is 7 MeV. Events that satisfy the three conditions written in the orange balloon are
selected as delayed event candidates. Then, a pair of events with time diﬀerence Δ𝑇 < 500 𝜇s and spacial
diﬀerence Δ𝑅 < 300 cm is tagged as IBD.

photoelectron the event has. The reconstructed events with a total charge above 1000 p.e. areremoved as events originating from atmospheric neutrinos and cosmic-ray muons. Note that the
OD-triggered events are not used, and the LE-triggered events or HE-triggered events are used inthis prompt event selection.
Selection of Delayed Event Candidates
Reconstructed Events that pass the following criteria are selected as IBD delayed event candidates:• reconstructed energy < 10 MeV• inside the ﬁducial volume (FV)
• (PMT hit timing goodness)2 −(PMT hit pattern goodness)2 > 0
The diﬀerence between the square of the goodness for PMT hit timing (called bsgood) and the
goodness for PMT hit pattern (called dirKS) is a parameter called “OvaQ.” Therefore, the last
criterion can be expressed as OvaQ>0.

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

51

Neutron Tagging
After reconstructed events are separated into IBD prompt event candidates and IBD delayed
event candidates, SNWATCH tags the pair of IBD prompt events and IBD delayed events. Here,also simple conditions for time diﬀerence Δ𝑇 < 500 𝜇s and spacial diﬀerence Δ𝑅 < 300 cm
are used to ﬁnd the association between IBD prompt event candidates and IBD delayed event
candidates. In this neutron tagging process, some non-IBD events (like ES) might be tagged by
accident and lost, and vice versa. These factors aﬀect pointing accuracy and their inﬂuences on
pointing accuracy are discussed in Section 4.1.

2.5.5 Determination of the Supernova Direction
To determine the supernova direction in SK, it is crucial to detect as many ES events as possiblethat have the supernova direction information as mentioned in Section 2.5.1. Though the neutrino
direction cannot be known directly, the recoil electrons scattered by the incoming neutrinos aredetected, which can be used to reconstruct the true supernova direction as follows.
Maximum Likelihood Fit
When a supernova-like event cluster is found, SNWATCH determines the supernova direction by
performing Maximum Likelihood Fit to the reconstructed events [53]. For i-th event, a likelihood
function 𝐿 𝑖 is deﬁned as:
𝐿𝑖 =

Õ
𝑟

reco
𝑁𝑟 ,𝑘 𝑡𝑟 ( 𝑓𝑖 ) 𝑝 𝑟 (𝐸 𝑖 , 𝑑ˆ𝑖 ; 𝑑ˆSN)

(2.20)

where the index 𝑟 stands for the type of the neutrino interaction, i.e., 𝑟 = IBD, ES of 𝜈¯e , ES of otherneutrino ﬂavors, or oxygen CC interaction. The index 𝑘 running from 1 to 5 represents the energy
bin in the unit of MeV: 7 ≤ 𝐸 < 10, 10 ≤ 𝐸 < 15, 15 ≤ 𝐸 < 22, 22 ≤ 𝐸 < 35, and 35 ≤ 𝐸 < 50,
respectively, where 𝐸 is the measured energy of the electron. These indices determine the numberof events 𝑁𝑟 ,𝑘 of the interaction 𝑟 in the 𝑘-th energy bin. 𝑡𝑟 is deﬁned according to the IBD ﬂag
𝑓𝑖 of i-th event and the reaction 𝑟 as:(
neutron tagging eﬃciency
𝑡𝑟=IBD =1 − (neutron tagging eﬃciency)(
0 ( 𝑓𝑖 = TRUE)
𝑡𝑟≠IBD =1 ( 𝑓𝑖 = FALSE).

( 𝑓𝑖 = TRUE)( 𝑓𝑖 = FALSE)(2.21)(2.22)

Here, the neutron tagging eﬃciency is ∼ 46% for 0.033% Gd concentration. 𝐸 𝑖 is the total electronenergy of 𝑖-th event and uniquely identiﬁes the index 𝑘. 𝑑ˆ𝑖 is the reconstructed direction of theChapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

52

reco is the supernova direction we would like to determine. The 𝑝 (𝐸 , 𝑑ˆ ; 𝑑ˆreco )i-th event and 𝑑ˆSN𝑟𝑖 𝑖 SN

function indicates a probability density function (PDF) for interaction 𝑟 as a function of the energy
𝐸 𝑖 and an inner-product of 𝑑ˆreco · 𝑑ˆ𝑖 = cos 𝜃 reco . In the determination of the PDF, SNWATCH
SN

SN

utilizes the SK Monte-Carlo (MC) simulations (described in Section 2.6): The generated MC
samples are divided into one-MeV bins from 7 to 35 MeV and a combined energy bin greaterthan 35 MeV. Next, by using the known true supernova direction 𝑑ˆtrue and a model function,SNtrue · 𝑑ˆMC distribution of the generated MC samples is ﬁtted, where 𝑑ˆMC indicatescos 𝜃 SN = 𝑑ˆSN𝑖𝑖

the 𝑖-th event direction of a generated MC sample. Fig. 2.19 illustrates the deﬁnition of 𝜃 SN .
An example of cos 𝜃 SN distribution is given in Fig. 2.20: it has ﬂat components and a peak atcos 𝜃 SN = 1, which originates from isotropic interaction events and ES events, respectively.

Fig. 2.19: 𝜃 SN is the angle between 𝑖-th event direction in SK 𝑑ˆ𝑖 (the blue arrow in the gray box) and thetrue (∼ supernova neutrino arrival direction) (the red arrow in the gray box). An
true supernova direction 𝑑ˆSN
ES event is illustrated as an example. The direction of the recoil electron corresponds to 𝑑ˆ𝑖 . By applying
reco (the green
Maximum Likelihood Fit to the distribution of cos 𝜃 SN , the reconstructed supernova direction 𝑑ˆSNdashed line) that we would like to determine is obtained in 1 set of MC. Δ𝜃 is the angle diﬀerence between
reco and 𝑑ˆtrue , and used to estimate pointing accuracy (see Section 2.5.6).
𝑑ˆSN
SN

(

A likelihood
L = exp

Õ

)
𝑁𝑟 ,𝑘

Ö

𝐿𝑖

(2.23)

𝑖𝑘,𝑟reco vector is determined at which the likelihood is maximized as
is constructed and the 𝑑ˆSN

𝜕L
𝜕L
= 0.
=
𝜕𝑁𝑟 ,𝑘 𝜕 𝑑ˆreco
SN(2.24)

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

53

Fig. 2.20: Typical cos 𝜃 SN distribution from [53] simulated with the Wilson model (see Section 3.1.1) at a
10 kpc supernova for the total electron energy range 7-50 MeV. The black cross and solid blue line represent
the simulation results and the ﬁtted likelihood function, respectively. The peak around cos 𝜃 SN = 1 comesfrom ES events.

reco contains two parameters, zenith and azimuth angle.
𝑑ˆSN

2.5.6 Pointing Accuracy
Pointing accuracy (or angular resolution) in SNWATCH is the indicator of the performance ofdetermining the supernova direction. To estimate the pointing accuracy, SNWATCH uses 3000 MC
samples. From the events included in one MC sample (a simulated supernova burst), one 𝑑ˆreco isSNdetermined as a result of the maximum likelihood ﬁt algorithm described in the previous Section
2.5.5. Therefore, the 3000 𝑑ˆreco vectors are obtained from 3000 MC samples. Pointing accuracy atSNtrue · 𝑑ˆreco . Fig. 2.21 shows the distribution
1𝜎 is derived from Δ𝜃 which is deﬁned as cos(Δ𝜃) = 𝑑ˆSN
SNof Δ𝜃 for 3000 MC samples. Pointing accuracy at 1𝜎 is the value of Δ𝜃 at which the integral of
the histogram from Δ𝜃 = 0 contains 68% of the 3000 MC samples.
SK-Gd aims to realize supernova pointing with the accuracy of ∼ 3◦ for supernovae at 10 kpc,
which allows the follow-up observation with large telescopes, as shown in Fig. 2.22.

2.5.7 Alert Issue
The supernova warning issued in the ﬁnal stage of SNWATCH includes the number of observed
neutrinos, the duration time of the neutrino burst, the universal time when the burst starts, andthe estimated supernova direction in the equatorial coordinates. The networks that SNWATCH
sends a warning are SNEWS 1.0 (SuperNova Early Warning System 1.0) [58, 59], IAU CBAT
(International Astronomical Union Central Bureau for Astronomical Telegrams) [60], ATEL (The
Astronomer’s telegram) [61, 62], and GCN (The Gamma-ray Coordinates Network) [63, 64].
SNWATCH has been running since 1996, and no golden alarm has been sent so far. [53].

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

54

Fig. 2.21: Δ𝜃 distribution of Wilson model (see Section 3.1.1 and two progenitor models (NK1 and NK2)
from Nakazato model (see Section 3.1.2) for 3000 MC samples of simulated supernova at 10 kpc without
true and the determined
neutrino oscillation from [53]. Δ𝜃 is the angle between the input supernova direction 𝑑ˆSN
reco . The value at which the integral of the distribution from Δ𝜃 = 0 covers 68% ofsupernova direction 𝑑ˆSN
3000 MC samples is deﬁned as the pointing accuracy at 1𝜎. The superimposed solid lines represent the ﬁtusing the von Mises-Fisher distribution [56].

SNWATCH aims to release the alarm within less than 1 minute from the supernova neutrino burst
detection in SK. The time between the detection and the alarm issue is limited by the processing
time of (1) event reconstruction, (2) supernova direction ﬁt, and (3) announcement. So far, (1) and(3) have reduced to less than one minute, but (2) still takes ∼ 5 minutes for a 10 kpc supernova withthe current Maximum Likelihood Fitter written in C++. The development of a new direction ﬁtter
written in python, HEALPix (Hierarchical Equal Area isoLatitude Pixelation of a sphere) [65]based ﬁtter, is ongoing. With this ﬁtter, the processing time for (2) is estimated to be reduced
signiﬁcantly to a few seconds.

2.6 Supernova Burst Neutrino Simulations in SK-Gd
Supernova bursts have neither occurred in the nearby universe nor have supernova neutrinos
been detected since the last supernova neutrino detection from SN1987A. Therefore, we need to
study supernova physics and the SK detector response to a supernova using simulations. Fig. 2.23
shows the ﬂow diagram of supernova simulation in SK-Gd. A supernova model, distance to andcoordinate of supernova, and the assumption on neutrino oscillation are input to the event vector
generator for SK called SKSNSim. Then, the output of SKSNSim is given to the detector simulator
for SK called SKG4. Next, mccomb_sn combines SKSNSim results with SKG4 results, adds noise,Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

55

Fig. 2.22: Detection prospects of galactic supernovae [57]. (Top) The histograms of dust-attenuated plateau
magnitudes of core-collapse supernovae and their respective percentage relative to the total core-collapse
supernovae. (Bottom) The typical ranges of optical magnitude and ﬁelds of view (FOV) of various opticaltelescopes are shown by shaded rectangles: ASAS-SN (All-Sky Automated Survey for SuperNovae), Blanco,
CFHT (Canada France Hawaii Telescope), Evryscope, LSST (Large Synoptic Survey Telescope), PanSTARRS (Panoramic Survey Telescope and Rapid Response System), Subaru, and ZTF (Zwicky Transient
Facility). The left-pointing arrow represents the optical magnitude sensitive to the naked eye. Pointing
Accuracy of SK (pure water, ∼ 5◦ ) and SK-Gd (∼ 3◦ ) are represented by the horizontal dashed lines andlabeled.

and applies software triggers. Finally, SNWATCH reconstructs the events generated with these SK
MC simulations, determines the direction of the supernova, and estimates its pointing accuracy(explained in Section 2.5.5 and Section 2.5.6). These tools utilize the data analysis framework
ROOT [66]. The details for SKSNSim, SKG4, and mccomb_sn are described below.

2.6.1 SKSNSimSKSNSim (Super-Kamiokande Supernova Simulation) is an event generator for supernovarelated neutrino interactions developed with C++. For a supernova at a given distance in anarbitrarily chosen direction and a given neutrino oscillation case, SKSNSim computes the expected
number of neutrino interactions listed in Section 2.5.1 and generates event vectors from the ﬂuxesof the input supernova model and cross sections. The cross section calculation is based on:
Strumia & Vissani (2003) [67] for IBD, Bahcall et al. (1995) [68] for ES, Suzuki et al. (2018) [69]Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

56

Fig. 2.23: Overview of supernova simulation in SK. A supernova neutrino emission data produced by asupernova model, distance to the supernova, position of the supernova, and the neutrino oscillation assumption(no oscillation, oscillation with NMO, or oscillation with IMO are input into SKSNSim. The simulated
supernova neutrino events in SK-Gd are generated with SKSNSim, SKG4, and mccomb_sn. SNWATCH
reconstructs the simulated supernova neutrino events, identiﬁes each reconstructed event, ﬂags IBD eventswith the neutron tagging described in Section 2.5.4, and applies supernova direction ﬁt to the non-IBD events.
Here, the 7 MeV threshold is used to select prompt event candidates as described in Section 2.5.4. Pointing
accuracy is estimated by repeating these sets of simulations 3000 times per a supernova model, a supernova
distance, a supernova position, and an oscillation type.

and Nakazato et al. (2018) [70] for oxygen CC interactions, and Langanke et al. (1996) [71] andKolbe et al. (2002) [72] for oxygen NC interactions. (In the latest version of SKSNSim, thebackward anisotropy [73] in the event topology of the oxygen CC interactions and the isotropic
event topology of the oxygen NC interaction are considered.)
SKSNSim was originally developed to read ﬂux data in a speciﬁc format, which had been abottleneck for using other supernova models with diﬀerent data formats. There are two options todeal with this diﬃculty: (1) Modifying SKSNSim, or (2) Modifying the data format of supernova
models. Since the latter was easier and more realistic, I converted the data of some supernova
models to the speciﬁc data format and simulated them. The method of data format uniﬁcation ispresented in Section 3.2.
Neutrino Oscillation in SKSNSim
In SKSNSim, the matter eﬀect for the three-ﬂavor neutrino oscillation inside the supernova is
considered based on the calculation in [74].
With neutrino oscillation assuming NMO, the relationship between the number of neutrinos

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

57

𝑔𝑒𝑛

generated in a collapsing star 𝑁 𝜈𝑖 and the number of neutrinos at the stellar surface 𝑁 𝜈𝑠𝑢𝑟for each𝑖
ﬂavor 𝑖 = 𝑒, 𝜇, 𝜏 is given by𝑔𝑒𝑛

𝑁 𝜈𝑠𝑢𝑟= 𝑁 𝜈𝑥e(2.25)𝑔𝑒𝑛𝑔𝑒𝑛
𝑁 𝜈𝑠𝑢𝑟= 𝑁 𝜈e + 𝑁 𝜈𝑥
𝑥
𝑔𝑒𝑛
𝑔𝑒𝑛
2
2
𝑁 𝜈𝑠𝑢𝑟¯e = 𝑁 𝜈¯e × cos 𝜃 12 + 𝑁 𝜈¯ 𝑥 × sin 𝜃 12
𝑔𝑒𝑛
𝑔𝑒𝑛
2
2
𝑁 𝜈𝑠𝑢𝑟¯ 𝑥 = 𝑁 𝜈¯e × sin 𝜃 12 + 𝑁 𝜈¯ 𝑥 × (1 + cos 𝜃 12 )
𝑔𝑒𝑛

𝑔𝑒𝑛

(2.26)(2.27)(2.28)

𝑔𝑒𝑛

where 𝑁 𝜈𝑥 represents 𝑁 𝜈𝜇 or 𝑁 𝜈𝜏 , while 𝑁 𝜈𝑠𝑢𝑟
= 𝑁 𝜈𝑠𝑢𝑟+ 𝑁 𝜈𝑠𝑢𝑟.
𝑥𝜇𝜏With neutrino oscillation assuming IMO, it is given by
𝑔𝑒𝑛

𝑔𝑒𝑛

𝑔𝑒𝑛

𝑔𝑒𝑛

𝑁 𝜈𝑠𝑢𝑟= 𝑁 𝜈e × sin2 𝜃 12 + 𝑁 𝜈𝑥 × cos2 𝜃 12e
𝑁 𝜈𝑠𝑢𝑟= 𝑁 𝜈e × cos2 𝜃 12 + 𝑁 𝜈𝑥 × (1 + sin2 𝜃 12 )𝑥𝑔𝑒𝑛𝑁 𝜈𝑠𝑢𝑟¯e = 𝑁 𝜈¯ 𝑥

𝑔𝑒𝑛𝑔𝑒𝑛
𝑁 𝜈𝑠𝑢𝑟¯ 𝑥 = 𝑁 𝜈¯e + 𝑁 𝜈¯ 𝑥 .

(2.29)(2.30)(2.31)(2.32)

Note that the matter eﬀect inside the earth is not considered in SKSNSim.

2.6.2 SKG4
SKG4 (Super-Kamiokande Geant4) is a Geant4-based detector simulator. Geant4 is a global
standard software package that simulates the passage of particles through matter [75, 76, 77].
It deals with material information (e.g., detector geometry, isotopes, density), physics of interactions (e.g., electromagnetics, optics, hadronic physics), and particle kinematics (e.g., energy,
momentum, position, and direction of a vertex). SKG4 is customized for SK detector, in which
Cherenkov radiation, photon scattering, absorption, and reﬂection by water (or Gd solution), theresponse of PMTs and their electronics are simulated. All the analyses in this thesis are performed
under the assumption of 0.078% Gd2 (SO4 )3 · 8H2 O concentration (corresponding to 0.033 % Gd
concentration). No dark noise is added and the software trigger is not applied at this step.

2.6.3 mccomb_sn
mccomb_sn (Monte Carlo Combine for Supernova) merges the result of SKSNSim and SKG4,
adds realistic dark noise, and applies software triggers. mccomb_sn processes data with 1 ms as
the minimum unit to avoid memory shortage due to the high event rate of a supernova. Such ahigh event rate causes the accidental coincidence that multiple events are misidentiﬁed as one.

58

Chapter 3
Summary of Supernova Models
This chapter summarizes the characteristics of six supernova models used in this thesis anddescribes the method of data format uniﬁcation for processing them with SK’s supernova event
generator SKSNSim.

3.1 Supernova Models
Since supernova burst simulations consume considerable computational resources, it is often
the case that supernova models simulate only the ﬁrst ∼ 1 s post bounce (e.g., [36]). To overcome
the limitation of computational resources, supernova burst neutrino emission simulations require
simpliﬁed assumptions and approximations (e.g., one-dimensional approaches in spherical symmetric geometry). The typical timescale of supernova burst neutrino emission is ∼ 10 s as observed
at SN1987A. To see a realistic detector response, supernova simulations over a long period are
preferred.
In many one-dimensional simulations, the shock wave does not revive, failing the explosion.
Such models assume some shock revival mechanisms (see Section 1.3.2) or artiﬁcially enhanceneutrino reaction rates for a successful explosion (see Section 3.1.5 for example). These attempts,
as well as diﬀerent progenitor masses and equations of state (EoS) adopted in the models, also
contribute to the diversity of supernova models.
To see the model diﬀerence in SK response and to demonstrate SK’s capability to discriminate
them, I selected the following ﬁve relatively long-term one-dimensional supernova models: thehistorically signiﬁcant Wilson model (see Section 3.1.1), two long-term one-dimensional models(Nakazato model and Mori model, see Section 3.1.2 and Section 3.1.3, respectively), and twoelectron-capture supernova models (Hüdelpohl model and Fischer model, see Section 3.1.4 andChapter 3 Summary of Supernova Models

59

Section 3.1.5, respectively). I also chose a pioneering three-dimensional Tamborra model (seeSection 3.1.6). The ﬁrst ∼ 0.1 s time evolution of each ﬂavor’s luminosity and mean energy foreach model are shown in Fig. 3.1. Time evolution with 20 s range is shown in Fig. 3.2.

1000

700
600
500
400
300
200
100

5

400
300
200
0
0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12
time post bounce [s]

25
20
15

(c) 𝜈𝑥 luminosity
25

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20
15
10

5

0
0.10

0.12

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

50(d) 𝜈e mean energy

500

100

10

0.02 0.04 0.06 0.08
time post bounce [s]600

x mean energy [MeV]10

0.02 0.00

700

00.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12
time post bounce [s]e mean energy [MeV]e mean energy [MeV]

15

800

(b) 𝜈¯e luminosity
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

900
x luminosity [1e + 50 erg/s]

800(a) 𝜈e luminosity
25

1000

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

900
e luminosity [1e + 50 erg/s]

e luminosity [1e + 50 erg/s]

6500
Wilson6000
Nakazato
5500
Mori
5000
Hudelpohl
4500
Fischer
Tamborra
4000
3500
3000
2500
2000
1500
1000
500
0
0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12
time post bounce [s]00.02 0.00

0.02 0.04 0.06 0.08
time post bounce [s](e) 𝜈¯e mean energy

0.10

0.12

0.02 0.00

0.02 0.04 0.06 0.08
time post bounce [s]

0.10

0.12

(f) 𝜈𝑥 mean energy

Fig. 3.1: Time evolution of luminosity (top) in the unit of 1050 erg s−1 and mean energy (bottom) in the unitof MeV for six supernova models listed in Table 3.1 for each neutrino ﬂavor, from -0.02 s to 0.12 s (the corebounce occurs at 0 s). Here, 𝜈 𝑥 means any of 𝜈 𝜇 , 𝜈 𝜏 , 𝜈¯ 𝜇 , and 𝜈¯ 𝜏 . The red, black, blue, orange, purple, andgreen lines represent Wilson model, Nakazato model, Mori model, Hüdelpohl model, Fischer model, andTamborra model, respectively, as indicated by the legend in each panel. The striking peak in (a) for somemodels corresponds to the neutronization burst, and a dip before the neutronization burst seen in Mori and
Hüdelpohl model corresponds to neutrino trapping (Section 1.3.2).

Chapter 3 Summary of Supernova Models

1054
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

1052

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra1053
e luminosity [erg/s]

e luminosity [erg/s]

1053

1054

1052

1051

1052

1051

1050 0

5

10
15
time post bounce [s]

20

1051

1050 0(a) 𝜈e luminosity

5

10
15
time post bounce [s]

20

15

25

Hudelpohl
Fischer
Tamborra

20

15

10

5

10

5

0

5

0
10
time post bounce [s]15(d) 𝜈e mean energy

20

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

20

25
x mean energy [MeV]e mean energy [MeV]

20

10
15
time post bounce [s]30
WilsonNakazatoMorie mean energy [MeV]255(c) 𝜈𝑥 luminosity

30
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

51050 0(b) 𝜈¯e luminosity

30

0

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

1053
x luminosity [erg/s]

1054

60

0
0

5

10
time post bounce [s]15(e) 𝜈¯e mean energy

20

0

5

10
time post bounce [s]1520(f) 𝜈𝑥 mean energy

Fig. 3.2: Same as Fig. 3.1 but shows longer time range until 20 s (the core bounce occurs at 0 s). Note thatluminosity is expressed in logarithmic scale in the unit of erg s−1 .

Chapter 3 Summary of Supernova Models

61

3.1.1 Wilson model
Wilson model [78] (also called “Livermore model”) is a one-dimensional core-collapse supernova model with a long period (from the start of the collapse to ∼ 18 s after the core bounce),
which was a pioneer work in the 1990s. Though it is dated and no longer preferred, it still has
a role as a baseline reference in supernova model papers today [53, 79]. The time evolution of
luminosity and mean energy for this model from -0.2 s to 5.2 s are shown in Fig. 3.3. Its progenitor
with 20𝑀 was to reproduce SN1987A’s light curve. The numerical simulation code developed
by Wilson and Mayle [80, 81] is used. In this thesis, the data scanned from Figure 1 of [78] isused, covering until 15 s after the core bounce.
40
Wilson model

4500
4000

e

3500

x

luminosity [1e + 50 erg/s]

e

e
e

30

x

25

3000
2500

20

2000

15

1500

10

1000

5

500
0

Wilson model

35

mean energy [MeV]

5000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](a) Luminosity

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](b) Mean energy

Fig. 3.3: Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy in the unit of MeV
from -0.2 s to 5.2 s for Wilson model. The core bounce occurs at 0 s. 𝜈e , 𝜈 𝜇 and 𝜈 𝜏 are represented by green,
red, and blue, respectively.

Chapter 3 Summary of Supernova Models

62

3.1.2 Nakazato model
Nakazato model [82] is a long-term one-dimensional model that includes eight sets of progenitor
mass and metalicity (four masses: 13, 20, 30, 50 𝑀 and two metallicities: 𝑍 =0.02, 0.004). It
realizes the simulation from the start of the collapse to 20 s after the core bounce by combining
a general relativistic neutrino-radiation hydrodynamic simulation (𝜈RHD) for the early phase andquasi-static evolutionary neutrino diﬀusion calculations for the PNS cooling phase. The time
evolution of luminosity and mean energy from -0.2 s to 5.2 s are shown in Fig. 3.4. The EoS
by Shen et al. (1998a, 1998b) [83, 84] is used in this model. Three parameters (100, 200, and
300 ms after the bounce) are prepared for the possible shock revival time. I focus on the 20 𝑀 ,𝑍 = 0.02 (solar metallicity) progenitor model with the shock revival at 200 ms after the bounce inthis thesis. Hereafter, the “Nakazato model” indicates this case.
40
Nakazato modeleluminosity [1e + 50 erg/s]

e
x

1000

Nakazato model

35

e

e

30

x

mean energy [MeV]

1500

25
20
15

500

10
5
0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](a) Luminosity

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](b) Mean energy

Fig. 3.4: Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy in the unit of MeV
from -0.2 s to 5.2 s for Nakazato model. The core bounce occurs at 0 s. 𝜈e , 𝜈 𝜇 and 𝜈 𝜏 are represented bygreen, red, and blue, respectively.

Chapter 3 Summary of Supernova Models

63

3.1.3 Mori modelMori model [85] is a one-dimensional core-collapse supernova model with 9.6 𝑀 progenitor
from the onset of core collapse to the PNS cooling phase (20 s after the core bounce). The time
evolution of luminosity and mean energy from -0.2 s to 5.2 s are shown in Fig. 3.5. It modiﬁes
general relativistic hydrodynamics code with a spherically symmetric geometry for the accretion
phase GR1D [86] to cover the PNS cooling phase. This model employs an EoS based on thedensity-dependent relativistic mean ﬁeld (DD2) [85].
40
e
e
x

Mori model

35

e
e

30

x

mean energy [MeV]Mori model

luminosity [1e + 50 erg/s]

6500
6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0

25
20
15
10
5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](a) Luminosity

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](b) Mean energy

Fig. 3.5: Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy in the unit of MeV
from -0.2 s to 5.2 s for Mori model. The core bounce occurs at 0 s. 𝜈e , 𝜈 𝜇 and 𝜈 𝜏 are represented by green,
red, and blue, respectively.

Chapter 3 Summary of Supernova Models

64

3.1.4 Hüdelpohl model
Hüdelpohl model [87] is a one-dimensional electron-capture supernova model with sphericallysymmetric geometry. A 8.8 𝑀 , O-Ne-Mg core progenitor modeled by Nomoto (1987) [88]is adopted. The time evolution of luminosity and mean energy from -0.2 s to 5.2 s are shownin Fig. 3.6. The simulation was performed using the neutrino radiation hydrodynamics code
PROMETHEUS-VERTEX, which is composed of the hydrodynamics solver PROMETHEUS [89]and the neutrino transport code VERTEX [90]. Shen’s EoS [83, 84] is used. For the set of neutrino
interactions, the model considers two cases: the Sf case which includes a “full” set of neutrino
interactions listed in Appendix A in Buras et al. (2006) [91] and the Sr case with a “reduced” set ofneutrino interactions omitting pure neutrino interactions (listed in [92]). I employed the results of
the Sf case in this thesis. This case covers the PNS cooling phase but has a short simulation period
until ∼ 9 s because its high-density eﬀects suppress neutrino opacities. Hereafter, “Hüdelpohl
model” refers to the Sf case.
40
Hudelpohl model

3500

e

3000

e

luminosity [1e + 50 erg/s]

x

2500

e

e

30

x

25

2000

20

1500

15

1000

10

500

5

0

Hudelpohl model

35

mean energy [MeV]

4000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](a) Luminosity

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](b) Mean energy

Fig. 3.6: Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy in the unit of MeV
from -0.2 s to 5.2 s for Hüdelpohl model. The core bounce occurs at 0 s. 𝜈e , 𝜈 𝜇 and 𝜈 𝜏 are represented bygreen, red, and blue, respectively.

Chapter 3 Summary of Supernova Models

65

3.1.5 Fischer model
Fischer model[93] is a one-dimensional supernova model including three progenitors: the 8.8 𝑀
O-Ne-Mg core progenitor modeled by Nomoto (1987) [88] (same as the one used in Hüdelpohl
model), and the 10.8, 18 𝑀 Fe-core progenitors by Woosley et al. (2002) [94]. The modelutilizes AGILE-BOLTZTRAN [95], a spherically symmetric, general relativistic hydrodynamics
code (AGILE) with a Boltzmann neutrino transport solver (BOLTZTRAN). The time evolutionof luminosity and mean energy from -0.2 s to 5.2 s are shown in Fig. 3.7. The EoS by Shen etal. (1998a, 1998b) [83, 84] is used. While the 8.8 𝑀 progenitor has successfully exploded, the10.8, 18 𝑀 progenitors have not exploded naturally. In the latter two cases, neutrino reaction
rates have been artiﬁcially enhanced to produce a successful explosion. In this thesis, I selected
the naturally-exploded 8.8 𝑀 case, and the data scanned from Figure 2 and 14 of [78] covering
until ∼ 6 s after the core bounce are used. Hereafter, the “Fischer model” indicates this data.

40

1500

35

e

30

luminosity [1e + 50 erg/s]

e
x

1000

Fischer modeleexmean energy [MeV]

Fischer model

25
20
15

500

10
5
0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](a) Luminosity

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
time post bounce [s](b) Mean energy

Fig. 3.7: Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy in the unit of MeV
from -0.2 s to 5.2 s for Fischer model. The core bounce occurs at 0 s. 𝜈e , 𝜈 𝜇 and 𝜈 𝜏 are represented by green,
red, and blue, respectively.

Chapter 3 Summary of Supernova Models

66

3.1.6 Tamborra model
Tamborra model [96] is a pioneer of three-dimensional simulation with energy-dependent neutrino transport. It has three progenitors with diﬀerent masses (11.2, 20, 27 𝑀 ). The simulation
time range is ∼ 350 ms for the 11.2 𝑀 , 20 𝑀 progenitor case and ∼ 550 ms for the 27 𝑀
progenitor case, and none of them has exploded successfully within these simulation periods. The
model uses the neutrino radiation hydrodynamics code PROMETHEUS-VERTEX. The EoS withcompressibility 𝐾 =220 MeV by Lattimer and Swesty (1991) [97], often referred to as LS EoS,
is used in this model. For the 20 and 27 𝑀 progenitor cases, quasi-periodic oscillation appears
in the neutrino signal due to Standing-Accretion-Shock Instability (SASI). This signal modulation
depends on the angular direction of the observer relative to the progenitor. For each progenitor
mass, this model considers three observer directions. I use the data for 27 𝑀 progenitor withthe “black” observer direction in [96] which is provided in the supernova simulation pipeline
SNEWPY [98]. Hereafter, “Tamborra model” indicates this case.

40

5000
4500

Tamborra model

4000

35

e

30

e

3500

x

25

2500

e
e

mean energy [MeV]luminosity [1e + 50 erg/s]

x

3000

20

2000

15

1500

10

1000

5

500
0
0.0

Tamborra model

0.1

0.2
0.3
0.4
time post bounce [s](a) Luminosity

0.5

0.6

00.0

0.1

0.2
0.3
0.4
time post bounce [s]

0.5

0.6

(b) Mean energy

Fig. 3.8: Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy in the unit of
MeV from 0.0 s (time of the bounce) to 0.6 s for Tamborra model. 𝜈e , 𝜈 𝜇 and 𝜈 𝜏 are represented by green,
red, and blue, respectively. The quasi-periodic oscillation features originate from Standing Accretion-Shock
Instability (SASI).

Chapter 3 Summary of Supernova Models

67

Table 3.1 summarizes the main proﬁles of the above six models employed in this thesis. Notethat the start times and the durations shown in the table are after the linear extrapolation describedin Section 3.2.1 and do not necessarily correspond to that of the published models.
Table 3.1: Summary of six supernova model data employed in this thesis.

Model Name

WilsonNakazatoMori

Hüdelpohl

Fischer

Tamborra

Dimension

1D

1D

1D

1D

1D

3D

progenitor mass [𝑀 ]

20

20

9.6

8.8

8.8

27

start time [s]

0.03

-0.05

-0.256

-0.02

0.0

0.011

duration [s]

14.96

20.05

19.95

8.98

6.10

0.54

EoS

-

Shen*

DD2**

Shen*

Shen*

LS***

* Equation of state by Shen et al. (1998a, 1998b) [83, 84].
** Equation of state based on density-dependent relativistic mean-ﬁeld model [99].
*** Equation of state by Lattimer and Swesty [97]3.2 Data Format Uniﬁcation
As mentioned in Section 2.6, the limitation that SKSNSim was able to accept only a speciﬁcformat of data prevented the study of SK responses using a variety of models with other data
formats. SKSNSim has a class to read “Nakazato format” in which the diﬀerential neutrino
number ﬂux Δ𝑁 𝑘,𝜈𝑖 (𝑡 𝑛 )/Δ𝐸 𝑘 and diﬀerential neutrino number luminosity Δ𝐿 𝑘,𝜈𝑖 (𝑡 𝑛 )/Δ𝐸 𝑘 at thetime 𝑡 𝑛 are provided for each neutrino ﬂavor 𝜈𝑖 (𝑖 = 𝑒, 𝜇, 𝜏) and energy bin 𝐸 𝑘 as described inAppendix of Nakazato et al. (2013) [82] *1.
To read the data in other formats, it is more practical to standardize the data format itself andinput it to SKSNSim than to develop a class in SKSNSim for reading every diﬀerent data format.
Therefore, I performed “data format uniﬁcation” for the models with non-“Nakazato format” data.
I prepared the lists of time-luminosity pairs (𝑡, 𝐿 𝜈𝑖 (𝑡)) and time-mean-energy pairs (𝑡, 𝐸 𝜈𝑖 (𝑡))by scanning the plots of the time evolution of luminosity and mean energy in the published papers.
The rest of this section describes how this “data format uniﬁcation” is conducted.

3.2.1 Linear Interpolation and Extrapolation
Besides Nakazato model, Mori model is provided in “Nakazato format” with slightly diﬀerent
energy binning 𝐸 𝑘 . Other non-“Nakazato format” models (Wilson model, Hüdelpohl model,*1 The “Nakazato format” data of [82] and its guide are available on the Web site http://asphwww.ph.noda.tus.ac.jp/snn/

Chapter 3 Summary of Supernova Models

68

Fischer model, and Tamborra model) need data format uniﬁcation. For these four models, I used
the same energy binning as that of Nakazato model. For Hüdelpohl model, the lists of (𝑡, 𝐿 𝜈𝑖 (𝑡))pairs and (𝑡, 𝐸 𝜈𝑖 (𝑡))-pairs are already provided in the repository of SK database *2. Regarding
Wilson model and Fischer model, I scanned the ﬁgures of luminosity vs. time and mean energy vs.
time using a web-based plot digitizing tool WebPlotDigitizer [100] for each neutrino ﬂavor to makethe lists of (𝑡, 𝐿 𝜈𝑖 (𝑡)) and (𝑡, 𝐸 𝜈𝑖 (𝑡)). Since the time data points 𝑡 of these three models are notcommon among neutrino ﬂavors 𝜈𝑖 , I performed linear interpolations and extrapolations to eachlist before making them into “Nakazato format” (described in the following Section 3.2.2-Section
3.2.4).
Note that Fischer model’s 𝜈e luminosity curve (the upper left panel of Figure 2 in Fischer etal. (2010) [93]) starts later than that of other ﬂavors, which requires extrapolation of 𝜈e luminosity
so that it has the same time range as the other ﬂavor’s luminosity data points. Since the maximum
luminosity and the rising edge of 𝜈e luminosity is out of the plotted region, linear extrapolation is
the only possible way to realize this.
For Tamborra model, I took advantage of SNEWPY [98] *3 which has the lists of (𝑡, 𝐿 𝜈𝑖 (𝑡)) and(𝑡, 𝐸 𝜈𝑖 (𝑡)) with a common time data point among ﬂavors.

3.2.2 Diﬀerential Number Flux Calculation
The goal of this “data format uniﬁcation” is to obtain the diﬀerential neutrino number ﬂux
Δ𝑁 𝑘,𝜈𝑖 (𝑡 𝑛 )/Δ𝐸 𝑘 [s−1 MeV−1 ] and diﬀerential neutrino number luminosity Δ𝐿 𝑘,𝜈𝑖 (𝑡 𝑛 )/Δ𝐸 𝑘[erg s−1 MeV−1 ] at the time 𝑡 𝑛 [s] for each neutrino ﬂavor 𝜈𝑖 (𝑖 = 𝑒, 𝜇, 𝜏) and energy bin 𝐸 𝑘 fromthe available pairs of (𝑡, 𝐿 𝜈𝑖 (𝑡)) and (𝑡, 𝐸 𝜈𝑖 (𝑡)). The time-integrated ﬂux of supernova neutrino[MeV−1 kpc−2 ] is represented as
1 𝐸 𝜈𝑖 ,totald𝐹 (𝐸 𝜈 )=𝑓 (𝐸 𝜈 ).
2
d𝐸 𝜈
4𝜋𝑑SN
𝐸 𝜈𝑖

(3.1)

where 𝑑SN [kpc] is the distance to the supernova, 𝐸 𝜈𝑖 ,total [MeV] represents the total energy emittedby 𝜈𝑖 , 𝐸 𝜈𝑖 [MeV] stands for the average energy of 𝜈𝑖 , and 𝑓 (𝐸 𝜈 ) is a normalized distribution
2 is calculated in SKSNSim, it does not need to befunction [70]. Since the distance term 1/4𝜋𝑑SN

considered here. As 𝑓 (𝐸 𝜈 ), I assume Fermi-Dirac distribution𝑓FD (𝐸 𝜈 ) =𝐸𝜈 2
2
3𝜁 (3)𝑇𝜈3𝑖 𝑒 𝐸𝜈 /𝑇𝜈𝑖 + 1*2 Prepared for developing SNWATCH. The data is conﬁrmed to reproduce the published plots.
*3 Available on the GitHub https://github.com/SNEWS2/snewpy(3.2)

Chapter 3 Summary of Supernova Models

69

where 𝜁 (3) ≈ 1.202 is the zeta function and
𝑇𝜈𝑖 =

𝐸 𝜈𝑖
180
𝜁 (3) 𝐸 𝜈𝑖 ≈
4
3.151
7𝜋

(3.3)

is the neutrino temperature in the units of MeV. By replacing the total energy 𝐸 𝜈𝑖 ,total [MeV]with the luminosity 𝐿 𝜈𝑖 (𝑡) [erg s−1 ] and substituting 𝐸 𝜈𝑖 = 𝐸 𝜈𝑖 (𝑡) in Eq. (3.1)-Eq. (3.3), theexpression of the diﬀerential number ﬂux [s−1 MeV−1 ] is obtained as
𝐿 𝜈𝑖 (𝑡)d2 𝑁 𝜈
2𝐸𝜈 2=
d𝐸 𝜈 d𝑡
𝐸 𝜈𝑖 (𝑡) 3𝜁 (3)𝑇𝜈3𝑖 𝑒 𝐸𝜈 /𝑇𝜈𝑖 + 1(3.4)

where 𝑇𝜈𝑖 ≈ 𝐸 𝜈𝑖 (𝑡)/3.151 [MeV].

3.2.3 Diﬀerential Number Luminosity Calculation
The diﬀerential number luminosity [ergs−1 MeV−1 ] can be computed from the diﬀerential number
ﬂux [s−1 MeV−1 ] as
Δ𝐿 𝑘,𝜈𝑖 (𝑡 𝑛 ) Δ𝑁 𝑘,𝜈𝑖 (𝑡 𝑛 )1.6022 × 10−6 erg=
× 𝐸𝑘 ×
Δ𝐸 𝑘
Δ𝐸 𝑘
MeV

(3.5)

3.2.4 Normalization for Reproducing Original Luminosity
In order to reproduce the original luminosity vs. time plot and mean energy vs. time plot fromthe “Nakazato format” table, a normalization factor is necessary. Such normalization factor iswritten as
Normalizing Factor at 𝑡 =original luminosity at 𝑡,
reproduced luminosity at 𝑡

(3.6)

where the original luminosity is 𝐿 𝜈𝑖 (𝑡) provided in the list and the reconstructed luminosity
𝐿 𝜈𝑖 ,reco (𝑡) is obtained by the energy-integration of the diﬀerential number luminosity as
𝐿 𝜈𝑖 ,reco (𝑡) =Õ Δ𝐿 𝑘,𝜈 (𝑡)
𝑖

𝑘

Δ𝐸 𝑘

× (𝐸 𝑘+1 − 𝐸 𝑘 ).

(3.7)

By multiplying Eq. (3.6) to the results of Eq. (3.4) and Eq. (3.5) and arranging them, the normalized“Nakazato format” tables of other models are obtained.

70

Chapter 4
Detector Response and Pointing Accuracy
As mentioned in Section 2.5, SK has the crucial role of detecting supernova neutrino and alerting
the supernova direction before its optical burst. Therefore, in order to understand the responseof SK in advance, it is necessary to simulate galactic supernovae (i.e., supernovae that occur
within about 10 kpc from the Earth) using various models. This chapter reports the evaluation ofSK’s response and pointing accuracy for supernova bursts of the six models described in Chapter
3 with considering neutrino oscillation cases. In Section 4.1, pointing accuracy with varying
energy threshold in SNWATCH is discussed to test the present 7 MeV threshold for selecting
prompt event candidates, using Nakazato model for a 10 kpc supernova assuming NMO. Using
the appropriate energy threshold determined in this section, a description and discussion of thedetector response and pointing accuracy for a supernova at 10 kpc for the six models assuming
three neutrino oscillation types are given in Section 4.2.

4.1 Energy Threshold Dependence of Pointing Accuracy
As mentioned in Section 2.6, SNWATCH currently running uses the energy threshold of 7 MeV
for selecting IBD prompt candidates (≥ 7 MeV) and calculating the angular resolution of thesupernova direction. The threshold has been selected as 7 MeV because backgrounds from thedecay of radioactive isotopes such as Rn etc., dominate the energy region below 7 MeV. However,
the inﬂuence of changing the energy threshold on the pointing accuracy has never been investigated.
It is vital to verify whether 7 MeV is the appropriate energy threshold to determine the supernova
direction with the best possible accuracy.
Pointing accuracy in SNWATCH is calculated using IBD-ﬂagged 𝜃 SN . As explained in Section
2.6, true interaction information of the simulated supernova burst is partially lost during the event

Chapter 4 Detector Response and Pointing Accuracy

71

reconstruction, identiﬁcation of prompt/delayed events, and/or neutron tagging. The ratio of what
interaction information is lost at which step depends on the threshold.
To examine how changing the energy threshold aﬀects pointing accuracy, I generated 1000 data
sets with the chain of simulations described in Section 2.6 and derived pointing accuracy using
Nakazato model assuming a supernova at 10 kpc with neutrino oscillation in NMO for energy
thresholds varying from 5 MeV and 9 MeV. Since the version of mccomb_sn and SNWATCH
I used here set the LE trigger threshold (described in Section 2.3.3) to 47 and the HE trigger
threshold to 50, the same value was used for 6-9 MeV threshold cases. Regarding the 5 MeV
threshold, I prepared the data in two cases for the LE trigger threshold: 47 and 44 because thediﬀerence in the trigger eﬃciency may aﬀect the result. Note that the version of SKSNSim usedin this study does not consider the oxygen NC reactions. Table 4.1 and Fig. 4.1 show the results ofpointing accuracy for each energy threshold.
Table 4.1: Pointing accuracy with various energy thresholds in SNWATCH.
Energy threshold
LE trigger threshold
Pointing accuracy at 1𝜎

5 MeV
44
4.53±0.14

5 MeV
47
4.53±0.14

6MeV47
4.27±0.14

7 MeV
47
4.17±0.13

8 MeV
47
4.17±0.13

9 MeV
47
4.35±0.14

Fig. 4.1: Pointing accuracy as a function of energy threshold for selecting prompt candidates in SNWATCH.

Although the statistical error is large (1000 simulations are not suﬃcient), the best accuracy
is somehow achieved at the 7-8 MeV threshold. Regarding the 5 MeV threshold cases, thediﬀerence in LE trigger threshold does not aﬀect pointing accuracy. To ﬁnd out the reason for thisChapter 4 Detector Response and Pointing Accuracy

72

energy threshold dependence, the purity and the eﬃciency of ES should be investigated. Valuable
direction information from ES events may be lost due to improper classiﬁcation during event
reconstruction, identiﬁcation, and neutron tagging. In other cases, events that are not really ES
events may get classiﬁed as ES events. How much these factors contribute to the pointing accuracy
was investigated and discussed below.

4.1.1 Event Selection in SNWATCH
The ﬂow of event classiﬁcation in SNWATCH with the deﬁnitions of the ES eﬃciency andpurity is described in Fig. 4.2. The four panels of Fig. 4.2 show how the true events generated
by SKSNSim, SKG4, and mccomb_sn are categorized with reconstruction and neutron tagging
in SNWATCH, for (a) IBD prompt interaction, (b) ES, (c) Oxygen CC interaction, and (d) Gd-𝛾
interaction (i.e., neutron capture on Gd). The deﬁnition of the term “identiﬁed/misidentiﬁed” and“tagged/not tagged” are as follows;
The word “identiﬁed” (indicated by the solid green arrow) means that a true supernova neutrino
interaction, such as IBD, ES, and Oxygen CC interaction, is classiﬁed as an IBD prompt candidate(top middle box in each panel). The IBD prompt candidates satisfy the selection criteria mentioned
in Section 2.5.4. The word “misidentiﬁed” means the opposite: a true supernova neutrino
interaction is classiﬁed as an IBD delayed candidate (top middle box in each panel) by accidentally
satisfying the condition for delayed candidate selection (described in Section 2.5.4). Examples of
the causes of the misidentiﬁcation in panel (a)-(c) are the incorrect reconstruction of the event, theenergy being lower than the energy threshold for selecting prompt candidates (i.e., below 7 MeV),or the event being outside the ﬁducial volume. Regarding panel (d), the cause of a misidentiﬁcation
might be that the event has too high energy (≥ 10 MeV) due to bad energy resolution of the detector
as a delayed candidate.
The word “tagged” (indicated by the solid magenta arrow) means that a prompt candidate is
selected as an IBD prompt event (panel (a)-(c)) because corresponding delayed candidate is found,or a delayed candidate is selected as an IBD delayed (panel (d)) because corresponding prompt
candidate is found. The word “not tagged” (indicated by the dashed magenta arrow) is the contrary.
If corresponding delayed (prompt) candidate is not found for a prompt (delayed) candidate, theprompt candidate is “not tagged.”Let’s take a look at the examples of appropriate event categorization. A true IBD event (panel(a)) should be identiﬁed as a prompt candidate and then tagged as an IBD prompt event with
the neutron tagging algorithm. A true ES event (panel (b)) should also be identiﬁed as a prompt
candidate, but it should not be tagged as an IBD prompt event because it is an ES event. In the same

Chapter 4 Detector Response and Pointing Accuracy

73

way, a true oxygen CC event (panel (c)) should be identiﬁed as an IBD prompt event. However,since ∼ 30% of oxygen CC interactions are accompanied by neutron capture as mentioned in
Section 2.5.1, it is possible to be “tagged” or “not tagged.” For a true Gd-𝛾 interaction, theappropriate course of classiﬁcation is “identiﬁed” as an IBD delayed candidate and then "tagged"
as an IBD delayed event.
Next, let’s look at the inappropriate event categorization instances. True ES events can be lostin the following two cases: (1) the true event is correctly identiﬁed as a prompt candidate but istagged as a prompt event by accident, (2) the true event is misidentiﬁed as a delayed candidate.
These losses contribute to the ineﬃciency in ES selection, worsening the pointing accuracy.
Contamination in the reconstructed ES events can also deteriorate the pointing accuracy. One
example is that a true Gd-𝛾 event is misidentiﬁed as a prompt candidate and is “not tagged” (i.e.,
fake ES indicated in panel (d)).

4.1.2 ES Eﬃciency and Ineﬃciency
With the event categorization described in Section 4.1.1, ES eﬃciency is deﬁned as
ES eﬃciency ≡the number of true ES events identiﬁed as prompt candidates and “not tagged”.
the number of true ES(4.1)

ES ineﬃciency due to the incorrect tagging, say, ES ineﬃciency (tagged as prompt), is
ES ineﬃciency (tagged as prompt event)the number of true ES events identiﬁed as prompt candidates and tagged≡,
the number of true ES(4.2)
and ES ineﬃciency due to misidentiﬁcaion, say, ES ineﬃciency (misidentiﬁed), is
ES ineﬃciency (misidentiﬁed) ≡the number of true ES events misidentiﬁed.
the number of true ES(4.3)

Fig. 4.3 shows ES eﬃciency and ineﬃciency for each factor as a function of the energy thresholdin SNWATCH. ES eﬃciency decreases with the energy threshold increases because more ES eventsare discarded. Whereas ES ineﬃciency (tagged as prompt) is almost threshold-independent andsmall, ES ineﬃciency (misidentiﬁed) ranges from 0.56 to 0.72 and gets higher as the energy
threshold becomes higher. Therefore, ES ineﬃciency due to misidentiﬁcation turned out to be
responsible for worse resolution in higher energy thresholds.

Chapter 4 Detector Response and Pointing Accuracy

74(a) Selection of IBD events.

(b) Selection of ES events.

(c) Selection of oxygen CC events.

(d) Selection of Gd-𝛾 events.

Fig. 4.2: Event selection ﬂow in SNWATCH for each interaction: (a) IBD, (b) ES, (c) Oxygen CC, and (d) Gd𝛾 (neutron capture on Gd). For (a)-(c), the true interaction written on the left side box is “identiﬁed” (indicatedby the solid green arrow) to be categorized as an IBD prompt candidate (top middle box) by satisfying theselection criteria described in Section 2.5.4, or “misidentiﬁed” (indicated by the dashed green arrow) to be
categorized as an IBD delayed candidate (bottom middle box) by satisfying the condition described in Section
2.5.4. Next, with the neutron tagging algorithm, the prompt candidate (or the delayed candidate) is “tagged”(indicated by the solid magenta arrow) or “not tagged” (indicated by the dashed magenta arrow). Regarding(d), the true Gd-𝛾 event is “identiﬁed” as an IBD delayed candidate (bottom middle box), or “misidentiﬁed”
as an IBD prompt candidate (top middle box). The box highlighted in yellow in each panel indicates the
position where the interaction of the panel should be classiﬁed. If a true Gd-𝛾 event is identiﬁed as an IBD
prompt candidate and then is “not tagged”, it can be a “fake ES” (indicated by the purple box on the right inpanel (d)). See the text for more details.

4.1.3 ES purity and Contamination to ES
ES purity is deﬁned as
ES purity ≡the number of true ES events identiﬁed as prompt candidates and “not tagged”.
the total number prompt candidates and “not tagged”(4.4)

Chapter 4 Detector Response and Pointing Accuracy

Fig. 4.3: ES eﬃciency and ineﬃciency as a function of energy threshold. The green circles represent ES eﬃciency with the LE trigger thresholdof 47. The red and blue circles stand for ES
ineﬃciency due to incorrect tagging and due tomisidentiﬁcation, respectively, with the LE trigger threshold of 47. The triangles of the corresponding colors indicate the LE trigger thresholdof 44.

75

Fig. 4.4: ES purity and the ratio of contamination to ES as a function of energy threshold. The
green circles represent ES purity with the LE trigger threshold of 47. The circles of other colors
stand for the ratio of contamination in ES due to
IBD (red), due to oxygen CC interactions (blue),
due to neutron captures including Gd-𝛾 (orange),and due to other events (gray), with the LE trigger
threshold of 47. The triangles of the corresponding colors indicate the LE trigger threshold of 44.

ES impurities, or contamination to ES is represented as
ES impurity (due to “X”)
the number of true “X” events identiﬁed as prompt candidates and “not tagged”≡,
the total number prompt candidates and “not tagged”(4.5)

where X indicates IBD or oxygen CC interactions or neutron capture or other backgrounds.
Fig. 4.4 shows the energy threshold dependence of ES purity and contamination to ES from eachfactor. For better pointing accuracy, it is better to have a high ES purity and low impurity. As canbe seen from the ﬁgure, the biggest contamination to ES is from IBD events identiﬁed as prompt
candidates and “not tagged” (red plots), ranging from 0.65 to 0.82. A noteworthy feature of thisﬁgure is the contamination from neutron captures (including Gd-𝛾, orange plots): it increases withthe threshold decrease. Thus, this factor is most responsible for deteriorated pointing accuracy inthe lower energy threshold. In particular, the contamination from neutron captures to ES exceeds
the ES purity (green plots) at the 5-6 MeV threshold while it is slightly less than the ES purity at
the 7 MeV threshold. It is found that the maximum ES purity (0.059) is achieved at the 7 MeV

Chapter 4 Detector Response and Pointing Accuracy

76

threshold.

4.1.4 Energy Threshold in SNWATCH
In conclusion, the leading cause of ES ineﬃciency comes from the misidentiﬁcation of ES,
resulting in worse pointing accuracy with the higher energy threshold. The contamination to
ES from neutron captures is responsible for worse pointing accuracy with the lower energy
threshold. This study on the energy threshold dependence of pointing accuracy in SNWATCH
ﬁrst demonstrated that the current 7 MeV energy threshold for selecting prompt candidates isappropriate.

4.2 Detector Response for Supernova at 10kpc
Data format uniﬁcation enabled several supernova models to be processed with SKSNSim,making it possible to study SK’s response to the simulated supernova bursts. “Nakazato format”
data for the six models described in Chapter 3 were processed with SKSNSim, SKG4 (with 0.03%
Gd concentration), mccomb_sn, and SNWATCH (with the 7 MeV threshold for selecting prompt
candidates), for a supernova at 10 kpc. For each model, the following three cases are assumed;
without oscillation (No Osc.), with neutrino oscillation in NMO, and with neutrino oscillation in
IMO. In the oscillation calculation in SKSNSim, sin2 𝜃 12 = 0.307 [3] is used (shown in Table 1.1).
The LE trigger threshold and the HE trigger threshold are set to 49 and 52, respectively, in bothmccomb_sn and SNWATCH. As mentioned in Section 2.5.6, SNWATCH uses 3000 MC samples
as the indicator of pointing accuracy. However, due to limited computer resources for this study,
I generated 1000 MC samples per model for every oscillation assumption. Note that a common
supernova position, arbitrarily chosen to be the position of the Sun at 0:00 on 23rd March 2011
(i.e., RA = 1h 41m 43.s 6, Dec = +0◦ 39012. 005), was used in the 1000 MC samples. This section
reports the results in the following order: the average number of events of 1000 MC samples foreach interaction generated by SKSNSim in Section 4.2.1, the average number of reconstructed
events for each interaction in Section 4.2.2, the oscillation-dependent diﬀerence in SK’s response in
Section 4.2.3, detection of neutronization burst in Section 4.2.4, and ﬁnally, the model-dependent
diﬀerence in SK’s response in Section 4.2.5.

4.2.1 Average Number of Generated Events in SK by SKSNSim
To understand the property of neutrino oscillation, we ﬁrst look at the diﬀerence in the numberof generated events for each interaction and each ﬂavor of neutrinos in SK water among models

Chapter 4 Detector Response and Pointing Accuracy

77

and oscillation assumptions. Table 4.2 show the average number of events of 1000 MC samples
for each interaction generated by SKSNSim for the six models, assuming a supernova at 10 kpc
for each neutrino oscillation assumption. The order of the number of generated events for eachinteraction among oscillation assumptions varies in models due to the diﬀerence in the compositionof the neutrino ﬂavor of the model in the oscillation assumption. For example, the order of thenumber of IBD events is No Osc. < NMO < IMO for Wilson, Nakazato, Mori, and Fischer
models, while it is comparable for Hüdelpohl model and the opposite for Tamborra model (i.e.,
IMO < NMO < No Osc.). For Wilson, Nakazato, and Fischer models, the number of 𝜈𝑒 -involved
ES events is similar within 2.05% among diﬀerent oscillation assumptions, whereas it varies 10.4%
for Mori, 9.00% for Hüdelpohl, and 28.2% for Tamborra model.
These features can be understood from Table 4.3, showing the average number of neutrinos ofeach ﬂavor interact with SK for each oscillation assumption. The numbers of 𝜈𝑖 for each oscillation
assumption are obtained by adding the number of events which involves 𝜈𝑖 listed in Table 4.2. For
the ﬁve models other than Tamborra model, the number of 𝜈¯𝑒 increases in IMO case comparedto No Osc. case, suggesting that the eﬀect of the 𝜈¯𝑒 increase due to 𝜈¯ 𝜇 , 𝜈¯ 𝜏 → 𝜈¯𝑒 is expected to
be stronger than the eﬀect of the 𝜈¯𝑒 decrease due to 𝜈¯𝑒 → 𝜈¯ 𝜇 , 𝜈¯ 𝜏 , as explained in Section 2.6.1(Eq. (2.29)-Eq. (2.32)). On the other hand, in Tamborra model, the number of 𝜈¯𝑒 is less in IMO
case than in No Osc. case, indicating the decrease of 𝜈¯𝑒 due to 𝜈¯𝑒 → 𝜈¯ 𝜇 , 𝜈¯ 𝜏 is stronger than the
opposite conversion. This can be also interpreted from Fig. 3.1, the time evolution of luminosityand mean energy, as follows. Mean energies of 𝜈¯𝑒 are similar among models (Fig. 3.1 (e)), but
luminosity of 𝜈¯𝑒 is greater in Tamborra model (the green line in Fig. 3.1 (b)) than in the othermodels, indicating that the number of 𝜈¯𝑒 produced at the supernova in the ﬁrst 0.1 s is larger in
Tamborra model than in the other models. Therefore, if we assume neutrino oscillation in IMO,
the eﬀect of the 𝜈¯𝑒 decrease is expected to be stronger than the 𝜈¯𝑒 increase, resulting in fewer
yields of IBD events than in the NMO and no oscillation assumptions.
The number of 𝜈𝑒 is the largest in NMO for Wilson, Nakazato, Mori, and Fischer models,suggesting the eﬀect of 𝜈 𝜇 , 𝜈 𝜏 → 𝜈𝑒 is stronger than that of 𝜈𝑒 → 𝜈 𝜇 , 𝜈 𝜏 in NMO case for thesemodels, as described in Section 2.6.1. This is not the case for Hüdelpohl model and Tamborra
model. Hüdelpohl model has a similar number of neutrinos of each ﬂavor among oscillation cases.
For Tamborra model, the 𝜈𝑒 decrease is stronger than the 𝜈𝑒 increase, resulting in less number of𝜈𝑒 with oscillation than without oscillation.
The number of oxygen interaction events in Table 4.2 shows a big diﬀerence among models;for example in No Osc. case, Wilson model has 722 oxygen interaction events in total, whereas
it is 33 events in total for Fischer model. These diﬀerences originate from the energy spectra ofcoming neutrinos; since the cross section of oxygen interactions is larger in higher neutrino energyChapter 4 Detector Response and Pointing Accuracy

78

Table 4.2: Average number of events at SK in the 32.5k m3 full volume for 1000 simulated supernova bursts
at 10 kpc for Wilson, Nakazato, Mori, Hüdelpohl, Fischer, and Tamborra models. Note that 𝜈 𝑥 represents 𝜈 𝜇and 𝜈 𝜏 .
Generated by
SKSNSim
IBD (𝜈¯e )ES (𝜈e )ES (𝜈¯e )ES (𝜈 𝑥 )ES (𝜈¯ 𝑥 )16 O CC (𝜈 )e
16 O CC (𝜈¯ )e16 O NC (𝜈 ,15 N)e
16 O NC (𝜈¯ ,15 N)e
16 O NC (𝜈 ,15 N)
𝑥
16 O NC (𝜈¯ ,15 N)
𝑥
16 O NC (𝜈 ,15 O)e
16 O NC (𝜈¯ ,15 O)e
16 O NC (𝜈 ,15 O)
𝑥
16 O NC (𝜈¯ ,15 O)𝑥
total

WilsonNo Osc.
7431
223
97
80
69
44
195
4
22
177
177
1
6
48
48
8622

Generated by
SKSNSim
IBD (𝜈¯e )ES (𝜈e )ES (𝜈¯e )ES (𝜈 𝑥 )ES (𝜈¯ 𝑥 )16 O CC (𝜈 )e
16 O CC (𝜈¯ )e16 O NC (𝜈 ,15 N)e
16 O NC (𝜈¯ ,15 N)e
16 O NC (𝜈 ,15 N)
𝑥
16 O NC (𝜈¯ ,15 N)
𝑥
16 O NC (𝜈 ,15 O)e
16 O NC (𝜈¯ ,15 O)e
16 O NC (𝜈 ,15 O)
𝑥
16 O NC (𝜈¯ ,15 O)𝑥
total

Hüdelpohl
No Osc.
NMO
3048
3052
146
124
53
53
43
47
38
38
12
32
30
31
1
3
3
3
6
4
6
6
0
1
1
1
1
1
2
2
3390
3398

NMO
8207
231
97
79
69
1034
329
89
43
93
156
24
12
25
42
10530

IMO
9970
229
98
80
69
729
633
63
89
119
112
17
24
32
30
12294

Nakazato
No Osc.
3542
173
63
60
52
48
46
4
5
31
31
1
1
9
8
4074

IMO
3049
132
53
46
38
26
33
2
3
4
6
1
1
1
1
3396

Fischer
No Osc.
1884
90
35
31
27
5
15
0
1
5
5
0
0
1
1
2100

NMO
3893
172
66
60
51
180
68
15
8
20
28
4
2
5
8
4580
NMO
1990
87
35
31
26
27
18
2
2
3
4
1
0
1
1
2228

IMO
4693
171
72
60
48
139
116
12
16
23
21
3
4
6
5
5389

Mori
No Osc.
3275
177
60
52
45
8
30
1
3
15
15
0
1
4
4
3690

NMO
3422
148
61
57
45
86
42
8
4
8
14
2
1
2
4
3904

IMO
3745
156
63
56
44
62
71
5
8
10
10
1
2
3
3
4239

IMO
2242
88
37
31
25
21
27
2
2
4
4
1
1
1
1
2487

Tamborra
No Osc.
3830
135
50
28
25
55
97
5
11
16
16
1
3
4
4
4280

NMO
3487
82
45
38
26
90
90
8
10
13
17
2
3
3
5
3919

IMO
2718
99
35
35
30
80
77
7
8
14
19
2
2
4
5
3135

Chapter 4 Detector Response and Pointing Accuracy

79

Table 4.3: Average number of neutrinos of each ﬂavor for each model arrived at SK for each oscillation
assumption. Note that 𝜈 𝑥 represents 𝜈 𝜇 and 𝜈 𝜏 .

𝜈𝑒
𝜈¯𝑒
𝜈𝑥
𝜈¯ 𝑥

WilsonNo Osc.
272
7751
305
294

𝜈𝑒
𝜈¯𝑒
𝜈𝑥
𝜈¯ 𝑥

Hüdelpohl
No Osc.
NMO
159
160
3135
3140
52
50
46
46

NMO
1378
8688
197
267

IMO
1038
10814
231
211

Nakazato
No Osc.
226
3657
100
91

IMO
161
3139
51
45

Fischer
No Osc.
95
1935
37
33

NMO
371
4037
85
87
NMO
117
2045
35
31

IMO
325
4901
89
74

Mori
No Osc.
186
3369
71
64

NMO
244
3530
67
63

IMO
224
3889
69
57

IMO
112
2309
36
30

Tamborra
No Osc.
196
3991
48
45

NMO
182
3635
54
48

IMO
188
2840
53
54

regions as shown in the cross section plot (Fig. 2.14), the detected number of oxygen interactions
depends on the neutrino energy. This will be discussed in Section 4.2.3 in terms of the energy
spectrum at SK.

4.2.2 Average Number of Reconstructed Events in SK
The average number of reconstructed events for each interaction in SK-Gd (with 0.03% Gdconcentration) is given in Table 4.4 for the six models, assuming a supernova at 10 kpc considering
three oscillation scenarios. For each model and each oscillation assumption, the number of eventsis derived by taking the average of 1000 MC samples (simulated by SKSNSim, SKG4, andmccomb_sn) that are reconstructed with SNWATCH (with the 7 MeV threshold), and applied theevent selection criteria used in the pointing accuracy estimation (see Section 2.5.4). Note that in
the realistic supernova simulation described in Section 2.6, the original information generated in
SKSNSim is lost in the mccomb_sn process. Therefore, the only way to estimate which type ofinteraction the reconstructed event was is to compare the time information the reconstructed eventwith the time information of of SKSNSim-generated event. To do this, the condition of less than
0.02 𝜇s time diﬀerence between the SKSNSim-generated event and the reconstructed event closest
to it are used. The numbers listed in Table 4.4 are less than those listed in Table 4.2. In fact, morethan half of ES events are lost during reconstruction and the event selection criteria described in
Section 2.5.4. The low energy ES events are mainly removed by the prompt candidate selection
criteria including the 7MeV cut and FV cut.

Chapter 4 Detector Response and Pointing Accuracy

80

Wilson model has the largest number of total reconstructed events among the six models. The
model with the smallest number of total events is Fischer model, which has the shortest data
period among the ﬁve one-dimensional models (∼ 6 s, see Table 3.1). Tamborra model, the only
three-dimensional model, has a comparable number of total events to Mori model despite the very
short simulation time range of less than 1 s.
The order of the number of IBD events for Wilson, Nakazato, Mori, and Fischer models is
No Osc. < NMO < IMO as shown in Table 4.4. The trend is the opposite in Tamborra model:
No Osc. > NMO > IMO. These characterisitics are the same as those shown in Table 4.2. For
Wilson, Nakazato, and Mori model, this trend is also consistent with the results reported in thepreceding studies (Abe et al. (2016) [53] and Mori et al. (2020) [85]).
The number of ES events from 𝜈e is the largest in NMO in Wilson, Nakazato, and Fischer
models. Regarding Wilson and Nakazato models, the tendency is the same as reported in thepreceding studies (Abe et al. (2016) [53]). For Mori model in Table 4.4, the number of ES events
considering all ﬂavors is consistent with the numbers reported in Mori et al. (2020) [85].
All the models have more oxygen CC events in NMO and IMO cases than in No Osc. case.
This feature originates from the larger cross section of oxygen CC interactions with higher energy
neutrinos, as later seen in Fig. 4.15. The average number of reconstructed oxygen NC events is lessthan 0.5 events (written as 0 events in Table 4.4), indicating they are lost by the prompt candidate
selection criteria and the time diﬀerence condition (less than 0.02 𝜇s between the generated andthe reconstructed closest to it).

4.2.3 Oscillation-Dependent Diﬀerence in SK’s Response
This section reports the diﬀerence in SK’s responses (time evolution, energy spectrum, cos 𝜃 SN
distribution) among No Osc., NMO, and IMO for each model. The reconstructed events in the time
evolution ﬁgures and cos 𝜃 SN distribution in this sub-section satisfy the same criteria as describedin 4.2.2. For energy spectra, the same criteria except for the 7 MeV cut are applied. Throughout
the section, the assumptions of No Osc., NMO, and IMO are displayed in ﬁgures in blue, green,
and red, respectively. It should be kept in mind that Tamborra model has a very short simulation
period of ∼ 0.5 s and the model does not explode within that period.
Time Evolution
Fig. 4.5, Fig. 4.6, and Fig. 4.7 shows the oscillation-dependent diﬀerence in the time evolution
considering all the neutrino interactions for each model until ∼ 20 s, 1.5 s, and 0.12 s, respectively.
The diﬀerent order in the total number of events shown in Table 4.4 roughly appears in theseChapter 4 Detector Response and Pointing Accuracy

81

Table 4.4: Average number of reconstructed events at SK-Gd (with 0.03% Gd concentration) in the 22.5k m3
ﬁducial volume for 1000 simulated supernova bursts at 10 kpc with Wilson, Nakazato, and Mori, Hüdelpohl,
Fischer, and Tamborra models. The event selection criteria described in Section 2.5.4 are applied, including
the 7 MeV energy threshold for selecting prompt candidates. To identify the interaction of the reconstructed
event, the condition of less than 0.02 𝜇s time diﬀerence between the SKSNSim-generated event and theclosest reconstructed event are applied. Note that 𝜈 𝑥 represents 𝜈 𝜇 and 𝜈 𝜏 .
Reconstructed
IBD (𝜈¯e )ES (𝜈e )ES (𝜈¯e )ES (𝜈 𝑥 )ES (𝜈¯ 𝑥 )16 O CC (𝜈 )e
16 O CC (𝜈¯ )e16 O NC (𝜈 ,15 N)e
16 O NC (𝜈¯ ,15 N)e
16 O NC (𝜈 ,15 N)
𝑥
16 O NC (𝜈¯ ,15 N)
𝑥
16 O NC (𝜈 ,15 O)e
16 O NC (𝜈¯ ,15 O)e
16 O NC (𝜈 ,15 O)
𝑥
16 O NC (𝜈¯ ,15 O)𝑥
total
Reconstructed
IBD (𝜈¯e )ES (𝜈e )ES (𝜈¯e )ES (𝜈 𝑥 )ES (𝜈¯ 𝑥 )16 O CC (𝜈 )e
16 O CC (𝜈¯ )e16 O NC (𝜈 ,15 N)e
16 O NC (𝜈¯ ,15 N)e
16 O NC (𝜈 ,15 N)
𝑥
16 O NC (𝜈¯ ,15 N)
𝑥
16 O NC (𝜈 ,15 O)e
16 O NC (𝜈¯ ,15 O)e
16 O NC (𝜈 ,15 O)
𝑥
16 O NC (𝜈¯ ,15 O)𝑥
total

WilsonNo Osc.
4879
69
22
34
28
27
126
0
0
0
0
0
0
0
0
5185

NMO
5364
106
25
28
27
660
208
0
0
0
0
0
0
0
0
6418

Hüdelpohl
No Osc.
NMO
1936
1939
38
39
9
8
12
12
10
10
7
19
19
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2031
2037

IMO
6465
95
30
30
26
465
394
0
0
0
0
0
0
0
0
7505

Nakazato
No Osc.
2221
43
10
18
15
29
28
0
0
0
0
0
0
0
0
2364

IMO
1935
39
8
12
10
16
21
0
0
0
0
0
0
0
0
2041

Fischer
No Osc.
1186
22
5
9
7
3
9
0
0
0
0
0
0
0
0
1241

NMO
2434
57
11
16
14
108
41
0
0
0
0
0
0
0
0
2681
NMO
1260
29
6
8
7
17
11
0
0
0
0
0
0
0
0
1338

IMO
2921
53
13
17
13
83
69
0
0
0
0
0
0
0
0
3169

Mori
No Osc.
2048
44
9
15
12
4
19
0
0
0
0
0
0
0
0
2151

NMO
2144
46
9
14
11
56
27
0
0
0
0
0
0
0
0
2307

IMO
2355
45
10
14
11
40
45
0
0
0
0
0
0
0
0
2520

IMO
1437
26
6
8
7
13
17
0
0
0
0
0
0
0
0
1514

Tamborra
No Osc.
2505
46
12
10
8
35
62
0
0
0
0
0
0
0
0
2678

NMO
2283
33
10
12
9
58
58
0
0
0
0
0
0
0
0
2463

IMO
1786
37
8
12
10
51
49
0
0
0
0
0
0
0
0
1953

Chapter 4 Detector Response and Pointing Accuracy

82

ﬁgures. From Fig. 4.6 (b), it can be seen that Nakazato model has a faster fall in the number ofWilson (total)
No Osc.
NMO
IMO

1500

1000

500

0

0

5

10

15

20

Nakazato (total)

2000

No Osc.
NMO
IMO

1500

1000

500

0

0

5

time [s]2500

Hudelpohl (total)
No Osc.
NMO
IMO

1500

1000

500

0

0

5

10

15

20

Mori (total)

2000

No Osc.
NMO
IMO

1500

1000

500

0

0

5

15

time [s](d) Hüdelpohl model (total)

20

Fischer (total)
No Osc.
NMO
IMO

1500

1000

500

0

0

5

10

15

20

(c) Mori model (total)

2500

2000

10

time [s](b) Nakazato model (total)
events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) Wilson model (total)

2000

10

2500

time [s]15

time [s](e) Fischer (total)

20

events/0.5s (average of 1000 simulations)

2000

2500

events/0.5s (average of 1000 simulations)2500

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

total events in IMO case (red) than in No Osc. and NMO cases.

2500

Tamborra (total)

2000

No Osc.
NMO
IMO

1500

1000

500

0

0

5

10

15

20

time [s](f) Tamborra (total)

Fig. 4.5: Oscillation-dependent diﬀerence in the time evolution of the number of total events until 20 s,covering the whole simulation period.

Whether the quasi-periodic neutrino signal modulation due to SASI seen in Tamborra model(the ﬂuctuation around 0.2 s and 0.5 s in Fig. 3.8) can be detected at SK is of interest. However, inthe ﬁrst 1.5 s time evolution in Tamborra model, Fig. 4.6 (f), such quasi-periodic features cannot
be seen.

Wilson (total)
No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

200
180

Nakazato (total)

160

No Osc.
NMO
IMO

140
120
100
80
60
40
20
0

−0.4 −0.2

00.2

time [s]Hudelpohl (total)

160

No Osc.
NMO
IMO

140
120
100
80
60
40
20
0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

180

0

0.8

1

1.2

1.4

Mori (total)

180

No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0

−0.4 −0.2

00.2

Fischer (total)
No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0

−0.4 −0.20time [s]

0.2

0.4

0.6

0.8

1

1.2

1.4

0.8

1

1.2

1.4

200
180

Tamborra (total)

160

No Osc.
NMO
IMO

140
120
100
80
60
40
20
0

−0.4 −0.20time [s](d) Hüdelpohl model (total)

0.6(c) Mori model (total)

200
180

0.4

time [s](b) Nakazato model (total)

200−0.4 −0.2

0.6

200

time [s](a) Wilson model (total)

00.4

events/25ms (average of 1000 simulations)

180

83
events/25ms (average of 1000 simulations)

200

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](e) Fischer (total)(f) Tamborra (total)

Wilson (total)
No Osc.
NMO
IMO

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

10

Nakazato (total)

9

No Osc.
NMO
IMO

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

time [sec]Hudelpohl (total)

8

No Osc.
NMO
IMO

6
5
4
3
2
1
0.02

0.04

0.06

0.08

0.1

time [sec](d) Hüdelpohl model (total)

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

9

0

0.08

0.1

0.12

9

Mori (total)

8

No Osc.
NMO
IMO

7
6
5
4
3
2
1
0
−0.02

0

0.02

Fischer (total)
No Osc.
NMO
IMO

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.06

0.08

0.1

0.12

(c) Mori model (total)

10
9

0.04

time [sec](b) Nakazato model (total)

10

0
−0.02

0.06

10

time [sec](a) Wilson model (total)

7

0.04

0.08

time [sec](e) Fischer (total)

0.1

0.12

events/1ms (average of 1000 simulations)9

events/1ms (average of 1000 simulations)10

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)Fig. 4.6: Oscillation-dependent diﬀerence in the time evolution of the number of total events until 1.5 s.

10
9Tamborra (total)

8

No Osc.
NMO
IMO

7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](f) Tamborra (total)

Fig. 4.7: Oscillation-dependent diﬀerence in the time evolution of the number of total events until 0.12 s.

Chapter 4 Detector Response and Pointing Accuracy

84

Whereas the time structure of the whole time range (Fig. 4.5) and the ﬁrst 1.5 s (Fig. 4.6) issimilar in the concentration of events within the ﬁrst ∼ 0.5 s and the decay after that, signiﬁcantdiﬀerence can be seen from that of the ﬁrst 0.12 s (Fig. 4.7). The peaks at ∼ 0 s observed in
No Osc. case (blue) for some models in Fig. 4.7 correspond to the neutronization burst.
The time evolution of for each interaction in the whole simulation period, until 1.5 s, until 0.12 s
are shown in Fig. 4.8-4.9, Fig. 4.10-4.11, and Fig. 4.12-4.13, respectively. These ﬁgures tell us
how many events of a speciﬁc interaction channel are observed on average at a certain time bin,which cannot be known from Table 4.4.
From Fig. 4.8 (a)-(f), Fig. 4.10 (a)-(f), and Fig. 4.12 (a)-(f), we can see the time structure of IBD
events. The order of IBD events of No Osc. < NMO < IMO described in Section 4.2.2 is kept inevery time bin for Wilson, Mori, and Fischer model, while it is not seen in the 0-0.5 s time bin for
Nakazato model. The faster fall in the IBD events observed in IMO case (red) than in No Osc. and
NMO cases (Fig. 4.10 (b)) comes from their diﬀerent time structure in Fig. 4.12 (b). The similar
number of IBD events for Hüdelpohl model among oscillation cases shown in Table 4.4 lasts until
the end of the simulation (Fig. 4.14 (d)).
The time structure of ES events for each model is shown in Fig. 4.8 (g)-(l) (until 20 s),
Fig. 4.10 (g)-(l) (until 1.5 s), and Fig. 4.12 (g)-(l) (until 0.12 s). The peaks at ∼ 0 s (especially in No Osc. (blue)) in Fig. 4.10 (g)-(l), and Fig. 4.12 (g)-(l) correspond to the 𝜈𝑒 increaseby neutronization burst described in Section 1.3.2. Detection of the peak of ES events due to theneutronization burst is discussed in the next Section 4.2.4.
The diﬀerence in the time evolution of oxygen CC events is shown in Fig. 4.9 (a)-(f) (until
20 s), Fig. 4.11 (a)-(f) (until 1.5 s), and Fig. 4.12 (a)-(f) (until 0.12 s). Although the number of
events is small, peaks due to the neutronization burst exist in some model at ∼ 0 s. It is clear from
Fig. 4.9 (a) that a larger number of oxygen CC events lasts until the end for Wilson model than forthe other models.

Wilson (IBD)No Osc.
NMO
IMO

1500

1000

500

5

10

15

20

No Osc.
NMO
IMO

1500

1000

500

0

0

5

time [s]2500

Hudelpohl (IBD)No Osc.
NMO
IMO

1500

1000

500

0

0

5

10

15

20

No Osc.
NMO
IMO

60
50
40
30
20
10
10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)Wilson (ES)5No Osc.
NMO
IMO

1500

1000

500

0

0

5

No Osc.
NMO
IMO

60
50
40
30
20
10
10

15

time [s](j) Hüdelpohl model (ES)20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Hudelpohl (ES)

5

0

0

5

20

60
50
40
30
20
10
0

0

5

10

15

20

Tamborra (IBD)2000

No Osc.
NMO
IMO

1500

1000

500

0

0

5

Fischer (ES)No Osc.
NMO
IMO

60
50
40
30
20
10
0

0

5

10

15

20

100
90

Mori (ES)80

No Osc.
NMO
IMO

70
60
50
40
30
20
10
0

0

5

10

15

20

(i) Mori model (ES)

90

70

10

time [s]

100

80

20

(f) Tamborra model (IBD)No Osc.
NMO
IMO

70

15

time [s]Nakazato (ES)

80

10

2500

(h) Nakazato model (ES)

90

0

500

time [s]

100

0

15

90

(g) Wilson model (ES)

70

10

100

time [s]801000(c) Mori model (IBD)(e) Fischer model (IBD)

90

0

1500

time [s]1000No Osc.
NMO
IMO

time [s]Fischer (IBD)

2000(d) Hüdelpohl model (IBD)

70

20

2500

time [s]8015Mori (IBD)

2000(b) Nakazato model (IBD)
events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) Wilson model (IBD)

2000

10

2500

time [s]events/0.5s (average of 1000 simulations)0Nakazato (IBD)

2000

events/0.5s (average of 1000 simulations)

0

2500

15

time [s](k) Fischer model (ES)20

events/0.5s (average of 1000 simulations)

2000

85
events/0.5s (average of 1000 simulations)2500

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

100
90

Tamborra (ES)80

No Osc.
NMO
IMO

70
60
50
40
30
20
10
0

0

5

10

15

20

time [s](l) Tamborra model (ES)Fig. 4.8: Oscillation-dependent diﬀerence in the time evolution of IBD events (top six panels) and ES events(bottom six panels) covering the whole simulation period for each model.

Wilson (16O CC)No Osc.
NMO
IMO

80

60
40

20

0

5

10

15

20

Nakazato (16O CC)

100

No Osc.
NMO
IMO

80

60
40

20

0

0

5

time [s]6016

Hudelpohl ( O CC)

40

No Osc.
NMO
IMO

30

20

10

0

0

5

10

15

20

No Osc.
NMO
IMO

0.6
0.5
0.4
0.3
0.2
0.1
5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)160Fischer ( O CC)

50

No Osc.
NMO
IMO

40

30

20

10

0

0

5

Hudelpohl (16O NC)
No Osc.
NMO
IMO

0.6
0.5
0.4
0.3
0.2
0.1
5

10

15

time [s](j) Hüdelpohl model (oxygen NC)

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

1

0

15

20

30

20

10

0

0

5

Nakazato ( O NC)
No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20

140

120

Tamborra (16O CC)

100

No Osc.
NMO
IMO

80

60
40

20

0

0

5

Fischer (16O NC)
No Osc.
NMO
IMO

0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

10

15

20

1
0.9

Mori (16O NC)

0.8

No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20

(i) Mori model (oxygen NC)

1

0.7

20

time [s]

0.9
0.8

15

(f) Tamborra (oxygen CC)

16

0.8

10

time [s](h) Nakazato model (oxygen NC)

0.90

No Osc.
NMO
IMO

time [s](g) Wilson model (oxygen NC)

0.7

10

1
0.9

time [s]0.840(c) Mori model (oxygen CC)(e) Fischer (oxygen CC)

Wilson ( O NC)

0

Mori (16O CC)

time [s]

1

0.7

50

time [s]16(d) Hüdelpohl model (oxygen CC)

0.8

20

60

time [s]0.915(b) Nakazato model (oxygen CC)
events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) Wilson model (oxygen CC)

50

10

60

time [s]events/0.5s (average of 1000 simulations)0120

events/0.5s (average of 1000 simulations)

100

140

15

time [s](k) Fischer (oxygen NC)

20

events/0.5s (average of 1000 simulations)

120

86
events/0.5s (average of 1000 simulations)

140

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

1
0.9

Tamborra (16O NC)

0.8

No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20

time [s](l) Tamborra (oxygen NC)

Fig. 4.9: Oscillation-dependent diﬀerence in the time evolution of oxygen CC events (top six panels) andoxygen NC events (bottom six panels) covering the whole simulation period for each model.

Wilson (IBD)No Osc.
NMO
IMO

120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0

−0.4 −0.2

00.2

time [s]200180

Hudelpohl (IBD)160

No Osc.
NMO
IMO

140
120
100
80
60
40
20
−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

10
8
6
4
2
0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)Wilson (ES)−0.4 −0.2

160

No Osc.
NMO
IMO

140

14
12
10
8
6
4
2
0.4

0.6

0.8

1

time [s](j) Hüdelpohl model (ES)

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

No Osc.
NMO
IMO

16

0.2

80
60
40
20
0

−0.4 −0.2

0

0.2

100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Nakazato (ES)16

No Osc.
NMO
IMO

12
10
8
6
4
2
−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

14
12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

1.2

1.4

180

Tamborra (IBD)160

No Osc.
NMO
IMO

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.2

1.4

20

Mori (ES)18

No Osc.
NMO
IMO

16
14
12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

(i) Mori model (ES)Fischer (ES)16

1time [s]

20
18

0.8

(f) Tamborra model (IBD)

18

0

0.6

time [s]

20

14

0.4

200

(h) Nakazato model (ES)

Hudelpohl (ES)0100time [s]20−0.4 −0.2120(c) Mori model (IBD)

120(g) Wilson model (ES)0140time [s]Fischer (IBD)time [s]181.4(e) Fischer model (IBD)

12

0

1.2

No Osc.
NMO
IMO

160

time [s]

20

14

1

180

(d) Hüdelpohl model (IBD)

16

0.8

200

time [s]180.6Mori (IBD)

180(b) Nakazato model (IBD)
events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) Wilson model (IBD)

0

0.4

200

time [s]events/25ms (average of 1000 simulations)

140

Nakazato (IBD)180

events/25ms (average of 1000 simulations)

160

200

0.8

1

time [s](k) Fischer model (ES)

1.2

1.4

events/25ms (average of 1000 simulations)

180

87
events/25ms (average of 1000 simulations)

200

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

20

Tamborra (ES)18

No Osc.
NMO
IMO

16
14
12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](l) Tamborra model (ES)Fig. 4.10: Oscillation-dependent diﬀerence in the time evolution of IBD events (top six panels) and ES events(bottom six panels) until 1.5 s for each model.

Wilson (16O CC)No Osc.
NMO
IMO

12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

20

15

10

5

0

−0.4 −0.2

00.2

time [s]20

Hudelpohl (16O CC)No Osc.
NMO
IMO

16
14
12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

0.5
0.4
0.3
0.2
0.1
−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](j) Hüdelpohl model (oxygen NC)

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Hudelpohl (16O NC)

0

12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

16
14
12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Fischer (16O NC)
No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

1

1.2

1.4

20

Tamborra (16O CC)

18

No Osc.
NMO
IMO

16
14
12
10
8
6
4
2
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.2

1.4

1

Mori (16O NC)

0.9

No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

time [s]

1
0.9

0.8

(f) Tamborra (oxygen CC)

Nakazato (16O NC)

0.8

0.6

time [s]

1
0.9

0.4

(c) Mori model (oxygen CC)(h) Nakazato model (oxygen NC)

1−0.4 −0.2

14time [s](g) Wilson model (oxygen NC)0

No Osc.
NMO
IMO

16

time [s]No Osc.
NMO
IMO

time [s]0.91.4(e) Fischer (oxygen CC)
events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)Wilson (16O NC)

0.6

0

1.2

Mori (16O CC)

18

time [s]

1

0.7

1

Fischer (16O CC)

18(d) Hüdelpohl model (oxygen CC)

0.8

0.8

20

time [s]0.90.6(b) Nakazato model (oxygen CC)
events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) Wilson model (oxygen CC)

18

0.4

20

time [s]events/25ms (average of 1000 simulations)

14

Nakazato (16O CC)

events/25ms (average of 1000 simulations)

16

25

0.8

1

time [s](k) Fischer (oxygen NC)

1.2

1.4

(i) Mori model (oxygen NC)
events/25ms (average of 1000 simulations)

18

88
events/25ms (average of 1000 simulations)

20

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

1

Tamborra (16O NC)

0.9

No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](l) Tamborra (oxygen NC)

Fig. 4.11: Oscillation-dependent diﬀerence in the time evolution of oxygen CC events (top six panels) andoxygen NC events (bottom six panels) until 1.5 s for each model.

Wilson (IBD)No Osc.
NMO
IMO

6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

No Osc.
NMO
IMO

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

time [sec]10

Hudelpohl (IBD)No Osc.
NMO
IMO

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

1.2
1
0.8
0.6
0.4
0.2
0.02

0.04

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

No Osc.
NMO
IMO

0

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

No Osc.
NMO
IMO

1
0.8
0.6
0.4
0.2
0.02

0.04

0.06

0.08

time [sec](j) Hüdelpohl model (ES)

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Hudelpohl (ES)

0

4
3
2
1
0
−0.02

0

0.02

0.06

0.08

0.1

0.12

Nakazato (ES)1.6

No Osc.
NMO
IMO

1
0.8
0.6
0.4
0.2
0

0.02

0.04

0.06

0.08

0.1

0.12

No Osc.
NMO
IMO

1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.12

Tamborra (IBD)9No Osc.
NMO
IMO

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.1

0.12

2

Mori (ES)1.8

No Osc.
NMO
IMO

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

(i) Mori model (ES)Fischer (ES)

1.6

0.1

time [sec]

2
1.8

0.08

(f) Tamborra model (IBD)

1.2

0
−0.02

0.06

time [sec]

2

1.4

0.04

10

(h) Nakazato model (ES)

1.2

0
−0.02

5

time [sec]

2

1.4

0.04

1.8

(g) Wilson model (ES)1.66(c) Mori model (IBD)No Osc.
NMO
IMO

time [sec]1.8

7time [sec](e) Fischer model (IBD)

Wilson (ES)

0
−0.02

0.12

No Osc.
NMO
IMO

8time [sec]

2

1.4

0.1

Fischer (IBD)9(d) Hüdelpohl model (IBD)

1.6

0.08

10

time [sec]

1.8

0.06

Mori (IBD)

9(b) Nakazato model (IBD)
events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)(a) Wilson model (IBD)

9

0.04

10

time [sec]events/1ms (average of 1000 simulations)

7

Nakazato (IBD)

9events/1ms (average of 1000 simulations)

8

10

0.08

time [sec](k) Fischer model (ES)

0.1

0.12

events/1ms (average of 1000 simulations)

989
events/1ms (average of 1000 simulations)10

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

2

Tamborra (ES)1.8

No Osc.
NMO
IMO

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](l) Tamborra model (ES)Fig. 4.12: Oscillation-dependent diﬀerence in the time evolution of IBD events (top six panels) and ES events(bottom six panels) until 0.12 s for each model.

Wilson (16O CC)No Osc.
NMO
IMO

1.2
1
0.8
0.6
0.4
0.2
0

0.02

0.04

0.06

0.08

0.1

0.12

No Osc.
NMO
IMO

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

time [sec]2

Hudelpohl (16O CC)No Osc.
NMO
IMO

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

No Osc.
NMO
IMO

0.5
0.4
0.3
0.2
0.1
0.02

0.04

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)Wilson (16O NC)

0

1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

No Osc.
NMO
IMO

0.5
0.4
0.3
0.2
0.1
0

0.02

0.04

0.06

0.08

0.1

time [sec](j) Hüdelpohl model (oxygen NC)

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Hudelpohl (16O NC)

0.6

0
−0.02

0.04

0.06

0.08

0.1

0.12

1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

Nakazato (16O NC)
No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.1

0.12

2

Tamborra (16O CC)

1.8

No Osc.
NMO
IMO

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.1

0.12

1

Mori (16O NC)

0.9

No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.08

(i) Mori model (oxygen NC)

Fischer (16O NC)

0.8

0.08

time [sec]

1
0.9

0.06

(f) Tamborra (oxygen CC)

1
0.9

0.04

time [sec](h) Nakazato model (oxygen NC)

1

0.7

1.2

time [sec](g) Wilson model (oxygen NC)

0.8

1.4

(c) Mori model (oxygen CC)

No Osc.
NMO
IMO

time [sec]0.9

No Osc.
NMO
IMO

1.6

time [sec](e) Fischer (oxygen CC)

0.6

0
−0.02

0.12

Mori (16O CC)

time [sec]

1

0.7

0.1

Fischer (16O CC)

1.6(d) Hüdelpohl model (oxygen CC)

0.8

0.08

2
1.8

time [sec]

0.9

0.06

(b) Nakazato model (oxygen CC)
events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)(a) Wilson model (oxygen CC)

1.8

0.04

2
1.8

time [sec]events/1ms (average of 1000 simulations)

0
−0.02

Nakazato (16O CC)

events/1ms (average of 1000 simulations)

1.4

2
1.8

0.08

time [sec](k) Fischer (oxygen NC)

0.1

0.12

events/1ms (average of 1000 simulations)

1.6

90
events/1ms (average of 1000 simulations)2
1.8

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

1

Tamborra (16O NC)

0.9

No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](l) Tamborra (oxygen NC)

Fig. 4.13: Oscillation-dependent diﬀerence in the time evolution of oxygen CC events (top six panels) andoxygen NC events (bottom six panels) until 0.12 s for each model.

Chapter 4 Detector Response and Pointing Accuracy

91

Energy Spectrum
The variation of the energy spectrum of IBD and ES for each model is shown in Fig. 4.14.
Fig. 4.15 shows the same as Fig. 4.14 but for oxygen CC and NC interactions. By the comparisonof Fig. 4.14 (a)-(f), It can be seen that for Wilson, Nakazato, Mori, and Fischer models, theenergy distribution of IBD events in IMO is characterized by higher energy components than in
No Osc. and NMO. This feature is most remarkable in Wilson model. Regarding the ES energy
distribution shown in Fig. 4.14 (g)-(l), more ES events with energies around 7 MeV are found in
No Osc. than in NMO and IMO. Except for Tamborra model, higher energy components are foundin the assumption with neutrino oscillation than without oscillation. Hüdelpohl model’s energy
spectra of the four interactions shown in Fig. 4.14 (d), (j), Fig. 4.15 (d), and (j) reveal that there islittle diﬀerence among oscillation assumptions in this model other than oxygen CC events, also as
indicated by Table 4.4. It is clear from Fig. 4.15 (a)-(f) that the ﬁve one-dimensional models have
similar characteristics that more yield of oxygen CC events with neutrino oscillation than without
neutrino oscillation and the energy distribution is similar in NMO and IMO.

Wilson (IBD)No Osc.
NMO
IMO

120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

Nakazato (IBD)No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0
0

10

20

30

energy [MeV]200

Hudelpohl (IBD)No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

180

No Osc.
NMO
IMO

10
8
6
4
2
20

30

40

50

60

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)Wilson (ES)

10

140

No Osc.
NMO
IMO

10
8
6
4
2
20

30

40

50

60

70

80

energy [MeV](j) Hüdelpohl model (ES)

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Hudelpohl (ES)

10

100
80
60
40
20
0
0

10

20

30

100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

No Osc.
NMO
IMO

14
12
10
8
6
4
2
0
0

10

20

30

40

50

60

70

80

90

100

No Osc.
NMO
IMO

14
12
10
8
6
4
2
0
0

10

20

30

40

50

60

80

90

100

80

90

100

90

100

90

100

200
180

Tamborra (IBD)No Osc.
NMO
IMO

160
140
120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

20
18

Mori (ES)No Osc.
NMO
IMO

16
14
12
10
8
6
4
2
0
0

10

20

30

40

50

60

70

80

(i) Mori model (ES)Fischer (ES)1670energy [MeV]

20
18

60

(f) Tamborra model (IBD)

Nakazato (ES)1650

energy [MeV]

20
18

40

(c) Mori model (IBD)(h) Nakazato model (ES)

12

0
0

120

energy [MeV]20

14No Osc.
NMO
IMO

140

energy [MeV]120(g) Wilson model (ES)

16

100

No Osc.
NMO
IMO

energy [MeV]1890(e) Fischer model (IBD)

12

0
0

80

Mori (IBD)

160

energy [MeV]

20

14

70

Fischer (IBD)

160(d) Hüdelpohl model (IBD)

16

60

200

energy [MeV]

18

50

180

(b) Nakazato model (IBD)
events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)(a) Wilson model (IBD)

180

40

200

energy [MeV]

events/1MeV (average of 1000 simulations)

140

180

events/1MeV (average of 1000 simulations)

160

200

70

energy [MeV](k) Fischer model (ES)

80

90

100

events/1MeV (average of 1000 simulations)

180

92
events/1MeV (average of 1000 simulations)

200

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

20
18

Tamborra (ES)No Osc.
NMO
IMO

16
14
12
10
8
6
4
2
0
0

10

20

30

40

50

60

70

80

energy [MeV](l) Tamborra model (ES)Fig. 4.14: Oscillation-dependent diﬀerence in the energy spectrum of IBD events (top six panels) and ES
events (bottom six panels) for each model. The energy region below the 7 MeV threshold for selecting prompt
candidates is shaded in light blue.

16

35

Wilson ( O CC)30

No Osc.
NMO
IMO

25
20
15
10
5

30

40

50

60

70

80

90

100

Nakazato ( O CC)No Osc.
NMO
IMO

4
3.5
3
2.5
2
1.5
1
0.5
0
0

10

20

30

energy [MeV]5
16

Hudelpohl ( O CC)No Osc.
NMO
IMO

4
3.5
3
2.5
2
1.5
1
0.5
0
0

10

20

30

40

50

60

70

80

90

100

No Osc.
NMO
IMO

0.6
0.5
0.4
0.3
0.2
0.1
40

50

60

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)Wilson (16O NC)

0.8

30

Hudelpohl ( O NC)
No Osc.
NMO
IMO

0.5
0.4
0.3
0.2
0.1
10

20

30

40

50

60

70

80

90

energy [MeV](j) Hüdelpohl model (oxygen NC)

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

16

0.6

0
0

3
2.5
2
1.5
1
0.5
0
0

10

20

30

3
2.5
2
1.5
1
0.5
0
0

10

20

30

40

50

60

70

80

90

100

No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

70

80

90

100

Fischer ( O NC)
No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

90

100

5
4.5

Tamborra (16O CC)No Osc.
NMO
IMO

4
3.5
3
2.5
2
1.5
1
0.5
0
0

10

20

30

40

50

60

70

80

90

100

90

100

1
0.9

Mori (16O NC)

0.8

No Osc.
NMO
IMO

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

70

80

(i) Mori model (oxygen NC)

16

0.8

80

energy [MeV]

1
0.9

70

(f) Tamborra (oxygen CC)

Nakazato (16O NC)

0.8

60

energy [MeV]

1
0.9

50

(c) Mori model (oxygen CC)

No Osc.
NMO
IMO

3.5

40

energy [MeV](h) Nakazato model (oxygen NC)

10.7

No Osc.
NMO
IMO

3.5

energy [MeV](g) Wilson model (oxygen NC)

0.8

100

Fischer ( O CC)

4energy [MeV]

0.9

90

(e) Fischer (oxygen CC)

1

20

80

Mori (16O CC)

4energy [MeV]

0.9

10

70

16

(d) Hüdelpohl model (oxygen CC)

0
0

60

5
4.5

energy [MeV]

0.7

50

(b) Nakazato model (oxygen CC)
events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)(a) Wilson model (oxygen CC)

4.5

40

5
4.5

energy [MeV]

events/1MeV (average of 1000 simulations)

20

16

events/1MeV (average of 1000 simulations)

10

5
4.5

70

80

energy [MeV](k) Fischer (oxygen NC)

90

100

events/1MeV (average of 1000 simulations)0093
events/1MeV (average of 1000 simulations)40

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

1
0.9

Tamborra (16O NC)
No Osc.
NMO
IMO

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

70

80

90

100

energy [MeV](l) Tamborra (oxygen NC)

Fig. 4.15: Oscillation-dependent diﬀerence in the energy spectrum of oxygen CC events (top six panels) andoxygen NC events (bottom six panels) for each model. The energy region below the 7 MeV threshold forselecting prompt candidates is shaded in light blue.

Chapter 4 Detector Response and Pointing Accuracy

94

Angular Distribution
Fig. 4.16 shows the variation of cos 𝜃 SN distribution for IBD and ES. Fig. 4.17 is the sameas Fig. 4.16 for oxygen CC and NC interactions. The shape of cos 𝜃 SN distribution depends on
the interaction type. Since the direction of positrons emitted in IBD interactions is isotropic,cos 𝜃 SN distribution is almost ﬂat as seen in Fig. 4.16 (a)-(f), though some of them are slightly
inclined to forward, i.e., cos 𝜃 SN ∼ 1. Wilson model has the steepest slope among the six models(Fig. 4.16 (a)), which can be interpreted from its higher mean energy than the other models. As
Fig. 4.14 (a) shows, Wilson model has more IBD events with higher energy than the other models,
especially in IMO, which indicates more positrons are likely to be emitted forward, resulting
in the forward-inclined distribution of cos 𝜃 SN . The cos 𝜃 SN distribution of ES events shown in
Fig. 4.16 (g)-(l) has a peak at cos 𝜃 SN ∼ 1 as described in Section 2.5.5. Regarding oxygen CC
events, cos 𝜃 SN distribution has a backward bias for every model. cos 𝜃 SN distribution of oxygen
NC events should be ﬂat for every model, however, the numbers of events here is too small to beobserved. These distributions reﬂect the angular dependence assumed in SKSNSim (mentioned
in Section 2.6.1).

180
160
140
120
100

20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

160

Hudelpohl (IBD)No Osc.
NMO
IMO

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

180

100

120
100

60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

Wilson (ES)No Osc.
NMO
IMO

20

10

0

0.2

cosθ SN

0.4

0.6

0.8

1

Hudelpohl (ES)No Osc.
NMO
IMO

20

10

0

0.2

cosθ SN

0.4

0.8

1

140
120
100

160
140
120
100

Fischer (IBD)No Osc.
NMO
IMO

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1

50

Nakazato (ES)30

No Osc.
NMO
IMO

20

10

0
−1 −0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

0.6(j) Hüdelpohl model (ES)

0.8

1

50

Fischer (ES)30

No Osc.
NMO
IMO

20

10

0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN(k) Fischer (ES)00.2cosθ SN

0.4

0.6

0.8

1

0.6

0.8

1

0.6

0.8

1

0.6

0.8

1

200
180
160
140
120
100

Tamborra (IBD)No Osc.
NMO
IMO

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

60

50

Mori (ES)
40

30

0.4

0.6

No Osc.
NMO
IMO

20

10

0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4(i) Mori model (ES)60

40

No Osc.
NMO
IMO(f) Tamborra (IBD)

60

40

Mori (IBD)(c) Mori model (IBD)180cosθ SN

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)500−1 −0.8 −0.6 −0.4 −0.2

0.6

160

(h) Nakazato model (ES)

60

30

0.4

200

(g) Wilson model (ES)

40

0.2

cosθ SN

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)500−1 −0.8 −0.6 −0.4 −0.20180(e) Fischer (IBD)60

30

No Osc.
NMO
IMO

80

(d) Hüdelpohl model (IBD)

40

Nakazato (IBD)

200(b) Nakazato model (IBD)

200

120

140

cosθ SN(a) Wilson model (IBD)

140

160

events/bin (average of 1000 simulations)40

No Osc.
NMO
IMO

180

events/bin (average of 1000 simulations)60

Wilson (IBD)

200

0.8

1

events/bin (average of 1000 simulations)

80

95
events/bin (average of 1000 simulations)

200

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

60

50

Tamborra (ES)4030

No Osc.
NMO
IMO

20

10

0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4(l) Tamborra (ES)Fig. 4.16: Oscillation-dependent diﬀerence in the cos 𝜃 SN distribution of IBD events (top six panels) and ES
events (bottom six panels) for each model.

No Osc.
NMO
IMO

30
25
20
15
10
5
0

0.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)(a) Wilson model (oxygen CC)

9
8

6
5

Hudelpohl (16O CC)No Osc.
NMO
IMO

4
3
2
1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

NMO
7

1

5
4
3
2
1
0
−1 −0.8 −0.6 −0.4 −0.2

Wilson (16O NC)
No Osc.
NMO
IMO

0.4
0.3
0.2
0.1
0

0.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)(g) Wilson model (oxygen NC)
1

0.8

0.6
0.5

Hudelpohl (16O NC)
No Osc.
NMO
IMO

0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

(j) Hüdelpohl model (oxygen NC)

0.4

0.6

0.8

1

9
8

6
5

Fischer (16O CC)No Osc.
NMO
IMO

4
3
2
1
0
−1 −0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1

0.8

0.6
0.5

Nakazato (16O NC)
No Osc.
NMO
IMO

0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

1

1

0.8

0.6
0.5

Fischer (16O NC)
No Osc.
NMO
IMO

0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6(k) Fischer (oxygen NC)

7
6
5Mori (16O CC)No Osc.
NMO
IMO

4
3
2
1
0
−1 −0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1

0.8

1

0.8

1

0.8

1

10
9
8
7
6
5

Tamborra (16O CC)No Osc.
NMO
IMO

4
3
2
1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1
0.9
0.8
0.7
0.6
0.5

Mori (16O NC)
No Osc.
NMO
IMO

0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6(i) Mori model (oxygen NC)

0.9

0.7

8

(f) Tamborra (oxygen CC)

0.9

0.7

9

(c) Mori model (oxygen CC)

10

7

10

cosθ SN(h) Nakazato model (oxygen NC)

0.9

0.7

events/bin (average of 1000 simulations)0.8

0−1 −0.8 −0.6 −0.4 −0.2

0.2cosθ SN

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

1

0.5

0

cosθ SN(e) Fischer (oxygen CC)

0.9

0.6

IMO

6

(d) Hüdelpohl model (oxygen CC)

0.7

No Osc.

8(b) Nakazato model (oxygen CC)

10

7

Nakazato (16O CC)

events/bin (average of 1000 simulations)0−1 −0.8 −0.6 −0.4 −0.2

9events/bin (average of 1000 simulations)

35

10

1

events/bin (average of 1000 simulations)40

96
events/bin (average of 1000 simulations)Wilson (16O CC)

45

events/bin (average of 1000 simulations)

50

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

1
0.9
0.8
0.7
0.6
0.5

Tamborra (16O NC)
No Osc.
NMO
IMO

0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6(l) Tamborra (oxygen NC)

Fig. 4.17: Oscillation-dependent diﬀerence in the cos 𝜃 SN distribution of oxygen CC events (top six panels)
and oxygen NC events (bottom six panels) for each model.

Chapter 4 Detector Response and Pointing Accuracy

97

4.2.4 Detection of Neutronization Burst
Neutronization burst is a rapid increase in 𝜈𝑒 emission within ∼ 0.1 s after the bounce described in
Section 1.3.2. As can be seen from the early stage of the time evolution of luminosity (Fig. 3.1 (a)),
the time at which the neutronization bursts occur and their amplitudes vary in models. It is therefore
worthwhile to investigate whether SK-Gd can detect it. Fig. 4.18 shows the model-dependent
diﬀerence in the time evolution of the average number of IBD events (dashed lines) and ES events(solid lines) for 1000 simulations from -0.02 s to 0.12 s for each oscillation assumption. Note that
ES of 𝜈𝑒 , 𝜈¯𝑒 , 𝜈 𝑥 , and 𝜈¯ 𝑥 are the ES events here. The plotted events satisfy the selection criteria
described in Section 4.2.2.
Without oscillation, the time structure of 𝜈𝑒 luminosity (Fig. 3.1 (a)) is reﬂected into that of ES
events (Fig. 4.18 (a)), indicating that the primary contribution to the ES peaks is from 𝜈𝑒 -involved
ES events. In each model, the peak’s excess over the ﬂat component can be considered as theES events of 𝜈𝑒 from the neutronization burst. Mori (blue) and Hüdelpohl (orange) model havestrong ES peaks at ∼ 0.005 s after the bounce. Wilson model (red) has a sharp peak of ES eventsat ∼ 0.04 s, whereas Nakazato model (black) has a smeared peak at ∼ 0.035 s. Though the dataof Fischer model (purple) and Tamborra model (green) used in this thesis do not seem to cover
the whole time range of neutronization burst (seen from Fig. 3.1), the ES peak is seen for thesemodels in the No Osc. case. An excess of ES events (solid) before the rise of IBD events (dashed)exists in every model.

events/1ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

98

2
1.8
1.6
1.4

No Osc.

1.2

IBD (dashed)
ES (solid)

1

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec]events/1ms (average of 1000 simulations)(a) No oscillation
2
1.8
1.6
1.4

NMO

1.2

IBD (dashed)
ES (solid)

1

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec]events/1ms (average of 1000 simulations)(b) NMO
2
1.8
1.6
1.4

IMO

1.2

IBD (dashed)
ES (solid)

1

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](c) IMO

Fig. 4.18: The model-dependent diﬀerence of the time evolution of IBD events (dashed) and ES events (solid)
from -0.02 s to 0.12 s (core bounce occur at 0 s) for (a) no oscillation, (b) NMO, and (c) IMO.

Chapter 4 Detector Response and Pointing Accuracy

99

With neutrino oscillation in NMO (Fig. 4.18 (b)), the ES peaks seen in the No Osc. case disappear
in most of the models; only Wilson and Mori models have weaker ES peaks than in No Osc.,
although they do not exceed the number of IBD events. These decreases compared to No Osc. casecan be interpreted from the neutrino oscillation formulae described in Section 2.6.1. To take
Mori model (blue) for example, the excess of ES events over the ﬂat component in No Osc. case𝑔𝑒𝑛corresponds to 𝑁 𝜈𝑒 in Eq. (2.25)-Eq. (2.26) *1. It is estimated as 10.9±0.10 events by subtracting
the ﬂat component (82.7 events per 1 s, obtained by the integral from 0.04 s to 0.12 s) from theintegral of peak component (13.51 events in total, obtained from the integral of −0.005 s to 0.026 s)
in Fig. 4.18 (a). In the same way, the excess of ES events over the ﬂat component in NMO casecorresponds to 𝑁 𝜈𝑠𝑢𝑟in Eq. (2.25)-Eq. (2.26), estimated as 1.32±0.04 events by subtracting the ﬂat
𝑒component (93.8 events per 1 s, obtained by the integral from 0.04 s to 0.12 s) from the integralof peak component (4.31 events in total, obtained from the integral of −0.002 s to 0.017 s) in
Fig. 4.18 (b). In other words, neutrino oscillation in NMO reduces the number of generated 𝜈𝑒from 10.9 events to 1.32 events. We can also estimate how the number of 𝜈 𝑥 has changed byneutrino oscillation: by substituting them into Eq. (2.25)-Eq. (2.26), the number of generated 𝜈 𝑥
𝑔𝑒𝑛and the number of 𝜈 𝑥 at the stellar surface are obtained as 𝑁 𝜈𝑥 = 1.32 and 𝑁 𝜈𝑠𝑢𝑟= 12.2.
𝑥With neutrino oscillation in IMO (Fig. 4.18 (c)), the ES peaks are stronger than those in NMO
case, but it is weaker than those in No Osc. case. This can be also understood from the neutrino
oscillation formulae Eq. (2.29)-Eq. (2.30) in the same way. To take Mori model for example again,
the excesses of ES events over the ﬂat component in IMO corresponds to 𝑁 𝜈𝑠𝑢𝑟in Eq. (2.29). It𝑒
is estimated as 4.31±0.07 events by subtracting the ﬂat component (90.6 events per 1 s, obtainedby the integral from 0.04 s to 0.12 s) from the integral of peak component (7.12 events in total.
obtained from the integral of −0.004 s to 0.027 s) in Fig. 4.18 (c). The change in the number of 𝜈 𝑥
𝑔𝑒𝑛

is derived by the substitution of 𝑁 𝜈𝑒 = 10.9, 𝑁 𝜈𝑠𝑢𝑟
= 4.31 and sin2 𝜃 12 = 0.307, cos2 𝜃 12 = 0.693
𝑒𝑔𝑒𝑛= 9.37 are obtained).
used in SKSNSim to Eq. (2.29)-Eq. (2.30) (𝑁 𝜈𝑥 = 1.39, 𝑁 𝜈𝑠𝑢𝑟𝑥

After all, it is diﬃcult to discriminate the neutrino mass ordering from the detection of ES eventsat the neutronization burst with SK-Gd due to small statistics. Hyper-Kamiokande detector may
capable of discriminating the mass ordering from the neutronization burst detection.

4.2.5 Diﬀerence in Models in NMO caseIn this section, the model dependence of SK’s responses (time evolution, energy spectrum,cos 𝜃 SN distribution) focusing on the NMO assumption is reported. (The corresponding ﬁgures*1 Since Fig. 4.18 shows the number of events after the event reduction described in Section 2.5.4, the actual number
𝑔𝑒𝑛of 𝑁𝜈𝑒 is expected to be more than those in this estimation.

Chapter 4 Detector Response and Pointing Accuracy

100

given in this section in the No Osc. and IMO cases are presented in Appendix A.) The reconstructed
events in the time evolution ﬁgures and cos 𝜃 SN distribution in this sub-section satisfy the prompt
candidate selection criteria described in Section 4.2.2. Throughout the section, the color of a modelin the ﬁgures showing model variation is expressed in the same manner as Fig. 3.1; Wilson modelin red, Nakazato model in black, Mori model in blue, Hüdelpohl model in orange, Fischer modelin purple, and Tamborra model in green. In the ﬁgures showing the variation in the interaction
channels, the colors in the same manner as Fig. 2.14 are used; IBD in red, ES in green, oxygen
CC interactions in blue, oxygen NC interactions in light blue, and total interactions in gray. We
should again keep in mind that Tamborra model does not explode within its very short simulation
period of ∼ 0.5 s.
Time Evolution
Fig. 4.19 shows the diﬀerence in the time evolution of the number of events until 20 s amonginteractions for each model. Fig. 4.20 shows the same but for each interaction among models.
Fig. 4.21 shows the diﬀerence in the time evolution of the number of event until 1.5 s amonginteractions for each model. Fig. 4.22 shows the same but for each interaction among models.
From Fig. 4.21, we can ﬁnd the signiﬁcant diﬀerence in the time structure of ES events (green)and oxygen CC events (blue); In Mori model (Fig. 4.21 (a)), the ES events excess over oxygen CC
events is observed at 0 s, which corresponds to the neutronization burst mentioned in Section 4.2.4(see Fig. 4.18 (b)). The ES excess over oxygen CC is seen in all the models other than Nakazato
model (seen in Fig. 4.21 (b)). In Nakazato model, characterized by the large number of oxygen
CC events within the ﬁrst 0.25 s as shown in Fig. 4.22, the yield of oxygen CC events exceeds thenumber of ES events. The time structure of Wilson model regarding oxygen CC is characterized
by the long-lasting oxygen CC events excess over the ES events. These excesses of oxygen CC
events over ES events are caused by larger cross section of oxygen CC interaction in higher energy
regions (shown in Fig. 2.14). Tamborra model has a similar characteristic to this, however, it isdiﬀerent from the other ﬁve models in the feature of an increasing number of events after the ﬁrst
neutrino emission peak; the number of events in the other models attenuates after the ﬁrst neutrino
emission peak. Fig. 4.22 shows the diﬀerence of the time evolution until 1.5 s among models foreach interaction.
Fig. 4.23 shows the time evolution of the number of events until 0.12 s among interactions foreach model. Fig. 4.24 shows the time evolution of the number of events until 0.12 s among models
for each interaction.

2000
1800

Wilson (NMO)

1600

total
IBD
ES
16
O CC
16
O NC

1400
1200
1000
800
600
400
200
0

0

5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

101

1400

Nakazato (NMO)
1200

total
IBD
ES
16
O CC
16
O NC

1000
800
600
400
200
0

0

5

time [s]1000Mori (NMO)

800

total
IBD
ES
16
O CC
16
O NC

700
600
500
400
300
200
100
0

0

5

10

15

20

900

Hudelpohl (NMO)

800

total
IBD
ES
16
O CC
16
O NC

700
600
500
400
300
200
100
0

0

5

total
IBD
ES
16
O CC
16
O NC

300

200

100

5

10

time [s](e) Fischer model

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)Fischer (NMO)

0

15

20

(d) Hüdelpohl model

600

0

10

time [s](c) Mori model

400

20

1000

time [s]50015(b) Nakazato model
events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) Wilson model

900

10

time [s]2500

Tamborra (NMO)
2000

total
IBD
ES
16
O CC
16
O NC

1500

1000

500

0

0

5

10

15

20

time [s](f) Tamborra modelFig. 4.19: Diﬀerence in the time evolution until 20 s among interactions for each model.

2500

IBD (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

2000

1500

1000

500

0

0

5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

102

100
90

ES (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

80
70
60
50
40
30
20
10
0

0

5

time [s]14016

O CC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

120
100
80
60
40
20

0

5

15

20

(b) ES

10

time [s](c) Oxygen CC interaction

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) IBD

0

10

time [s]

1
0.9

16

O NC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20

time [s](d) OxygenNC interaction

Fig. 4.20: Diﬀerence in the time evolution until 20 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

200
180

Wilson (NMO)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

103

140

Nakazato (NMO)
120

total
IBD
ES
16
O CC
16
O NC

100
80
60
40
20
0

−0.4 −0.2

00.2

time [s]100Mori (NMO)

80

total
IBD
ES
16
O CC
16
O NC

70
60
50
40
30
20
10
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

90

30

20

10

0.2

0.4

0.6

0.8

time [s](e) Fischer model

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

total
IBD
ES
16
O CC
16
O NC

0

1.4

total
IBD
ES
16
O CC
16
O NC

70
60
50
40
30
20
10
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(d) Hüdelpohl model

Fischer (NMO)−0.4 −0.2

1.2

time [s]6001Hudelpohl (NMO)

80(c) Mori model

40

0.8

100

time [s]500.6(b) Nakazato model
events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) Wilson model

90

0.4

time [s]200180

Tamborra (NMO)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](f) Tamborra modelFig. 4.21: Diﬀerence in the time evolution until 1.5 s among interactions for each model.

140

IBD (NMO)
120

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

104

30

ES (NMO)

25

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

5

0

−0.4 −0.2

00.2

time [s]30
16

O CC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

5

0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.2

1.4

(b) ES

0.6

0.8

time [s](c) Oxygen CC interaction

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) IBD25

0.4

time [s]

1
0.9

16

O NC (NMO)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

time [s](d) OxygenNC interaction

Fig. 4.22: Diﬀerence in the time evolution until 1.5 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

5

Wilson (NMO)

4.5

total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

105

5
4.5

Nakazato (NMO)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

time [sec]5Mori (NMO)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

4.5

2.5
2
1.5
1
0.5
0

0.02

0.04

0.06

time [sec](e) Fischer model

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

total
IBD
ES
16
O CC
16
O NC

0
−0.02

0.1

0.12

0.1

0.12

total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

(d) Hüdelpohl model

Fischer (NMO)

3

0.12

time [sec]

5

3.5

0.1

Hudelpohl (NMO)(c) Mori model

4

0.08

5

time [sec]

4.5

0.06

(b) Nakazato model
events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)(a) Wilson model

4.5

0.04

time [sec]5
4.5

Tamborra (NMO)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

time [sec](f) Tamborra modelFig. 4.23: Diﬀerence in the time evolution until 1.5 s among interactions for each model.

109IBD (NMO)

8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

106
1

0.9

ES (NMO)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

time [sec]

1
16

0.8
0.7
0.6
0.5

O CC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.1

0.12

(b) ES

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)(a) IBD

0.9

0.04

time [sec]

1
0.9

16

O NC (NMO)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

time [sec](c) Oxygen CC interaction

0.04

0.06

0.08

time [sec](d) OxygenNC interaction

Fig. 4.24: Diﬀerence in the time evolution until 1.5 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

Energy Spectrum
Fig. 4.25 shows the energy spectra among interactions for each model. It is obviously seen thatthe energy contribution from IBD events is dominant for all models. Fig. 4.26 shows the diﬀerencein the energy spectra among models for each interaction. It is clear that Wilson (red) and Tamborra(green) model have higher mean energy of IBD events (Fig. 4.26 (a)), indicating the mean energyof 𝜈¯𝑒 is higher in these models, which can be seen in Fig. 3.2 (e).

250

Wilson (NMO)
total
IBD
ES
16
O CC
16
O NC

200

150

100

50

0
0

10

20

30

40

50

60

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

107

140

Nakazato (NMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
0

10

140

Mori (NMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

80
60
40
20
0
0

10

20

30

40

50

60

energy [MeV](e) Fischer model

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

total
IBD
ES
16
O CC
16
O NC

100

40

50

60

70

80

90

100

Hudelpohl (NMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

energy [MeV](d) Hüdelpohl model

Fischer (NMO)

120

30

140

energy [MeV](c) Mori model

140

20

energy [MeV](b) Nakazato model
events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)energy [MeV](a) Wilson model

140

Tamborra (NMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

energy [MeV](f) Tamborra modelFig. 4.25: Diﬀerence in the energy spectra among interactions for each model. The energy region below the7 MeV threshold for selecting prompt candidates is shaded in light blue.

180

IBD (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

160
140
120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

ES (NMO)

35

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
0

10

20

30

40

50

60

(a) IBD(b) ES16

O CC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5

20

40

energy [MeV]

35

10

108

energy [MeV]

40

0
0

events/1MeV (average of 1000 simulations)

200

30

40

50

60

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

70

80

90

100

90

100

40
16

O NC (NMO)

35

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
0

10

20

30

40

50

60

energy [MeV]energy [MeV](c) Oxygen CC interaction(d) OxygenNC interaction

7080

Fig. 4.26: Diﬀerence in the energy spectra among models for each interaction: (a) IBD, (b) ES, (c) oxygen CC,
and (d) oxygen NC. The energy region below the 7 MeV threshold for selecting prompt candidates is shadedin light blue.

Angular Distribution
Fig. 4.27 shows the cos 𝜃 SN distribution of each interaction for each model. The comparisonof the cos 𝜃 SN distribution among models are presented in Fig. 4.28. It is natural that the angular
distribution for each interactino is model-independent.

300

Wilson (NMO)

250

total
IBD
ES
16
O CC
16
O NC

200

150

100

50

0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy
160
140

100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

total
IBD
ES
16
O CC
16
O NC

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

140

total
IBD
ES
16
O CC
16
O NC

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN(e) Fischer model

0.6

0.8

1

Hudelpohl (NMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)Fischer (NMO)

100

0.4

0.4

0.6

0.8

1

(d) Hüdelpohl model

160

120

0.2

160

(c) Mori model

140

0cosθ SN

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Mori (NMO)

100

total
IBD
ES
16
O CC
16
O NC

(b) Nakazato model

160

120

Nakazato (NMO)

120(a) Wilson model

140

109

160
140

Tamborra (NMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

(f) Tamborra modelFig. 4.27: Diﬀerence in the cos 𝜃 SN distribution among interactions for each model.

1

160
140

IBD (NMO)

120

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Chapter 4 Detector Response and Pointing Accuracy

110

120

60

40

20

0
−1 −0.8 −0.6 −0.4 −0.2

16

O CC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

40
35
30
25
20
15
10
5
0

0.2

cosθ SN

0.4(c) Oxygen CC interaction

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)00.2cosθ SN

0.4

0.6

0.8

1

0.8

1

(b) ES500−1 −0.8 −0.6 −0.4 −0.2

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra80(a) IBD45

ES (NMO)

100

1
16

0.9

O NC (NMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6(d) OxygenNC interaction

Fig. 4.28: Comparison of the cos 𝜃 SN distribution among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

4.3 Pointing Accuracy for Supernova at 10 kpc
Fig. 4.29 shows the distribution of Δ𝜃 of 1000 simulations (described in Section 2.5.6) for eachmodel and oscillation assumption, and the derived pointing accuracy for the six models with threeoscillation assumptions are shown in Table 4.5. The pointing accuracy depends on the models,varying from ∼ 3◦ to ∼ 7◦ . Although the statistical error is large in some models, it can be seen that

Chapter 4 Detector Response and Pointing Accuracy

111

in which oscillation assumption the best resolution is achieved is diﬀerent among the models. With
neutrino oscillation, the better pointing accuracy is achieved in NMO case in Wilson, Nakazato,
and Fischer models, while in Mori, Hüdelpohl, and Tamborra models, the better pointing accuracy

100

90

90

Wilson (1σ resolution [°])

80

No Osc. (3.01 ± 0.10)
NMO(2.51 ± 0.08)
IMO(2.81 ± 0.09)

70
60
50
40
30
20

60
50
40
30
20

0
0

0
0

6

8

10

12

14

16

18

20

No Osc. (4.51 ± 0.14)
NMO(4.01 ± 0.13)
IMO(4.27 ± 0.14)

70

10
4

90

Nakazato (1σ resolution [°])

80

10
2

100

2

4

6

8

12

14

16

18

60
50
40
30
20
10
6

8

10

30
20

2

4

6

8

12

14

16

∆θ [°](d) Hüdelpohl model (total)

18

20

12

14

16

18

20

100

80

Tamborra(1σ resolution [°])

90

No Osc. (7.15 ± 0.23)
NMO(6.07 ± 0.19)
IMO(6.93 ± 0.22)

70
60
50
40
30
20

0
0

10

(c) Mori model (total)

10
4

40

∆θ [°]

number of simulations

No Osc. (5.41 ± 0.17)
NMO(5.11 ± 0.16)
IMO(5.01 ± 0.16)

2

50

0
0

20

Fischer(1σ resolution [°])

90

number of simulations

number of simulations

10

100

Hudelpohl(1σ resolution [°])

7060(b) Nakazato model (total)

100

80

No Osc. (4.91 ± 0.16)
NMO(4.55 ± 0.14)
IMO(4.55 ± 0.14)70∆θ [°](a) Wilson model (total)

90

Mori (1σ resolution [°])

8010∆θ [°]

00

number of simulations

100

number of simulations

number of simulations

is achieved in IMO case.

80

No Osc. (4.61 ± 0.15)
NMO(5.09 ± 0.16)
IMO(4.67 ± 0.15)

70
60
50
40
30
20
10

2

4

6

8

10

12

∆θ [°](e) Fischer (total)

14

16

18

20

0
0

2

4

6

8

10

12

14

16

18

20

∆θ [°](f) Tamborra (total)

Fig. 4.29: The Δ𝜃 distribution of each oscillation case for each model. The blue, green, and red histograms
represent No Osc., NMO, and IMO, respectively. The dashed line and the arrow in each histogram of thecorresponding color indicate the pointing accuracy at 1𝜎, i.e., the value of Δ𝜃 up to which the integral of thehistogram covers 68% of the 1000 simulations (see Section 2.5.6). The pointing accuracy for each oscillation
assumption in units of degree is also shown in the legend. The shaded region (light blue) indicates the target
pointing accuracy (≤ 3◦ ).

Since pointing accuracy is roughly determined by the balance between the number of IBD eventsand ES events, which depends on the number of neutrinos of each ﬂavor and neutrino oscillation.
The diversity in the number of IBD and ES events among models shown in Table 4.4 produces thediﬀerence in the ratio of ES/IBD, resulting in the diﬀerence in the oscillation assumption in which
the best pointing accuracy is achieved. Table 4.6 shows the ratio of the number of ES relative to thenumber of IBD events. For the models other than Mori and Hüdelpohl models, the oscillation typewith the higher ratio corresponds to the oscillation type in which the better resolution is achieved.

Chapter 4 Detector Response and Pointing Accuracy

112

In Mori and Hüdelpohl models, although the ES/IBD ratio is the highest in No Osc. the numberof events is too small and it is not signiﬁcant.
Table 4.5: Pointing accuracy at 1𝜎 in the unit of degree for six models with three oscillation cases. For eachmodel, the gray column represents which of NMO and IMO provides better pointing accuracy.

Pointing accuracy [◦ ]WilsonNo Osc.
3.01±0.10

Pointing accuracy [◦ ]Mori
No Osc.
4.91±0.16

Pointing accuracy [◦ ]Fischer
No Osc.
7.15±0.23

NMO
2.51±0.08

NMO
4.55±0.14

NMO
6.07±0.19

IMO
2.81±0.09

Nakazato
No Osc.
4.51±0.14

NMO
4.01±0.13

IMO
4.27±0.14

IMO
4.55±0.14

Hüdelpohl
No Osc.
5.41±0.17

NMO
5.11±0.16

IMO
5.01±0.16

IMO
6.93±0.22

Tamborra
No Osc.
4.61±0.15

NMO
5.09±0.16

IMO
4.67±0.15

Table 4.6: The ratio of ES relative to IBD for six models with three oscillation cases. For each model, thegray column represents which of the NMO and IMO provides a higher ratio of ES/IBD.

ES/IBD

WilsonNo Osc.
0.031±0.003

ES/IBDMori
No Osc.
0.039±0.004

ES/IBD

Fischer
No Osc.
0.036±0.006

NMO
0.035±0.003

NMO
0.037±0.004

NMO
0.040±0.006

IMO
0.028±0.002

Nakazato
No Osc.
0.039±0.004

NMO
0.040±0.004

IMO
0.033±0.003

IMO
0.034±0.004

Hüdelpohl
No Osc.
0.036±0.004

NMO
0.036±0..004

IMO
0.036±0.004

IMO
0.033±0.005

Tamborra
No Osc.
0.030±0.004

NMO
0.028±0.004

IMO
0.038±0.005

4.4 Conclusion
Before the systematic study on SK’s response and pointing accuracy using the six models, I
examined whether the current 7 MeV energy threshold for selecting prompt event candidates in
SNWATCH is appropriate. I investigated the energy threshold dependence of pointing accuracy
for the ﬁrst time. Though the statistical error is large, it is found that the pointing accuracy becomesworse with both the higher energy threshold (9 MeV) and the lower energy threshold (5-6 MeV).

Chapter 4 Detector Response and Pointing Accuracy

113

The ineﬃciency in ES events selection due to misidentiﬁcation of ES events is responsible for theworse pointing accuracy in higher energy regions, and the contamination to ES events by neutron
capture events is the main cause of the worse pointing accuracy in lower energy regions. As aresult, the 7 MeV threshold for the prompt event candidate selection seems to be appropriate.
Thorough Section 4.2.2-4.3, I systematically examined SK’s response and pointing accuracy ofa supernova at 10 kpc considering three neutrino oscillation assumption for each model for theﬁrst time. This was enabled by unifying the input data format of the model data. SK’s response
varies in models; it reﬂects the diﬀerence in the time and energy structure, indicating that thesupernova model discrimination using SK’s response is possible. Detection of the neutrino signalof the neutronization burst might be possible in some models, but not in others. Unfortunately,even if the neutronization signal is detected, SK-Gd is not capable of diﬀerentiating the neutrinomass ordering, due to the small statistics. Regarding the eﬀect of mass ordering on SK’s response,
it is not easy to understand in a uniﬁed way across models. This is because each model’s ﬂux andenergy of each neutrino ﬂavor is quite diﬀerent, and each has its characteristic response throughneutrino oscillations.
The pointing accuracy of SNWATCH for a supernova at 10 kpc varies in models and neutrino
oscillation assumptions, ranging from ∼3-7◦ . SK-Gd has been aimed to determine the galactic
supernova direction within 3◦ accuracy using Wilson model as mentioned in Section 2.5.6. It isconﬁrmed that SK-Gd achieves the 3◦ accuracy in pointing supernova in Wilson model which has
the largest number of events among the six models. However, in other models, the 3◦ accuracy is notachieved due to less neutrino ﬂuxes. Thus, the eﬀorts to improve the S/N ratio in small statistics
cases, such as modifying the reconstruction algorithm and supernova direction determination
algorithm, are essential. Several developments for improving pointing accuracy are ongoing.

114

Chapter 5Conclusion
Super Kamiokande (SK) aims to determine galactic supernova direction from the supernova burst
neutrino detection. SK’s real-time supernova monitoring system SNWATCH [53] reconstructs thesupernova direction and issues an alert for multi-messenger observation of core-collapse supernova.
To take advantage of the enhanced neutron detection eﬃciency to 75% by gadolinium (Gd) loading
to SK water with 0.011% concentration in 2020 and 0.033% concentration in 2022 (SK-Gd project),developments for upgrading SNWATCH have been ongoing. To determine the supernova direction,
extracting as many elastic scattering (𝜈 + e− → 𝜈 + e− ) events as possible is crucial in SNWATCH.
It is conducted by identifying inverse beta decay (IBD) events (𝜈¯e +p → e+ + n) that do not have theinformation of supernova direction, using the coincidence of the prompt signal from e+ (≥ 7 MeV)
and the delayed signal from gamma rays emitted by neutron capture.
First, I checked the energy threshold of the prompt candidate selection in SNWATCH andconﬁrmed the current 7 MeV threshold is appropriate. Then I studied SK’s response to supernova
bursts using various supernova models and evaluated pointing accuracy with the 7 MeV threshold.
I investigated SK’s responses to supernova bursts at a distance of 10 kpc considering neutrino
oscillations for six supernova models. The latest SK Monte Carlo (MC) simulations were employed.
The data format uniﬁcation of supernova models that I performed enabled this systematic study.
Through the study, it was found;(1) SK’s response varies in models; it reﬂects the diﬀerence in the time and energy structure,indicating that the supernova model discrimination using SK’s response is possible.
(2) Detection of the neutrino signal of the neutronization burst (an explosive 𝜈e emission
within the ﬁrst 0.1 s after the core bounce) might be possible in some models, but notothers. Unfortunately, even if the neutronization burst signal is detected, SK-Gd is notcapable of diﬀerentiating the neutrino mass ordering due to the small statistics.

Chapter 5 Conclusion

115(3) The eﬀect of mass ordering on SK’s response is not easy to understand in a uniﬁed way
across models. This is because each model’s ﬂux and energy of each neutrino ﬂavor is quite
diﬀerent, and each has its typical response through neutrino oscillation.
(4) The pointing accuracy for a supernova at 10 kpc varies in models and neutrino oscillation
assumptions, ranging from 3◦ to 7◦ . SK-Gd has been aimed to determine the galactic
supernova direction within 3◦ accuracy using Wilson model, as mentioned in Section 2.5.6.
It is conﬁrmed that SK-Gd achieves 3◦ accuracy in pointing a galactic supernova in Wilson
model, which has the largest number of events among the six models. However, in othermodels, the 3◦ accuracy is not achieved due to less neutrino ﬂuxes. Further improvements inevent reconstruction, separating IBD events from other events, and determining supernova
direction are essential.
In future studies, quantitative discrimination of supernova models using SK’s responses reported
in this thesis should be investigated. Another task to be addressed is to explore more variety ofsupernova models, including recent three-dimensional models. To improve pointing accuracy,
there is an urgent need to upgrade the supernova direction determination algorithm. One idea
might be to utilize the WIT system [101] which takes lower energy data than SNWATCH. We needto investigate SK-Gd’s capability of identifying which of supernova candidates is the explodedone (e.g., whether SK-Gd can discriminate supernova candidates illustrated in Fig. 1.12 with 10◦
accuracy).

116

Appendix A
Diﬀerence in SK Response among Models
Figures which are not included in Section 4.2.5 are listed here. For the time evolution and cos 𝜃 SN
distribution, the reconstructed events satisfying the prompt event selection criteria described in
Section 2.5.4 and the time diﬀerence condition (less than 0.02 𝜇s between the generated event andthe reconstructed event closest to it) are shown.

Appendix A Diﬀerence in SK Response among Models

117

A.1 Diﬀerence in Models in No Oscillation case

2000
1800

Wilson (No Osc.)

1600

total
IBD
ES
16
O CC
16
O NC

1400
1200
1000
800
600
400
200
0

0

5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)A.1.1 Time Evolution

1400

Nakazato (No Osc.)
1200

total
IBD
ES
16
O CC
16
O NC

1000
800
600
400
200
0

0

5

time [s]1000Mori (No Osc.)

800

total
IBD
ES
16
O CC
16
O NC

700
600
500
400
300
200
100
0

0

5

10

15

20

900

Hudelpohl (No Osc.)

800

total
IBD
ES
16
O CC
16
O NC

700
600
500
400
300
200
100
0

0

5

total
IBD
ES
16
O CC
16
O NC

300

200

100

5

10

time [s](e) Fischer model

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)Fischer (No Osc.)

0

15

20

(d) Hudelpohl model

600

0

10

time [s](c) Mori model

400

20

1000

time [s]50015(b) Nakazato model
events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) Wilson model

900

10

time [s]2500

Tamborra (No Osc.)
2000

total
IBD
ES
16
O CC
16
O NC

1500

1000

500

0

0

5

10

15

20

time [s](f) Tamborra modelFig. A.1: Diﬀerence in the time evolution until 20 s among interactions for each model.

2500

IBD (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

2000

1500

1000

500

0

0

5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

118

100
90

ES (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

80
70
60
50
40
30
20
10
0

0

5

time [s]14016

O CC (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0

0

5

15

20

(b) ES

10

15

time [s](c) Oxygen CC interaction

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) IBD120

10

time [s]

1
0.9

16

O NC (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20

time [s](d) OxygenNC interaction

Fig. A.2: Diﬀerence in the time evolution until 20 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

200
180

Wilson (No Osc.)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

119

140

Nakazato (No Osc.)
120

total
IBD
ES
16
O CC
16
O NC

100
80
60
40
20
0

−0.4 −0.2

00.2

time [s]100Mori (No Osc.)

80

total
IBD
ES
16
O CC
16
O NC

70
60
50
40
30
20
10
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

90

30

20

10

0.2

0.4

0.6

0.8

time [s](e) Fischer model

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

total
IBD
ES
16
O CC
16
O NC

0

1.4

total
IBD
ES
16
O CC
16
O NC

70
60
50
40
30
20
10
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(d) Hudelpohl model

Fischer (No Osc.)−0.4 −0.2

1.2

time [s]6001Hudelpohl (No Osc.)

80(c) Mori model

40

0.8

100

time [s]500.6(b) Nakazato model
events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) Wilson model

90

0.4

time [s]200180

Tamborra (No Osc.)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](f) Tamborra modelFig. A.3: Diﬀerence in the time evolution until 1.5 s among interactions for each model.

140

IBD (No Osc.)
120

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

120

30

ES (No Osc.)

25

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

5

0

−0.4 −0.2

00.2

time [s]30
16

O CC (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

5

0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(b) ES

0.6

0.8

1

time [s](c) Oxygen CC interaction

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) IBD25

0.4

time [s]

1
0.9

16

O NC (No Osc.)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](d) OxygenNC interaction

Fig. A.4: Diﬀerence in the time evolution until 1.5 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

5
4.5

Wilson (No Osc.)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

121

5
4.5

Nakazato (No Osc.)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

time [sec]5Mori (No Osc.)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

4.5

2
1.5
1
0.5
0

0.02

0.04

0.06

time [sec](e) Fischer model

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

total
IBD
ES
16
O CC
16
O NC

2.5

0
−0.02

0.1

0.12

total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

(d) Hudelpohl model

Fischer (No Osc.)

3

0.12

time [sec]

5

3.5

0.1

Hudelpohl (No Osc.)(c) Mori model

4

0.08

5

time [sec]

4.5

0.06

(b) Nakazato model
events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)(a) Wilson model

4.5

0.04

time [sec]

5
4.5
4
3.5
3

Tamborra (No Osc.)

2.5

total

2

IBD

1.5

ES

1

16

O CC

16

O NC

0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](f) Tamborra modelFig. A.5: Diﬀerence in the time evolution until 0.12 s among interactions for each model.

9

IBD (No Osc.)

8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.7
0.6
0.5

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.3
0.2
0.1
0.02

ES (No Osc.)

1.6

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.02

0

0.02

0.04

0.06

(b) ESO CC (No Osc.)01.8(a) IBD

0.4

0
−0.02

2

time [sec]

16

0.8

122

time [sec]1
0.9

events/1ms (average of 1000 simulations)

10

0.04

0.06

0.08

time [sec](c) Oxygen CC interaction

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

0.08

0.1

0.12

1
0.9

16

O NC (No Osc.)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](d) OxygenNC interaction

Fig. A.6: Diﬀerence in the time evolution until 0.12 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

Appendix A Diﬀerence in SK Response among Models

123Appendix A Diﬀerence in SK Response among Models

124

Wilson (No Osc.)
total
IBD
ES
16
O CC
16
O NC

200

150

100

50

0
0

10

20

30

40

50

60

70

80

90

100

total
IBD
ES
16
O CC
16
O NC

100
80
60
40
20
0
0

10

20

30

total
IBD
ES
16
O CC
16
O NC

80
60
40
20

30

40

50

60

70

80

90

100

140

140

total
IBD
ES
16
O CC
16
O NC

100
80
60
40
20

30

40

50

60

90

100

100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

(d) Hudelpohl model

Fischer (No Osc.)

120

80

energy [MeV]

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

70

total
IBD
ES
16
O CC
16
O NC

(c) Mori model

20

60

Hudelpohl (No Osc.)

120

energy [MeV]1050(b) Nakazato model

100

0
0

40

(a) Wilson model

120

20

Nakazato (No Osc.)

120

energy [MeV]Mori (No Osc.)

10

140

energy [MeV]

140

0
0

events/1MeV (average of 1000 simulations)250

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)A.1.2 Energy spectra

140

Tamborra (No Osc.)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

energy [MeV]energy [MeV](e) Fischer model(f) Tamborra model

80

90

100

Fig. A.7: Diﬀerence in the energy spectra among interactions for each model. The energy region below the7 MeV threshold for selecting prompt candidates is shaded in light blue.

180

IBD (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

160
140
120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
0

10

20

30

40

50

60

(b) ESO CC (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5

30

ES (No Osc.)

35(a) IBD

16

20

40

energy [MeV]

35

10

125

energy [MeV]

40

0
0

events/1MeV (average of 1000 simulations)

200

40

50

60

70

energy [MeV](c) Oxygen CC interaction

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

70

80

90

100

40
16

O NC (No Osc.)

35

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
0

10

20

30

40

50

60

70

80

90

100

energy [MeV](d) OxygenNC interaction

Fig. A.8: Diﬀerence in the energy spectra among models for each interaction: (a) IBD, (b) ES, (c) oxygen CC,
and (d) oxygen NC. The energy region below the 7 MeV threshold for selecting prompt candidates is shadedin light blue.

Appendix A Diﬀerence in SK Response among Models

126

300

Wilson (No Osc.)

250

total
IBD
ES
16
O CC
16
O NC

200

150

100

50

0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)A.1.3 Angular Distribution
160
140

100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

total
IBD
ES
16
O CC
16
O NC

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Mori (No Osc.)

100

140

total
IBD
ES
16
O CC
16
O NC

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN(e) Fischer model

0.6

0.8

1

Hudelpohl (No Osc.)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)Fischer (No Osc.)

100

0.4

0.4

0.6

0.8

1

(d) Hudelpohl model

160

120

0.2

160

(c) Mori model

140

0cosθ SN(b) Nakazato model

160

120

total
IBD
ES
16
O CC
16
O NC

120

(a) Wilson model

140

Nakazato (No Osc.)

160
140

Tamborra (No Osc.)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

(f) Tamborra modelFig. A.9: Diﬀerence in the cos 𝜃 SN distribution among interactions for each model.

1

160
140

IBD (No Osc.)

120

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models
120

100

ES (No Osc.)80

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

60

40

20

0
−1 −0.8 −0.6 −0.4 −0.2

O CC (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

6
5
4
3
2
1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4(c) Oxygen CC interaction

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

16

7

0.2

0.4

0.6

0.8

1

(b) ES1080cosθ SN(a) IBD

9

127

1
16

0.9

O NC (No Osc.)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

(d) OxygenNC interaction

Fig. A.10: Diﬀerence in the cos 𝜃 SN distribution among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

Appendix A Diﬀerence in SK Response among Models

128Appendix A Diﬀerence in SK Response among Models

129

A.2 Diﬀerence in Models in IMO case

2500

Wilson (IMO)
2000

total
IBD
ES
16
O CC
16
O NC

1500

1000

500

0

0

5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)A.2.1 Time Evolution

1400

Nakazato (IMO)
1200

total
IBD
ES
16
O CC
16
O NC

1000
800
600
400
200
0

0

5

time [s]1000Mori (IMO)

800

total
IBD
ES
16
O CC
16
O NC

700
600
500
400
300
200
100
0

0

5

10

15

20

900

Hudelpohl (IMO)

800

total
IBD
ES
16
O CC
16
O NC

700
600
500
400
300
200
100
0

0

5

total
IBD
ES
16
O CC
16
O NC

300

200

100

5

10

time [s](e) Fischer model

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)Fischer (IMO)

0

15

20

(d) Hudelpohl model

600

0

10

time [s](c) Mori model

400

20

1000

time [s]50015(b) Nakazato model
events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) Wilson model

900

10

time [s]2500

Tamborra (IMO)
2000

total
IBD
ES
16
O CC
16
O NC

1500

1000

500

0

0

5

10

15

20

time [s](f) Tamborra modelFig. A.11: Diﬀerence in the time evolution until 20 s among interactions for each model.

2500

IBD (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

2000

1500

1000

500

0

0

5

10

15

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

130

100
90

ES (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

80
70
60
50
40
30
20
10
0

0

5

time [s]14016

O CC (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0

0

5

15

20

(b) ES

10

15

time [s](c) Oxygen CC interaction

20

events/0.5s (average of 1000 simulations)

events/0.5s (average of 1000 simulations)(a) IBD120

10

time [s]

1
0.9

16

O NC (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20

time [s](d) OxygenNC interaction

Fig. A.12: Diﬀerence in the time evolution until 20 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

200
180

Wilson (IMO)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

131

200
180

Nakazato (IMO)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

00.2

time [s]100Mori (IMO)

80

total
IBD
ES
16
O CC
16
O NC

70
60
50
40
30
20
10
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

90

total
IBD
ES
16
O CC
16
O NC

50
40
30
20
10
0

0.2

0.4

0.6

0.8

time [s](e) Fischer model

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)Fischer (IMO)−0.4 −0.2

1.4

total
IBD
ES
16
O CC
16
O NC

70
60
50
40
30
20
10
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(d) Hudelpohl model

90

0

1.2

time [s]

100

60

1

Hudelpohl (IMO)80(c) Mori model

70

0.8

100

time [s]800.6(b) Nakazato model
events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) Wilson model

90

0.4

time [s]200180

Tamborra (IMO)

160

total
IBD
ES
16
O CC
16
O NC

140
120
100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time [s](f) Tamborra modelFig. A.13: Diﬀerence in the time evolution until 1.5 s among interactions for each model.

140

IBD (IMO)
120

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

100
80
60
40
20
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

132

30

ES (IMO)

25

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

5

0

−0.4 −0.2

00.2

time [s]30
16

O CC (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

20

15

10

5

0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.2

1.4

(b) ES

0.6

0.8

1

time [s](c) Oxygen CC interaction

1.2

1.4

events/25ms (average of 1000 simulations)

events/25ms (average of 1000 simulations)(a) IBD25

0.4

time [s]

1
0.9

16

O NC (IMO)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−0.4 −0.2

0

0.2

0.4

0.6

0.8

1

time [s](d) OxygenNC interaction

Fig. A.14: Diﬀerence in the time evolution until 1.5 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

5
4.5

Wilson (IMO)
total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

133

10
9

Nakazato (IMO)
total
IBD
ES
16
O CC
16
O NC

8
7
6
5
4
3
2
1
0
−0.02

0

0.02

time [sec]

5
4.5

total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

4.5

2
1.5
1
0.5
0

0.02

0.04

0.06

time [sec](e) Fischer model

0.08

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

total
IBD
ES
16
O CC
16
O NC

2.5

0
−0.02

0.1

0.12

total
IBD
ES
16
O CC
16
O NC

4
3.5
3
2.5
2
1.5
1
0.5
0
−0.02

0

0.02

0.04

0.06

0.08

(d) Hudelpohl model

Fischer (IMO)

3

0.12

time [sec]

5

3.5

0.1

Hudelpohl (IMO)(c) Mori model

4

0.08

5

time [sec]

4.5

0.06

(b) Nakazato model
events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)(a) Wilson modelMori (IMO)

0.04

time [sec]

5
4.5
4
3.5
3

Tamborra (IMO)

2.5

total

2

IBD

1.5

ES

1

16

O CC

16

O NC

0.5
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

time [sec](f) Tamborra modelFig. A.15: Diﬀerence in the time evolution until 0.12 s among interactions for each model.

9

IBD (IMO)

8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

7
6
5
4
3
2
1
0
−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

1.4
1.2
1

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.6
0.4
0.2
0.02

ES (IMO)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

(b) ESO CC (IMO)00.9(a) IBD

0.8

0
−0.02

1

time [sec]

16

1.6

134

time [sec]2
1.8

events/1ms (average of 1000 simulations)

10

0.04

0.06

0.08

time [sec](c) Oxygen CC interaction

0.1

0.12

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

events/1ms (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

0.08

0.1

0.12

0.1

0.12

1
0.9

16

O NC (IMO)

0.8

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.02

0

0.02

0.04

0.06

0.08

time [sec](d) OxygenNC interaction

Fig. A.16: Diﬀerence in the time evolution until 0.12 s among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

Appendix A Diﬀerence in SK Response among Models

135Appendix A Diﬀerence in SK Response among Models

136

Wilson (IMO)
total
IBD
ES
16
O CC
16
O NC

200

150

100

50

0
0

10

20

30

40

50

60

70

80

90

100

total
IBD
ES
16
O CC
16
O NC

100
80
60
40
20
0
0

10

20

30

total
IBD
ES
16
O CC
16
O NC

80
60
40
20

30

40

50

60

70

80

90

100

140

140

total
IBD
ES
16
O CC
16
O NC

100
80
60
40
20

30

40

50

60

90

100

100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

90

100

(d) Hudelpohl model

Fischer (IMO)

120

80

energy [MeV]

70

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

70

total
IBD
ES
16
O CC
16
O NC

(c) Mori model

20

60

Hudelpohl (IMO)

120energy [MeV]1050(b) Nakazato model

100

0
0

40

(a) Wilson model

120

20

Nakazato (IMO)

120energy [MeV]Mori (IMO)

10

140

energy [MeV]

140

0
0

events/1MeV (average of 1000 simulations)250

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)A.2.2 Energy spectra

140

Tamborra (IMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

energy [MeV]energy [MeV](e) Fischer model(f) Tamborra model

80

Fig. A.17: Diﬀerence in the energy spectra among interactions for each model. The energy region below the7 MeV threshold for selecting prompt candidates is shaded in light blue.

180

IBD (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

160
140
120
100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

90

100

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
0

10

20

30

40

50

60

(b) ESO CC (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5

30

ES (IMO)35(a) IBD

16

20

40

energy [MeV]

35

10

137

energy [MeV]

40

0
0

events/1MeV (average of 1000 simulations)

200

40

50

60

70

energy [MeV](c) Oxygen CC interaction

80

90

100

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

events/1MeV (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models

70

80

90

100

90

100

40
16

O NC (IMO)

35

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
0

10

20

30

40

50

60

70

80

energy [MeV](d) OxygenNC interaction

Fig. A.18: Diﬀerence in the energy spectra among models for each interaction: (a) IBD, (b) ES, (c) oxygen CC,
and (d) oxygen NC. The energy region below the 7 MeV threshold for selecting prompt candidates is shadedin light blue.

Appendix A Diﬀerence in SK Response among Models

138

300

250

200

150

Wilson (IMO)
total
IBD
ES
16
O CC
16
O NC

100

50

0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)A.2.3 Angular Distribution
160
140

100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

total
IBD
ES
16
O CC
16
O NC

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Mori (IMO)

100

140

total
IBD
ES
16
O CC
16
O NC

80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN(e) Fischer model

0.6

0.8

1

Hudelpohl (IMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)Fischer (IMO)

100

0.4

0.4

0.6

0.8

1

0.8

1

(d) Hudelpohl model

160

120

0.2

160

(c) Mori model

140

0cosθ SN(b) Nakazato model

160

120

total
IBD
ES
16
O CC
16
O NC

120

(a) Wilson model

140

Nakazato (IMO)

160
140

Tamborra (IMO)
total
IBD
ES
16
O CC
16
O NC

120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6(f) Tamborra modelFig. A.19: Diﬀerence in the cos 𝜃 SN distribution among interactions for each model.

200

IBD (IMO)

180
160

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

140
120
100
80
60
40
20
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)

Appendix A Diﬀerence in SK Response among Models
120

80

60

40

20

0
−1 −0.8 −0.6 −0.4 −0.2

O CC (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

30
25
20
15
10
5
0
−1 −0.8 −0.6 −0.4 −0.2

0

0

0.2

cosθ SN

0.2

cosθ SN

0.4(c) Oxygen CC interaction

0.6

0.8

1

events/bin (average of 1000 simulations)

events/bin (average of 1000 simulations)16

35

WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.4

0.6

0.8

1

0.8

1

(b) ES50

40

ES (IMO)

100(a) IBD

45

139

1
16

0.9

O NC (IMO)
WilsonNakazatoMori
Hudelpohl
Fischer
Tamborra

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−1 −0.8 −0.6 −0.4 −0.2

00.2

cosθ SN

0.4

0.6(d) OxygenNC interaction

Fig. A.20: Diﬀerence in the cos 𝜃 SN distribution among models for each interaction: (a) IBD, (b) ES,(c) oxygen CC, and (d) oxygen NC.

140

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146

147

List of Figures

1.1

Neutrino Mass Ordering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

1.2

Δ𝜒2 proﬁle of 𝛿𝐶 𝑃 for NMO (left panel) and IMO (right panel) [6]. . . . . . . .

7

1.3

Δ𝜒2 proﬁle of 𝜃 23 [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.4

Expected and measured neutrino ﬂuxes and energy from various sources [7]. . .

8

1.5

Zenith angle distributions of atmospheric neutrino events at Super-Kamiokande IIV [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

1.6

Oscillation probabilities assuming NMO [8]: (a) 𝜈 𝜇 → 𝜈e oscillation. . . . . . .

11

1.7

Schematic picture of nuclear reactions in the Sun: (a) pp-chain reaction and (b)CNO cycle.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

1.8

Expected spectrum of solar neutrino ﬂuxes from diﬀerent nuclear processes [9].

13

1.9

Expected DSNB signal and the background (reactor 𝜈¯e and charged current eventsby atmospheric neutrinos) by inverse beta decay search [27]. . . . . . . . . . . .

16

1.10

Optical light curve for each spectral supernova type [28]. . . . . . . . . . . . .

17

1.11

Schematic picture of evolutionary phases of core-collapse supernova burst, fromthe onset of core-collapse to proto-neutron star cooling [32]. . . . . . . . . . . .

1.12

20

Positions of core-collapse supernova candidates within 1 kpc of the Earth illustrated in equatorial coordinate system [43]. . . . . . . . . . . . . . . . . . . . .

26

2.1

Overview of the Super-Kamiokande Detector and related facilities [44]. . . . . .

28

2.2

(a) Super Modules separating the ID and the OD and supporting the PMTs [44].
(b) Detector coordinate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

2.3

Schematic picture of 20-inch PMT [44]. . . . . . . . . . . . . . . . . . . . . .

30

2.4

Quantum eﬃciency of a photocathode as a function of wavelength [nm . . . . .

30

2.5

Pulse height distribution for one photoelectron [44]. . . . . . . . . . . . . . . .

31

2.6

Transit time spread at one photoelectron signal, tested using a typical PMT with
410 nm wavelength light [44]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

List of Figures

148

2.7

Geomagnetic compensation coils surrounding the inner surface of the SK tank [45]. 32

2.8

Schematic illustration of the air puriﬁcation system (Rn-reduced air generator). .

33

2.9

Cherenkov ring observation at SK. . . . . . . . . . . . . . . . . . . . . . . . .

34

2.10

Picture of a QBEE board [48]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

2.11

Block diagram of the data acquisition system for SK [48]. . . . . . . . . . . . .

37

2.12

Neutron capture eﬃciency as a function of Gd concentration in water by mass [51]. 40

2.13

Schematic illustration of SK-Gd water system [50]. . . . . . . . . . . . . . . .

2.14

Cross sections of neutrino interactions in SK as a function of neutrino energy [52]. 44

2.15

Block diagram of SNWATCH [53]. . . . . . . . . . . . . . . . . . . . . . . . .

46

2.16

Deﬁnition of 𝜃 dir,𝑖 and 𝜃 𝑖 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.17

(a) Deﬁnition of (𝜃 𝑖 , 𝜙𝑖 ) [55]. (b) Correction term 𝑆(𝜃, 𝜙) for eﬀective photocathode area of the 𝑖-th PMT [55]. . . . . . . . . . . . . . . . . . . . . . . . .

2.18

41

49

Schematic illustration of the prompt event selection, the delayed event selection,and the neutron tagging used in SNWATCH. . . . . . . . . . . . . . . . . . . .

50

2.19

Deﬁnition of 𝜃 SN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

2.20

Typical cos 𝜃 SN distribution from [53] simulated with the Wilson model (seeSection 3.1.1) at a 10 kpc supernova for the total electron energy range 7-50 MeV. 53

2.21

Δ𝜃 distribution of Wilson model and Nakazato model for 3000 MC samples ofsimulated supernova at 10 kpc without neutrino oscillation from [53]. . . . . . .

54

2.22

Detection prospects of galactic supernovae [57]. . . . . . . . . . . . . . . . . .

55

2.23

Overview of supernova simulation in SK. . . . . . . . . . . . . . . . . . . . . .

56

3.1

Time evolution of luminosity (top) in the unit of 1050 erg s−1 and mean energy(bottom) in the unit of MeV for six supernova models listed in Table 3.1 for eachneutrino ﬂavor, from -0.02 s to 0.12 s (the core bounce occurs at 0 s). . . . . . .

3.2

Same as Fig. 3.1 but shows longer time range until 20 s (the core bounce occurs
at 0 s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3

61

Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy
in the unit of MeV from -0.2 s to 5.2 s for Nakazato model. . . . . . . . . . . .

3.5

60

Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy
in the unit of MeV from -0.2 s to 5.2 s for Wilson model. . . . . . . . . . . . .

3.4

59

62

Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy
in the unit of MeV from -0.2 s to 5.2 s for Mori model. . . . . . . . . . . . . . .

63

List of Figures
3.6

149

Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy
in the unit of MeV from -0.2 s to 5.2 s for Hüdelpohl model. The core bounce
occurs at 0 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.7

64

Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy
in the unit of MeV from -0.2 s to 5.2 s for Fischer model. The core bounce occurs
at 0 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.8Time evolution of (a) luminosity in the unit of 1050 erg s−1 and (b) mean energy
in the unit of MeV from 0.0 s (time of the bounce) to 0.6 s for Tamborra model.

4.1

66

Pointing accuracy as a function of energy threshold for selecting prompt candidates in SNWATCH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

65

71

Event selection ﬂow in SNWATCH for each interaction: (a) IBD, (b) ES, (c) Oxygen CC, and (d) Gd-𝛾 (neutron capture on Gd). . . . . . . . . . . . . . . . . . .

74

4.3

ES eﬃciency and ineﬃciency as a function of energy threshold. . . . . . . . . .

75

4.4

ES purity and the ratio of contamination to ES as a function of energy threshold.

75

4.5

Oscillation-dependent diﬀerence in the time evolution of the number of total
events until 20 s, covering the whole simulation period. . . . . . . . . . . . . .

4.6

Oscillation-dependent diﬀerence in the time evolution of the number of total
events until 1.5 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7

83

Oscillation-dependent diﬀerence in the time evolution of the number of total
events until 0.12 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.8

82

83

Oscillation-dependent diﬀerence in the time evolution of IBD events (top six
panels) and ES events (bottom six panels) covering the whole simulation period
for each model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.9

85

Oscillation-dependent diﬀerence in the time evolution of oxygen CC events (topsix panels) and oxygen NC events (bottom six panels) covering the whole simulation period for each model. . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.10

Oscillation-dependent diﬀerence in the time evolution of IBD events (top six
panels) and ES events (bottom six panels) until 1.5 s for each model. . . . . . .

4.11

88

Oscillation-dependent diﬀerence in the time evolution of IBD events (top six
panels) and ES events (bottom six panels) until 0.12 s for each model. . . . . . .

4.13

87

Oscillation-dependent diﬀerence in the time evolution of oxygen CC events (topsix panels) and oxygen NC events (bottom six panels) until 1.5 s for each model.

4.12

86

89

Oscillation-dependent diﬀerence in the time evolution of oxygen CC events (topsix panels) and oxygen NC events (bottom six panels) until 0.12 s for each model. 90

List of Figures
4.14

Oscillation-dependent diﬀerence in the energy spectrum of IBD events (top six
panels) and ES events (bottom six panels) for each model. . . . . . . . . . . . .

4.15

95

Oscillation-dependent diﬀerence in the cos 𝜃 SN distribution of oxygen CC events(top six panels) and oxygen NC events (bottom six panels) for each model. . . .

4.18

93

Oscillation-dependent diﬀerence in the cos 𝜃 SN distribution of IBD events (topsix panels) and ES events (bottom six panels) for each model. . . . . . . . . . .

4.17

92

Oscillation-dependent diﬀerence in the energy spectrum of oxygen CC events(top six panels) and oxygen NC events (bottom six panels) for each model. . . .

4.16

150

96

The model-dependent diﬀerence of the time evolution of IBD events (dashed)
and ES events (solid) from -0.02 s to 0.12 s (core bounce occur at 0 s) for (a) no
oscillation, (b) NMO, and (c) IMO. . . . . . . . . . . . . . . . . . . . . . . . .

98

4.19

Diﬀerence in the time evolution until 20 s among interactions for each model. . 101

4.20

Diﬀerence in the time evolution until 20 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 102

4.21

Diﬀerence in the time evolution until 1.5 s among interactions for each model. . 103

4.22

Diﬀerence in the time evolution until 1.5 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 104

4.23

Diﬀerence in the time evolution until 1.5 s among interactions for each model. . 105

4.24

Diﬀerence in the time evolution until 1.5 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 106

4.25

Diﬀerence in the energy spectra among interactions for each model. The energy
region below the 7 MeV threshold for selecting prompt candidates is shaded inlight blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.26

Diﬀerence in the energy spectra among models for each interaction: (a) IBD,(b) ES, (c) oxygen CC, and (d) oxygen NC. The energy region below the 7 MeV
threshold for selecting prompt candidates is shaded in light blue. . . . . . . . . 108

4.27

Diﬀerence in the cos 𝜃 SN distribution among interactions for each model. . . . . 109

4.28

Comparison of the cos 𝜃 SN distribution among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 110

4.29

The Δ𝜃 distribution of each oscillation case for each model. . . . . . . . . . . . 111

A.1

Diﬀerence in the time evolution until 20 s among interactions for each model. . 117

A.2

Diﬀerence in the time evolution until 20 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 118

A.3

Diﬀerence in the time evolution until 1.5 s among interactions for each model. . 119

List of Figures
A.4

151

Diﬀerence in the time evolution until 1.5 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 120

A.5

Diﬀerence in the time evolution until 0.12 s among interactions for each model.

A.6

Diﬀerence in the time evolution until 0.12 s among models for each interaction:

121(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 122
A.7

Diﬀerence in the energy spectra among interactions for each model. The energy
region below the 7 MeV threshold for selecting prompt candidates is shaded inlight blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

A.8

Diﬀerence in the energy spectra among models for each interaction: (a) IBD,(b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . . . . . . 125

A.9

Diﬀerence in the cos 𝜃 SN distribution among interactions for each model. . . . . 126

A.10

Diﬀerence in the cos 𝜃 SN distribution among models for each interaction: (a) IBD,(b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . . . . . . 127

A.11

Diﬀerence in the time evolution until 20 s among interactions for each model. . 129

A.12

Diﬀerence in the time evolution until 20 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 130

A.13

Diﬀerence in the time evolution until 1.5 s among interactions for each model. . 131

A.14

Diﬀerence in the time evolution until 1.5 s among models for each interaction:(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 132

A.15

Diﬀerence in the time evolution until 0.12 s among interactions for each model.

A.16

Diﬀerence in the time evolution until 0.12 s among models for each interaction:

133(a) IBD, (b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . 134
A.17

Diﬀerence in the energy spectra among interactions for each model. . . . . . . . 136

A.18

Diﬀerence in the energy spectra among models for each interaction: (a) IBD,(b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . . . . . . 137

A.19

Diﬀerence in the cos 𝜃 SN distribution among interactions for each model. . . . . 138

A.20

Diﬀerence in the cos 𝜃 SN distribution among models for each interaction: (a) IBD,(b) ES, (c) oxygen CC, and (d) oxygen NC. . . . . . . . . . . . . . . . . . . . . 139

152

List of Tables

1.1

Oscillation parameters [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2

Summary of solar neutrinos produced in the pp-chain reactions. . . . . . . . . .

12

1.3

Observational classiﬁcation of supernovae. . . . . . . . . . . . . . . . . . . . .

17

1.4

Summary of nuclear burning [33, 34]. . . . . . . . . . . . . . . . . . . . . . .

21

2.1

Threshold energy 𝐸 𝑡 ℎ for some particles observed at SK. . . . . . . . . . . . .

35

2.2

Summary of software trigger types, thresholds, time windows for recording thesignals when the trigger is issued (𝑡 = 0) to search the related events, andfrequencies of the trigger issue. . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

38

Natural abundance and thermal neutron capture cross section for isotopes relevant
to SK-Gd [50]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.1

Summary of six supernova model data employed in this thesis. . . . . . . . . .

67

4.1

Pointing accuracy with various energy thresholds in SNWATCH. . . . . . . . .

71

4.2

Average number of events at SK in the 32.5k m3 full volume for 1000 simulated
supernova bursts at 10 kpc for Wilson, Nakazato, Mori, Hüdelpohl, Fischer, andTamborra models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3

Average number of neutrinos of each ﬂavor for each model arrived at SK for each
oscillation assumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4

78
79

Average number of reconstructed events at SK-Gd (with 0.03% Gd concentration)in the 22.5k m3 ﬁducial volume for 1000 simulated supernova bursts at 10 kpc
with Wilson, Nakazato, and Mori, Hüdelpohl, Fischer, and Tamborra models. .

4.5

81

Pointing accuracy at 1𝜎 in the unit of degree for six models with three oscillation
cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.6

The ratio of ES relative to IBD for six models with three oscillation cases. . . . 112