Doctoral Dissertation
博士論文
Search for Neutrinos associated with Solar Flares inSuper-Kamiokande(スーパーカミオカンデにおける太陽フレア由来のニュートリノ探索)

A Dissertation Submitted for the Degree of Doctor ofPhilosophy
December 2021
令和 3 年 12 月博士 (理学) 申請
Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科
物理学専攻
Kohei Okamoto
岡本 幸平

Abstract
Neutrinos associated with solar flares (solar flare neutrinos) provide information on particle
acceleration mechanisms during the impulsive phase of solar flares. Solar flare neutrino search
was conducted using the Super-Kamiokande detector with search time windows set by using datafrom solar observation satellites. Furthermore, we have established another approach to set the
search windows for solar flare neutrinos analyzing the data of coronal mass ejections, and thenperformed the first attempt to search for neutrinos from solar flares occurring on the invisible
side of the Sun. Twenty-three solar flares above the X5.0 class were selected which occurred on
the visible side of the solar surface between April 1996 and May 2018. And ten solar flares wereselected from the invisible side which accompanies with coronal mass ejections whose emission
speed is faster than 2000 km s−1 . Then, the neutrino events coincident with the solar flares weresearched for using the Super-Kamiokande detector. The Super-Kamiokande data is divided into
two samples as high-energy samples (above 100 MeV) and low-energy samples (16 - 100 MeV).
For the solar flares occurring on the visible side of the Sun, there are two solar flares occurring on
the visible side of the Sun with one high-energy neutrino candidate in the search time windows.
For the other eighteen solar flares on the visible side, there are not any neutrino candidates. The
solar flares with the neutrino candidate occurred on November 4th, 2003, and September 6th,
2017, and expected background rates are 0.20 event/flare and 0.12 event/flare, respectively. They
are statistically consistent with the expected background rate. For the solar flares occurring on
the invisible side, there are two solar flares with two high-energy neutrino candidates and twosolar flares with one high-energy neutrino candidate. There are not any neutrino candidates withthe other solar flares. The expected background rate for each solar flare on the invisible side is
0.62 event/flare. They are statistically consistent with the expected background rate. Therefore,
the upper limit of solar flare neutrino fluence at 90% confidence level was calculated for eachsolar flare. The fluence upper limits at 90% confidence level for the solar flares occurring on
the visible side of the Sun without neutrino candidates are 5.6 × 105 cm−2 . For the solar flares
occurring on the invisible side, The fluence upper limits at 90% confidence level in the energy
region from 100 MeV to 10 GeV are 5.6 × 105 cm−2 , 8.2 × 105 cm−2 and 1.2 × 106 cm−2 for solar
flares with zero, one and two neutrino candidates, respectively. From the obtained fluence upper
limits, the upper limits on the conversion factor, η, which is the eﬃciency of energy conversion
from the total energy of solar flare to the energy of the neutrinos, is estimated. In the case of
the largest solar flare on November 4th, 2003, it is determined as η < 0.004, which is two ordersof magnitude smaller than the estimation by Fargion and Moscato. Therefore, this experimental
result suggests that the theoretical assumption of the energy conversion during solar flares should
be re-considered. In addition, the fluence upper limit at 90% confidence level for the solar flareoccurring on the invisible side on November 7th, 2003, which followed the largest solar flare,is 1.2 × 106 cm−2 . The fluence upper limits at 90% confidence level in the energy region from
16 to 100 MeV for the solar flares occurring on the visible and invisible side of the Sun are
1.7 × 107 cm−2 . In order to compare the results with the other experimental fluence limits, theii

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model independent fluence upper limit below 100 MeV is also obtained. The result does not
rule any theoretical models but gives the most stringent upper limits on the fluence of solar flare
neutrinos in the tens of MeV region.

Acknowledgments
I would first like to express my gratitude to Prof. Masayuki Nakahata for giving me the opportunity to do research at Super-Kamiokande. He showed me around the Kamioka Mine even before
I entered the graduate school and gave me a historical background of the Kamiokande from its
beginning to the present. He also gave me various advice and support for my research. I would
not have been able to complete this research without his support.
I would like to thank Dr. Yuuki Nakano for giving me so much of his time to help me withall aspects of the radon detector calibration experiments and solar flare research. He taught me
how to connect pipes, how to make slide presentations, and how to analyze data from SuperKamiokande. In addition to my research, I also learned how to prepare for drinking parties anddelicious food in Toyama, which made my research in Kamioka enjoyable.
Prof. Yoshitaka Itow of Nagoya University provided me with the necessary environment to
conduct research on solar flares and taught me the basics.
Associate Professor Satoshi Masuda of Nagoya University taught me the basics of how toanalyze data from solar observation satellites and how to accelerate particles in solar flares.
Thanks to Dr. Masuda, I have a better understanding of solar flares.
Dr. Shintaro Ito of KEK analyzed the high-energy data in the search for neutrinos from solar
flares, and made the event displays.
I would like to express my gratitude to Associate Professor Hiroyuki Sekiya for providing
me with various experimental materials, including the detector itself, and a lot of advice on
the calibration experiment of the radon detector. When I broke the radon detector due to mycarelessness, he encouraged me to find out what the cause was as soon as possible and to restore
it immediately.
Prof. Yasuo Takeuchi of Kobe University gave me advice on calibration experiments of radon
detectors and data analysis of Super-Kamiokande. He also came to our drinking party and oﬀered
us some delicious drinks.
I would like to thank my members in Kamioka, Dr. Asato Orii, Dr. Masatoshi Kobayashi, Dr.
Ryosuke Akutsu, Mr. Yutaro Sonoda, Dr. Akira Takenaka, and Mr. Takumi Suzuki, Nobuyuki
Kato, Pedersen Juan William, and Toshiki Mochizuki for making my life in Kamioka enjoyable.
I would like to express my sincere gratitude to my high school baseball teammates, Ryo Abe,Rin Abe, Ryo Izaki, Tomoyuki Ito, Ryosuke Oshima, Arata Okawa, Kaoru Okamoto, Takuya Kijima, Yuji Sunazuka, Toshiyuki Tanaka, Tsubasa Tsuchiya, Shotaro Tsunoda, Hiroshi Nagatomi,
Hiroshi Nagayama, Ryosuke Ninomiya, Yudai Hakata, Tatsumi Hiraga, Naoya Fukushima, Yunosuke Hosokawa, Yuji Norihashi, Shunpei Murakami, Masayuki Yokoyama, Wataru Yoneda, andYuta Watanabe, for their continuous support and friendship even after graduating from highschool.
Finally, I would like to express my sincere gratitude to my family for their support.

iv

Contents
1 Introduction to Solar Flares and Neutrinos
1.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Sun and Its Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Observations of Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Soft X-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 Hard X-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3 γ-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.4 Coronal Mass Ejection (CME) . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Particle Acceleration in Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Predictions for Solar Flare Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Current Situaion and Importance of Solar Flare Neutrino Detection . . . . . . .

1
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1
4
6
9
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10
11
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15

2 Super-Kamiokande Detector
2.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Overview of the Super-Kamiokande detector . . . . . . . . . . . . . . . . . . . . .
2.3 PMTs for SK Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 20-inch PMTs (ID PMTs) . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Compensation Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 SK Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Water and Air Purification System . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Water Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Air Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Data Acquisition and Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 DAQ system of SK-I to SK-III . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 DAQ system for SK-IV . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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20
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22
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25
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3 Search Time Window Determination
3.1 The Importance of Determining Search Time Window . . . . . . . . . . . . . . .
3.2 The Visible Side Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Solar Flare Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Time Window Determination . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 The Invisible Side Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Search window for solar flares at invisible side . . . . . . . . . . . . . . . .
3.3.2 Solar Flare Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Time Window Determination . . . . . . . . . . . . . . . . . . . . . . . . .

31
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34
47
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49
49

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CONTENTS
3.4

Summary of the Search Time Windows. . . . . . . . . . . . . . . . . . . . . . .

50

4 Detector Calibration
4.1 ID PMT Calibraion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Water Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Absolute Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52
52
55
58

5 Simulation
5.1 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 High-Energy neutrino interactions . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Low-Energy neutrino interaction . . . . . . . . . . . . . . . . . . . . . . .
5.2 SK Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Solar Flare Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 SK Data Analysis
6.1 High-Energy Event Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.3 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.4 Fourth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.5 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.6 Final Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.7 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Low-Energy Event Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.5 Summary of Low-Energy Sample . . . . . . . . . . . . . . . . . . . . . . .
6.3 Summary for SK Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73
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86

7 Results and Discussions89
7.1 Visible Side Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2 Invisible Side Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.3 Fluence Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.4 Discussions and Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8 Conclusion

125

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8

The schematic diagram of the Sun’s layered structure . . . . . . . . . . . . . . .
The yearly occurrence rate of the solar flares and CMEs . . . . . . . . . . . . . .
The frequency of solar flares as a function of their total energy. . . . . . . . . . .
A schematic view of magnetic reconnection site. . . . . . . . . . . . . . . . . . . .
Numerical simulation results of solar flare by T.Yokoyama and K.Shibata . . . .
The prediction of Solar Flare neutrino flux by Kocharov . . . . . . . . . . . . . .
The prediction of solar flare neutrino flux by Takeishi et al. . . . . . . . . . . . .
The prediction of solar flare neutrino flux by Fargion and Moscato . . . . . . . .

4
5
6
7
8
14
15
16

2.1 Schematic illustration of the Super-Kamiokande detector . . . . . . . . . . . . . .
2.2 The schematic view of 20-inch PMT. . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Quantum eﬃciency as a function of incident photon wavelength. . . . . . . . . .
2.4 Single photoelectron distribution of the ID PMT. . . . . . . . . . . . . . . . . . .
2.5 Transit time distribution of the ID PMT. . . . . . . . . . . . . . . . . . . . . . .
2.6 A schematic view of the compensation coils of SK. . . . . . . . . . . . . . . . . .
2.7 Water purification system of the Super-Kamiokande detector . . . . . . . . . . .
2.8 Air purification system of the Super-Kamiokande detector . . . . . . . . . . . . .
2.9 The schematic view of analog input blocks of ATM. . . . . . . . . . . . . . . . .
2.10 The schematic view of the DAQ system for the SK-I to SK-III inner detector. . .
2.11 The schematic view of DAQ system for SK-I to SK-III outer detector. . . . . . .
2.12 Block diagram of the QTC and its surroundings. . . . . . . . . . . . . . . . . . .
2.13 Schematic view of the data acquisition system of SK-IV. . . . . . . . . . . . . . .

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24
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26
26
27
28
29

3.1
3.2
3.3
3.4
3.5
3.6
3.7

Normalized time profiles of selected emissions from the solar flare occurring on
October 28, 2003. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An example solar flare occurring on October 28, 2003, showing the soft X-ray light
curve observed by the GOES satellite and the derivative of the flux of soft X-rays.
Energy spectra of γ-rays associated with the solar flare occurring on November 2,
2003, as recorded by the RHESSI satellite. . . . . . . . . . . . . . . . . . . . . . .
Count rates recorded by the LEP detector when this solar flare occurring on
October 28, 2003 are color-coded (white-blue-green-yellow-red-black). . . . . . .
Light curve associated with the solar flare occurring on October, 28, 2003 asrecorded by the GEOTAIL satellite. . . . . . . . . . . . . . . . . . . . . . . . . .
Light curves of the solar flare occurring on November 2, 2003. . . . . . . . . . . .
Distributions of the width of time window determined by each method. . . . . .
vii

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40
41
44

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LIST OF FIGURES
3.8

Time duration as a function of the peak intensity of soft X-ray. Black dots, Red
squares, Green up-triangles, Blue down-triangles, and Light blue stars show soft
X-ray, Detivative of soft X-ray, Hard X-ray(100–800 keV), Line γ-ray, and Hard
X-ray(above 50 keV) emissions, respectively. . . . . . . . . . . . . . . . . . . . . .
3.9 Time diﬀerence distribution after subtracting the peak timing of soft X-rays. . .
3.10 Relationship between each channel’s peak timing after subtracting the peak timeof soft X-rays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.11 The correlation between the speed of the CMEs and the peak intensity of soft
X-rays from solar flares monitored by the GOES satellite. . . . . . . . . . . . . .

45
46
48
49

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

Relative gain distribution of the ID PMTs. . . . . . . . . . . . . . . . . . . . . . 53
Picture of Ni-Cf source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Charge distribution in units of pC obtained in the absolute gain calibration. . . . 55
The position dependence of the photon detection probability in the detector . . . 56
The schematic diagram of the timing calibration system . . . . . . . . . . . . . . 57
A typical TQ distribution for one readout channel . . . . . . . . . . . . . . . . . 58
Timing distribution added over all the readout channels in Qbin=14 (photoelectron). 59
Timing resolution σt (square) and σ ′ t (triangle) as a function of charge (photoelectron) for SK-IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.9 The schematic view of the calibration system for water transparency . . . . . . . 61
4.10 The comparison between laser MC and calibration data. . . . . . . . . . . . . . . 62
4.11 Typical fitted water coeﬃcient functions used in the MC. . . . . . . . . . . . . . 63
4.12 Time variation of water transparency. . . . . . . . . . . . . . . . . . . . . . . . . 63
4.13 Summary of absolute energy scale measurements for each SK phase. . . . . . . . 64
4.14 A schematic diagram of LINAC calibration system. . . . . . . . . . . . . . . . . . 64
4.15 The linearity of the germanium detector. . . . . . . . . . . . . . . . . . . . . . . . 65
4.16 The diﬀerence between the data and the fitted line in Fig. 4.15. . . . . . . . . . . 65
4.17 The diﬀerence of the Neﬀ between the LINAC calibration data and the MC simulation in SK-IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1
5.2
5.3

68
69

5.4
5.5
5.6

Cross-section for the CCQE scattering of muon neutrino and muon anti-neutrino.
Cross-section for single pion production of the muon neutrino. . . . . . . . . . . .
Comparison between experimental data and calculated curves of the total crosssections of the CC interaction for ν and ν̄. . . . . . . . . . . . . . . . . . . . . . .
IBD cross-section on a free proton as a function of neutrino energy. . . . . . . . .
The energy distribution of solar flare neutrinos from Fargion. . . . . . . . . . . .
The energy distribution of solar flare neutrinos from Fargion. . . . . . . . . . . .

6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8

The schematic view of high-energy event type. . . . . . . . . . . . . . . . . . . .
The schematic view of the cable hole and veto counter. . . . . . . . . . . . . . . .
Basic idea of finding ring candidates. . . . . . . . . . . . . . . . . . . . . . . . . .
Definition of θi and ϕi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Angular dependence of acceptance of PMT . . . . . . . . . . . . . . . . . . . . .
cut criteria for spalltion likelihood . . . . . . . . . . . . . . . . . . . . . . . . . .
final sample distribution (SK I-III) . . . . . . . . . . . . . . . . . . . . . . . . . .
final sample distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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80
82
82
87
88
88

7.1

The time distributions of high-energy neutrino events around the solar flares occurring on the visible side of the Sun on November 6th, 1996 (top), July 14th,
2000 (upper-middle), April 2nd, 2001 (lower-middle), and April 6th, 2001 (bottom). 92

70
71
72
72

LIST OF FIGURES
7.2

ix

The time distributions of high-energy neutrino events around the solar flares
occurring on the visible side of the Sun on April 15th, 2001 (top), October
23rd, 2003 (upper-middle), October 28th, 2003 (lower-middle), and October 29th,
2003 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.3 The time distributions of high-energy neutrino events around the solar flares occurring on the visible side of the Sun on November 2nd, 2003 (top), November
4th, 2003 (upper-middle), January 20th, 2005 (lower-middle), and September 7th,2005 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.4 The time distributions of high-energy neutrino events around the solar flares occurring on the visible side of the Sun on September 8th, 2005 (top), September
9th, 2005 (upper-middle), December 5th, 2006 (lower-middle), and December 5th,
2006 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.5 The time distributions of high-energy neutrino events around the solar flares occurring on the visible side of the Sun on August 9th, 2011 (top), March 7th,
2012 (upper-middle), September 6th, 2017 (lower-middle), and September 10th,2017 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.6 The time distributions of low-energy neutrino events around the solar flares occurring on the visible side of the Sun on November 6th, 1996 (top), July 14th,
2000 (upper-middle), April 2nd, 2001 (lower-middle), and April 6th, 2001 (bottom). 97
7.7 The time distributions of high-energy neutrino events around the solar flares
occurring on the visible side of the Sun on April 15th, 2001 (top), October
23rd, 2003 (upper-middle), October 28th, 2003 (lower-middle), and October 29th,
2003 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.8 The time distributions of low-energy neutrino events around the solar flares occurring on the visible side of the Sun on November 2nd, 2003 (top), November
4th, 2003 (upper-middle), January 20th, 2005 (lower-middle), and September 7th,2005 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.9 The time distributions of low-energy neutrino events around the solar flares occurring on the visible side of the Sun on September 8th, 2005 (top), September
9th, 2005 (upper-middle), December 5th, 2006 (lower-middle), and December 5th,
2006 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.10 The time distributions of low-energy neutrino events around the solar flares occurring on the visible side of the Sun on August 9th, 2011 (top), March 7th,
2012 (upper-middle), September 6th, 2017 (lower-middle), and September 10th,2017 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.11 The time of observed neutrino events for the solar flare on November 4th, 2003 (left),and July 6th, 2017 (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.12 The energy distribution of the neutrino events observed in the time window forsolar flares occurring on the visible side of the Sun and that of the backgroundsample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.13 The angular distribution of the neutrino events from solar flares occurring on
November 4th, 2003, and that of signal simulation sample. . . . . . . . . . . . . . 104
7.14 The angular distribution of the neutrino events from solar flares occurring on
September 6th, 2017, and that of signal simulation sample. . . . . . . . . . . . . 104
7.15 The time distributions of high-energy neutrino events around the solar flares occurring on the invisible side of the Sun on April 18th, 2001 (top), November
2nd, 2003 (upper-middle), November 7th, 2003 (lower-middle), and November
9th, 2003 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

x

LIST OF FIGURES
7.16 The time distributions of high-energy neutrino events around the solar flares
occurring on the invisible side of the Sun on July 24th, 2005 (top), June 4th,
2011 (upper-middle), July 23rd, 2012 (lower-middle) December 13th, 2014 (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.17 The time distributions of low-energy neutrino events around the solar flares occurring on the invisible side of the Sun on July 24th, 2005 (top), June 4th,
2011 (upper-middle), July 23rd, 2012 (lower-middle) December 13th, 2014 (bottom).109
7.18 The time distributions of low-energy neutrino events around the solar flares occurring on the invisible side of the Sun on July 24th, 2005 (top), June 4th,
2011 (upper-middle), July 23rd, 2012 (lower-middle) December 13th, 2014 (bottom).110
7.19 The time diﬀerence between the two events observed within the search windows
for solar flares on November 8th, 2003 and July 24th, 2005. . . . . . . . . . . . . 111
7.20 The number of neutrino candidates in the search time window per one solar flare. 112
7.21 The energy distribution of the neutrino events observed in the time window forsolar flares occurring on the invisible side of the Sun and that of the backgroundsample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.22 The angular distribution of the neutrino events from the solar flare occurring on
November 7th, 2003, and that of signal simulation sample. . . . . . . . . . . . . . 114
7.23 The angular distribution of the neutrino events from the solar flare occurring on
November 7th, 2003, and that of signal simulation sample. . . . . . . . . . . . . . 114
7.24 The angular distribution of the neutrino events from the solar flare occurring on
July 23rd, 2005, and that of signal simulation sample. . . . . . . . . . . . . . . . 115
7.25 The angular distribution of the neutrino events from the solar flare occurring on
July 23rd, 2005, and that of signal simulation sample. . . . . . . . . . . . . . . . 115
7.26 The angular distribution of the neutrino events from the solar flare occurring on
June 4th, 2011, and that of signal simulation sample. . . . . . . . . . . . . . . . . 116
7.27 The angular distribution of the neutrino events from the solar flare occurring on
July 23rd, 2012, and that of signal simulation sample. . . . . . . . . . . . . . . . 116
7.28 The comparison between predicted fluence by solar flare neutrino models andfluence upper limits obtained in this study. Red solid lines (black dashed line)
show predicted neutrino fluence of each model (fluence upper limit). . . . . . . . 119
7.29 The fluence limit obtained by the SK-I, II, III, and IV together with the otherexperimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

List of Tables
1.1
1.2
1.3

Three flavor ν oscillation parameters obtained from diﬀerent global analysis ofneutrino data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Classification of a Solar Flare. . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the predicted solar flare models. . . . . . . . . . . . . . . . . . . . .

3
9
14

2.1
2.2
2.3
2.4
2.5
2.6
2.7

The list of critical energies of charged particles in water. . . . . . . . . . . . . . .
The summary of 20-inch PMT charactaristics. . . . . . . . . . . . . . . . . . . . .
The Current flowing in the compensation coils. . . . . . . . . . . . . . . . . . . .
The summary of SK phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The summary of Hardware Trigger threshold in SK-I to SK-III. . . . . . . . . . .
Observable charge range for each of the three input channels of QBEE. . . . . . .
The summary of software trigger in SK-IV. . . . . . . . . . . . . . . . . . . . . .

18
20
21
22
27
28
30

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8

Observation targets for each solar satellite. . . . . . . . . . . . . . . . . . . . . . 32
Summary of satellites and energy ranges in this study. . . . . . . . . . . . . . . . 32
List of solar flares selected for this study. . . . . . . . . . . . . . . . . . . . . . . 33
Time windows determined for soft X-rays, derivative of soft X-rays and hard X-rays. 42
Time windows determined for line γ-rays (RHESSI) and hard X-rays (GEOTAIL). 43
Summary of timing information obtained in this study. . . . . . . . . . . . . . . . 45
Summary of results from fits in Fig. 3.10. . . . . . . . . . . . . . . . . . . . . . . 47
The summary of the search windows estimated in this study for energetic CMEs
occurring on the invisible side of the Sun. . . . . . . . . . . . . . . . . . . . . . . 50
3.9 The time windows that used to search for neutrinos from solar flares on the visible
side in this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10 The time windows that used to search for neutrinos from solar flares on the invisible side in this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1

Summary of absolute gain values in SK. . . . . . . . . . . . . . . . . . . . . . . .

53

6.1
6.2
6.3

Reduction eﬃciency after each FC reduction step . . . . . . . . . . . . . . . . . .
Reduction eﬃciency after each low-energy reduction step . . . . . . . . . . . . . .
Background event rate of each SK phase. . . . . . . . . . . . . . . . . . . . . . .

79
86
86

7.1

The summary of two events observed within the search window for neutrinos
associated with the solar flare occurring on the visible side of the Sun. . . . . . . 90
The summary of events observed within the search window for neutrinos associatedwith the solar flare occurring on the invisible side of the Sun. . . . . . . . . . . . 105
The summary of fluence limits for the low-energy sample. . . . . . . . . . . . . . 117

7.2
7.3

xi

xii

LIST OF TABLES
7.4
7.5
7.6

The summary of fluence limits for the low-energy sample. . . . . . . . . . . . . . 118
The summary of fluence upper limits for the high-energy sample. . . . . . . . . . 121
The summary of fluence upper limits for the high-energy sample. . . . . . . . . . 122

Chapter 1

Introduction to Solar Flares andNeutrinos
In this chapter, the physics of neutrinos, solar flares, and neutrino emission associated with solar
flares are discussed.

1.1

Neutrinos

Neutrinos are elementary particles with no electric charge and interact with other particles via
the weak force and gravity only. Neutrinos interact with other matter only rarely, so if neutrinos
which are produced by high-energy phenomena in the universe can be observed, they can be used
to investigate phenomena occurring at the source. So far, neutrinos from fusion reactions at thecenter of the Sun [1], supernova explosions [2] and Blazer [3] have been observed.

1.1.1

Neutrino oscillation

One of the important properties of neutrinos is neutrino oscillation. They were thought to beparticles with zero mass in the standard model of particle physics. However, neutrino oscillation
was discovered with observations of atmospheric and solar neutrinos, with the consequence thatneutrinos have masses [4, 5]. The flavor eigenstates of neurinos, |να ⟩ (α = e, µ, τ ), can be
expressed as superposition of their mass eigenstates, |νi ⟩ (i = 1, 2, 3):∑|να ⟩ =
Uαi |νi ⟩ ,(1.1.1)iwhere U is a 3 × 3 unitary matrix which is call Pontecorvo-Maki-Nakagawa-Sakata (PMNS)
matrix [6, 7]. This PMNS matrix can be written by using 4 independent parameters, which are
mixing angles θ12 , θ23 , θ13 and the Charge-Parity (CP) violation phase δCP :




1
0
0
c13
0 s13 e−iδCPc12 s12 0 −s12 c12 0
010
U = 0 c23 s23  
0 −s23 c23
0
0 1−s13 eiδCP 0c13c12 s13s12 c13s13 e−iδCPc13 s23  ,(1.1.2)= −s12 c23 − c12 s13 s23 e−iδCP c12 c23 − s12 s13 s23 eiδCPs12 s23 − c12 s13 c23 eiδCP
c12 s23 − s12 s13 c23eiδCP
c13 c23
1

2

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

where cij = cos θij and sij = sin θij . If sin δCP ̸= 0, the PMNS matrix contains imaginary parts,
which cause CP violation. In vaccum, the time evolution of of a mass eigenstate can be derived
from the Schrödinger equation,id|νi (t)⟩ = H |νi (t)⟩ = Ei |νi (t)⟩dt
|νi (t)⟩ = exp(−iEi t) |νi (0)⟩ ,(1.1.3)(1.1.4)

where Ei is the energy of mass eigenstate, H represents Hamiltonian and t is a travering time of
the neutrino. From Eqs. 1.1.1 and 1.1.4, The flavor eigenstate |να ⟩ at a time t can be written as∑|να (t)⟩ =Uαi exp(−iEi t) |νi (0)⟩(1.1.5)i

When the mass of a neutrinos, m2i , are too small compared to their momenta, pi , an approximation,√Ei =p2i + m2i ≈ pi +m2i
m2
≈p+ i ,
2pi
2Ei

(1.1.6)

where the neutrino energy, expressed as E ∼ |pi | ∼ |pj |. Then, Eq. 1.1.5 becomes as following:|να (t)⟩ =∑Uαi exp(−ipt) exp(−

im2i t) |νi (0)⟩2EUαi exp(−ipt) exp(−

im2i t †)Uβi |νβ ⟩ .
2E

i

=

∑
i,β

(1.1.7)the να → νβ transition probability P (να → νβ ) is calculated as:
P (να → νβ )

=
=

=

=

=

| ⟨νβ |να (t)⟩ |2∑
im2 t † 2||
Uαi exp(−ipt) exp(− i )Uβi
2E
i,β
(
)
∑ †
i(m2i − m2j )t†Uαi Uβi Uαj Uβj exp −
2E
i,j
(
)
∑ †
i∆m2ij L†
Uαi Uβi Uαj Uβj exp −2Ei,jδαβ − 4∑††Uβi Uαj Uβj) sin2 (Re(Uαi

i>j

+

2

∑
i>j

†
†
Im(UαiUβi Uαj Uβj) sin(∆m2ij L)4E

∆m2ij L)2E

(1.1.8)where ∆m2ij ≡ m2i − m2j is a mass-squared diﬀerence, t is replaced with a travel distance L = ctand δαβ is the Kronecker’s delta. According to this equation, neutrino oscillation will happen
when at least two neutrino masses are not degenerate (mi ̸= mj ) and there is nonzero mixing angle (θij ̸= 0). Neutrino oscillation in a vauum can be described by six parameters: three mixing

1.1. NEUTRINOS

3

angles (θ12 , θ23 , θ13 ), two mass squeared diﬀerence1 (∆m212 , ∆m223 ), and a CP phase (δCP ). These
parameters have been measured by using various neutrino sources: solar, reactor, atmospheric
and accelerator neutrinos. The parameters θ12 , ∆m212 are measured by solar neutrino experiments [8–10]. Atmospheric neutrino and accelerator neutrino experiments [11–14] establishedthe parameters, θ23 , ∆m223 . Measurements at reactor experiments [15–17] established that the
mixing angle, θ13 , was small but nonzero. The value of the CP phase (δCP ) is still unknown
but Tokai to Kamioka (T2K) experiment [18] showed non-zero δCP with 95% Confidence Level(C.L.). The best fit values of global analysis of neutrino data are summarized in Table. 1.1.
There are two possibilities of mass hierarchy, which depend on the ordering of the neutrino mass
eigenstates. The order, m1 < m2 < m3 (m3 < m1 < m2 ), is called to Normal Ordering (NO)(Inverted Ordering (IO)).
Table 1.1: Three flavor ν oscillation parameters obtained from diﬀerent global analysis of neutrino
data. In all cases the numbers labeled as NO (IO) are obtained assuming NO (IO), i.e., relative
to the respective local minimum.
Parameter
Best fit valueNO+0.13
sin2 θ12 [10− 1]
3.10−0.12+0.18
2
sin θ23 [10− 1]
5.63−0.24+0.066sin2 θ13 [10− 2]
2.237−0.065
δCP [◦ ]221+39
−28
+0.21
2
−5
∆m21 [10 eV]
7.39−0.20+0.029∆m223 [10−3 eV]
2.454−0.031
IO+0.13
sin2 θ12 [10− 1]
3.10−0.12+0.17
2−
sin θ23 [10 1]
5.65−0.22+0.0652−sin θ13 [10 2]2.259−0.065◦
δCP [ ]
282+23−25+0.21∆m221 [10−5 eV]
7.39−0.20∆m223 [10−3 eV] −2.510+0.030−0.031

1 ∆m2 + ∆m2 + ∆m2 = 0
12
23
31

4

1.2

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

The Sun and Its Activity

The sun is a multi-layered, spherical mass of gas that is composed of hydrogen and helium witha radius of about 7.0 × 105 km. The structure is as follows:• Core – The region where the nuclear fusion reaction occurs. Its size is about
1.0 × 105 km, which is 20% of the solar radius.
• Radiative zone – In this region, convection cannot occur. Therefore, The energy generated in the core is transferred by means of radiation rather than by
convection. It appears between 20% and 70% of the solar radius.
• Convective zone – between 70% of the solar radius and the visible surface.
• Photosphere – The light emitted to the outside of the Sun is generated in thislayer, which corresponds to the visual stellar surface.
• Chromosphere – A dilute gas layer on the photosphere. It is several thousand
to ten thousand kilometers thick.
• Corona – The Sun’s corona extends 10 solar radii into outer space and is mosteasily seen during a total solar eclipse.

CoronaChromosphere

Photosphere

Convective Zone

Radiative Zone

Core
0

0.2

0.7

1
Solar RadiusFigure 1.1: The schematic diagram of the Sun’s layered structure. The scale is based on a solar
radius as unit.
Solar activity goes through an 11-year cycle of activity and quiescence. As shown in Figure 1.2,
the frequency of solar flares is synchronized with the sunspot number, and about 3,000 solar flare
events are observed per year during the maximum season.

5

4000

300

3500

Number of Solar Flares
Number of CMEs
Number of Sun Spots

3000

250

200

2500
2000

150

1500

100

1000
50
500
0

1996 1998 2000

2002 2004

2006 2008 20102012

02014 2016 2018
Year

Figure 1.2: The yearly occurrence rate of the solar flares and CMEs, and the monthly variationof the number of the sun spots at the surface of the Sun during solar cycle 23 and 24. The
number of solar flares, CMEs and sunspots are taken from NOAA’s solar flare list2 , LASCOCME Catalog3 and Sunspot Index and Long-term Soalr Observations4 , respectively.

1 https://www.ngdc.noaa.gov/stp/solar/solarflares.html
2 https://cdaw.gsfc.nasa.gov/CME list/UNIVERSAL/1999 02/univ1999 02.html
3 https://wwwbis.sidc.be/silso/datafiles

Sun Spot Number[Month-1]

Number of Solar Flares or CMEs [Event Year-1]

1.2. THE SUN AND ITS ACTIVITY

6

1.3

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

Solar Flares

A solar flare is a process in which magnetic energy is converted into thermal, kinetic, and particle
acceleration energy in the outer layers of the solar atmosphere which is shown as chromosphereand corona in Fig. 1.1. The amount of energy generated by a single solar flare is typically1026 − 1032 erg, making it the largest energy release event in the solar system. The typicaltimescale for energy release is 100−1000 seconds based on electromagnetic wave observation [19].
Solar flares occur mainly in the vicinity of active regions which is seen as a sunspot. The frequencyof flares depends on the solar activity cycle and can be more than 10 events per day during the
maximum period, while it can be only one event per month during the minimum period asshown in Fig. 1.2. Figure 1.3 shows the relationship between the frequency of solar flares andtheir energy.

Figure 1.3: The frequency of solar flares as a function of their total energy. The higher theenergy released, the smaller the frequency of flares [20].

Solar flares accelerate ionized particles, such as electrons and protons, and carry nonthermalenergy from the acceleration site to the energy loss site in the chromosphere.
Neutral particles associated with solar flares are important to testify to theoretical aspectsof particle accelerations in magnetic reconnection because they can escape from the accelerationsite. Their observations reveal both spatial and time profiles of primary particle acceleration
while primary and secondary charged particles are trapped by a magnetic field.

Magnetic Reconnection
Magnetic reconnection is thought to play an important role in solar flares because magnetic
energy is converted into kinetic and thermal energy of particles in a short period which agrees with

1.3. SOLAR FLARES

7

solar flare observations. When antiparallel magnetic field lines are pressed against each other inthe plasma, a surface current called a current sheet flows between them. As long as the current isflowing, the opposing lines of magnetic force do not connect, but if the current dissipates for somereason, the lines of magnetic force are reconnected, and the strong magnetic tension of the newly
created lines of magnetic force causes the plasma to accelerate violently [21]. Figure 1.4 shows
the schematic view of magnetic reconnection site. Figure 1.5 shows the numerical simulation
result of magnetic reconnection. The numerical simulation of magnetic reconnection reproduces
well the cusp shape as seen in soft X-ray observations.

Figure 1.4: A schematic view of magnetic reconnection site. Black solid arrows show magnetic
force lines, the light blue cross shows current which is perpendicular to the magnetic force. Basedon Fig.1 of Ref. [21].

8

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

Figure 1.5: Numerical simulation results by T.Yokoyama and K.Shibata [22]. The top andbottom figures show the temporal evolution of temperature and density distribution, respectively.
The arrows show the velocity, and the lines show the magnetic field lines. The units of length,
velocity, time, temperature, and density are 3000 km, 170 kms−1 , 18 s, 2 × 106 K, and 109 cm−3
respectively. In the initial condition (t = 0) a dense region is located near the bottom of thesimulation box in which the density is about 105 times that of another region.

1.4. OBSERVATIONS OF SOLAR FLARES

1.4

9Observations of Solar Flares

Solar flares have been observed since the first observation in 1859 with electromagnetic waves invarious wavelength ranges. In this section, the observational information on solar flares which isused in this study are described.

1.4.1

Soft X-ray

Soft X-rays are originally produced by bremsstrahlung from electrons in thermal motion. Because
the energy of a particle accelerated by a solar flare is finally converted into thermal energy, thetotal intensity of the soft X-ray is used to represent the total energy released by the solar flare.
A peak value of the soft X-ray flux in the range of 1–8 Å (1.5–12 keV) observed by Geostationary
Operational Environmental Satellite (GOES) is widely used as an indicator in the classification ofsolar flares. The correspondence between the classifications and the peak intensity of the X-rays
is shown in Table 1.2. On the basis of this classification, a solar flare whose peak value exceeds
1.0 × 10−4 W/m2 (X1.0 class) is considered to be the largest order [23].
Table 1.2: The Classification of a Solar Flare.
Solar Flare Class Soft X-ray intensity [W/m2 ]A
10−8 –10−7
B
10−7 –10−6
C
10−6 –10−5
M
10−5 –10−4
X> 10−4

1.4.2

Hard X-ray

Hard X-rays are produced by bremsstrahlung from nonthermal electrons and the energy ranges
from a few keV to MeV. Such non-thermal electrons are accelerated by the solar flare; hence
they provide information about the energy distribution of the nonthermal electrons. Nonthermal
electrons lose their energy by scattering in the solar atmosphere and eventually generate thermal
bremsstrahlung. In contrast with soft X-rays, hard X-rays provide information about the electron
acceleration site and its time frame.
It is empirically known that the peak times of the hard X-ray flux occur close to the inflection
points of the soft X-ray light curve [24]. Therefore, by diﬀerentiating the light curve of soft Xrays with respect to time, we obtain a light curve similar to that of hard X-rays, and we cansimilarly extract information about electron acceleration.

1.4.3

γ-ray

Because neutrinos are produced via hadronic decay, the timing of these interactions should be
identified in order to determine the search window. The time profile of γ-rays is the most important in this study because observation of γ-rays implies the acceleration and nuclear reactions ofprotons. In a solar flare, there are several diﬀerent reactions which produce γ-rays; γ-rays due
to bremsstrahlung from high energy electrons, γ-rays due to electron-positron annihilation, line
γ-rays due to neutron capture on hydrogen nuclei, and γ-rays due to de-excitation from nuclei,
such as carbon (12 C) and oxygen (16 O) [25,26]. Among these, line γ-rays due to neutron capture
on hydrogen nuclei are the most important channel and are discussed below, along with γ-ray

10

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

emission due to neutral pions. Hard X-ray and γ-ray had been observed by Reuven Ramaty HighEnergy Solar Spectroscopic Imager (RHESSI) satellite from 2003 to 2018. This spacecraft wasable to make an image of solar flares with 3 keV to 17 MeV energy range. So, not only temporal
information but also the precise position of solar flares can be obtained from RHESSI’s data.

1.4.4

Coronal Mass Ejection (CME)

CMEs are known as phenomena associated with solar flares. It is a shock wave of plasma whichis accelerated in solar flare location. The observation of CMEs occurring on the invisible side of
the Sun is performed by coronagraph method with the LASCO, the Large Angle Spectroscopic
Coronagraph on the Solar and Heliospheric Observatory (SOHO) [27, 28]. The catalog of CMEs
observed by the SOHO spacecraft is maintained by NASA [29]2 and this catalog summarizes thetime of CMEs emission and its locations. CMEs can be observed even if the active region is
on the invisible side of the Sun. Therefore, this information is useful for making a search time
window for solar flares on the invisible side.

2 https://cdaw.gsfc.nasa.gov/CME_list/

1.5. PARTICLE ACCELERATION IN SOLAR FLARES

1.5

11

Particle Acceleration in Solar Flares

When solar flares occur, high-energy particles that do not normally exist in the solar atmosphere
are observed. Therefore, the particles must be accelerated by some acceleration mechanism
during solar flares, but it has not been clarified yet. In this section, candidates for the acceleration
mechanism are described. It is noted that three candidates are listed below, but many otherparticle acceleration mechanisms have been considered and their combination is also possible.

Stochastic Acceleration (Fermi’s second-order)
There is an acceleration mechanism called stochastic acceleration, which was proposed by E.
Fermi in 1949 [30]. Charged particles are accelerated to high energy by repeated collisions witha molecular cloud with a magnetic field.
Consider the case where a charged particle with energy E and speed vp collides with amolecular cloud moving at speed vm [31]. The change in energy in one collision can be writtenas∆E± /E = ±2(vm /vp )(1.5.1)

where ∆E+ is the energy obtained in a head-on collision with a molecular cloud, and that ina rear collision is ∆E− .
Frequency of frontal and rear collision per unit time Rfront and Rrear are
1 + vm /vp
tcoll
1 − vm /vp
Rfront =tcoll
Rrear =

(1.5.2)(1.5.3)where tcoll is the average time taken from the first collision to the next one. Thus, the energychange per unit time can be written asdE= Rrear ∆E+ + Rfront ∆E− = 4
dt

(

vm
vp

)2

E
tcoll

(1.5.4)This is called quadratic acceleration because the increment in energy is proportional to thesquare of vm /vp . It takes a very long time for a charged particle to be accelerated to high energy
since the speed of a molecular cloud vm is very small compared to the speed of charged particle
vp . The application of statistical acceleration to particle acceleration in solar flares has been
made by various theorists [32–36].

Shock Wave Acceleration
If the location of the stochastic acceleration process is near the shock wavefront, the collisions
between the molecular cloud and the charged particles are not random, and more eﬃcient acceleration occurs. This mechanism is most eﬀective if shocks with an angle of the upstream
magnetic field to the shock normal larger than 45◦ [37]. In this acceleration mechanism, theincremental energy of the particle is proportional to vm /vp .

12CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

Coherent Acceleration
The origin and strength of the electric field in a solar flare are not clear but acceleration models
with an electric field have been considered. A possible way that an electric field will appear ina solar flare is magnetic reconnection. The first suggestion that particle acceleration is caused
by magnetic reconnection in solar flares was made by Giovanelli [38]. Magnetic reconnection has
been applied to solar flare models.
There have been several attempts to estimate the electric field produced by resistive tearing
mode instability but the results disagree. The reason for the disagreement is that induced electricfields depend on the small-scale structure of the magnetic field and the transport properties of
the instability.

1.6

Predictions for Solar Flare Neutrinos

Last several decades, an emission model of solar flare neutrinos has been theoretically discussed [39–44]. For example, Fargion and Moscato predicted a possibility of observing neutrinos
from a large solar flare of energy greater than 1032 erg using Super-K and IceCube [42]. On theother hand, Takeishi et.al. predicted a rather small possibility of observing neutrinos even inHyper-Kamiokande [45] by numerical simulations [44]. In this section, general knowledge of pion
production by proton collision and the theoretical predictions of solar flare neutrino flux at the
Earth will be introduced.
If protons are accelerated during solar flares to suﬃciently high energies (more than about
300 MeV), pions are produced by collisions with other nuclei in the solar atmosphere [46, 47].
The main mechanism for the production of charged pions, the source of neutrinos, is as follows:p + p → ∆++ + n → p + π + + n↗ p + p + π0p + p → ∆+ + p↘ p + n + π+

(1.6.1)(1.6.2)or by scattering with neutrons, produced as follows:
p + n → ∆+ + n↗ n + π+ + n↘ p + π− + p(1.6.3)p + n → ∆0 + p↗ p + p + π−
↘ p + n + π0

(1.6.4)The proton energy threshold required for pion production can be derived from the kinetics
of proton scattering. When a solar flare occurs, the accelerated protons are inelastically diﬀused
by the protons in the solar atmosphere, which is considered to be almost stationary. Let A bean accelerated proton and B be a proton at rest, and let TA be the kinetic energy and p be themomentum of proton A in the system where proton B is at rest. The total kinetic energy of A
and B in the center-of-mass system is T , and we consider the case of forward scattering. Letting
the total energy be E, since E 2 − p2 c2 is invariant under the Lorentz transformation, we have
(TA + 2mp c2 )2 − p2 c2 = (2T + mp c2 )4(1.6.5)where mp is the mass of proton and c is the speed of light in the vacuum, respectively. On theother hand, TA can be written as√
TA = p2 c2 + m2p c4 − mp c2(1.6.6)

1.6. PREDICTIONS FOR SOLAR FLARE NEUTRINOS

13

From Eqs. 1.6.5 and 1.6.6, we have[
TA = 4T 1 +T
2mp c2](1.6.7)

In a center-of-mass system, the sum of the momenta of proton A and proton B is zero, so
the state in which both A and B are at rest after the collision satisfies the law of conservation of
momentum. Therefore, the energy produced in this collision is 2T . Considering that a particleof mass m is produced in this collision, the condition 2T ≥ mc2 must be satisfied.
From Eq. 1.6.7, we can find the minimum value of TA to be charged pions generated, which
is
]
[
mπ
TA ≥ 2mπ c 1 +4mp
2(1.6.8)where mπ is invariant mass of pion. Substituting mp = 938MeV/c2 and mπ = 139.5M eV /c2 , we
get the minimum kinetic energy of the proton required to produce a pion as

Tth = 293 MeV(1.6.9)Therefore, the amount of proton with kinetic energy greater than Tth is important for estimating the amount of solar flare neutrinos.
There are mainly three predictions for solar flare neutrino flux at the Earth with diﬀerent
assumptions. Generation of solar flare neutrinos was simulated assuming the isotropic and beamlike proton acceleration with the Monte Carlo methods by Kocharov, Kovaltsov, and Usoskin [43],and Takeishi et al. [44]. For Fargion’s and Moscato’s prediction [42], the neutrino flux was
estimated using the amount of energy taken up by pion production out of the total energy ofsolar flares.

Prediction of Kocharov, Kovaltsov, and Usoskin
They performed Monte Carlo simulations of particle production reactions in the solar atmosphere,
and present the expected number of neutrino events for two cases. In the first model, protons
that are isotropically accelerated are scattered by the solar atmosphere to produce pions, and asolar flare on the visible side of the sun is assumed. In the second model, protons are accelerated
as beam-like and scattered with protons in the photosphere of the Sun to produce pions. It iscorresponding to a solar flare on the invisible side of the Sun.

Prediction of Takeishi et al.
As in Kocharov, the proton energy spectrum is assumed to have a power spectrum and the numberof protons contributing to neutrino production Np (> 500 MeV) is estimated from the numberof protons with the energy above 30MeV obtained from γ-ray observations. The calculation isdone for two conditions: the case where the power index is 3 and the highest proton energy is
10 GeV, and the case where the power index is 1 and the highest proton energy is 100 GeV. The
results are several orders of magnitude smaller than those from Fargion and Kocharov, and they
indicate that it is diﬃcult to observe solar flare neutrinos with the Super-Kamiokande detector.

14

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

Figure 1.6: The prediction of Solar Flare neutrino flux by Kocharov [43]Prediction by Fargion and Moscato
Fargion [42] calculated the neutrino energy spectrum by considering the energy conversion fromthe magnetic reconnection into proton accelerations. Assuming the conversion eﬃciency is 10%,
Fargion estimated several neutrino interactions in the SK detector when solar flare classified as
the largest explosion (≥ 1032 erg) occurs at the invisible side of the Sun as listed in Table 1.3.
The ν generation conditions and numbers of the expected event in Super-Kamiokande (SK)are summarized in Table 1.3.

Table 1.3: Summary of the predicted solar flare models.
Model
Kocharov, Kovaltsov, and Usoskin [43]Takeishi et al. [44]Fargion and Moscato [42]Power index
of parent proton
3–4
1
3
1
-

ν generation condition
isotropic
beam likeisotropic
beam likeisotropic
isotropic

The number of expected
event in SK [/flare]
1.36 × 10−4
0.85
9.0 × 10−5
3.8 × 10−6
0.75
7.5

1.7. CURRENT SITUAION AND IMPORTANCE OF SOLAR FLARE NEUTRINO DETECTION15

Figure 1.7: The prediction of Solar Flare neutrino flux by Takeishi et al. [44]1.7

Current Situaion and Importance of Solar Flare Neutrino Detection

In 1988, the Homestake experiment reported an excess of neutrino events when energetic solar
flares occurred. This observation suggested a relation between solar flares and the neutrino
capture rate on 37 Cl [48, 49] and proposed neutrino magnetic moment spin precession to explain
the time variation of the capture rate [50, 51]. However, the Kamiokande [52], SNO [53] andBorexino [54] experiments searched for neutrino signals using diﬀerent solar flare samples andfound no excess of signals related to solar flares.
Observations of solar flare neutrinos are important in the following two respects. The first is
the investigation of the acceleration mechanism of hadrons in solar flares. If the neutrino energy
spectrum can be measured, it will tell us the conditions of the accelerated protons, and this will
provide new insights into the mechanism of ion acceleration in solar flares. The second is thatneutrinos from solar flares on the invisible side of the Sun could be directly observed. In thecase of a solar flare occurring on the invisible side of the Sun, the generated neutrinos penetrate
through the Sun to reach the Earth. Therefore, if we can observe neutrinos originating from solar
flares on the invisible side of the Sun, we may be able to obtain information on the acceleration
mechanism toward the center of the Sun.

16

CHAPTER 1. INTRODUCTION TO SOLAR FLARES AND NEUTRINOS

Muon and Tau Neutrinos Spectra from Solar Flares

81

Fig. 1 1.8:
SolarThe
neutrino
Flare fluxes
over known
neutrino background:solar neutrinos
by known
Figurepredictionof solarflare neutrino
flux by Fargion
and Moscato[42]
nuclear activities as well as the expected Supernova Relic fluxes and the atmospheric noises.
The Solar flare are estimated on the Earth at peak activity of the flare supposed to held
100 s. The two primordial flavour νe , ν e and their correspondent νµ , νµ are shown before
their oscillation while flying and mixing toward the Earth. Their final flavour are nearly equalin all states νe ,νµ , ντ and are not shown for sake of simplicity; however each final νe ,νµ , ντ ,νe ,νµ ,ντ fluxes are almost corresponding to the lower curve for the electron neutrino spectra.
Both highest and lowest activities are described following an up-going (poor flux) or downgoing (richer flux) scenario. The primary solar flare spectra is considered like the atmosphere
one at least within the energy windows Eνµ ! 10−3 GeV up to 10 GeV.

cm. The secondary muons µ do not loose much of their energy (≤ 1%) in ionization, (Eµ ≤E
0.1 − 1 GeV) during their nearly free decay: the muon flight distance is Lµ = mµµ Γµ −1 C =
E

dE

µ
−5
π
6.58 · 104 ( mµµ ) cm, and the ionization losses are: dE
MeV cm−1 . In conclusion
dx # dx # 10
most of the solar flare energy will contribute to downward muon energy, with an efficiency ηnear unity. At deeper regions, near h < −700 km where the solar density is n" ≥ 1020 cm−3 ,a GeV-muon will dissipate most of its energy in ionization before decaying. In that case theenergy ratio between muon relics and primary protons is much smaller than unity. Only asmall fraction of inward protons will reach by a random walk such deeper regions and we may
conclude that, in general, the flare energy relations are:EπF L ≡ ηEFL ≤ EFL

Chapter 2

Super-Kamiokande Detector
In this chapter, the detection principle, the overview of the Super-Kamiokande detector, thewater and air purification system and the data acquisition are described.

2.1

Cherenkov Radiation

The Cherenkov light is the light emitted when a charged particle passes through a dielectric
medium with a speed faster than the speed of light in vacuum. It is in the form of a cone along
the trail of a charged particle. The angle θc between the trajectory of the charged particle andthe direction of the Cherenkov light is given ascos θc =1βn(2.1.1)

where n is the refractive index of the dielectric medium and β is the velocity of the charged particle
when the velocity of light in vacuum, c, is 1. In water, n is about 1.34, and the Cherenkov angle
is about 42 degrees for a particle with β ∼ 1.
Since a charged particle must have a velocity faster than the speed of light in the medium toemit the Cherenkov light, the velocity of the charged particle satisfies
β>

1
.
n

(2.1.2)The lowest energy of the charged particle that satisfies this condition, which is called criticalenergy Ec , can be expressed as
Ec = √

nm0.
n2 − 1(2.1.3)where m0 is the mass of the charged particle. Table 2.1 shows the summary of critical energies
for typical charged particles in water.
The Cherenkov light is detected as a ring pattern in SK, from which the point of occurrenceof the event, the direction of travel of the charged particle, and the time of occurrence of theevent can be reconstructed.
The number of emitted photons N depends on the wavelength of the emitted photon λ:
)
(
1
dN
1
,
(2.1.4)= 2πα 1 − 2 2
dxdλ
n β
λ2
17

18

CHAPTER 2. SUPER-KAMIOKANDE DETECTOR

Table 2.1: The list of critical energies of charged particles in water.
Charged Particle Invariant Mass [MeV/c2 ] Critical Energy Ec [MeV]
Fukuda et al. / Nuclear Instruments and Methodse±in Physics Research A 501(2003) 418–462
425
0.511
0.767
µ±
105.7
157.4
π±
139.7
207.9
ing other locations within Japan,
1991

1992

1993

1994

1995

1996

1997

ne was determined to be the most
Excavationn for the experiment for many
Water lengthTankamiokande experimentwhere
had xbeenstands for the pathof the particle, and α ∼ 1/137 is the fine structure constant.
The number
photons
integrated
from 300 to 600 nm with respect to λ (the sensitive
pleted and made significant
phy- of emitted
Water Purification
wavelength
region
of
SK
PMTs)
is
about
340
photons/cm.
s; the mine was still in operation
Electronics
lities (electricity, water, air ducts,
Electronics Installtion
ications); its rock structurewas
2.2 Overview
of the Super-Kamiokande detector
very stable. A suitable site was
PMT Production
The Super-Kamiokande (SK) detector is a 50 kton water Cherenkov detector located in Hida
the mine for the new experiment,
PMT Installation
City,
Prefecture, Japan [55]. It is located at 36◦ 25′ 32.6′′ N latitude and 137◦ 18′ 37.1′′ Eting main tunnel; thus
it Gifuwould
longitude,
about 370 mCommissioning
above sea level, approximately 1000 m under the Ikenoyama-mountain.
to excavate a new tunnel,
whose
The detector is a cylindrical water tank 39.3 m in diameter and 41.4 m high as shown in Figure 2.1.
substantial fraction of the total
Data Taking

Because it is covered by a overburden about 1000 m thick, the event rate of muons from theatmosphere, which are the background of this analysis, are reduced to 1/100,000 compared toFig. 3. Super-Kamiokande construction schedule.
miokande project wasthat
approved
at the ground level. About 11,000 photomultiplier tubes are installed on the inner surface
Ministry of Education,
Science,of thedetector to detect the Cherenkov light.

ure in 1991 for total funding of
100 M. The US portion of thewas primarily to build the OD
roved by the US Department ofor $3 M. In addition the US has
about 2000 20 cm PMTs recycled
xperiment.
the cavity started in 1991, andction was completed by Decemer-Kamiokande was successfullynd began operations on April 1,
ed. By May 1, 1996, minor initial
he DAQ were cleared up and data
earnest. While earlier data are
Fig. 4. A sketch of the Super-Kamiokande detector site, undere number of interrupted runs
Figure 2.1: Schematic
illustration of the Super-Kamiokande detector. Taken from [55].
Mt. Ikenoyama.
ril, 1996 are normally discardedin physics analyses except for
ment, as well as the experiment control room, ard-going muons. Fig. 3 shows theseparate cavity housing the water purification
eline.
2.3
PMTs
for SKtoilet
Detectorsystem,facilities, and a parking area forew of the detector and othermine
vehicles.
A intobranchtunnelwinds
downward
wn in Fig. 4. In the inset
atthe
The SK detector structure is divided
an inner
detector(ID)and an outer detector (OD),aroundthetankandprovidesaccesstheinner detector has aorner, a sectional viewofMt.
with a stainless steel frame called a supermodule between them. toThediameter of 33.8 m pressure
and a heightof 36.2atm.theIt canstorebottom.
about 32.5
kton of ultrapure water and is
hatch
tank
Additionalhown, with Super-Kamiokandehalls for the electron LINAC located above andunder the peak where the tunnels
behind the main tank cavity and for equipment
storage are also provided.
hich houses the 50 kton tank is
The main tunnel also provides access to othere mine’s main horizontal truck
experiments at the Kamioka Observatory such ass 1800 m long at approximately
KamLAND. As a safety backup the experimental
bove mean sea level, as shown inareas can also be reached by mine train from thesu tunnel, named after the rivermine company’s surface facilities in Higashi–, provides access to the tank top,
Mozumi village.
nics huts and calibration equip-

2.3. PMTS FOR SK DETECTOR

19

equipped with 111291 20-inch photomultiplier tubes facing inward. This 20-inch photomultipliertube covers about 40% of the surface area of ID. The surfaces of ID other than the 20-inch
photomultiplier tubes are covered with black sheets to optically separate it from OD and inorder to prevent light leak from one side to the other. On the other hand, OD surrounds ID
with a thickness of 2 m and is capable of storing about 17.5 kton of ultrapure water. 1885 8-inch
photomultiplier tubes with a wavelength shifter plate of 60 cm wide and 60 cm high are mounted
in the OD layer. The wall and supermodule sides of the OD layer are covered with a highlyreflective Tyvek sheet in order to increase light collection eﬃciency in OD.

2.3.1

20-inch PMTs (ID PMTs)

The model number of the 20-inch photomultiplier tube (hereafter ID PMT or 20-inch PMT) usedin the inner tank is Hamamatsu R3600 and has a spherical shape with a diameter of 20-inch (50cm). Figure 2.2 shows a schematic diagram of the ID PMT. As shown in Fig. 2.3, the quantum
eﬃciency is wavelength dependent, and it is 22% at 390 nm. The sensitive wavelength range
is 280-660 nm. Figures 2.4 and 2.5 shows the pulse height distribution and the transit time
distribution for one photoelectron. The performance is summarized in Table 2.2. From the 2ndphase of SK (i.e. from 2002), the ID PMTs are covered with fiber-reinforced plastic (FRP) andacrylic cases to prevent a chain reaction implosion.

~ 70000

cable length
φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

water proof structure( 610 20 )

~ 720

(mm)

2.3.2

Quantum efficiency

Figure 2.2: The schematic view of 20-inch PMT. Taken from [55].

Compensation
0.2 Coils

Since the photoelectrons produced on the photocathode are collected by the electric field to thedynode, the geomagnetic field aﬀects the collection eﬃciency of the photoelectrons. In orderto reduce the eﬀect of geomagnetic field in the detector, 26 sets of coils are wound around the
0.1
tank to cancel out the geomagnetic
field inside the tank. Thanks to the eﬀect of these coils, themagnetic field in the tank is below 100 mG everywhere. Figure 2.6 shows a schematic view of thecompensation coils of SK and Table 2.3 shows the currents which are flowing in the compensationcoils.
0

1 This is the number in the 3rd and300
500 for the 600
700
4th phases400
of SK. Those
1st and 2ndphases are 11146 and 5182,

respectively. SK phases are explained in Sec. 2.4

Wave length (nm)

photwater proof structure( 610 20 )~ 720

CHAPTER 2. SUPER-KAMIOKANDE DETECTOR

Quantum efficiency

20

(mm)

0.2

0.1

0

300

400

500

600
700
Wave length (nm)Figure 2.3: Quantum eﬃciency as a function of incident photon wavelength. Taken from [55].

Table 2.2: The summary of 20-inch PMT charactaristics [55].
Model number
Hamamatsu R3600
Material of photocathode
Bialkali (Sb-K-Cs)
Quantum Eﬃciency
22% at λ ∼ 390 nm
Dynode type
Venetian blind type, 11 stages
Pressure tolerance
Pressure tolerance
Gain
107 at 2000 V
Dark current
200 nA at gain = 107
Dark noise rate
∼ 3 kHz at gain = 107
Transit time
90 nsec typical at gain = 107
Transit time spread
2.2 nsec at single photoelectron

2.4

SK Phases

Since the start of observations in April 1996, Super-Kamiokande has been divided into six dataacquisition phases. Table 2.4 summarizes the performance of the Super-Kamiokande detectors
in each phase.

SK-I
The data of SK-I was collected from April 1996 to July 2001. In July 2001, the faulty PMTs
were replaced. Later, while pouring ultrapure water into the detector, a PMT at the bottom
ruptured, causing other PMTs to rupture in a chain reaction. As a result of this accident, 6777
of the PMTs in the inner detector and 1100 of the PMTs in the outer detector were lost.

SK-II
After the accidental breakage of the PMTs, the number of PMTs in the inner tank was decreased
to 5182, and the data were taken from October 2002. The ID PMTs were equipped with shock
wave protection cases.

2.5. WATER AND AIR PURIFICATION SYSTEM

21

Figure 2.4: Single photoelectron distribution of the ID PMT. Taken from [55].

Table 2.3: The Current flowing in the compensation coils [56].
Coils in Fig. 2.6
A
B
C
D
E
F
G
Current [A]
31.35 31.35 31.35 28.80 30.10 28.60 30.10

SK-IIINew PMTs were installed to replace the ones lost due to the PMT breakage accident. As a resultof this work, the number of PMTs in the inner tank was 11129 and the coverage rate was 40%
again.

SK-IV
In August 2008, the electronics for data acquisition were redesigned, and a new set of electronics
called QBEE was introduced in SK-IV, replacing the ATM used in SK-I, SK-II, and SK-III.

SK-V
After refurbishing the tank for “Super Kamiokande Gadolinium” (SK-Gd), the observation was
resumed using ultrapure water.

SK-VI (SK-Gd)
Gadolinium with a concentration of 0.01% was added to improve the detection eﬃciency ofneutrons in July 2020.

2.5

Water and Air Purification System

The ultrapure water used in the Super-Kamiokande detector is purified from groundwater in the
Kamioka mine. The groundwater contains many impurities. The impurities absorb and scatter

22

CHAPTER 2. SUPER-KAMIOKANDE DETECTOR

Figure 2.5: Transit time distribution of the ID PMT. Taken from [55].

Table 2.4: The summary of SK phases.
SK Phase
Start Date
Stop Date
Number of ID PMT
Gadolinium dope
PMT Acrylic caseElectronics

SK-I
Apr. 1996
Jul. 2001
11146
×
×
ATM

SK-II
Oct. 2002
Oct. 2005
5182
×
◦
ATM

SK-III
Jul. 2006
Aug. 2008
11129
×
◦
ATM

SK-IV
Sep. 2008
May 2018
11129
×
◦
QBEE

SK-V
Jan. 2019
Jul. 2020
11129
×
◦
QBEE

SK-VI
Jul. 2020
Running
11129
◦
◦
QBEE

light and reduce light transmission, as well as radioactive impurities create background events inneutrino observation. So, it is necessary to remove them. In addition to this, the bedrock contains
many radioactive elements, and the air inside the mine, for example, has a concentration of radon
more than 100 times higher than the air on the ground. In the Super-Kamiokande experiment,
the air outside the mine is purified and blown to the experimental area which includes dome of
the SK detector, water system area and etc.

2.5.1

Water Purification System

The ultrapure water production system as shown in Fig. 2.7 in SK. A diﬀerent system has
been used for gadolinium dissolution in 2020, but the details are omitted because the data inultrapure water were used in this study. The following is a brief description of the ultrapure
water production process.
• 1µm filter – Removes dust particles larger than 1 µm in size.
• Heat exchanger – The water pump used for circulation and the photomultipliertubes emit heat. This heat causes the water temperature to rise, which increases

2.5. WATER
ANDSUPER-KAMIOKANDE
AIR PURIFICATION SYSTEM
CHAPTER
3. THE
DETECTOR

23

Figure 3.11:Figure
Schematic
view of thecompensationcoils. They
composedof 26[56].
sets of coils
2.6: A schematicviewof the compensationcoils areof SK.
Taken from
deployed outside the water tank. Taken from [33].
5. Radon-lessdissolving
the airdark
noise andsystemcauses convection inside the tank. To prevent the rise in theRadon-lessairtemperature,
is dissolved thein thewater, andit improves
theisradon
removalefficiency inwatertemperatureof thesupply water
adjusted
to be about
13 degrees
Celsius.
the following
vacuumdegasifier step.
• Ion exchanger – Removes metal ions dissolved in the water.

6. Reverse osmosis filter• UV
sterilizer– Irradiates
ultraviolet
to kill bacteria that breed in the
A reverse
osmosisfilterremoves withparticulates
in light
the water.
water.

7. Vacuum
degasifier system• Rn-free-air
dissolving system – In order to improve the removal eﬃciency ofRadon andair gasgases
in the water.
Dissolved
oxygenthe growthofradon
in arethe contained
vacuum degassing
process,
the air withtheencourages
radon removed
asbacteria.much
A vacuum
degasifier
removesgases
dissolvedinthewater.
The
removalefficiency
as possible is dissolved in pure water.
for radon
andoxygen gas is estimated to be about 96% and 99%, respectively.
• Reverse osmosis filter – Perform filtration using osmotic pressure to remove
organic
compounds with a molecular weight of about 100.
8. Cartridge
ion exchanger• Vacuum
degasifier(polisher)– Removesfurther
gases dissolvedin water.
Cartridge
ion exchanger
reduces ionsin the water.
• Cardridge Ion Exchanger – Cartridge ion exchanger further reduces ions in the

9. Ultra filter
water.
An ultrafilter, which consists of hollow fiber membrane filters, removes particulates whose
Ultra Filter– Removes
dust particles larger than 10 nm in size.
size is •greaterthan ∼
10 nm insmall
diameter.
• Membrane Degasifier – Removes gases dissolved in the water.

10. Membrane degasifier
A membrane degasifier further reduces radon gas dissolved in the water. The removal
2.5.2 Air Purification Systemefficiency for radon gas at this step is estimated to be about 83%.
Figure 2.8 shows the outline of the air purification system. The process of air purification isAfterthesebelow.
processes, the radon concentration in the supply water is estimated to be 1.74 ±shown
0.14 mBq/m3 , and in the return water, it is 9.06 ± 0.58 mBq/m3 [35]. Locations of the water
inlets and outlets in the SK tank are shown in Fig. 3.13.

3.2.4

Air Purification System

The radon concentration level in the air in the mine is about 100 times higher than outside.
This “radon rich” air contaminates the water in the detector. Therefore, an air purification
system is located outside the mine, and radon reduced air is sent to the experimental site as

24

Y. Nakano, T. Hokama, M. Matsubara et al.

CHAPTER 2. SUPER-KAMIOKANDE DETECTOR

Nuclear Inst. and Methods in Physics Research, A 977 (2020) 164297

Fig. 1. Schematic diagram of the SK-IV water system. Purified water is supplied through inlets at the bottom and drained from outlets in both the bottom and top regions asshown in details in Fig.
2.
Figure2.7: Water purification system of the Super-Kamiokande detector. Taken from [57].

reduced. For this purpose, we have developed a new measurement
system to monitor the Rn concentration in purified water. Herein we
present details of the system as well as results of in-situ measurements
at Super-K.
This paper is organized as follows. In Section 2 we describe theSuper-K detector and its water system as well as summarize the historyof Rn studies at Super-K. Section 3 presents a new method of extracting
Rn from water and subsequently describes the design and data analysis
of a system to measure the extracted Rn. We discuss backgroundlevels and systematic uncertainties accompanying this measurementin Section 4 before presenting measurement results in Section 5. In
Section 6, we discuss several possible Rn sources in the Super-K tank.
Finally in Section 7, we conclude this study and outline prospects forthe future. Note that we use the term Rn to refer specifically to 222 Rn
in this paper, unless otherwise stated.

background due to electrons from the decay of 214 Bi (Rn daughter).
The Q-value of this decay is E max = 3.27 MeV. In order to understandthis background and its contribution to the analysis of solar neutrinos,
precise measurements of the Rn concentrations in the water of SK-IV
detector and in the outputs of the system are necessary.
2.1. Water purification system

The original water purification system for Super-K has been described in Ref. [38]. During the first phase of Super-K (SK-I), it consistedof mechanical 1 m filters, a heat exchanger (HE1), mixed-bed deionization resins (Ion Exchanger, IE), ultraviolet (UV) sterilizers, avacuum degasifier (VD), a high-quality IE (Cartridge Polisher, CP), andultrafilters (UF). Their ordering here is the same as that of their appear2. The Super-Kamiokande detector
ance in the recirculation process. Over the intervening 20 years, the system has been continuously
upgraded
to reduce
and improve
Figure 2.8: Air purification system of the Super-Kamiokande
detector.
Taken
from impurities[55].
Super-K is a water Cherenkov detector containing 50 000 tonnes ofcontrol over the detector environment. For example, a reverse-osmosis
highly purified water that is viewed by 11 129 20-in. photomultiplier
membrane (RO) was added to the recirculation line during the second
tubes (PMTs) [14]. It is located roughly 1000 m underground (2700 m
phase of operations (SK-II), and an additional heat exchanger (HE3)water equivalent) inside the Ikenoyama mountain in Gifu prefecture,
was installed during the third phase (SK-III). Furthermore, at the begin• coordinate
Compressor– ofCompresses
theairz),to 7-8.5
atm.
Japan. We define the local
systemthe detector as(x, y,
ning of SK-IV an upgraded heat exchanger (HE4) was added to system
where (x, y) represents the plane of the cylinder as viewed from above
order to further control the input water temperature and thereby• within
Filterthe– Dustis tankremovedfromtheis air. inThere
are three types of filters: 0.3 µm,
and z represents the heightdetector[14]. The
originsuppress convection in the tank water, which causes Rn and otherplaced at the center of the tank.
0.1 µm, and 0.01 µm.
impurities to mix into the fiducial region of the detector (details below).
After the installation of new front end electronics in 2008 [15], thethe water temperature is controlled at 13.06 ˝ C with an
fourth phase of Super-K •(SK-IV)
started and was concluded
10 years
Dehumidification,
CO2 removal
systemAfterwards– Removes
H2 O and CO2 contained inaccuracy of 0.01 ˝ C [16,39]. The total circulation rate during SK-IV waslater in May 2018. With improvements
the air. in the water circulation system,
60 ton/h, which doubles that of SK-III. Fig. 1 shows the configuration
calibration methods [16], and event selection, the detector’s energyof the system
the end of carbon,
SK-IV.
threshold was lowered to•3.5Activated
MeV in termsof electron– recoil
kinetic en-air throughcharcoalBy passing
the atactivatedradon conergy [9]. These upgrades have also allowed for precision measurements
WaterissuppliedtoSuper-K
through inlets at the bottom region oftained in the air is adsorbed.
of the electron recoil energy spectrum and the Super-K data together
the inner detector (ID), which is shown in Fig. 2. The inlets extend up
with data from SNO provide
the strongest
constraint
on the solar
to zradon= *16.5removal
m in the eﬃciency,
tank, which is
40 cm isbelow
• Cooled
activatedcharcoal– Toelecincreaseradon
ad- the bottom edge oftron neutrino survival probability [9,17]. However, experimental data
the fiducial
volumeused for analysis [9]. The ID is separated opticallysorbedbyactivatedcarboncooledto−40
degreesCelesius.
from other solar neutrino experiments, including radiochemical exfrom the outer detector (OD) by a Tyvek sheet [16], but the water inperiments [18–20], water Cherenkov experiments [21–24], and liquid
the tank still flows from ID to OD. As shown in Fig. 2, water is drained
scintillator experiments [25–31] have not yet demonstrated the upturn
through outlets placed at the top region of the tank and at the bottomof the recoil energy spectrum expected from the MSW effect. This nullregion of the OD for recirculation and purification. The outlets placed
observation has motivated several theoretical explanations includingin the OD drain water from its barrel region (‘‘OD barrel’’).
models with sterile neutrinos [32–34], mass-varying neutrinos [35],
There are twelve inlets placed at the bottom of ID and four outlets
and non-standard interactions [36,37].
placed in OD. As a result of this configuration and the precise temAt energies below 5 MeV Super-K has observed an excess of events
perature control enabled by HE4, the water tank above z = *11 m
close to the detector structure near the bottom and barrel regions ofexperiences laminar flow, and therefore lower Rn backgrounds, while
the detector [9]. However, due to the limited energy resolution of thedetector [13], this energy region overlaps with that of the primarythat below this level undergoes convection [16].
22.6. DATA ACQUISITION AND ELECTRONICS

2.6

25

Data Acquisition and Electronics

From the start of SK observations until August 2008, an electronic circuit called Analog-TimingModules (ATM) was used for data acquisition. In September 2008, a new electronic circuit called
QTC-Based Electronics Ethernet (QBEE) and software trigger system were introduced. In thissection, these two types of DAQ system are described.

2.6.1

DAQ system of SK-I to SK-III

DAQ system for Inner Detector
Figures 2.9 and 2.10 show a schematic view of analog input blocks of ATM and the DAQ system
of SK-I to SK-III. The ATM combines the functions of an analog-to-digital converter (ADC) anda time-to-digital converter (TDC) to record the integrated charge and arrival time of each PMT
signal. 12 PMT signals are fed to a ATM board. The PMT signal in current splitter is divided
into four signals.
When one of the PMT signal is sent to the ATM channel and its amplitude is greater than
-1 mV (0.25 photoelectron), the ATM channel converts the amplitude and detection time ofthe signal into an analog charge and holds it. At the same time, the ATM board sends ananalog signal whose amplitude is proportional to the number of hit channels (HITSUM signal)to the trigger module. All HITSUM signals are summed up, and if the total amplitude exceeds
a threshold, a global trigger is issued. When a global trigger is generated, all ATMs digitize
the charge and time information which is held in the previous step. The digital signals are sent
to and stored at SMP (Super Module Partner). These data are sent to the online computers,
finally.
DAQ system for Outer Detector
A schematic diagram of the OD data acquisition system for SK-I to -III is shown in Fig. 2.11.
A single coaxial cable feeds high voltage to each PMT and carries back its analog signals. Eachchannel is connected to a custom paddle card which fans out the voltage to 12 PMTs. These
cards also pick oﬀ the analog PMT signals through a high voltage capacitor and resistor network,
allowing a single cable to be used for both HV and signal.
A signal from one OD PMT is sent to a charge-to-timing converter (QTC) module, whichconverts it to a rectangular pulse whose width is proportional to the input charge. Similarly
to ID, a HITSUM signal is generated at the QTC module and sent to the trigger module. If a
global trigger is issued, the leading edge and the width of the pulse is converted to the timing
and charge information of the OD PMT by the TDC module.
Hardware Trigger
There are three types of global triggers for ID and one type for OD. The SLE trigger rate is mostsensitive to the detector ambient background level, for example, γ-rays from rock, β-rays from214
Bi and so on. Therefore, the SLE trigger threshold value was changed many times. They havediﬀerent threshold voltage values, and their values are summarized in Table 2.5.

2.6.2

DAQ system for SK-IV

Figures 2.12 and 2.13 shows the block diagram of the QTC and its surroundings and the dataacquisition system of SK-IV. One QBEE module has eight QTCs (Charge to Time Converters),
and each QTC handles the signals of three PMTs. When a signal is sent to a QBEE channel,

26

CHAPTER 2. SUPER-KAMIOKANDE DETECTOR

PMTSUMHITSUM

PMT
signalCurrent splitter
Amplifierchannelcontroll
Discri.

controll
TAC-A
to ADC

splitted signal A

QAC-A

&

TAC-B
splitted signal B

QAC-B

trigger

Figure 2.9: A schematic view of the analog input blocks of the ATM. Only one channel is shownin the figure. Dashed arrows show the PMT signal, its split signals, and accumulated time andcharge signals. Solid arrows show the logic signals which control the processing of the analog
signals. Taken from [55].

Inner DAQ
×6

20-inch PMT

×8• PMT × 11146

SCH
ATM

• ATM × 946

× 20

× 240

ATM
GONG

TKO

interface
SMP
×6

trigger signal(to ATMs)HITSUM(from ATMs)• online computer
server × 9
host × 1

onlinecomputer(server)

Ultra-Sparc

VME

trigger logic• SMP × 48

Ultra-Sparc

onlinecomputer(host)

VME
interface
TRG

Ultra-Sparc

FDDI

onlinecomputer(server)

NIM

Figure 2.10: The schematic view of the DAQ system for the SK-I to SK-III inner detector.
Arrows show data flow. Taken from [55].

2.6. DATA ACQUISITION AND ELECTRONICS

27

Figure 2.11: The schematic view of DAQ system for SK-I to SK-III outer detector. Taken
from [55].

Table 2.5: The summary of Hardware Trigger threshold in SK-I to SK-III. About -11 mV corresponds to one PMT hit.
SK Phase
SK-I
SK-II
SK-III
HE−340 mV−180 mV−320 mV
LE−320 mV−152 mV−302 mV
SLE−260 → −180 mV −110 mV −212 → −186 mV
OD−380 mV−380 mV−380 mV

28
712

ARTICLE IN PRESSCHAPTER 2. SUPER-KAMIOKANDE DETECTOR

H. Nishino et al. / Nuclear Instruments and Methods in Physics Research A 610 (2009) 710–717

Fig. 3. Block diagram of the QTC and its surroundings. PMT signals, transmitted through coaxial cables, are divided among three QTC gain ranges. Combined with the
input circuits, the QTC provides full analog signal processing for the PMT signals. Output signals are generated by LVDS drivers and read by TDCs.

Figure 2.12: Block diagram of the QTC and its surroundings. PMT signals, transmitted throughcoaxial cables, are divided into three QTC gain ranges.
Combinedwiththelargest
inputgain
circuits,
the is "0:3
discriminator
thresholdfor therange (Small)
Table 1
Specificationof theQTC
QTCprovidesfull analog signal processing for the toPMT
signals.
Output signals
generated"14 mV.
Which discriminatoroutput areamong
the three ranges isused to trigger charging is also determined by control registers.
LVDS drivers and read Self-trigger
by TDCs.
Taken from [58].
Type byof trigger
by discriminator

The discriminator threshold can be increased by using a lower
gain range for the trigger. A channel can be disabled by disabling
all three of its ranges. The charge dynamic range can be controlled
by the gain of the V=I converter and the amount of constantDiscriminator
Tablethreshold
2.6: Observable charge range for each of the three
inputcurrent;
channelsof QBEE.
[58].less jitter
dischargea largerdischargeTaken
currentfrom
produces
Charge dynamic range
and has a smaller
charge[pC/count]
dynamic range. Discharge current should
Channel Observable range [pC] Charge
resolution
be optimized to achieve the best resolution over the required
Small
0–51
Charge resolution
dynamic range. 0.1
Integral (non)linearity
To minimize 0.7
power consumption, the QTC is designed toMedium0–357
Timing resolution
operate with a 4.9
single þ 3:3 V power supply. The band gap
High
0–2500reference of þ1:2 V drives the internal bias circuit and built-in
Power dissipation
6-bit/8-bit control DACs.
Process
Number of input channels
Processing speed
Charge integration gate
Number of gains

Package3! 900 ns/ cycle
400 ns1)
3 (Ratio 1: 17 : 49
"0:3 ! " 14 mV (small range)
0.2 ! 51 pC (small)
1 ! 357 pC (medium)
5 ! 2500 pC (large)! 0:2 pC (small)o 7 1%
0.3 ns (2 pC, " 3 mV)
o 0:1 ns ð4 100 pC)
o 100 mW/ ch
0:35 mm CMOS
100 pin CQFP

2.2. Design of the analog circuit

and its amplitude exceeds the threshold, 1/4 photoelectrons, the QTC module integrates thesignal and outputs a rectangular pulse, whose leading-edge
represents
signalcircuits
timingThis subsection
describesthe
the analog
that andare crucial todescribed in Section 2.2.2. The QTC output signal with null input
QTC performance,
tohandleaccurate
impedance
matching
at thewidth
represents
theintegrated
charge.
The
rectangular
pulse
is
sent
to
the
TDC
moduleandsignal can be measured by asserting the PEDESTAL signal.
input circuit block, wide-band signal amplification in the LNA,
digitized.
The
digitized
charge andtiminginformationis sent to the front-end PC through theThetimer blockcontains
three important
timers:a charging
noise suppression by band limitation at the discriminator block,
timer,
a discharging
timer,
and beinga VETO processed
timer. These by
timerseach (Field
Ethernet
cable
after
FPGA
Programmable
Gate
Array).
The
frontand signal
delay by the LPF
for precise
chargeintegration.
generate timing gates by ramps with constant discharge current
end PCs arrange the received data in a timing order and send them to the merger PCs, where aand comparators. The time length for these gates are controlled by
2.2.1. External input circuit
software trigger
is issued.
digital-to-analog
converters(DACs) for discharge current and forshown in Fig. 4, there is an external input circuit which
comparator
In thresholdorder tolevels.
improve the charge resolution at a few As
p.e.
levels and to handle a wider range ofcontains a termination resistor, gain-adjusting attenuators, and
Fig.
5
shows
the
timing
chart
for
QTC
operation.
The
charging
2.6
charges than ATM, QTC has three gain range channels(Small,Medium,andHigh).
DC blocking capacitors
outsideof theQTC. InTable
order tosatisfy thetimer, triggered by the discriminator output signal, operates for
shows
the
observablechargerange
andresolution.
Overall,thecharge
range
is
0.2
pC
to
2500
requirementfor
impedance
matchingatprecisionfor o 0:1%
! 400 ns. Soon after the end of the charge gate, the discharging
U-turned reflection signal, an external resistor network is used fortimerpC.
operates for ! 350 ns. During the charge gate, the switch
the input signal termination while the QTC input impedance isbetween the V=I converter and charging capacitor closes and
10 k O. This external resistor network is also used to determine
input charge accumulates in the capacitor. During the discharge
the gains of the three QTC gain stages. In our application for the SK
Triggerthe discharging current source andgate,Software
the switch between
detector, input signals are divided by two 17 dB p attenuators into
capacitor closes, and arriving input signals are ignored. The
the three gain stages, for which the ratio of the divided signals istrailingedge mergerof the QTC
outputrepresents
the time
In thePC,
the signal
softwaretriggering
is whenperformedbylooking for events where the number of
1. Then the divided signals are fed into the QTC via the DC
1: 17 : 49
the PMTs
integrated
voltagedecreases
the comparator
hitsignal
within
200 nsec,
N200to, exceeds
a certain blocking
threshold.
Table
2.7 summarizes
the trigger
capacitors
to avoid
direct current injection.
threshold level; thus, the QTC output signal widens as the input

types,
N200At thresholds,
and typicalevent
signalgets larger.
the end of the dischargegate, reset
andrates.
VETO The time width for an event with LE or HE
trigger
is 40 All
µsec.
the caseof thetheVETO
SLEtimertrigger,
event
time widthis set to 1.3 µsec to reduce
Low-noiseamplifiersignals
are issued.
QTCIn
circuits
exceptare the2.2.2.
Fig. 6AFTshows(AFTer)
the LNA, which
amplifies
input PMT
reinitialized
and the ofbaseline
the LPF
outputis restored
to avoid
the amountdata.of The
SHE(SuperHigh
Energy) andtriggers
weretheadded
for signals.
The LNA is a resistor feedback inverting amplifier with a cascodeundesired effects for the next incoming signals. Input signals
70, andthe study of supernova relic neutrinos. The SHE trigger
is triggered when N200 exceeds
within ! 150 ns after the discharge gate are ignored. In total,
stage. Resistive rather than capacitive
feedback is used to handle
the AFT
triggeris issued
not with
issuedthe SHEis CALissued.
signals
wideandbandwidth.
The trigger
signal pathis devoted toprocessing
time forone input
signal is only
! 900 ifns.the OD trigger is
Some
QTCtheoperations
and gateis lengths
be configured
calibration.
A commoncalibration
pulse cansupplied toWhen
AFT trigger
issued,candata
are acquiredcharge
without
settinga trigger
thresholdforbe500
all ranges of all channels. The path can be switched on and off by athrough register settings. The dynamic range of the gate length is150–1000 ns. The discriminator threshold is controlled by a DAC
MOSFET single-pole single-throw (SPST) switch controlled byregister settings.
and by the gain of the discriminator’s amplifier. The configurable

2.6. DATA ACQUISITION AND ELECTRONICS

29

Figure 2.13: Schematic view of the data acquisition system of SK-IV. In the left part, newly
developed front-end electronics boards connected with PMTs are shown. In the right part,components of the new online system are shown. The data are transferred from QBEEs to theorganizer PC via 100 Base-T (broken line), Gigabit Ethernet (solid line) or 10-Gigabit Ethernet(bold solid line). Taken from [59].

30

CHAPTER 2. SUPER-KAMIOKANDE DETECTOR

Table 2.7: The summary of software trigger in SK-IV.
Trigger type
SLE
LE
HE
SHE (before Sep. 2011)
SHE (after Sep. 2011)

N200 threshold [hit]
34
47
50
70
58

Recorded event time width [µsec]
1.3
40
40
40
40

Event rate [Hz]
∼3500
∼40
∼ 10
-

µsec after the event.
The SHE and AFT triggers can detect 2.2 MeV γ-rays emitted when neutrons are captured
by hydrogen nuclei. The hit threshold of the SHE trigger was lowered from 70 to 58 in September
2011.

Chapter 3

Search Time Window
Determination
This chapter describes the importance of determining the time window and how it was done inthis thesis.

3.1

The Importance of Determining Search Time Window

The GOES satellite provides data relating only to the intensity of soft X-rays produced bythermal electrons. Hence, the GOES data may not be particularly useful for identifying the time
window for the search for solar flare neutrinos because neutrinos originate from interactions ofprotons.
In the previous study, Wasseige [60] proposed a method for determining the search window
for solar flare neutrinos using γ-rays above 70 MeV for neutral pion decays (π 0 → 2γ) observedby the Fermi-LAT satellite. The appearance of neutral pions implies the production of neutrinos
in solar flares because charged pions are expected to be produced simultaneously with neutralpions. Therefore, it is natural to set the search window for solar flare neutrinos based on theoccurrence time frame of γ-ray emission caused by neutral pions. However, as the Fermi-LAT
satellite data is available only after its launch in 2008, this method cannot be applied to thesolar flares before that time, notably to the largest solar flare on record November 04, 2003, class
X28.0 [61]. For those reasons, an alternative method must have been developed to determine thetime window for the flare neutrino search.
Neupert [24] pointed out an empirical correlation between the soft X-ray flux and the integralof the microwave flux during solar flares (hereafter Neupert eﬀect). In many flares, the behaviorof the time derivative for the soft X-ray intensity is similar to a temporal variation of the radio,
hard X-ray and γ-ray flux during the impulsive phase. Although the statistics are low, Veronig etal. [62] examined the moment of appearance for the γ-ray including that from π 0 in large flare andfound the time coincidence with the moment of main energy release determined by hard X-rays
and line γ-rays. Kurt et al. [63] systematically analyzed the γ-rays from π 0 decays and neutron
emissions recorded by the SONG (SOlar Neutrons and Gamma rays detector) detector [64] andcompared their time profiles with those of soft X-ray by GOES and ULYSSES [65], hard Xray by Yohkoh [66] and RHESSI [67], line γ-ray by INTEGRAL (INTErnational Gamma-Ray
Astrophysics Laboratory) [68]. The temporal relation among the γ-ray emission from π 0 decay,
the derivative of soft X-ray and hard X-ray is shown in Fig. 3.1. Therefore, we used the time31

32

CHAPTER 3. SEARCH TIME WINDOW DETERMINATION

Table 3.1: Observation targets for each solar satellite. Circles (⃝) show the main target whoseenergy and timing can be measured by the satellite’s devices. Triangles (△) indicate secondary
target, hardly detectable by the satellite as direct measurements; the counting rate alone canindirectly imply target existence. Details are described in the later sections.
Satellite
Launch year End year Soft X-ray Hard X-ray Line γ-ray γ-ray
GOES
1975
–
⃝
△
–
–
RHESSI
2002
2018
⃝
⃝
⃝
⃝
GEOTAIL
1992
–
–
△
△
△

Table 3.2: Summary of satellites and energy ranges in this study. As described in the main text,
GEOTAIL cannot measure the energy of neutral particles above 50 keV.
Type
Satellite
Energy range (wave length)
Soft X-ray
GOES
1.5–12 keV (1–8 Å)Hard X-ray
RHESSI
100–800 keVLine γ-ray
RHESSI
2.218–2.228 MeV
Hard X-ray and soft γ-ray GEOTAIL
Above 50 keV

profile of the time derivative for the soft X-ray instead of the γ-ray emission from π 0 decay todetermine search time windows.

3.2

The Visible Side Solar Flares

The flares on the visible side are observed by various satellites, which provide data in a wide rangeof wavelengths. To search for solar flare neutrinos, we used public data from solar satellites andcomputational resources of the Center for Integrated Data Science (CIDAS) at Nagoya University.
In this study, we analyzed the data recorded by three satellites; GOES, RHESSI, and GEOTAIL.
The main targets of each satellite are summarized in Table 3.1.
Using CIDAS, we analyzed the GOES satellite’s soft X-ray data, as well as the RHESSI
satellite’s hard X-ray and γ-ray data, as summarized in Table 3.2. For the analysis of GEOTAIL
data, we used the raw data to recover hard X-rays above 50 keV including soft γ-rays.

3.2.1

Solar Flare Event Selection

We used data obtained by the GOES satellite to select solar flares for our neutrino search because
the GOES satellite series have continually monitored solar flares since 1975. Its long operation
permits the use of the same indicator in comparisons between older and more recent flares.
For this study, we first registered all solar flares occurring from 1996 to 2018 in the NOAA list.
Then, we selected the 23 solar flares whose peak soft X-ray intensity exceeds 5.0×10−4 W/m2 (X5.0
class). The date, class, and location on the Sun (active region, so-called AR) for each selected
flare are summarized in Table 3.3.

3.2. THE VISIBLE SIDE SOLAR FLARES

33

Table 3.3: List of solar flares selected for this study. The data, class and active region (AR) location are taken from a National Oceanic and Atmospheric Administration
source (NOAA, https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solarflares/x-rays/goes/xrs/).
Date
Class AR location
1997 Nov. 6
X9.5
S18W63
2000 Jul. 14
X5.7
N22W07
2001 Apr. 2
X20.0
S21E832001 Apr. 6
X5.6
S21E31
2001 Apr. 15 X14.4
S20W852001 Aug. 25 X5.8
S17E342001 Dec. 13
X5.3
N16E092002 Jul. 23
X5.1
S13E72
2003 Oct. 23
X5.4
S21E88
2003 Oct. 28 X17.2
S16E08
2003 Oct. 29 X10.0
S15W02
2003 Nov. 2
X9.2
S14W56
2003 Nov. 4 X28.0
S19W832005 Jan. 20
X7.1
N14W61
2005 Sep. 7
X18.2
S11E77
2005 Sep. 8
X5.4
S12E752005 Sep. 9
X6.2
S12E67
2006 Dec. 5
X9.0
S07E682006 Dec. 6
X6.5
S05E642011 Aug. 9
X7.4
N14W692012 Mar. 7
X5.4
N22E122017 Sep. 6
X9.4
S09W342017 Sep. 10
X8.3
S08W88

34

3.2.2

CHAPTER 3. SEARCH TIME WINDOW DETERMINATIONTime Window Determination

Soft X-rays (GOES)
A typical soft X-ray light curve observed by the GOES satellite is shown in the top panel ofFig. 3.2. In the NOAA list, the timing at which four consecutive flux increases occur wasdetermined as the start time of each solar flare. The flare end time was typically determined as
the timing at which the event’s flux decline to half the value of its peak. However, this end timedepends on the flare class which makes unsuitable for our analysis. We, therefore, set the flareend time as the timing at which the flux declines to 1.0 × 10−4 W/m2 (X1.0 class).
To extract information about light curve brightening correlated with particle acceleration, we
took a calculation of the time derivative of the light curve as shown in the bottom panel of Fig. 3.2.
For setting the time window, we first fitted the light curve with a Gauss function (A exp{(t −tpeak )2 /σ 2 }). We then selected the region of [tpeak − 3σ, tpeak + 3σ] as the search window.
Hard X-ray (RHESSI)The RHESSI satellite was launched in February 2002 to monitor solar flares. It records electromagnetic waves in the range of 3 keV to 17 MeV and can observe continuous spectra frombremsstrahlung of high energy electrons, line γ-rays of 2.223 MeV, and γ-rays from 12 C and 16 O
nuclei [67]. Owing to its wide energy range, the RHESSI satellite provides important informationfor extracting acceleration time scales for electrons, protons, and ions.
In this study, we scanned the energy spectrum in the range of 100–800 keV for hard X-ray
analysis as shown in the top panel of Fig. 3.3 (a). We then determined the count rate within
this energy range using the front detector on the RHESSI. To set the search window, we fitted
the light curve via a combination of basic functions. For the fitting, we used a constant value forthe background before the brightening, a linear function for the brightening phase of the light
curve, and an exponential function for the dimming phase. The start time (tstart ) was definedas the time when the liner function intercepts the background constant. The time window wasdetermined by selecting the region where the exponential function is 2σ beyond the backgroundconstant. The end time (tend ) is the last point satisfying this condition. In this way, the searchwindow by hard X-ray is determined as [tstart , tend ].
Line γ-rays (RHESSI)For line γ-ray analysis, we first scanned the energy spectrum before and after each solar flareas shown in the top panel of Fig. 3.3 (a). Here we defined the energy spectrum before (after)as OFF (ON) FLARE. Then, we took a ratio between them as shown in the bottom panel ofFig. 3.3 (a). When we confirmed the line γ-ray in the spectrum after the solar flare, we plotted
the light curve using the energy range of 2.218–2.228 MeV as shown in Fig. 3.3 (b). To determine
the search window, we used the same method described above for hard X-rays. It is reported inRef. [70] that line γ-ray signal of neutron capture is delayed by 100 sec because it takes some time
for the neutron to be thermalized and captured by hydrogen in the solar atmosphere. Therefore,
we selected the region of [tstart − 100 sec, tend ] as the time window for line γ-rays.
GEOTAIL satellite hard X-ray events
The GEOTAIL satellite was launched in July 1992 to observe the Earth’s magnetosphere. Its
main targets are electrical field, magnetic field, plasma, and high energy particles in the magnetosphere. The LEP (low energy particle) instrument mounted on the satellite, can measurecounts of ions and electrons independently based on energy-per-charge separation [71]. The LEP

3.2. THE VISIBLE SIDE SOLAR FLARES

35

detector consists of an electrostatic analyzer and particle counters: microchannel plates for ions,and channel electron multipliers for electrons.
GEOTAIL has occasionally been exposed to the intense fluxes of energetic ions >50 MeV andphotons of >50 keV after strong solar flares or giant flares of magnetars [72–74]. These energetic
ions and photons do not follow the electrostatic analyzer’s energy-per-charge regulation, butrather penetrate through the satellite wall and hit the particle counters directly. For the solar
flare case, energetic photons include hard X-ray photons from bremsstrahlung by high energy
electrons, as well as line γ-ray photons from nuclear interactions. Figure 3.4 shows an exampleof this situation. During the interval 10:35:00–11:35:00 UTC on October 28, 2003, GEOTAIL
was in the solar wind upstream of the Earth’s bow shock and continued to measure solar windparticles as well as nonthermal ions (10–40 keV/q) accelerated by the bow shock. However,during the interval 11:01:40–11:15:30 UTC, GEOTAIL was hit by the solar flare hard X-ray
photons, which produced the energy-independent stripes in the first to third panel of Fig. 3.4.
It is noted that tailward-flowing solar wind ions (less than ∼20 keV/q colored with yellow-redblack) overwrapped with the hard X-ray stripes as shown in the fourth panel of Fig. 3.4. The
penetration depth for hard X-ray photons from the satellite wall to the counter depends on thesatellite spin phase so that the colors of the energy-independent stripes diﬀer slightly sector
by sector. The electron detector (not shown) responded to the solar flare hard X-ray photons
similarly. However, because the form factor of the electron detectors is two orders of magnitude
smaller than that of the ion detectors, the apparent contribution of solar flare hard X-ray photons
is much weaker.
In the present study, we estimated the time profiles of particle acceleration by selecting datafrom the four sectors and the energy range that was not “contaminated” by ions, taking countaverages every 12 s. Figure 3.5 shows the photon counts from 10:50:00 to 11:20:00 UTC, ascalculated from the data in the dawnward, sunward, and duskward sectors in Fig. 3.4. Finally,
the time window for GEOTAIL is determined using the same method as that used in the analysis
for line γ-ray above, because a component of the GEOTAIL signal contains line γ-rays.
Because all satellite data are available for the solar flare occurring on November 2, 2003, weused this example to illustrate the method for the time window determination developed in thisstudy, shown in Fig. 3.6.
The analysis results for 23 solar flares selected in this study are summarized in Tables 3.4
and 3.5. It is noted that, we failed to obtain the time window determined by the derivativeof soft X-ray for the solar flare occurring on September 9, 2005, because the brightening of its
soft X-ray light curve was relatively slow and the derivative of soft X-ray was not large enough.
Figure 3.7 summarizes the distribution of timing window duration for each channel. On the basisof these results, the average time duration for each channel is as follows;• Soft X-ray: 4, 178 s• Derivative of soft X-rays: 700 s• Hard X-rays: 944 s• Line γ-rays from neutron capture: 1, 586 s• Hard X-rays (GEOTAIL): 776 s

(Arb. units)

1
0.5

𝑑𝐼SXR /𝑑𝑡

GOES
1–8 Å

10−3
10−4

0

(a)
SPR-N

SONG

40–100 keV
0.5

0

(b)
(Arb. units)

1
INTEGRAL/SPI
𝛾-lines

0.5
0

0

0.4
Neutrons

0Counts (s−1 )(Arb. units)

0.5

10− 1
10−3

1

101

10

11:03:4

10− 1
10−3

1

SONG

𝛾 > 90 MeV

11:02:1

10−5

(c)
1

101

10−5

0.75–2 MeV
6–10.5 MeV
Photons (cm −2 s−1 MeV−1 )(Arb. units)

1

Photons (cm −2 s−1 MeV−1 )Advances inCHAPTER
Astronomy3. SEARCH TIME WINDOW DETERMINATION(W m −2 )36

10Figure 5: The restored incident
October 28, 2003 (from [35]). Re
black curves electron bremsstrah
the pion-decay gamma-ray spec
to a power law with varying inde
to a power law with an exponent

found in [35]. The importa
when power law spectrum cstrahlung extended up to v
1(100 MeV) was observed. W
decay contribution in this sp
0.5
estimate the upper limits o0
11:03:51 a sharp increase of gam
11:02
11:04
11:06
11:08
11:10
above 40 MeV occurred. The
UT (h:m)substantially in this momenappeared at energies above 3(e)neutral pions (see Figure 5).
Figure 4: Normalized time profiles of selected emissions fromcontinuum created by prima
Figure 3.1: Normalized
timeof (a)
selectedemissionsfromthe solar (b)flare occurring on
October
28, profiles
2003, flare:
soft X-ray
flux andits derivative;
with a break around 40 Me
October 28, 2003.(a)hardsoftX-ray
X-ray40–100
flux andits derivativefrom GOES;(b) hard
X-ray 40-100 keV
keV from
CORONAS-F/SPR-N(blackcurve);
release episode.
from CORONAS-F/SPR-N(blackcurve);
gamma-rays fromSONG
MeV
gamma-rays
from
CORONAS-F/SONG
0.75–2
MeV 0.75-2(red) and
6– (red) and 6-10.5
Comparing narrow gamm10.5γ-rays
MeV (green);(c) gamma-lines from[46];(red,(d) left y-axis) andMeV (green); (c) linefrom INTEGRAL/SPI;(d) INTEGRAL/SPI
γ-rays > 90 MeV
pion-decay
gamma-rays> 90SONG.
MeV (red,𝑦-axis) andrightTaken from [63]. flux at 100 MeV
neutrons (black, righty-axis) from(e)leftmagnetic
fieldneutronschange(black,rate [69].
has showed that the spectrum
𝑦-axis) from CORONAS-F/SONG; (e) magnetic field change rate
tons had also changed from[48].
to power law with spectral iThis spectrum shape remaine
the total intensity was decrea
by the SONG instrument beginning from 11:02:11 to 11:12:30
was the end of our measurem(see Figure 4). This Figure presents also summarized intensityof hard X-rays and 𝑑𝐼SXR /𝑑𝑡
reach their maximum valueof the 4.4 + 6.1 MeV gamma-lines (INTEGRAL with thewith the time interval of ma
SPI spectrometer [46]) and the magnetic field change rate
decay emission.
obtained with ∼1 min cadence [48].
High-energy neutrons w
The detailed study of SONG hard X-ray and gammadetector beginning at 11:06:2
ray emission measurement of this flare and neutrons can be(Arb. units)(d)3.2. THE VISIBLE SIDE SOLAR FLARES

37

10− 2

Soft X ray

Flux [W/m2]

10− 3

10− 4

Count rate [Count/3 s]

10− 5

20000

Derivative Soft X ray

15000
10000
5000
0
− 500010/28 10/28 10/28 10/28 10/28 10/28 10/28 10/28 10/28
10:00 10:20 10:40 11:00 11:20 11:40 12:00 12:20 12:40

Figure 3.2: An example solar flare occurring on October 28, 2003, showing the soft X-ray light
curve (top) observed by the GOES satellite and the derivative of the flux of soft X-rays (bottom).
In the top panel, the horizontal axis is universal time and the vertical axis is the flux of soft
X-rays. The black dotted horizontal line indicates a flux of 1.0 × 10−4 W/m2 . The region drawn
in gray shows the time window selected in this study. In the bottom panel, the horizontal axis
is universal time and the vertical axis is the derivative of the flux of soft X-rays with respect totime. The blue dots and the green region depict the data and their error, respectively; the red
curve is the result of Gaussian fitting. The gray region shows the time window selected by thisstudy.

CHAPTER 3. SEARCH TIME WINDOW DETERMINATION

102
(a)

Count rate[Counts/4sec]

Flux [cm-2 s-1 keV-1]

38

ON FLARE

10OFF FLARE

1
10−1

Ratio of Flux (ON FLARE/OFF FLARE)

10−2
4
3.5
3
2.5
2
1.5
1
0.5
0

102

(ON FLARE)/(OFF FLARE)

100

(b)
80
60
40
20
0
11/02 11/02 11/02 11/02 11/02 11/02 11/02 11/02 11/02
16:50 17:00 17:10 17:20 17:30 17:40 17:50 18:00 18:10

Universal Time (2003)

103

104

Energy [keV]

Figure 3.3: (a) Energy spectra of γ-rays associated with the solar flare occurring on November
2, 2003, as recorded by the RHESSI satellite. The blue solid histograms show ON FLARE andthe pink dashed histograms represent OFF FLARE. The horizontal axis shows energy in keV
and the vertical axis in the top panel shows the flux of γ-rays in units of cm−2 sec−1 keV−1 The
vertical axis in the bottom panel shows the ratio between fluxes in dimensionless units. (b) Light
curve of the solar flare as shown in (a). The horizontal axis shows universal time and the verticalaxis shows the count rate in units of count per 4 s. The blue points and green bars depict thedata and their error, respectively. The red curves show the fitting results and the shaded region
shows the time window determined by this method.

3.2. THE VISIBLE SIDE SOLAR FLARES

39

Figure 3.4: Count rates recorded by the LEP detector when this solar flare occurring on October28, 2003 are color-coded (white-blue-green-yellow-red-black). The horizontal axis shows theuniversal time (HH:MM) of particle detection. The vertical axis shows the energy of nonthermal
ions in units of energy-per-charge (5–40 keV/q). Four panels, top to bottom, show ion counts
in the four sectors pointed dawnward, sunward, duskward, and tailward, respectively, where theion flow directions are defined with respect to the relative magnetosphere geometry of the Sun
and Earth.

CHAPTER 3. SEARCH TIME WINDOW DETERMINATIONCount rate[Counts/detector/12sec]

40

900
800
700
600
500
400
300
200
100
0

10/28
10:50

10/28
11:00

10/28
11:10

10/28
11:20

Figure 3.5: Light curve associated with the solar flare occurring on October, 28, 2003 as recordedby the GEOTAIL satellite. The horizontal axis shows the universal time, and the vertical axis
shows count rate in units of [counts/detector/12 s]). Red points show the data, and blue lines
show the fitting results. This flare is the same flare as shown in Fig. 3.4.

3.2. THE VISIBLE SIDE SOLAR FLARES

41

Soft X ray−3

Flux [W/m 2 ]

10

−4

10

−5

Count rate [Count/4 s]

Count rate [Count/4 s]

Count rate [Count/3 s]

10

Derivative Soft X ray

10000
8000
6000
4000
2000
8000
7000
6000
5000
4000
3000
2000
1000

Hard X ray (100 - 800 keV)Line γ ray(2.2 MeV)

80
60
40
20

Count rate [Count/12 s]

0

250
200
150
100
50

11/02
17:00

Hard X ray (>50 keV)

11/02
17:10

11/02
17:20

11/02
17:30

11/02
17:40

11/02
17:50

11/02
18:00

11/02
18:10

Figure 3.6: Light curves of the solar flare occurring on November 2, 2003. Gray regions show thetime windows extracted by the analysis methods developed in this study. From top to bottom,
the panels show the light curves for soft X-rays, derivative of soft X-rays, hard X-rays (100–800 keV), line γ-rays (2.223 MeV), and hard X-rays (GEOTAIL, above 50 keV), respectively.
For the hard X-ray light curve (above 50 keV), the count rate gradually increased from 17:40
onward because protons in the range of 30–50 MeV were observed. These protons masked othercounts due to plasma particles and hard X-ray photons.

Table 3.4: Time windows determined for soft X-rays, derivative of soft X-rays and hard X-rays. The time is described in units of UTC([HH:MM:SS]).
Date
Soft X-rays (GOES)
Derivative of soft X-rays (GOES)
Hard X-rays (RHESSI)
tstarttend∆t [s]
tstarttend∆t [s]
tstarttend∆t [s]
1997 Nov. 6 11:49:00 12:12:21 1,401 11:52:13 11:54:58
165
–
–
–
2000 Jul. 14 10:03:00 11:05:03 3,723 10:08:44 10:28:31
1,187
–
–
–
21:32:00 22:56:12 5,052 21:35:10 21:52:57
1,067
–
–
–
2001 Apr. 2
19:10:00 19:43:15 1,995 19:12:32 19:21:31
539
–
–
–
2001 Apr. 6
2001 Apr. 15 13:19:00 14:23:39 3,879 13:43:48 13:51:03
435
–
–
–
2001 Aug. 25 16:23:00 17:36:18 4,398 16:28:36 16:33:38
302
–
–
–
2001 Dec. 13 14:20:00 14:41:57 1,317 14:24:25 14:31:05
400
–
–
–
2002 Jul. 23 00:18:00 01:08:27 3,027 00:25:08 00:31:36
388
00:25:44 00:36:46
562
931
–
2003 Oct. 23 08:19:00 09:13:9
3,249 08:20:32 08:36:03––
2003 Oct. 28 09:51:00 12:36:54 9,954 10:59:30 11:10:57
687
–
–
–
2003 Oct. 29 20:37:00 21:23:39 2,799 20:38:46 20:50:07
681
–
–
–
2003 Nov. 2 17:03:00 18:07:03 3,843 17:12:01 17:26:03
842
17:15:41 17:39:22 1421
2003 Nov. 4 19:29:00 21:10:12 6,072 19:36:59 19:56:03
1,144
–
–
–
2005 Jan. 20 06:36:00 08:05:48 5,388 06:39:22 06:57:12
1,070
06:43:27 06:57:57
870
17:17:00 18:48:57 5,517 17:23:34 17:39:48
974
–
–
–
2005 Sep. 7
2005 Sep. 8
20:52:00 21:31:48 2,388 21:00:27 21:08:05
458
–
–
–
2005 Sep. 9
19:13:00 21:20:36 7,656
–
–
–
–
–
–
2006 Dec. 5
10:18:00 10:56:09 2,289 10:24:18 10:35:43
685
–
–
–
2006 Dec. 6
18:29:00 19:16:30 2,850 18:41:29 18:47:06
337
18:42:33 18:49:19
406
290
–
–
–
2011 Aug. 9 07:48:00 08:11:47 1,427 08:00:50 08:05:40
2012 Mar. 7 00:02:00 01:31:34 5,374 00:04:21 00:25:16
1,255
–
–
–
2017 Sep. 6
11:53:00 13:30:00 5,820 11:54:39 12:03:20
521
–
–
–
2017 Sep. 10 15:35:00 17:26:06 6,666 15:49:12 16:06:32
1,040
15:54:42 16:19:03 1,461

42
CHAPTER 3. SEARCH TIME WINDOW DETERMINATION

3.2. THE VISIBLE SIDE SOLAR FLARES

43

Table 3.5: Time windows determined for line γ-rays (RHESSI) and hard X-rays (GEOTAIL).
Time is described in units of UTC ([HH:MM:SS]).
Date
Line γ-ray (RHESSI)Hard X-ray (GEOTAIL)
tstarttend∆t [s]
tstarttend∆t [s]
1997 Nov. 6–––
11:50:55 11:57:04
369
2000 Jul. 14
–
–
–
–
–
–
2001 Apr. 2
–
–
–
–
–
–
2001 Apr. 6
–
–
–
–
–
–
–
–
–
13:43:42 13:51:58
469
2001 Apr. 15–––
16:28:29 16:34:54
385
2001 Aug. 25
2001 Dec. 13
–
–
–
–
–
–
2002 Jul. 23 00:26:28 00:56:22 1,794–––
2003 Oct. 23
–
–
–
–
–
–
2003 Oct. 28–––
10:59:45 11:17:36 1,071
2003 Oct. 29
–
–
–
–
–
–
2003 Nov. 2 17:14:14 17:36:41 1,347 17:13:08 17:37:11 1,443
2003 Nov. 4–––
19:38:35 19:53:32
897
2005 Jan. 20 06:42:54 07:09:52 1,618–––
2005 Sep. 7–––
17:32:44 17:45:32 7678
–
–
–
–
–
–
2005 Sep. 8
2005 Sep. 9
–
–
–
–
–
–
2006 Dec. 5
–
–
–
–
–
–
2006 Dec. 6
–
–
–
–
–
–
2011 Aug. 9
–
–
–
–
–
–
–
–
–
–
–
–
2012 Mar. 72017 Sep. 6
–
–
–
–
–
–
2017 Sep. 10
–
–
–
–
–
–

Figure 3.8 shows the time duration of search windows as a function of the maximum valueof the soft X-ray peak. The correlation coeﬃcients between the maximum value of the soft
X-ray peak and the time duration of search windows are 0.436 for soft X-rays, 0.341 for soft
X-rays (derivative), 0.236 for hard X-rays (100–800 keV), −0.344 for line γ-rays, and 0.307 forhard X-rays (>50 keV). Therefore, no strong correlation is found among them, as summarizedin Table 3.6.
To investigate the diﬀerence in time profile between channels, we calculated the time elapsed
between the peak timing of a given channel and the peak timing of soft X-rays (Fig. 3.9), because
the peak timing of each channel is earlier than that of soft X-rays. The mean diﬀerences are−320 s for the derivative of soft X-rays, −482 s for hard X-rays, −471 s for line γ-rays, and−342 s for hard X-rays (GEOTAIL).
Each panel in Fig. 3.10 shows the time correlation between two variables: on the x-axis, thepeak timing of soft X-rays; on the y-axis, a given channel after subtracting the peak timing ofsoft X-rays. To extract the diﬀerence between peak timings, the plots are fitted with a linear
function; the fitting results are summarized in Table 3.7. The y-intercept of the linear function
gives the diﬀerence in peak timings.
In Fig. 3.10 (c), the fitting results are 0.9±0.1 for the slope and 7±55 s for the y-intercept. We
found a good timing correlation between the derivative of soft X-rays and hard X-rays because
the y-intercept is close to the origin of coordinates (0, 0), thus confirming the Neupert eﬀectCHAPTER 3. SEARCH TIME WINDOW DETERMINATION

3.5
3

Entries

23

2.5
2
1.5
1

Number of flare [flares/100s]

Number of flare [flares/100s]

44

3.5
3

Entries

2.5
2
1.5
1
0.5

0.5

00 500 10001500 200025003000 350040004500 5000

00 500 10001500 200025003000 350040004500 5000

Time window width [s]3.5
3Entries

5

2.5
2
1.5
1
0.5

Number of flare [flares/100s]

Time window width [s]Number of flare [flares/100s]

22

3.5
3

Entries

3

2.5
2
1.5
1
0.5

00 500 10001500 200025003000 350040004500 5000

00 500 10001500 200025003000 350040004500 5000
Time window width [s]Number of flare [flares/100s]

Time window width [s]3.5
3Entries

7

2.5
2
1.5
1
0.5
00 500 10001500 200025003000 350040004500 5000
Time window width [s]Figure 3.7: Distributions of the width of time window determined by each method: (a) light
curve of soft X-rays, (b) derivative of the light curve of soft X-rays, (c) hard X-rays, (d) line
γ-rays, and (e) hard X-rays (GEOTAIL). The Horizontal axis shows the duration of the time
window. The vertical axis shows the number of entries.

3.2. THE VISIBLE SIDE SOLAR FLARESe 16 of 26

45

K. Okamoto et al.

Time duration as aof the peak intensity ofy. Black dot, red square,
triangle, blue
ngle, and light blue star
X-ray, derivative ofy, hard0 – 800 keV), line
d hard50 keV), respectively.

Figure 3.8: Time duration as a function of the peak intensity of soft X-ray. Black dots, Red
squares, Green up-triangles, Blue down-triangles, and Light blue stars show soft X-ray, Detivativeof soft X-ray, Hard X-ray(100–800 keV), Line γ-ray, and Hard X-ray(above 50 keV) emissions,
respectively.

Table 3.6: Summary of timing information obtained in this study. Average time durations arecalculated from the distributions shown in Fig. 3.7. Correlation coeﬃcients are calculated fromthe distribution shown in Fig. 3.8. The diﬀerences in peak timing are calculated relative to asoft X-ray peak time of 0 (Fig. 3.9).
Entries Average duration Correlation Peak timing[s]
coeﬃcientdiﬀerence [s]Soft X-ray
23
4, 1780.436–
Soft X-ray (derivative)
22
700
0.341
−320
Hard X-ray
5
944
0.236
−482
Line γ-ray
31, 586−0.344−471
Hard X-ray (GEOTAIL)
7
776
0.307
−342

Time difference distribution after subtracting the peak timing of soft X-rays. The horizontal axis
time difference in units of seconds and the vertical axis shows the entry per 50 s.

016). Assuming this time window, the expected background rate can be reduced toCHAPTER 3. SEARCH TIME WINDOW DETERMINATION

Number of flare [/50 sec] Number of flare [/50 sec]

Number of flare [/50 sec]

Number of flare [/50 sec]

46

5
4
3
2
1
1
0.8
0.6
0.4
0.2
1
0.8
0.6
0.4
0.2

Derivative Soft X ray
EntriesMean
Std Dev

21
−320
197.3

Hard X ray(100 - 800 keV)

EntriesMean
Std Dev

5
−482
219

Line γ ray(2.2 MeV)
EntriesMean
Std Dev

3−471.7230.4

1Hard X ray (>50 keV)
0.8
Entries70.6
Mean−342.4
Std Dev
240.9
0.4
0.2
−1000 −800 −600 −400 −2000200 400 600 800
Peak timing difference from Soft X-ray [sec]1000

Figure 3.9: Time diﬀerence distribution after subtracting the peak timing of soft X-rays. The
horizontal axis shows the time diﬀerence in units of seconds; the vertical axis shows the entry
per 50 s.

3.3. THE INVISIBLE SIDE SOLAR FLARES

47

Table 3.7: Summary of results from fits in Fig. 3.10. Each axis in Fig. 3.10 represents the time
elapsed between the peak timing of a given channel and that of soft X-rays.
Figure 3.10
x-axisy-axisFitting result χ2 /d.o.f(a)Soft X-ray
Hard X-ray(1.1 ± 0.4)x
1.0/3(derivative)(100–800 keV) +(41 ± 166)(b)
Soft X-ray
Line γ-ray(1.4 ± 1.1)x
0.3/1(derivative)+(331 ± 548)(c)Soft X-ray
Hard X-ray(0.9 ± 0.1)x
0.3/4(derivative)(>50 keV)+(7 ± 55)(d)
Hard X-ray
Line γ-ray(1.0 ± 0.5)x
0.1/1(100–800 keV)(141 ± 286)

between them. Notably, this confirmation takes place by comparing the peak timing without
considering the shape of light curves.
In Fig. 3.10 (d), the y-intercept is 141 ± 285 s, suggesting that the peak timing of line γ-rays
is delayed from that of hard X-rays (100–800 keV). If the acceleration of both electrons and ionsoccurs simultaneously, this diﬀerence between their timings is explained by considering neutron
capture since the neutron capture time is estimated to be 100 sec [70, 75].
Figure 3.10 (e) overlays the plots shown in Fig. 3.10 (a) and Fig. 3.10 (b). We found thatthe peak timing of hard X-rays is earlier than that of line γ-rays, where their diﬀerence is about
100 s.

3.3

The Invisible Side Solar Flares

3.3.1

Search window for solar flares at invisible side

As briefly explained in Section 1.6, proton flux directed back to the Sun generates a nuclear
cascade in the solar atmosphere. Such flux results in a narrow beam of relativistic protons witha rather hard spectrum from solar flares on the invisible side of the Sun. Hence the searches
for neutrinos associated with solar flares occurring at the invisible side provide information
about the acceleration mechanism of downward going proton flux. However, no satellite, except
for a limited number of planet explorers, directly monitors an explosive phenomenon at theinvisible side before the launch of STEREO (Solar Terrestrial Relations Observatory) satellites
in 2006 [76]. The STEREO satellites have performed the CME imaging [77] and indeed observed
the solar high energy particles originated from the CMEs occurring on July 23rd, 2012 [78].
The time of CMEs allows one to infer the occurrence time of a solar flare on the invisible sideof the Sun because large energetic solar flares are usually accompanied by CMEs. Andrews [79]found the association rate of CMEs with solar flares increases with the flare’s peak flux of soft
X-rays, fluence, and time duration.
As explained in Section 1.4, the observation of CMEs occurring on the invisible side of the
Sun is performed by coronagraph method with the LASCO on SOHO. The catalog of CMEs
observed by the SOHO spacecraft is maintained by NASA [29]1 and this catalog summarizes thetime of CMEs and its locations.
1 https://cdaw.gsfc.nasa.gov/CME_list/

CHAPTER 3. SEARCH TIME WINDOW DETERMINATION

1000
800

Line γ Peak Timing - SoftX PeakTiming [sec]HardX Peak Timing - SoftX PeakTiming [sec]

48

(a)

600
400
200
0
−200
−400
−600

1000
800

400
200
0
−200
−400
−600

−800

−800

−1000

−1000

1000

1000

800

−1000 −800 −600 −400 −200 0 200 400 600 800 1000
Derivative Peak Timing - SoftX PeakTiming [sec]Line γ Peak Timing - SoftX PeakTiming [sec]Geotail Hardx Peak Timing - SoftX PeakTiming [sec]−1000 −800 −600 −400 −200 0 200 400 600 800 1000
Derivative Peak Timing - SoftX PeakTiming [sec]

(c)

600
400
200
0
−200
−400
−600

800

400
200
0
−200
−400
−600
−800

−1000

−1000

Peak Timing difference [sec]

(d)

600

−800

−1000 −800 −600 −400 −200 0 200 400 600 800 1000
Derivative Peak Timing - SoftX PeakTiming [sec]

(b)

600

−1000 −800 −600 −400 −200 0 200 400 600 800 1000
HardX Peak Timing - SoftX PeakTiming [sec]

1000
800

(e)

600
400
200
0
Hard X (100 - 800 keV)

−200
−400

Line γ

−600
−800
−1000

−1000 −800 −600 −400 −200 0 200 400 600 800 1000
Derivative Peak Timing - SoftX PeakTiming [sec]Figure 3.10: Relationship between each channel’s peak timing after subtracting the peak timeof soft X-rays. The fitting results are summarized in Table 3.7. For (e), the plots shown in both(a) and (b) are overlaid.

3.3. THE INVISIBLE SIDE SOLAR FLARES

49

Figure 3.11: The correlation between the speed of the CMEs and the peak intensity of soft X-rays
from solar flares monitored by the GOES satellite. The black plus signs show the parameters
taken from the catalog [29]. The blue line shows the regression line.

3.3.2

Solar Flare Event Selection

Yashiro et.al. [29] statistically examined a possible correlation between the kinetic energy of
CMEs and the intensity of the solar flare monitored by the GOES satellite and found a weak
positive correlation between them. Based on that study, we collected about 20, 000 CMEs listedin NASA and evaluated the threshold of the speed of CMEs associated with the solar flare with
X class. Figure 3.11 shows the correlation between the speed of the CMEs and the intensity ofsoft X-rays from solar flares. As expected, we found a weak positive correlation between them.
Finally, we conservatively determined the threshold as 2000 km s−1 in order to select the solar
flare of X class. This criterion roughly corresponds to solar flares with X2.0.

3.3.3

Time Window Determination

Yashiro et.al. [29] also investigated the time diﬀerence between the CMEs and the solar flares.
That study found the standard deviation of time diﬀerence is 1020 s from its distribution. In thisstudy, we set the start time of the search window to be 3060 s before the time of CMEs emission,
which corresponds to three standard deviation of the time diﬀerence. For the end time, we
conservatively set 4178 s after the time of CME emission, where this wide duration is determinedfrom the light curve of soft X-ray recorded by GOES since all processes, such as acceleration,energy release, etc, occurring during a solar flare complete within this time duration. Hence,the search window for solar flares occurring on the invisible side of the Sun is the same time
duration, which corresponds to 7238 s in total.
In this analysis, we selected energetic CMEs whose speed is more than 2000 km s−1 . Ten CMEs
from 1996 April to 2018 May were selected with this criterion. Table 3.8 summarizes the date,search window and location of the selected CMEs.

50

CHAPTER 3. SEARCH TIME WINDOW DETERMINATION

Table 3.8: The summary of the search windows estimated in this study for energetic CMEs
occurring on the invisible side of the Sun. The date, time, and active region (AR) are taken fromSOHO LASCO CME CATALOG [29].
DateTime [UTC]tstarttend
AR location Speed [km s−1 ]2001 Apr. 18
02:06:24
01:15:24 03:16:02
SW90b2464.2
2002 Jul. 18
18:58:20
18:07:20 20:07:58
E90b
2191.3
2002 Jul. 19
16:04:34
15:13:34 17:14:12
S15E902046.6
2003 Nov. 2
09:00:23
15:13:34 17:14:12
SW90b2036.02003 Nov. 7
15:32:19
14:41:19 16:41:57
W90b
2237.02003 Nov. 9
05:57:57
05:06:57 07:45:29
E90b2008.1
2005 Jul. 24
13:35:51
12:44:51 14:45:29
E90b
2527.82011 Jun. 4
21:42:42
20:51:42 22:52:20
N16W1532425.52012 Jul. 23
02:10:07
01:19:07 03:19:45
S17W132
2003.2
2014 Dec. 13
13:57:34
13:06:34 15:07:12
S20W143
2221.6

3.4

Summary of the Search Time Windows

We determined the search time windows with the time profile of soft X-ray, the derivative ofsoft X-ray, hard X-ray, and line γ-ray emissions for the twenty-three solar flares on the visible
side. The line γ-rays should be from hadronic processes and directly indicate neutrino existence
in a solar flare. This method can be applied to three solar flares. The derivative of soft X-ray
light curve can be applied to all solar flares observed by GOES and would be substituted for thetime window determined by the γ-ray emission from π 0 . For the reason above, the search time
windows that are determined from the line γ-rays and the derivative of soft X-rays are finallyused in this study.
We determined the search time window for ten solar flares on the invisible side with CMEdata from LASCO. Although the time window was almost 10 times longer than that for the solar
flares on the visible side, it enabled us to search for the solar flares on the invisible side.
Tables 3.9 and 3.10 show summaries of time windows which are used to search for solar flare
neutrinos in this study.

3.4. SUMMARY OF THE SEARCH TIME WINDOWS

51

Table 3.9: The time windows that used to search for neutrinos from solar flares on the visible
side in this study. The time is described in units of UTC ([HH:MM:SS]).
Date
Derivative of soft X-rays (GOES)
Line γ-ray (RHESSI)
start
end
duration [s]
start
end
duration [s]1997 Nov. 6 11:52:13 11:54:58
165
–
–
–
2000 Jul. 14 10:08:44 10:28:31
1,187
–
–
–
2001 Apr. 2
21:35:10 21:52:57
1,067
–
–
–
19:12:32 19:21:31
539
–
–
–
2001 Apr. 6
2001 Apr. 15 13:43:48 13:51:03
435
–
–
–
2001 Aug. 25 16:28:36 16:33:38
302
–
–
–
400
–
–
–
2001 Dec. 13 14:24:25 14:31:05
2002 Jul. 23 00:25:08 00:31:36
388
00:26:28 00:56:22
1,794
2003 Oct. 23 08:20:32 08:36:03
931
–
–
–
687
–
–
–
2003 Oct. 28 10:59:30 11:10:57
2003 Oct. 29 20:38:46 20:50:07
681
–
–
–
2003 Nov. 2 17:12:01 17:26:03
842
17:14:14 17:36:41
1,347
1,144
–
–
–
2003 Nov. 4 19:36:59 19:56:03
2005 Jan. 20 06:39:22 06:57:12
1,070
06:42:54 07:09:52
1,618
2005 Sep. 7
17:23:34 17:39:48
974
–
–
–
2005 Sep. 8
21:00:27 21:08:05
458
–
–
–
19:13:00 21:20:36
7,656
–
–
–
2005 Sep. 9
2006 Dec. 5
10:24:18 10:35:43
685
–
–
–
2006 Dec. 6
18:41:29 18:47:06
337
–
–
–
2011 Aug. 9 08:00:50 08:05:40
290
–
–
–
2012 Mar. 7 00:04:21 00:25:16
1,255
–
–
–
2017 Sep. 6
11:54:39 12:03:20
521
–
–
–
2017 Sep. 10 15:49:12 16:06:32
1,040
–
–
–

Table 3.10: The time windows that used to search for neutrinos from solar flares on the invisible
side in this study. The time is described in units of UTC ([HH:MM:SS]). The durations are
7238 s for all solar flares in this table.
Date
start
end
2001 Apr. 18 01:15:24 03:16:02
2002 Jul. 18 18:07:20 20:07:58
2002 Jul. 19 15:13:34 17:14:12
2003 Nov. 2 15:13:34 17:14:12
2003 Nov. 7 14:41:19 16:41:57
2003 Nov. 9 05:06:57 07:45:29
2005 Jul. 24 12:44:51 14:45:29
2011 Jun. 4 20:51:42 22:52:20
2012 Jul. 23 01:19:07 03:19:45
2014 Dec. 13 13:06:34 15:07:12

Chapter 4

Detector Calibration
In this chapter, ID PMT calibration, water transparency calibration, and energy scale calibrationin SK are briefly described. A more detailed explanation about the calibrations is described inRef. [80].

4.1

ID PMT Calibraion

The energy and vertex of an event are reconstructed from the charge and timing information of
hit PMTs.

Relative Gain of Each PMT
In order to calibrate the charge of the PMT, gain, a factor that converts from the observed
charge in a PMT in a unit of pico Coulomb (pC) to the number of photoelectrons, is needed.
There were two steps to obtain this value for all PMTs. First, the relative diﬀerence of the PMT
gain, which is called “Relative gain”, is measured, Then, the overall average gain, which is called“Absolute gain”, is determined.
To measure the relative gain diﬀerence, a stable light source emitting constant-intensity flashes
is deployed at a certain position in the tank. There are two measurements: the first uses highintensity flashes from which every PMT gets multiple photoelectrons. The second measurement
uses low-intensity flashes in which tens of PMTs get hits, i.e. occupancy of hits in each PMT ismuch less than 0.1, and the observed charge is mainly from single photoelectron. The averagecharge for the ith PMT, Qobs,i of the first measurement and the number of hits for the ith PMT,
Nobs,i , from the second measurement can be parameterized as follows:

Qobs,i∝Is × ai × εqe,i × Gi ,(4.1.1)

Nobs,i∝Iw × ai × εqe,i(4.1.2)where Is and Iw are the aberage intensities of high and low intensity flashes, respectively, ai is
acceptance of ith PMT, εqe,i is quantum eﬃciency (QE), and Gi is the ith PMT’s gain. Then,
relative gain of each PMT was extracted by taking the ratio of Eqs.4.1.1 and 4.1.2. Figure 4.1
shows the distribution of the relative gain of the ID PMTs after being normalized by the overall
average gain.
52

detector (left). The red points indicate the locations of the standard PMTs. These PMTs served as references fortrical relationship to the light source (right). (For interpretation of the references to color in this ﬁgure caption,

4.1. ID PMT CALIBRAION

0.00

53

Mean 1.000
RMS 0.059

1000

1.27

500

0
0.6

4

6

0.8

1
1.2
relative gain

1.4

Fig. 10. Distribution of relative gain of PMTs.

Figure 4.1: Relative gain distribution of the ID PMTs. Values are normalized to their mean
ID-PMTs from theirvalue. Taken from [80]Eqs. (1) and (2), except for a factor common to all PMTs:
Q obs ðiÞAbsolute GainGðiÞ p:ð3Þ
N obs ðiÞhes in which only
The absolute gain isdetermined using the charge distribution of the single photoelectron signal
can be reasonably
and is obtained using a Ni-Cf source calibration. Figure 4.2 is a picture of the Ni-Cf source which
the relative
gainof eachcanbe obtainedby normalunt the numberis ofused in Then
SK. γ-rays
with totalenergyof 7-9ID-PMT
MeV from
thermalneutron captureon nickel emit
18′
Cherenkov
photons,andthephoton
yield
is
about
0.004
p.e.
s/PMT/event.
These
signals are
izationwiththeaverage
gain
over
all
PMTs.
t is greater thanconsideredtobesinglephotoelectron
contributions.
Theobserved
chargedistribution
To perform this calibration we need a means to change the is shown
ight source is not
in Fig. 4.3.
The
meanof the charge
distribution
corresponds
to the source
absolute isgain value
intensityof value
the ﬂashesof thelight source.
The light
mplicating factors
and it is shown in Tab. 4.1.
nitrogen-laser-driven dye laser (Section 3.1.8). To manipulate theNobs(i) are almost
overall intensity of the light delivered into the ID, we used a ﬁlter
4.1: density
Summaryﬁltersof absolute
gain values
in SK.
wheel withTable
neutralbetweenthe dyelaser, and the
SK Phase Absolute gain value [pC/p.e.]
ð1Þ
optical ﬁber that feeds light into the diffuser ball.
SK-I
2.055
Fig. 10 shows
the ratio (3) for2.297
each PMT, the RMS of the
SK-II
ð2Þ
distribution wasSK-III
found to be 5.9%.2.243
Since the HV value for each
SK-IV to make Qobs be
2.645
PMT was determined
the same, we infer that thisof high and low
deviationisduetodifferences
in
QE
among
PMTs. The observed
ance of ID-PMT i,
ratio in Eq. (3) for each PMT, normalized by the average over all
old is sufﬁciently
PMTs,
want to track, have
Relative
QE contributed to a table of relative gain differences among
PMTs. These factors for relative gain differences of each PMT aren change makes
In order to measure energy using the number of photoelectrons from PMTs, the QE of each PMT
ld enables usis toalso needed. How to determine the relative QE for each PMT is described here. If the intensity
in probability offor
a light source is low enough, the observed hit probability should be proportional to the QE, as
18
old among PMTs.
4.1.2. Afactor
MC simulation
used to predictthenumber of photons
can be seen from
Eq.commonThe
I s =I w is alsoiseliminatedby thisnormalization.
In the arriving
aking the ratio of
actual measurement, Nobs was corrected by occupancy.

54

into this low-charge rbrated the relative gains. In this section, we describe the data weused and present the results of absolute gain calibration.
For this measurement, a uniform and stable source of singlephotoelectron level light is required. We used a “nickel source”
×103
2500
that isotropically emits gamma rays. The gamma rays have about
9 MeV from thermal neutron capture on nickel from the reaction
CHAPTER 4. DETECTOR CALIBRATION
58
Ni(n; γ)59Ni. A 252Cf source provides neutrons. More details can

2000
1500
1000

500
0

0

0.2

Fig. 13. The single-pe ddistribution was implemen
The dashed line shows t
Fig. 11. Picture of the nickel source which was manufactured by CI Kogyo. The ballFigure 4.2: was
PictureofofNi-Cf
This3.5ballof 6.5 kgof Cf
NiO
andwas
3.5 kgof polyethylene.
nickel data in SK-IV. The d
made
6.5 kgsource.
of NiO and
kg is
ofmadepolyethylene.
Thesourceinserted
into(neutron
the centersource)of the ballheld therea brassrod.
The Cf source
wasandinserted
intobythe
centerof the ball. Taken from [80]. of the QBEE, and the ratio

×103

at each PMT and we took the ratio of the2500observed number of hits to the predicted number of
6hits. It is noted that when this calibration was conducted, the water was convected in the10
entiredetector to make its quality uniform and the remaining cause of the geometrical eﬀect is only
the acceptance from the source to each 2000
PMT. Figure 4.4 shows the position dependence10
of5 thephoton detection probability of each PMT. In Fig. 4.4, the number of observed hits is correctedwith the distance between the Ni-Cf source and the position of ith PMT, ri , as well as the10PMT
41500
acceptance ai :Nobs,i × ri2 /ai .
(4.1.3)3
10

1000
Even after this correction, some position
dependence remains because of reflection from neigh2boring surfaces, and scattering and absorption by the water. These further corrections10were
estimated by the MC. Once these light propagation eﬀects are considered, the remaining diﬀer500
ence is attributed to the QE of individual PMTs.
10

Timing Calibration

00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

1

0

5

10 15 20 2

The time response of each readout channel, including PMTs andpCreadout electronics, has to bepcalibrated for precise reconstruction of the event vertices and track directions. The response
Fig. 12.
The single-pe
distributions
in pC unit forsourcein SK-III. lengths
The rightofplot
shows the same histog
time of readout
channels
can vary
due to diﬀerences
innickeltransittimedataof PMTs,PMT
showsdata withnormal PMT
gain, the electronics.
dashed line shows
the data thewithresponse
double gain
andofhalf threshold, andsignal cables,
andtherelative
diﬀerencesof readout
In addition,time
readout channels depends on the detected charge of PMTs, since the rise time of a large pulse isfaster than that of a smaller one. This is called the “time-walk” eﬀect. This was calibrated byinjecting various intensities of light into PMTs. A schematic diagram of the timing calibration
system is shown in Fig. 4.9. A nitrogen laser light source whose wavelength is shifted to 398 nm
by a dye is used. The nitrogen laser pulse is split into two outputs, one goes to the trigger PMT
which creates an external trigger for timing calibration events, and the other is sent to the dyelaser module to generate laser pulses. The dye laser pulse with a wavelength of 398 nm and aactured by CI Kogyo. The balle. The Cf source was insertedrod.

Fig. 13. The single-pe distributions for our MC simulation (solid line). This
distribution was implemented while we were still using the ATM-based electronics.
The dashed line shows the distribution of number of photoelectrons from thenickel data in SK-IV. The difference between them is due to the threshold functionof the QBEE, and the ratio is also put into our MC simulation.

4.2. WATER TRANSPARENCY

55

106
105
104
103
102
10
2 2.5 3 3.5 4 4.5 5

1

0

5

10 15 20 25 30 35 40 45 50

pC

pC

kel source data in SK-III. The right plot shows the same histogram in logarithmic scale. The solid line in the left ﬁgure
Figure 4.3: Charge distribution in units of pC obtained in the absolute gain calibration. Taken
ne shows the data with double gain and half threshold, and the dotted line is linear extrapolation.
from [80].

pulse width of 0.2 ns passes through a variable filter to adjust the laser intensity. The filtered
light is distributed into the whole ID PMTs through a diﬀuser ball.
From this calibration, two-dimensional correlation distribution of timing versus pulse height(charge) called TQ-distributions is obtained. A typical TQ distribution for one readout
channel is shown in Fig. 4.6. Calibration constants, called the TQ-map , are derived byfitting the TQ distribution to polynomial functions. The timing resolution of the SK detector isevaluated using the vertically sliced distributions of the TQ-distribution. This was conducted byfitting the sliced one-dimentinal timing distribution for each charge region with an asymmetric
Gaussian:()−(t − Tpeak )2



A
exp
+ B1 (t > Tpeak )
 1
σt2
(
)
f (t) =
(4.1.4)−(t − Tpeak )2


A
exp
+
B
(t
≤
T
)
 2
2
peak
σ ′ 2twhere A1 , A2 , B1 , B2 , σt and σ ′ t are fit parameters. A typical timing distribution for a certain
charge region and fit functions are shown in Fig. 4.7. The obtained timing resolutions are plotted
as a function of observed charge in Fig. 4.8.

4.2

Water Transparency

Water transparency is important in determining the number of generated Cherenkov photons
from the number of observed photoelectrons because the photons are observed after passing

56

CHAPTER 4. DETECTOR CALIBRATION
261

K. Abe et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 253–272

normalized hit probability

1.3
1.2
1.1
1
0.9
0.8
0.7

-1500

-1000

-500

0

500

1000

1500

z (cm)
1.3

1.3

1.2

1.2

1.1

1.1

1

1

0.9

0.9

0.8

0.8

0.7

0

1000

2000

3000

0.7

0

1000

2000

x 103

3000
x 103

Fig. 14. Hit probability as a function of PMT position. The vertical axis shows the number of hits normalized by average value of all the PMTs. The upper ﬁgure shows thebarrel PMTs where the horizontal axis denotes the z (cm) position of PMTs. The lower ﬁgures show top (left) and bottom (right) PMTs, where the horizontal axis shows thesquare of the distance from the center (cm2). The red thick line shows the data, and the blue thin line shows MC. The MC was not corrected by QE differences in each PMT.
(For interpretation of the references to color in this ﬁgure caption, the reader is referred to the web version of this paper.)Figure 4.4: The position dependence of the photon detection probability in the detector. The
vertical axis values are normalized by the average value of all PMTs. The top plot shows thePMTs
the sidewall,
the horizontal
ofdetermine
PMTs howin cm.
bottomleft
PMT, Z
weposition
cannot easily
many The
photonsreached it.
by this on
assumption
below 0.3 andpC becomes
negligible afteraxis
con- is the
Therefore,
we used axis
MC simulation
to predictofsideringplot
the truediscriminationthresholdand the PMTs,
small amount(right)shows
the top(bottom)and thehorizontal
is the square
ofthe
thenumberdistance
photons arriving at each PMT, and took the ratio of the observedof charge. The value averaged over the whole pC 2region wasfromtheas thedetector
centerin pC
unitof cm the
. red
show
data
and blue
pointsnumberof hits
to predicted
numberof hits. show MC. Taken
deﬁnedconversion
factor fromto single-pe;value pointsof
For this measurement, we use the nickel source used inthis conversion
factor was 2.243 pC to single-pe. At the beginning
from
[80]
of SK-IV, we repeated this measurement and found the newconversion factor to be 2.658 pC per photoelectron. This difference
comes from a long-term increase in the PMT gain. No clear reason
has been identiﬁed for this increase, but it is accounted for inphysics analyses.
The single-pe distribution, as constructed above, is also implemented in MC simulations. The solid line in Fig. 13 is the same as
the one we pieced together in Fig. 12, with the axis converted frompC to photoelectron. For simulations of multiple photons in IDPMTs, we sum values drawn from this distribution. The nickelsource data are also used to extract the threshold behavior for MC
simulations. The dashed histogram in Fig. 13 is the experimentallyobserved distribution and has the threshold folded into it. In MC
simulations, we use the ratio of the observed (dashed) and partly
observed, partly extrapolated (solid) histograms in Fig. 13 toimplement single-hit threshold behavior.

absolute gain measurements (Section 3.1.4). In addition, theuniformity of water quality throughout the tank is quite important, since any non-uniformity in water properties causes the hit
probability to depend on the PMT position not just because of
relative geometry, but also because of the exact conditions along
the photon path. As discussed in Section 2.4, this condition can be
identiﬁed by measuring the temperature proﬁle throughout the
ID. We conducted this calibration when the water convected over
the whole ID volume.19 It was also conﬁrmed that no signiﬁcant
top–bottom asymmetry of water quality existed because nodifferences in the standard PMTs appeared between top andbottom. We used nickel source data from that day for thismeasurement.
Fig. 14 shows the position dependence of the hit probability
with the following corrections:through the water in the tank. To calibrate the absorption and scattering of light in water, lasersthat have various wavelengths are used. Figure 4.9 shows the schematic view of the calibration
system for water transparency. The sidewall of the detector is divided into five regions, and theparameters of the scattering component are estimated from the hit timing and charge of the
PMTs in each region. Water absorption and scattering parameters are determined by comparing
MC simulations with data obtained from laser irradiation. Figure 4.10 shows the comparison ofTime-Of-Flight subtracted hit timing distributions between best-tuned laser MC and calibration2
data. The number of photons with a wavelength N(λ)
in waterdecreases gradually accordingð4Þto
obs ðiÞ # RðiÞ =aðθ ðiÞÞ3.1.5. Relative differences in QEs
Values for QE differ from PMT to PMT. Here we describe 0
how
we determine the relative QE for each PMT. If the intensity of alight source is low enough, the observed hit probability should be
proportional to the value of QE for the PMT, as can be seen from0
Eq. (2). While we can count the number of hits measured by eachwhere i again indexes the ID-PMTs, R(i) is the distance from thesource position to the PMT position, and aðθÞ is the acceptance as aI(λ) = I (λ) exp(−l/L(λ))(4.2.1)function of incident angle θ [4]. Even after this correction, someposition dependence still remains because of reﬂection from

where l is the travel length of the light, I (λ) is the initial intensity, I(λ) is the intensity at l, andThe data were taken on October 12, 2006 when was just after SK-III started.
L(λ) is the total attenuation length caused by scattering and absorption, which we call watertransparency. The total attenuation length caused by scattering and absorption, L(λ), is definedasL(λ) =

191
αabs (λ) + αsym (λ) + αasymm (λ)(4.2.2)

0.85 bottom
0.8

barrel

-150

-100

top
-50

0

barrel50

100bottom150

degreed QE factor and normalized by its average over all PMTs. The left side of the ﬁgure shows the setup. The
he top-center point. The color of the points in the right scatter plot corresponds to the PMT production period
4.2. inWATER
TRANSPARENCY
he references to color
this ﬁgure
caption, the reader is referred to the web version of this paper.)57

ation.

90
80
70
60
50
40

Fig. 20. Schematic view of the timing calibration system.

Figure 4.5: The schematic diagram of the timing calibration system. Taken from [80]Optical fiber30

where αabs (λ), αsym (λ) and αasymm (λ) are parameters for absorption, symmetric scattering and20
asymmetric scattering, respectively. Those factors
are parametrized
stainlesssleeve as follows:
10
103

0

mm
P1φ mm
+
C,
λ(4
)
P4
P5
(λ)
=
×
1.0
+
,
MgO α10000
ppm
sym
λ4
λ2
(
)
P7
2
αasymm (λ) = P6 × 1.0 + 5mm
×
(λ
−
P
)
,
8
λ4
αabs (λ)=

P0 ×(4.2.3)(4.2.4)(4.2.5)e average for eachof the references towhere the second term C in the first line is the amplitude basedφon mm
the experimental data forrsion of this paper.)P3> 464 nm [81] and C = P0 × P2 × (λ/500) for < 464 nm, P0−8 are constant coeﬃcients.
1500ppm
2.3mm
These parameters are used in MgO
MC andtuned by thiscalibration. Figure 4.11 shows typicalfitted water parameters used in MC. The points are the data obtained in April 2009.
The water transparency is also measured by the Cherenkov light from cosmic ray muons
pulse heights ofpassing through the detector. The water transparency measured by cosmic ray muons gives anr than that of averagedawater transparency weighted over the spectrum of Cherenkov photons and the quantum
eﬃciency as a function of wavelength.
Since this transparency
essentially what we need in theect. The overall
Fig. 21. Cross-sectionof the diffuserisball.
physics
analysis,
this
water
transparency
is
used
for
correcting
thenumber of hit PMTs and thee calibrated bynumber of photoelectrons for the energy measurement. Details of the method to measure theng the intensity
water transparency by muons are described in Ref. [80]. Figure. 4.12 shows the measured water
intensity
is varied
by a variable
optical ﬁlter. We use the opticaltransparency
over theperiod analyzed
in this thesis.

ming calibration
urce for timing
a gas ﬂow lasera wavelength ofponse 2-in. PMT
0.37 ns). This
light injection.
8 nm by a dye,spectrum, light
PMTs is almost

ﬁlter to measure the time responses of readout channels at various
pulse height. The ﬁltered light is guided into the detector by an
optical ﬁber (400 μm core) and injected into a diffuser ball locatednear the center of the tank to produce an isotropic light. Fig. 21
shows a cross-section of the diffuser ball. Directional variations in
the photon emission time of the diffuser ball were measured to beless than 0.2 ns.
Timing calibrations for SK ID readout channels were conductedbased on two-dimensional, timing versus pulse height (charge),
correlation tables that are called “TQ distributions”. Fig. 22 shows a

58

CHAPTER 4. DETECTOR CALIBRATION

K. Abe et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 253–272

Q (p.C.)

tqmap of cable # 00010
1230

265

0 1 2 3 4 5 6 7 8 9 10

1.0
0.9

1220

0.8
0.7

1210

T (ns)

0.6
1200

0.5
0.4

1190

0.3

Entries 561679

1180

0.2
0.1

1170

0

20

40

60

80

100

120

140

160

0.0

180

QBin
Fig. 22. Typical TQ distribution for a readout channel. The horizontal axis is charge (Qbin) of each hit, and the vertical axis is time-of-ﬂight-corrected timing (T) of the hits.
Larger (smaller) T corresponds to earlier (later) hits in this ﬁgure.

Figure 4.6: A typical TQ distribution for one readout channel. The horizontal axis corresponds
to observed charge. The vertical axis shows detection timing. Larger value in the vertical axis
The calibration constants, called the “TQ-map”, are derived bycorresponds to earlier hits in this plot. Taken from [80]ﬁtting the TQ distribution to polynomial functions. A TQ-map

includes overall process time and the time-walk effect; eachreadout channel has its own TQ-map.
In the laser event selection, we require that the monitor PMT isﬁred. The ﬁred timing deﬁnes the reference timing of the laser
ﬂashed. For laser events, we apply a timing correction, called timeof-ﬂight (TOF)of ﬂight
from theThecorrection,
method thatusedsubtracts
for the time
absolute
energycalibration in SK depends on the energy range. The
diffuser ballto the respective
PMT position
using
group
velocity
methods(or control
samples)which
arelisted below are related with this study.
of light with the measured wavelength, ! 398 nm. Using the
TOF-corrected hit timing,“laser hits”
are deﬁned
as hits
in a time• “High”
energystopping
muons(1-10 GeV)
window 750 ns around the hit timing of the monitor PMT.
stopping(200-500 MeV)
The selected laser •hits“Low”
of each energy
readout channel
are muonsdivided into
180 bins of charge, called “Qbin”s. Each Qbin is deﬁned as the• γ-rays from neutral pions (about 130 MeV)
amount of charge from the PMT in pC; they are deﬁned on a linear
scale from 0 to 10 pC (0.2
pC/Qbin)and on a logarithmic
scale from• Decayelectronsfrom stoppingmuons (about 50 MeV)
10 to 3981 pC (50 log ðpCÞ/Qbin). After the TQ distributions are
Fig. 23. Timing distribution added over all the readout channels in Qbin ¼14• LINAC
20MeV)( ! 1 photoelectron). The result of the ﬁt to an asymmetric Gaussian is shown by
divided into 180 Qbins,
the timingcalibration
distribution (below
is smoothedby athe solid curve.
Gaussian to minimize statistical ﬂuctuations. Although the timing
accuracyof Gaussian,
the absoluteenergyscale is checked by comparing data from all calibration
distribution in The
each Qbin
is almostthe timing
distributions have sourcesa small asymmetricbecause of an asymmetricconditions to connect Fi(x) (i ¼1, 2, 3) at Qbin ¼ 10 andwith the feature
MC simulation.
time response of PMT and contributions from direct and indirect
Qbin ¼ 50. F 1 ðxÞ and F 2 ðxÞ have 4 ﬁt parameters each, and 7 ﬁtlight; direct light causes early hits, while indirect light causes lateparameters in F 3 ðxÞ. Thus, the number of ﬁt parameter is 15 inhits due to reﬂection and scattering. In order to take the asymtotal. The parameters resulting from the ﬁt are saved in a database
metric feature into account, the timing distribution in each Qbin isas the TQ-map and are used to correct the time response of eachenergyGaussian,calibration,
eventsthat
stoppedin SK,
which is called “stopping muons”, areﬁtted to anFor
asymmetric
whichmuon
providesthe peaktimingreadoutchannel.
and standard
deviation.
peak timing
standard deviations
resolution ofby
thetrack
SK detector
is evaluatedusing theused.
The Themomentumofand
Cosmic-Ray(CR) muon The
cantiming
be determined
lengthsince thefor respective
chargesare (dE/dx)
ﬁtted by polynomial
functions dependdata set The
as usedfor theTQ-mapTo evaluate
theenergyloss
is approximately
constant samein water.
track
lengthis evaluation.
defined bytheing on Qbin:
timing resolution, all PMT timing distributions, corrected by theirdistance between the entering position at the detector
and the vertex position of the subsequent
TQ-maps, are accumulated in each Qbin and the timing distribuNpolNðxÞ $ p0decayþ p1 x þelectron.
p2 x2 þ ⋯ þpStopping
ð6Þ the following criteria are used:Nxmuons which satisfy
tions in Qbins are ﬁtted by an asymmetric Gaussian that is deﬁned,

4.3

Absolute Energy Calibration“High” Energy Stopping Muons

Qbin r 10 : F 1 ðxÞ $ pol3ðxÞ

2

2

ð7Þ
f ðt;oft 4theT peakdetector.
Þ $ A1 ' expð & ðt & T peak Þ =st Þ þB1• The entering position is at the top
wallþ ðx &direction
10Þ
Qbin r 50 : F 2 ðxÞ $ F 1 ð10Þ• The
is downward.
'½F ′1 ð10Þ þ ðx & 10Þ ' pol3ðx &10Þ)ð8Þ

• Only one decay electron is detected.

Qbin 4 50 : F 3 ðxÞ $ F 2 ð50Þ þ ðx & 50Þ ' pol6ðx &50Þ

ð9Þ

where F ′1 in Eq. (8) is a derivation of F1, that is introduced forcontinuity between F 1 ðxÞ and F 2 ðxÞ at Qbin ¼ 10. In Eqs. (8) and (9),F 1 ð10Þ and F 2 ð50Þ are introduced to satisfy the boundaryf ðt; t r T peak Þ $ A2 ' expð & ðt & T peak Þ2 =st ′2 Þ þ B2

ð10Þ
ð11Þ

where Ai, Bi (i¼ 1,2), st and s′t are ﬁt parameters (note that, in theseequations, a larger t corresponds to earlier hits). The ﬁt parametersneed to satisfy a boundary condition, A1 þ B1 ¼ A2 þ B2 , to connect
two Gaussian functions at t ¼ T peak . As an example, Fig. 23 shows
the timing distribution and the function resulting from the ﬁt for
Qbin¼14.

0.1
40

60

80

100

120

140

160

180

0.0

QBin

e horizontal axis is charge (Qbin) of each hit, and the vertical axis is time-of-ﬂight-corrected timing (T) of the hits.
4.3. ABSOLUTE ENERGY CALIBRATION
his ﬁgure.

59map”, are derived by
unctions. A TQ-map
me-walk effect; eacht the monitor PMT ise timing of the laser
rrection, called timeme of ﬂight from theusing group velocity! 398 nm. Using thened as hits in a timee monitor PMT.
nnel are divided into
in is deﬁned as there deﬁned on a linear
ogarithmic scale from
TQ distributions are
Fig. 23. Timing distribution added over all the readout channels in Qbin ¼14
distribution
added
allﬁtthechannels.
The isobserved
charge region! 1 photoelectron).
The
resultoverof theto readout
an asymmetric
Gaussianshown byon is smoothedFigure
by a 4.7: (Timing
used
in
the
distribution
is
about
3
pC
(1
photoelectronlevel).
The
resultofthe fit to an
the
solid
curve.
Although the timing
asymmetric
Gaussian
is
shown
by
the
solid
curve.
Taken
from
[80]
the timing distribuse of an asymmetricconditions to connect Fi(x) (i ¼1, 2, 3) at Qbin ¼ 10 andm direct and indirect
Qbin ¼ 50. F 1 ðxÞ and F 2 ðxÞ have 4 ﬁt parameters each, and 7 ﬁtof Thus,the muonis 7 <ofL ﬁt< 30m.
rect light causes late • Reconstructedparameters inrange
F 3 ðxÞ.
thetrack
numberparameteris 15 in
The first three
are used to
select vertical
downward-going
muons
that have a clear
er to take the asymtotal.criteria
The parameters
resultingfrom theﬁt are saved ina database
Cherenkov
ring.
canarebe wellThe
fourthcriterionofselects
ution in each Qbin
isastheTherefore,
TQ-map itand
usedreconstructed.
to correct thetime
response
each high energy
muon events.
ides the peak timing
readout channel.
standard deviations
The timing resolution of the SK detector is evaluated using the“Low” Energy
Stopping
Muons
al functions dependsame data
set as used
for the TQ-map evaluation. To evaluate thetimingresolution,all
PMT
timing
distributions,corrected
The momentum of stopping muons having
low energy(< 500 MeV/c)canbybetheirestimated using
TQ-maps,in each the
Qbin
and the angle
timinganddistributheð6Þ
Cherenkov
angle. are
Theaccumulated
relationship between
Cherenkov
momentum can be
tions
in Qbins are ﬁtted by an asymmetric Gaussian that is deﬁned,
expressed asfollows:√
ð7Þ
f ðt; t 4 T peak Þ $ A1 ' expð & ðt & T1peak Þ2 1=s2t Þ þB1 m2
ð10Þ
cos θc ==1+ 2(4.3.1)nβn
P (θc )
22f ðt; t r T peak Þ $ A2 ' expð & ðt & T peak Þ =st ′ Þ þ B2
ð11Þ
where
θ
is
the
Cherenkov
angle,
n
∼
1.33
is
the
refractionindex
ofwater,
βis the speed of
c
10Þ)
ð8Þ
′
1,2),(c),st andareinvariantﬁt parameters(notein these respectively.
where
Ai, Bi (i¼muon in a unitof speedof light
m isstthe
mass, andP isthat,
momentum,equations,largerthet corresponds
to earlierhits). The ﬁt parameters
Stopping muons
which asatisfy
following criteria
are used:
0Þ
ð9Þ
need
to
satisfyaboundary
condition,Aþ
B1 ¼ A2 þ B2 , to connect
1• The entering position is at the top wall of the detector.
two Gaussian functions at t ¼ T peak . As an example, Fig. 23 shows
hat is introduced for• The direction is downward.
the timing distribution and the function resulting from the ﬁt for10. In Eqs. (8) and (9),• Only one decay electron is detected.
Qbin¼14.
tisfy the boundary• Total number of photoelectrons in the ID is less than 1,500 p.e.′ s (750 p.e.′ s for
SK-II).
The first three criteria are the same as those for the “high” energy stopping muon events. The
fourth criterion selects “low” energy cosmic muons having momenta less than 380 MeV/c.

60

CHAPTER 4. DETECTOR CALIBRATION

266

K. Abe et al. / Nuclear Instruments and Methods in Physics Research A 7

Fig. 27 compares
distributions after
the target of theposition). The lef
right peak represe
black sheets. The tof the time distrasymmetric scatte
MC. We generateparameters and se
difference betwee
The number odecreases gradualTiming Resolution (ns)

6
5
4
3
2
1
0
10-1

1

10

102

103

IðλÞ ¼ I 0 ðλÞe % ðl=LðλÞÞwhere l is the trav
IðλÞ is the intensi′
Fig. 24. Timing resolution st (square) and st (triangle) as a function of charge
caused by scatteri
Figure 4.8:(photoelectron)
Timing resolution
σt (square) and σ ′ t (triangle) as a function of charge (photoelecfor SK-IV.
parency. LðλÞ is detron) for SK-IV. Taken from [80]1Fig. 24 shows the timing resolution, i.e. the standard deviation
LðλÞ ¼αabs ðλÞ þ αsym
st and s′t , as a function of charge. They are implemented in the SK
γ-rays from
NeutralPionsBy implementing both s and s′ , SK detector
detector
simulation.
where αabs ðλÞ, αsymtt
0 simulation reproduces timing distributions of data, e.g. LINAC
Single π events are produced by Neutral Current (NC) interactions of atmospheric neutrinos
tuning parameters−17
21
in the detector.
Theπdecaysintotwophotonswithalifetime
of
8.5
×
10
sec,
i.e.
almostcalibration0 data, better than by implementing only st.
functions and do n
immediately inThethe task
waterofCherenkov
detectors.
The invariant
mass ofthe
π0 canbe calculatedusingThe absorption
real-time
monitoringis to monitor
deviationofthe reconstructed
momentum of oftworeadout
γ-rays aschannels during SK detector operathe time-response
λ (nm) is empirica√tion, and to apply a correction
to the TQ-map as necessary.
P
Mπ0 = 2Pγ,1 Pγ,2 (1 − cos θ)(4.3.2)
αabs ðλÞ ¼ P 0 ' 41 þ
For the real-time monitoringof the time response of readout
λSK theemploysa nitrogen
laser(Laserγ-rays,
Sciencewhere Pγ,1channels,
and Pγ,2 are
momentaof the two
obserbed
andInstruments,
θ is the opening angle
VSL-337
DLM-120 dye laser system). This laser system uses
where the second t
between the
γ-rays. πand0 like events which satisfy the following criteria are used:sealed nitrogen as a gain medium and is better suited fordata for λ Z 464 n• Two electron-like rings are detected.
continuous operation than the gas-ﬂow laser that used for the
C ¼ P 0 ' P 2 ' ðλ=5
• TQ-map
An electronfrom muon This
decaylaser
is notalso
detected.
evaluation.
emits fast pulsing light of lessns FWHM,and the wavelengthof the lightis 337.1• thanVertex4position
is reconstructedwithin the Fiducial
Volume(FV).nm. The
is used for λ r 46
wavelength of the laser light is shifted by a dye system to 398 nm.
from a ﬁt to the da
The second criterion rejects events in which charged pions are produced with the π 0 or Charged
The
light
outputofthedyesystemisinjected
into
the
same
data of April 2009
Current (CC) events.
diffuser ball as used for TQ-map evaluation.
The angular di
For real-time monitoring, SK uses a ﬁxed light intensity that iscomponents,“sym
Decay Electrons from Stopping Muons
adjusted to obtain an averaged SK ID occupancy of ! 99% and an
scattered photon a
Stopping muons
producedecayofelectron
Decay electrons
have a continuous
specaveraged
charge! 20 events.
photoelectrons
per readout
channel energy
atprobability increastrum whichmaximum.
is called theThe
Michelspectrum.
The
mean
of
the
energyspectrum
is
about
37
MeV.
frequency of the ﬂashing laser light is ! 0:03 Hz, anding occurs for cos
The selection criteria for decay electron are listed follows:a typical 24-h operation provides a statistical accuracy of ! 0:05 ns
Rayleigh and sym
for monitoring the time response of the readout channels.
scattering consists
Fig. 25 shows timing-offset values as a function of time for atypically has a fo
typical readout channel; here, the timing offset is deﬁned as thesize is greater thdifference between the measured time response from real-timescattered angle funmonitoring and that from pre-deﬁned TQ-map. As shown in theof the particle si
ﬁgure, the time responses of readout channels have been stable“asymmetric” αasy
within 7 0:1 ns for a few years.
mined from
!
P4
α
ð
λ
Þ
¼
'
1:
sym
3.2. Calibration for photon tracking
4Charge (p.e.)λ-12009/10/19

2010/11/26

2012/01/02

2013/02/07

DateFig. 25. Timing-offset values with respect to pre-deﬁned TQ-map for a typicalchannelas a functionof time. The error bar on each point indicates 61
4.3.readout
ABSOLUTE
ENERGYCALIBRATION
statistical uncertainty.

0.003
0.002
0.001
0.004
0.003
0.002
0.001
0.004
0.003
0.002
0.001
1500

Fig. 27. Typical TOF
down-going laser beand MC (red histogr
trons. The top plot iplots correspond to t
indicated in Fig. 26. T
used to measure thethe right region is u
3.2.2. (For interpreta
is referred to the we

10-1

Inverse water transparency (1/m)

Fig. 26. Real-time laser system for measurements of absorption and scattering of
FigureThe schematicof thecalibration
systemfor water
The sidethe 4.9:
Cherenkov
light inview
water
and
reﬂectivity
at thePMT transparency.
surface. Analysis
waswallof the detector is divided into five regions, and the parameters of the scattering component are
performed using PMTs belonging to ﬁve divisions of the barrel region, B1–B5, andestimated from the hit timing and charge of the PMTs in each region. Taken from [80]top. The blue shaded circle spot at the bottom region indicates the beam target
used in the TOF calculation. (For interpretation of the references to color in thisﬁgure caption, the reader is referred to the web version of this paper.)• Time interval from a stopping muon is 2.0 to 8.0 µsec.

10-2

The number of hit PMTs in a 50 nsec window is greater than 60 hits (30 hits
Each• parameter
was determined by applying the same analysis
for SK-II).
2(χ method)on the real data from each laser run. The symmetric• The goodness of vertex fit which is defined as Eq. 6.2.6 is greater than 0.5.
scattering
is relatively
stable• Vertexcoefﬁcient
position is reconstructedwithinthe FV(the RMS/mean was about
10-3
3% August 2008 – November 2012). Both the absorption and
The first criterion involves the eﬃcient timing of decay electron tagging. The second criterion
asymmetricscattering
coefﬁcients
have onrelatively
rejects
γ-rays of 6 MeV
or more emitted
from muon capture
nucleons. larger timeTheabsolute
energyscale
iscalibrated
byvariousmethods
fordiﬀerenttime
momentum
ranges.
dependence (about 20–40% and 20–60% in the same
period,To estimate the systematic uncertainty of the energy scale, the ratio of values between data andrespectively). Since asymmetric scattering is one order of magniMC in each calibration method is used as shown in Fig. 4.13.
tude smaller than absorption, the time variations in water trans10-4
parency
are mainly caused by absorption.
LINAC
calibration30
As described
Sectionwater
depenFor energy
calibration forinlowest
energy2.4,
region(3.5 <quality
E < 20 has
MeV)position
in SK analysis,
a linearthe calibration
holethepositionsare data
fixed andaccelerator
for electrons
is used [83].isSince
dence. (LINAC)
The verticaldependence
determinedfromnickeltheobtained
length of theevery
beam pipe
isalso
fixed,
thecalibration
data
were
taken
at
the
fixed
pointsmonth and monitored with the real-time 9Xe
as shown in Fig. 4.14.
Fig. 28. Typical ﬁtted
systemasmeasuredescribed
in Section
3.1.2.
A similarin
In order tothe energyof the single
electron
generated z-dependenceby the LINAC calibration
the data obtained insystem,germanium
detector
used. in
Thisother
germanium
detector
is calibrated
with
γ-raysasfrom symmetric scatterin
the awater
qualityis isseencontrol
sampledata,
suchdecay electrons from cosmic-ray stopping muons. Fig. 30 shows
the top line shows t
the top–bottom asymmetry of the hit probability normalized by
the average of all the PMTs as a function of time. The top–bottom
asymmetry (αtba) is deﬁned by
SK-IV time perio
absorption, as dαtba ¼ ð〈N top 〉 # 〈N bottom 〉Þ=〈Nbarrel 〉ð18Þdependence ofmultiplying αabs
where 〈N top 〉; 〈Nbottom 〉 and 〈Nbarrel 〉 are the averages of the hit
probabilities of top, bottom and barrel of SK, respectively. The
Aðz; tÞ ¼ 1 þ z & β ðaverage of the hit probability on the top PMTs is about 5% smaller

62

CHAPTER 4. DETECTOR CALIBRATION
267

K. Abe et al. / Nuclear Instruments and Methods in Physics Research A 737 (2014) 253–272

0.004
0.003
0.002
0.001
0.004
0.003
0.002
0.001
0.004
0.003
0.002
0.001

2010/11/26

2012/01/02

2013/02/07

Date

set values with respect to pre-deﬁned TQ-map for a typicals a function of time. The error bar on each point indicates
nty.

0.004
0.003
0.002
0.001
0.004
0.003
0.002
0.001
0.004
0.003
0.002
0.001
1500

1600

1700

1800

1900

ns
Fig. 27. Typical TOF-subtracted (see text) timing distributions for the vertical
down-going laser beam with the wavelength at 405 nm between data (black circle)

Figure 4.10: The comparison
between laser MC and calibration data. Typical Time-Of-Flightand MC (red histogram, the best tune) normalized by observed total photoelectrons. The top plot
thevertical
PMTs at thedown-going
SK tank top wall. laser
The second
to bottom
subtracted timing distributions
foris forthebeamwith the wavelength atplots correspond to the ﬁve barrel wall regions from top to bottom of the SK tank as
405 nm between data
(blackcircle)andMC(redhistogram,
thebest
tuned) normalized byindicated in Fig. 26. The time region between the left two blue solid vertical lines isused tophotoelectrons.
measure the absorptionTheand scattering
described
this Section
3.2.1
observed number of total
top plot
is forinthe
PMTs
atand
the SK tank top wall.
the right region is used for the measurement of reﬂection described in Section
The second to the sixth
plots
correspond
to
the
five
barrelwall
regions
from
top to bottom of
3.2.2. (For interpretation of the references to color in this ﬁgure caption, the reader
the SK. Taken from [80]is referred to the web version of this paper.)laser system for measurements of absorption and scattering of
ht in water and reﬂectivity at the PMT surface. Analysis was
MTs belonging to ﬁve divisions of the barrel region, B1–B5, anded circle spot at the bottom region indicates the beam target
lculation. (For interpretation of the references to color in thisreader is referred to the web version of this paper.)

10-1

bout 20–40% and 20–60% in the same time period,
ince asymmetric scattering is one order of magnian absorption, the time variations in water transinly caused by absorption.
d in Section 2.4, water quality has position depenical dependence is determined from the nickel datay month and monitored with the real-time Xe
ribed in Section 3.1.2. A similar z-dependence in
ity is seen in other control sample data, such ass from cosmic-ray stopping muons. Fig. 30 showsm asymmetry of the hit probability normalized by
all the PMTs as a function of time. The top–bottomba) is deﬁned by

N bottom 〉Þ=〈Nbarrel 〉ð18Þ

Nbottom 〉 and 〈Nbarrel 〉 are the averages of the hit
top, bottom and barrel of SK, respectively. The
hit probability on the top PMTs is about 5% smaller
he bottom PMTs, as discussed in Section 2.4. The
measurements are in accordance over the entire

Inverse water transparency (1/m)

60
Ni(n,γ)Ni reaction (9.0 MeV and etc.), 137 Cs (0.662
MeV),
Co (1.33 MeV). Figures 4.15 andAbsorption
Total
Symmetric
Asymmetric4.16 show the output charge of the Ge detector as
a functionof γ-ray energy and the diﬀerence ofthe deviation between data and thefitted line. The electron energy measured by the germanium
10-2detector is used as input of MC simulation for LINAC calibration. After the LINAC calibrationr was determined by applying
the issame
analysisdatataken,
the SK simulation is tuned to match the detector response. Figure 4.17 shows thethe real data from each laser run. The symmetricdiﬀerence of the eﬀective number of hit PMTs, Neﬀ , which is defined in Eq. 6.2.4 after tuningﬁcient is relatively stable (the RMS/mean was about-3
in SK-IV.and
The conversion 10
functionfrom Neﬀ to energy is determined by MC simulation of
08 – November 2012). Both MC
the absorption
mono-energetic
electrons.
attering coefﬁcients have relatively
larger time

10-4
300

325

350

375

400

425

450

475

500

Wavelength (nm)Fig. 28. Typical ﬁtted water coefﬁcient functions used in the SK-MC. The points are
the data obtained in April 2009. The each lines through the points for absorption,
symmetric scattering and asymmetric scattering show the ﬁtted functions while
the top line shows the total of all ﬁtted functions added together.

SK-IV time period. Since the time variation is mainly caused byabsorption, as described above, the vertical position and timedependence of the water quality is introduced in SK-MC by
multiplying αabs by a factor Aðz; tÞ in Eq. (13):Aðz; tÞ ¼ 1 þ z & β ðtÞ

for z Z # 11 m

¼ 1 # 11 & βðtÞfor z r #11 m

ð19Þ

f absorption and scattering ofhe PMT surface. Analysis was
the barrel region, B1–B5, andon indicates the beam target
he references to color in thission of this paper.)ying the same analysis
aser run. The symmetric
he RMS/mean was aboutoth the absorption andrelatively larger timen the same time period,is one order of magniariations in water trans-

63

10-1

Inverse water transparency (1/m)

4.3.

Fig. 27. Typical TOF-subtracted (see text) timing distributions for the vertical
down-going laser beam with the wavelength at 405 nm between data (black circle)
and MC (red histogram, the best tune) normalized by observed total photoelectrons. The top plot is for the PMTs at the SK tank top wall. The second to bottom
plots correspond to the ﬁve barrel wall regions from top to bottom of the SK tank as
indicated in Fig. 26. The time region between the left two blue solid vertical lines isused to measure the absorption and scattering described in this Section 3.2.1 andthe right region is used for the measurement of reﬂection described in Section
ABSOLUTE
ENERGY CALIBRATION
3.2.2. (For interpretation of the references to color in this ﬁgure caption, the reader
is referred to the web version of this paper.)

Total

Absorption

Symmetric

Asymmetric

10-2

10-3

10-4

ssed in Section 2.4. The
ordance over the entire

Water Transparency [m]300 325 350 375 400 425 450 475 500
lity has position depenned from the nickel data
Wavelength (nm)with the real-time Xe
Fig. 28. Typical ﬁtted water coefﬁcient functions used in the SK-MC. The points are
imilar z-dependence inthe data obtainedin April
2009. The eachlines throughpointsabsorption,
Figure 4.11: Typicalfitted watercoeﬃcientfunctionsused inthethe
MC.forThepoints are the dataol sample data, such as
symmetric
scattering
asymmetricscattering show
the ﬁttedscattering,
functions whileobtained in April
2009.
Each andcurvesfor absorption,
symmetric
and asymmetricg muons. Fig. 30scatteringshows show
the top line shows the total of all ﬁtted functions added together.
CHAPTERTHE SUPER-KAMIOKANDE
DETECTOR
the fitted3.function
for each case while
the black curve shows the total of all fitted
obability normalized
by added together. Taken from [80]functionsof time. The top–bottom
SK-IV time period. Since the time variation is mainly caused byabsorption, as described above, the vertical position and time
ð18Þ
dependence of the water quality is introduced in SK-MC by
multiplying αabs by a factor Aðz; tÞ in Eq. (13):he averages of the hitof SK, respectively. The
SK-I
SK-II SK-III
SK-IV
Aðz; tÞ ¼ 1 þ140z & β ðtÞ for z Z # 11 m
MTs is about 5% smaller

120¼ 1 # 11 & βðtÞ100

for z r #11 m

ð19Þ

80
60
40
20
0

2000/01/01 2004/12/31 2009/12/31 2014/12/31

Date
Figure 3.36: Time variation of water transparency (water attenuation length). Absolute values

Figure 4.12: Timevariationofdetector
water configurationstransparency.
Absolute
values among
are sensitive
to the detector
are sensitive
to theand cannot be compareddifferent detector
phases.
configurations andcan not be compared among diﬀerent detector phases.

Figure 3.37: Schematic view of the laser light injector system for the reflectivity measurement of

64

CHAPTER 4. DETECTOR CALIBRATION

PHYS. REV. D 97, 072001 (2018)

ATMOSPHERIC NEUTRINO OSCILLATION ANALYSIS …

( MC - Data ) / Data [%]

4
SK-I

SK-II

SK-III

SK-IV

2

0

-2

Decay electron
Neutral current π0
Sub-GeV stopping µ
Multi-GeV stopping µ

-4

103

102

104

102

103

104

102

103

104

102

103

104

Momentum [MeV]

FIG. 3. Absolute energy scale measurements for each SK period. Vertical error bars denote the statistical uncertainty and horizontal
error bars4.13:
the momentum
rangeofspannedby eachanalysis.scale measurements for each SK phase. The percentFigure
Summary
absolute
energyage of diﬀerences between data and MC are shown. Vertical error bars denote the statisticalcorresponds to a total livetime of 5,326 days, 2,519 of
most discrepant sample from this study in each run period.
uncertainty
and horizontal error bars denote thewhich
momentum
range spannedby eachanalysis.
K. Okamoto
The total systematic error is assigned taking this value
are from SK-IV. Super-Kamiokande’s
atmosphericTaken[82]. with the time variation of the energy neutrino data are separated into three broad categories, fullysummedfrom
in quadrature

LINAC datascale, which is measured using the variation in the averagereconstructed momentum of Michel electrons and thevariation in the stopping muon momentum divided byrange. An example of the latter showing the energy scalestability since SK-I appears in Fig. 4. Note the SK-III
period was subject to poor and volatile water transparency
conditions, resulting in a comparatively turbulent energy
scale. The stability seen in the SK-IV period is a result of
SKpurification(y=0 plane)
improvements in the water
system and in
Position 7
corrections
ave= 0.995182 ± 0.000001 for the time variation of the PMT response.
The total energy scale uncertainty in each period has been
estimated as 3.3% in SK-I,LINAC
2.8% in SK-II, 2.4% in SK-III,and 2.1% in SK-IV.

contained (FC), partially contained (PC) and upward-going
muons (Up-μ) that are further sub-divided into the final
analysis samples. Fully contained events have a reconstructed vertex within the 22.5 kton fiducial volume,
defined as the region located more than 2 m from the
ID wall, and with no activity in the OD. The FC data are
sub-divided based upon the number of observed Cherenkov
rings, the particle ID (PID) of the most energetic ring,and visible energy or momentum into combinations of
single- or multi-ring, electron-like (e-like) or muon-like(μ-like), and sub-GeV (E < 1330.0 MeV) or multi-GeV(E > 1330.0 MeV).
Additional
Controlroomselections are made basedon the number of observed electrons from muon decays andthe likelihood of containing a π 0 . For the SK-I, -II, and -III
B. Sample selection
data periods the latter selection is based on [16] and for SKIV it is performed using the improved algorithm presented
Year (20XX)
Z=+12m
The current analysis
utilizes
atmospheric
neutrino data
① ④ ⑦ in [6]. After all selections there are a total of 14 FC analysis
collected during each of the SK run periods andsamples. Events with a fiducial vertex but with energy
Position 8
ave = 0.995918 ± 0.000001
deposition in the OD are classified as PC. Based on the
SK-I
SK-II
SK-III
SK-IV
energy deposition within the OD, PC events are further
0.04
Z=0 m
② ⑤ ⑧ classified into “stopping” and “through-going” subsamples.
The Up-μ sample is composed of upward-going muon
0.02
events produced by neutrino interactions in the rocksurrounding SK or in the OD water. Accordingly, lightYear (20XX)
0
deposition in both the OD and ID is expected and the
Z=-12 m ③ ⑥ ⑨ sample is divided into “through-going” and “stopping”
Position
9-0.02
subsamples for events that cross or stop within the ID,
ave = 1.004998 ± 0.000001
respectively. Through-going events with energy deposition
consistent with radiative losses are separated into a “show-0.04
X= -12 m, -8 m, -4 m ering” subsample. The 19 analysis samples defined for each2000.12.31
2005.12.31
2010.12.31
2015.12.31
the SK run periods are summarized in Table II. Zenith
Schematic view for theof
LINAC
calibration
angle
distributionsof each sample are shown in Fig. 5.
FIG. 4. 4.14:
EnergyAscale
stability measured
as a functionof datecalibration system. Orange squares show steering
Figureschematic
diagramof LINAC
Distributions
of
the
true
(The
electronisshot
at(-4,0,12)m)neutrino energy for the FC, PC,
Year(20XX)
since the start of SK operations. The energy scale is taken as themagnets
and circled numbers show injection points
mono-energitic
Basedon event
Fig.1
andofUp-μevent categorieselectrons.
appear in Fig.
6. Their
average of the reconstructed momentum divided by range ofofstopping
Ref.
[83]
rates
over
the
lifetimeoftheexperiment
have
been
stableat
4
18 MeVcosmic ray muon data in each bin. The vertical axis
8.3 FC events per day, 0.73 PC events per day, and 1.49
shows the deviation of this parameter from the mean value for
18 Upμ events per day, as shown in Fig. 7. In total 27, 505 μ-likeeach SK period separately. Error bars are statistical.

on dependence of Neﬀ ratio MC/data
Position 4
ave = 0.995952 ± 0.000001

2

1.02

1

1.01

1

1

9

0.99

8

0.98

78

10

12

14

16

18

20

0.978

Year (20XX)

1.03

Neff MC/data

3

Position 5
ave = 1.002554 ± 0.000001

2

1.02

1

1.01

1

1

9

0.99

8

0.98

7
8

10

12

14

16

18

20

0.97
8

Year (20XX)

1.03

Neff MC/data

3

Position 6
ave = 1.005266 ± 0.000001

2

1.02

1

1.01

1

1

9

0.99

8

0.98

7
8

10

12

14

16

18

20

Year (20XX)

8 MeV

12 MeV

0.97
8

10

12

14

16

18

20

10

12

14

16

18

20

10

12

14

16

18

20

Deviation from mean

1.03

Neff MC/data

3072001-7

4.3. ABSOLUTE ENERGY CALIBRATION65

MCA channel

3000
2500
2000
1500

MCA channel

3000
1000

χ2 / ndf
p0
p1

895.4 / 15
-6.84 ± 0.004479
0.1916 ± 3.421e-06

2500
500
20000

0

1500

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
True energy (keV)

1000

(E

obs

- Efit)/E

fit

0.003
Figure 4.15:
The linearity of the germanium detector. The red line shows a linear fuction used
for fitting. The vertical axis shows the output from the germanium detector (Multi Channel
500
Analyser 0.002
channels)
and the horizontal axis shows the energy of the calibration γ-ray sources inunit of keV.

0
0.001

0

0

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
True energy (keV)

(E

obs

- Efit)/E

fit-0.001

0.003-0.0020.002-0.00300.0011000 2000 3000 4000 5000 6000 7000 8000 9000 10000
True energy (keV)0-0.001-0.002-0.00301000 2000 3000 4000 5000 6000 7000 8000 9000 10000
True energy (keV)

Figure 4.16: The diﬀerence between the data and the fitted line in Fig. 4.15. The horizontal axis
shows the energy of γ-ray in unit of keV and the vertical axis shows the diﬀerence.

66

1.5

1.5

Neff (Data-MC)/MC [%]n

9
Neff (Data-MC)/MC [%]F THE SK-IV

CHAPTER 4. DETECTOR CALIBRATION

1.0
0.5
0.0

-0.5

0.5
0.0

-0.5

-1.0

-1.5

1.0

4

x=-12.4m, z=+12.1m

x=-12.4m, z=0.0m

x=-12.4m, z=-12.0m

x=-8.1m, z=+12.1m

x=-8.1m, z=0.0m

x=-8.1m, z=-12.0m

x=-3.9m, z=+12.1m

x=-3.9m, z=0.0m

x=-3.9m, z=-12.0m

6

8

10

12

14

16

18

-1.0

20

-1.5

4

6

8

2010 Energy [MeV]

10

12

14

16

18

20

2012 Energy [MeV]

1.5

1.5

y scale in SK-IV

Neff (Data-MC)/MC [%]onducted LINAC
alyzed calibration
event reconstrucFor the LINAC
from the trigger
pe is required. To
ion by hit timing
fined in Sec. III A)
occasionally overs beyond 3 from

Neff (Data-MC)/MC [%]Neff (Data-MC)/MC [%]sts of an electron
1.0
1.0
collimators, mag0.5
0.5
of the system are
0.0
0.0
of the beam pipe
-0.5
-0.5
ctor and a single
-1.0
-1.0
e detector. The
-1.5
-1.5
nto the detector,
468
10 12 14 16 18 20
468
10 12 14 16 18 20
2016 Energy [MeV]2017 Energy [MeV]by elastic scatterneutrinos.
FIG.
12. The di↵erence of the N LINAC
betweenthe calibration
4.17: The diﬀerence of the Neﬀ between thee↵calibration data and the MC siminjected into theFiguredata
and Thethemarkers
MC simulation.
Theofmarker
shows The
theredposition
ulation in SK-IV.
show the positions
the calibration.
horizontal lines
The energy of in-shows of±0.5%.
the calibration. The red horizontal lines shows ±0.5%.
18.9 MeV in total
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0

x=-12.4m
x=-8.1mx=-3.9m
±0.5%
-15

-10

-5

0

5

10
15
Vertex z [m]FIG. 13. The di↵erence of the Ne↵ between the calibration
data and the MC simulation after taking the weighted average. The marker shows the position of the calibration. The
blue horizontal lines shows ±0.5%.

Chapter 5

Simulation
In this chapter, the Monte Carlo (MC) simulation for solar flare neutrinos in SK is described.

5.1

Neutrino Interactions

For events with neutrino energies above 100 MeV (defined as “high-energy” events as follows),
the tools for atmospheric neutrino oscillation analysis were used, and for events with energies
below 100 MeV (defined as “low-energy” events as follows), the tools for solar neutrino analysis
and supernova neutrino searches were used in this study. More detailed information about data
reduction will be described in Chap. 6.

5.1.1

High-Energy neutrino interactions

For High-Energy events, neutrino interactions inside the detector are simulated based on NEUT[84]. They are classified into two categories, Charged Current (CC) and Neutral Current (NC)interactions. A neutrino exchanges a W ± boson with the target in the CC interaction. Afterthe CC interaction, a charged lepton is left in the final state. By distinguishing the flavor of
the charged lepton inside the detector, the flavor of incoming neutrino can be identified. On theother hand, in the NC interaction, a neutrino interacts with the target mediated by a Z 0 boson.
After this NC interaction, no signs of the neutrino flavor are left within the detector.
In the NEUT simulation, the following interactions are considered:• CC and NC (quasi-)elastic scattering. CCQE (NCQE): ν + N → l(ν) + N ′ (N ).
• CC meson exchange current, CCMEC : ν + N N ′ → l + N ′′ N ′′′ ,• CC and NC single meson production: ν + N → l(ν) + N ′ (N ) + meson,• CC and NC coherent pion production, CCCOH (NCCOH): ν + 16 O → l(ν) +16
O + π,• CC and NC deep inelastic scattering, CCDIS (NCDIS): ν + N → l(ν) + N ′ (N ) +hadrons,
where N ,N ′ ,N ′′ , and N ′′′ stand for nucleons, l stands for a charged lepton, and ν stands for aneutrino.
Brief explanations for each interaction are described below.
67

3. SIMULATION

68

56

CHAPTER 5. SIMULATION

and Pauli blocking of the nucleon. The outgoing momentum of the nucleons in
the interactions is required to be larger than the Fermi surface momentum to allow
quasi-elastic
scattering to occur. The Fermi surface momentum is set to 225 MeV/c,(Quasi-)Elastic
Scattering
which is required to reproduce the quasi-elastic peak in electron scattering. The
For the CCQE
interaction
NEUT,with
Llewellyn
Smith[134,modelis used.systematic
The CCQE crossNEUT
model was incomparedother models
135] [85]to estimateof neutrino
interactions
nuclearshowsexperimental
the crosssections as uncertainties
a function ofincoming
neutrinoandenergyin effects.
NEUTFigureand 3.7
variousresults
the quasi-elastic scattering from the experimental data and the calculations
are shown insection
Fig. of
5.1.
from the NEUT library.

Figure 3.7: Cross-section for the CCQE scattering of muon neutrino (left panel)

Figure 5.1: Cross-section
for the CCQE
scatteringmuon(left freepanel)and muon antiand muon anti-neutrino(right panel).
Solidoflines
showneutrinos
the calculated
targets,
neutrinos (rightpanel).
the calculated
curves forfreetargets,
and the dashedand thedashedSolidlines lines
show show
the calculated
bound targets.
Data
pointsare taken
from
ANL [136]bound(crosses),
BNL [137](triangles), Gargamelle[138–140](circles),lines show thecalculated
targets.
Experimental
data points
are from:
ANLSer[86], BNL [87],[141] (asterisks),
and SKAT(stars).
The
figurewas taken from Hayato
Gargamelle pukhov[88], Serpukhov[89], andSKAT[142]
[90].
Taken
from
[84].
[121].
The NC elastic scattering cross-sections were estimated from the CC cross-section
by the following relations [143, 144]:

CC meson exchange current

σ NC (νp → νp) = 0.153 × σ CCQE (νn → e − p)

(3.13)The CCQE interaction is approximated so that the neutrino interacts with a single nucleon only
σ NC (ν p between→ ν p) =the0.218
× σ CCQE(3.14)
p→e + n)
if it ignores the direct correlation
nucleonsin (νthenucleus.
However,
it is suggested
that a process in which an NC
incoming neutrino interacts
with multiple nucleons in the targetNCσ (νn → νn) = 1.5 × σ (νp → νp)(3.15)
nucleus simultaneously by MiniBooNE experiment [91]. The Meson Exchange Current (MEC)
model by Nieves et al. [92] σisNCadopted
in NEUT.
(ν n → ν n)
= 1.0 × σ NC (ν p → ν p)
(3.16)CC and NC single meson production
Single meson
production
occurs
via a baryon
resonance excitation state in a neutrino interaction
3.2.2
Meson
Exchange
Current
as following:
The CCQE interaction is approximated so that the neutrino interacts with a single
nucleon only if it ignores the direct correlation between
the nucleons in the nucleus.
ν + N → l(ν) + N ∗ ,In reality, however, the interaction between nucleons must introduce some direct
N ∗ →neutrino
N ′ + meson
correlation, such that the incident
interacts simultaneously with multiple(5.1.1)(5.1.2)where N ∗ is the baryon resonance, and a single meson is produced from N ∗ .
When the invariant mass of the hadron system, W , is less than about 2.0 GeV/c2 , theinteractions are dominant hadron production processes. Figure 5.2 shows the cross-sections of
single pion production as a function of incoming neutrino energy.
CC and NC coherent pion production
The reaction in which a single pion has the same charge as the incoming weak current can begenerated by the interaction between an oxygen nucleus and the neutrino. This interaction iscalled coherent pion production. Because the momentum transmitted to the oxygen nucleus is

69

Y. Hayatocm2)

νµ p → µ− p π+σ(ν µ )(10

−38

1.2

σ(ν µ )(10

−38

cm2)

5.1. NEUTRINO INTERACTIONS
2480

1
0.8

1
0.9

νµ n → µ− p π0

0.8
0.7
0.6
0.5

0.6

0.4

0.4

0.3
0.2

0.2

0.1

σ(ν µ )(10

−38

cm2)

0
1
0.9

1

10

0

Eν (GeV)1

10Eν (GeV)−νµ n → µ n π+

ANL Radecky, Phys.Rev.D 25, 1161 (1982)

0.8

ANL Campbell, Phys.Rev.Lett. 30, 225 (1973)

0.7

ANL Barish, Phys.Rev.D 19, 2521 (1979)

0.6

BEBC Allen Nucl.Phys.B 264, 221 (1986)

0.5

BEBC Allen Nucl.Phys.B 176, 269 (1980)

0.4
BEBC Allasia Nucl.Phys.B 343, 285 (1990)

0.3
BNL Kitagaki Phys.Rev.D 34, 2554 (1986)

0.2

FNAL Bell Phys.Rev.Lett. 41, 1008 (1978)

0.1
0

1

10

Eν (GeV)Fig. 2. Cross-sections of (a) ⌫µ p ! µ p⇡ + , (b) ⌫µ n ! µ p⇡ 0 , (c) ⌫µ n ! µ n⇡ + .
FigureSolid
5.2: lines
Cross-section
for single pion
productionExperimentalof the muon data
neutrino.
show the calculated
cross-sections.
pointsTheare solid
sum- lines
show marized
the calculated
The experimental data are summarized in the bottom rightin the cross-section.
table.
panel [93–100]. Taken from [84]In the determination of the angular distribution of pion in the final state,
we use Rein and Sehgal’s method for the P33 (1232) resonance. For the othervery small,the angular
distributionof the outgoing
leptons andin the forward
resonances,directional
distributionof generated
pionpionsis setare
topeaked
be isotropic
indirection.
Coherent
pion
productionissimulated
based
on
the
Rein
and
Sehgalmodel[101].
the Adler Frame (resonance rest frame). With the Rein and Sehgal’s model,
it is possible to calculate the cross-sections for each individual resonance if we
CC andNCthe
deepinelastic scattering
ignoreinterferences.
Using this characteristics, we made the probability
functions towhetherthetheintermediate
is Ptarget
withoften
The interactionof determine
incident neutrinos
withconstituent resonancequarks of thenucleon33 or notthe single-resonancecross-sections.
The angular
distributionof the⇡ + invariant
has been mass
generates
multiple hadrons via
CC deep inelastic
scattering(DIS). Whenof themeasured
hadron system,
than[14]
1.3 andGeV/cthis processfrom
becomesdominant. Forfor ⌫p W!, µis greaterp⇡ + modethe2 ,prediction
the simulation
2
interactions
with
W
<
2.0
GeV/c
,
only
pions
are
producedasgeneratedhadronsin thethe final
agrees well with the data. We also consider the Pauli blocking eﬀect in2state.decay
Since thishadronic
invariantmass
region,
W
<
2.0
GeV/c
,
is
overlappedwiththeof resonances by requiring that the momentum of nucleon should beregion
for thesinglepion production
the multiple This
pion production
simulatedas the DIS
larger thanthe Fermi interaction,
surface momentum.
suppressesistheinteraction
process.
cross-section by a few percent. The pion-less delta decay is also considered
Figure 5.3 shows the total cross-section of the CC interaction, including CCQE, single mesonand 20%ofDIS.
the events do not have a pion and only the lepton and the nucleon
productions,andare generated.
As described, the Rein and Sehgal’s model provide us the amplitudes of
5.1.2 Low-Energy neutrino interaction
neutrino resonance productions. Therefore, it is also possible to calculate
For Low-Energy
events, neutrino
interactions
insideare simulated
based oninversthe cross-sectionsof single
photon, K
andtheEtadetector
productions
by changing
thebeta-decay(IBD):
decay probabilities of the resonances. We also included these interactions inν¯e + p → e+ + n.
(5.1.3)the simulation program.
The IBD cross-section is the largest in the energy region of the low-energy sample and can beanalytically expressed. Only IBD was considered to obtain a conservative limit because otherCHAPTER 5. SIMULATION

These values are estimated from the experimental results [29, 30].

σ/Eν (10-38cm2 GeV-1)

70(¯⌫ N ! ⌫¯X)
= 0.39 0.02 ⇥ ((E⌫ 3.)/3.)(¯⌫ N ! µ+ X)(3 GeV < E⌫ < 6 GeV) ,(¯⌫ N ! ⌫¯X)
= 0.37 (E⌫ 6 GeV) .
(¯⌫ N ! µ+ X)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

GRV94LOGRV94LO (w/ B-Y corr.)
GRV98LO
GRV98LO (w/ B-Y corr.)

CCFR 90
CDHSW 87
GGM-PS 79

0

10

CHARM 88
BNL 80
CRS 8020

30 50

BEBC-WBB 79
IHEP-JINR 96
IHEP-ITEP 79

CCFRR 84
SKAT

100

200

150

250

Eν (GeV)Fig. 3. Neutrino and anti-neutrino charged current total cross-section. The upFigure per
5.3: 4 Comparison
betweenandcurves oflines corresponds
to experimental
neutrino anddata
lower
4 calculatedlines corresponds
to thethe total
anti crosssectionsneutrino.
of the CCTheinteraction
for
ν
and
ν̄.
The
experimental
data
were
taken
from
CCFR
meanings of each lines and corresponding data points are shown [102],
CDHSW [103], GGM-PS [104], CHARM [105], BNL [106], CRS [107], BEBC-WBB [108], IHEPin the figure. (CCFR90 [18], CDHSW87 [19], GGMPS79 [20], CHARM88 [21],JINR [109], IHEP-ITEP [110], CCFRR [111], and SKAT [112]. Taken from [84]
BNL80 [22], CRS80 [23], BEBCWBB79 [24], IHEPJINR96 [25], IHEPITEP79 [26],
CCFRR84 [27], SKAT [28]).

In NEUT, both PYTHIA/JetSet and our own codes are used to generateinteractions are not known precisely, especially about energy and angular distributions of exiting
the deep inelastic scattering events because PYTHIA/JetSet was developed
γ-ray emissions. Although only IBD is considered in this thesis, obtained flux limit will be
to simulateinteractions
anddoes[113]
not fitfor theenergies.
conservative.
In thishigher
study,energy
Strumiaand Vissani’s
model
is usedforlower
the IBD
cross-section
Therefore,
we use the experimental results to generate an event whose W is
as shown
in Fig. 5.4.
2

5.2

less than 2 GeV/c . For those small W events, we assume KNO scaling todetermine the value of W [31]. The multiplicity of pions is determined by
the function described before, which was also obtained experimentally. The
B
forward–backward asymmetry of pion multiplicity(nF⇡ /n⇡ ) in the hadronic
SK
Detector
Simulation
center of mass system is included as follows:

F NEUT
The secondary particles producednby
propagated
0.35are+ 0.41ln W 2 in the SK detector simulation using
⇡
=
.
(2)
a GEANT3 based simulation called
SKDETSIM.
InteractionsnB
0.5 + 0.09
ln (W 2 ) of the particles in water, particle⇡
decays, and production of Cherenkov photons are simulated in SKDETSIM. Detector responses
includingthevaluewaterwasproperty,
opticalmodeling
as wellas PMTandelectronics [32].
responses to theThisobtainedfromthe resultof theBEBC
experimentproduced photons are simulated based on the detector calibration results (See Chap. 4). The
opening angle of the Cherenkov ring is calculated using Eq. 2.1.1. For the propagation of charged
particles, the number of Cherenkov photons and their wavelengths are calculated using Eq. 2.1.4.

Cherenkov photons produced by the charged particles can be scattered or absorbed in water.
The probability of either of these processes occurring is characterized by parameters that dependon the transparency of the water, which is also based on the detector calibration results. When
the Cherenkov photons arrive at the wall of the tank, reflections on the surface can occur. The
calculated reflection value, including the polarization, is used for the SKDETSIM.
SK is an experiment that spans 20 years, and the detector conditions have fluctuated somewhat. Short-term fluctuations include water transparency fluctuations and long-term fluctuations include increased gain in PMT. In order to incorporate these changes into the simulation,a time-dependent detector simulation has been introduced in SKDETSIM.

5.3. SOLAR FLARE NEUTRINO FLUX

71

Figure 5.4: IBD cross-section on a free proton as a function of neutrino energy as calculated byStrumia and Vissani [113].

5.3

Solar Flare Neutrino Flux

The generation processes of solar flare neutrinos in theoretical models are described in Chap. 1.
The assumptions of the total energy of the solar flare neutrinos and the solar atmosphere modelare diﬀerent in each model, and the flux predictions of the solar flare neutrinos reaching theearth in each model are derived by the Monte Carlo simulation. The neutrino energy spectrum
from the solar flare neutrino model was used as input to simulate the solar flare neutrino signal.
For the high-energy MC sample, the expected visible energy spectrum of solar flare neutrinos
is obtained based on the atmospheric neutrino simulations using a re-weighting method. In the
re-weighting method, the result is obtained by re-weighting each simulated event with the ratioof the actual neutrino energy spectrum of solar flares and that of atmospheric neutrinos. Theenergy spectra thus obtained for various solar flare simulations are shown in Fig. 5.5 and 5.6.

CHAPTER 5. SIMULATION

Entry

72

105

Input spectrum(νe(νe)+νµ (νµ ))104

After reduction(νe(νe)+νµ (νµ ))

103
102
10
1
10-1
10-2
10-3

103

104
Visible Energy [MeV]

Entry

Figure 5.5: The energy spectra of solar flare neutrino from Fargion and Moscat [42]. The
horizontal axis is reconstructed positron kinetic energy and the vertical axis shows the numberof events. The yellow-green histograms represent the energy spectrum of the generated events,
and the magenta histograms represent the energy spectrum after the reduction (See Chap. 6) isapplied.

1200

Input Spectrum

1000

After Reduction
800

600

400

200

0
0

20

40

60

80

100

120

140

160
180
e+ Total Energy

Figure 5.6: The energy spectra of solar flare neutrinos from Fargion and Moscat [42]. The
horizontal axis is the visible energy in SK and the vertical axis shows the number of events. The
yellow-green histograms represent the energy spectrum of the generated events, and the magenta
histograms represent the energy spectrum after the reduction (See Chap. 6) is applied.

Chapter 6

SK Data Analysis
In this chapter, a method to search for events in the Super-Kamiokande detector is described.
Solar flare neutrinos are considered to have energies ranging from several MeV to several GeV.
For events with energies above 100 MeV (defined as “high-energy” events hereafter), the tools
for the atmospheric neutrino oscillation analysis were used, and for events with energies below
100 MeV (defined as “low-energy” events hereafter), the tools for the solar neutrino analysis andthe supernova neutrino search were used in this study. The data sets obtained by those tools aredescribed below.

6.1

High-Energy Event Analysis

The atmospheric neutrino events observed in Super-Kamiokande can be classified into several
types, as shown in Fig. 6.1. If a neutrino interacts in the inner detector (ID) and productedcharged particles lose all their energy in ID, the event is called a fully contained (FC) event. If
a neutrino interacts in ID and deposits energy both in the inner and outer detectors, the event
is called a Partially Contained (PC) event. When a muon-neutrino interacts with the rock inthe vicinity of the detector, the generated muon enters from the outer detector (OD) and emit
Cherenkov light in OD and ID. Downward-incident events are not used in the analysis because it
is diﬃcult to distinguish them from cosmic-ray muon backgrounds, but upward-incident eventsare used in the analysis of neutrino oscillations because they are mainly induced by neutrino
interactions. They are called upward-going muons (UPMU).
In this study, we analyzed only the FC data sample, since the energy of solar flare neutrinos
peaks around 70 MeV, and the track of the charged particles is usually contained in ID. The
event selection method for the FC sample is described below.

6.1.1

First Reduction

The number of triggered events in a day is about 106 events/day, most of which are due todownward cosmic ray muons and low-energy radioactive events. To remove such background,the following conditions are given as the first step of the FC event selection.
• PE300 > 200 p.e.’s : The PE300 , the total number of photoelectrons observed in
ID within 300 ns, is greater than 200 photoelectrons (p.e.’s).
• NHITA800 < 55 : Number of OD hits within a range of ±400 ns around theevent trigger, NHITA800 , is less than 55.
73

74

CHAPTER 6. SK DATA ANALYSIS

FC

PC

UPMU

Figure 6.1: Three types of high-energy events at SK. The solid arrows show charged particles
and dashed lines show neutrinos.

The first condition corresponds to a threshold of about 22MeV/c for the electron momentum,
which cuts out most low-energy events such as radiation background. The second condition is
to cut out cosmic ray muons that come into the detector.

6.1.2

Second Reduction

In the second stage of the FC event selection, the following conditions are given.
• PEmax /PE300 < 0.5 : The ratio of the largest number of photoelectrons among
all hit ID PMTs, PEmax , to the total number of photoelectrons PE300 is lessthan 0.5.
• NHITA800 < 25 (30 for SK-IV) or PEtot > 100, 000 p.e.’s (50,000 p.e.’s for SK-II): NHITA800 is less than 25 (30 for SK-IV) or total number of photoelectrons in
the inner tank PEtot is more than 100,000 photoelectrons (50,000 photoelectrons
for SK-II).
The first condition cuts out events where one PMT has an extremely large signal comparedto the surrounding PMTs due to electrical noises in the PMTs, and the second condition further
cuts out events such as cosmic ray muons left over from the first event selection.

6.1.3

Third Reduction

A third reduction comprises of several cuts optimized to reduce various types of muons, flasher
events, low energy radioactive events, and electric noise events.
Through-going Muon Cut
A high energy cosmic-ray muon that passes through ID is called a through-going muon. To
eliminate these events, a through-going muon fitter is applied if an event that PEmax is greaterthan 231 p.e.’s and number of ID PMT hits is more than 1000 hits. The fitter finds them by6.1. HIGH-ENERGY EVENT ANALYSIS

75

maximizing the following goodness
goodness = ∑

1

1
i σi2

×

(
exp
−
2

∑ 1
i

σi

(t′ i − t0 )2 × (σi × 1.5)2),(6.1.1)

where σi is the timing resolution of i-th PMT, t′ i is the i-th PMT’s time-of-flight corrected
residual time and t0 is chosen so that the goodness is maximal at each tested entering andexiting point. The event rejection criteria are as follows:• goodness > 0.75 : The goodness greater than 0.75.
• NHITAin > 10 or NHITAout > 10 : NHITAin (NHITAout ) is the number of OD
PMT hits located within 8 m from the reconstructed entering (exiting) point ina fixed 800 nsec timing window.
When those criteria are met, the event is rejected as a through-going muon.
Stopping Muon Cut
Stopping muons are cosmic-ray muons that stop inside ID. In a similar manner to through-going
muons, a special stopping muon fitter identifies a cluster of earliest timing ID PMT hits as amuon entering point from those PMT’s position, and the fitting goodness is evaluated using
Eq. 6.1.1. The criteria to reject those events are following:• goodness > 0 : The stopping muon fit is succeeded, the goodness is greater than0.
• NHITAin > 10 : If NHITAin is greater than than 10.
When those criteria are met, the event is rejected as a stopping muon.
Cable Hole Muon Cut
There are cable holes on the top of the SK tank to supply HV on PMTs and take PMT signals.
The cosmic-ray muons that enter through cable holes are removed using the veto counters, as
shown in Fig. 6.2. When one of the veto counters hit and the distance between the cable holeand the reconstructed vertex is less than 4 m, the event is rejected.
Low Energy Event Cut
In order to reject low energy events in the high-energy analysis, the following rejection criteria
are applied:• NHIT < 500 : The number of ID PMT hits (NHIT) is less than 500.
• N50 < 50 (N50 < 25 for SK-II) : N50 is the maximum number of ID PMT hits ina sliding 50 nsec window after subtracting the photon time-of-flight. The vertex
position used for the time-of-flight subtraction is reconstructed with a dedicatedlow energy event fitter.

CHAPTER 5. DATA SET

76

CHAPTER 6. SK DATA ANALYSIS

Figure 5.9: Schematic view of the veto counter. It is composed of a plastic scintillator plate andFigure506.2:
The Taken
schematic
cm PMT.
from view[107]. of the cable hole and the veto counter. Plastic scintillation
counters are used as veto counters for four large cable holes.

Flasher Event Cut
Reject distribution compared to events produced by charged
RejectFlasher 10
eventsoften have a broad timing
10
10
SK-IV
SK-IV
SK-IV
particles. The flasher After
event
rejection
criteria
areasfollows:
Final Sample
After 2nd Reduction
2nd Reduction
6

10

Data

6

5

10

ATM ν MC

Number of Events [/hit]

5

Number of Events [/hit]

Number of Events [/hit]

6

105

Data

ATM ν MC
1010• NHITmin,100 > 15 (For SK-I): NHITmin,100 is the minimum
number of ID
PMT
hits
in
a
sliding100
nsec
timingwindow
from
+300
nsec
to
+800
nsec
after
the
10
10
10
triggertiming.
10
10
10

104
3

2

4

3

2

4

3

2

•10 NHIT < 800 and NHITmin,100> 10 (For SK-II to SK-IV): NHIT is the number
10
10of ID PMT hits.
1
0 50 100150200250300350400450500

10 50 100150200250300350400450500

N50 [hit]
Accidental Coincidence
Event Cut

N50 [hit]

1
0 50 100150200250300350400450500

N50 [hit]

Figure 5.10:
variableactivities
N50 distributionsof events
with less coincide.
than 500 ID
hitscosmicin
A cosmic-ray
muonReduction
and low energy
sometimes
accidentally
In PMTcase the
SK-IV.
The
atmospheric
neutrino(ATMν)
MC
histograms
arenormalizedby
SK-IV
livetime
ray muon comes in the detector several hundred
nsec after the low energy activity, the event
two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term
triggerandis theissuedby the low energy activity, and no obvious OD PMT hits are found around the“Final Sample” refers to events after all the FC event selection criteria. Vertical error bars on
trigger timing. The event rejection criteria are as follows to prevent them from contaminating
the data points denote the statistical uncertainty.
the data set:

• PELATE > 5, 000 p.e.’s (PELATE > 2, 500 p.e.’s for SK-II) : PELATE is the total
number of photoelectrons in ID within a fixed 500 nsec timing window from+300 nsec to +800 nsec after the trigger timing.
56

6.1. HIGH-ENERGY EVENT ANALYSIS

77• NHITALATE > 20 : NHITALATE is the number of OD PMT hits within a fixed
500 nsec timing window from +300 nsec to +800 nsec after the trigger timing.

6.1.4

Fourth Reduction

To remove remaining flasher events, an intelligent pattern matching algorithm is applied. The
flasher events usually repeat with similar hit patterns, because the flasher events occur when alight is emitted from a flasher PMT. The algorithm tries to find if two diﬀerent events in which
PMT hit patterns are similar or not. The procedure of the algorithm of the pattern matching is
as follows:• Divide ID wall into 1,450 patches of a 2 × 2 m square.
• Calculate the correlation factor r by comparing the total charge in each patchof two events, A and B. The correlation is defined as:
r=

A
B
B
1 ∑ (QAi − ⟨Q ⟩) × (Qi − ⟨Q ⟩),N i
σA × σB(6.1.2)B
where N is the number of patches, QA
i (Qi ) is the ith patch’s total observedAB
charge in event A (B), ⟨Q ⟩ (⟨Q ⟩) is the average charge over all patches in
event A (B), σ A (σ B ) is is the standard deviation of the observed charge in
event A (B).

• Calculate the distance (DISTmax ) between the PMTs with the maximum pulse
heights in the two compared events.
• If DISTmax is less than 75 cm, an oﬀset value (0.15) is added to r.
• If r exceeds a threshold (rthr ), events A and B are recognized as matched. The
rthr is defined as
(
)
B
PEA
300 + PE300
rthr = 0.168 × log+ 0.13,(6.1.3)2where PE300 is the total number of photoelectrons observed in ID within 300
nsec.
• Repeat the above calculation over 10,000 events around the target event andcount the number of matched events.
• Remove the events with large r, or a large number of matched events.

6.1.5

Fifth Reduction

The fifth reduction is designed to remove still remaining cosmic ray muons and flasher events.
Stopping Muon Cut
The remaining stopping muons are rejected more tightly than that of the third reduction. The
goodness which is defined by Eq.6.1.1 and NHITAin , the number of OD PMT hits located within
8 m from the reconstructed entering point, are used again. The criteria follows:• goodness ≥ 0.5 and NHITAin ≥ 5 : This is a tighter criteria condition than thatof in the third reduction.

78

CHAPTER 6. SK DATA ANALYSIS

Invisible Muon Cut
If the momentum of cosmic ray muon is too low to generate Cherenkov light, it can not be
detected. They are called an invisible muon. A cluster of OD PMT hits, which are produced
earlier than the ID trigger timing and are induced by the muon before its decay, are often foundin such events. Events satisfying at least one of the following criteria are rejected as invisible
muon events:• PEtot < 1, 000 p.e.’s (500 p.e.’s for SK-II) and NHITAearly,200 ≥ 5 and NHITAsum ≥10 : PEtot is the total ID PMT charge and NHITAearly,200 is the maximum number of OD PMT hits in a sliding 200 nsec timing window from −9000 nsec to−200 nsec from the trigger timing. NHITAsum is defined as following:
NHITAsum ={NHITAearly,200 + NHITA500 (dOD < 500cm)
NHITAearly,200 + NHITA500 (otherwise)(6.1.4)

where NHITA500 is the number of OD PMT hits in a fixed 500 nsec timing
window from −200 nsec to +300 nsec from the trigger timing, and dOD is the
distance between the position of the OD PMT hit cluster in NHITAearly,200 andthe position of the OD PMT hit cluster in NHITA500 .
Flasher Event Cut
In order to further reject flasher events, there are flasher rejection criteria at the fifth reduction
step. The goodness-of-vertex fit and the variable described in the third reduction NMIN100 are
used. The criteria are as follows:• goodness-of-vertex < 0.4 and NHITmin,100 > 6 : The goodness-of-vertex fit isdescribed in Sec. 6.1.7.

6.1.6

Final Sample Selection

After five reduction steps, the neutrino events that satisfy the following three criteria are finallyselected in this study.
• The number of hit PMTs in the largest OD hit cluster (NHITAC) is less than
16 (10 for SK-I).
• The reconstructed vertex (dwall ) of neutrino interaction is located at more than
200 cm away from the ID wall.
• The visible energy (Evis ) obtained from the reconstruction algorithm should begreater 100 MeV for an electron.
The overall eﬃciency of the FC sample selections for the true neutrino events is estimated by
the signal MC as shown in Tab. 6.1.6. Here, we use atmospheric neutrino MC events for thesignal eﬃciency estimation. The background contamination i.e. non-neutrino events in the final
sample is estimated to be about 0.1% based on the eye-scant of the selected events.
In addition to this, the search time window which is described in Chap. 3 is applied to searchneutrinos associated with solar flares.

6.1. HIGH-ENERGY EVENT ANALYSIS

79

Table 6.1: Reduction eﬃciency after each FC reduction step calculated by the signal MC.
Eﬃciency
SK-I SK-II SK-III SK-IV
1st Reduction 100.0 99.96
100.0
100.0
2nd Reduction 100.0 99.90
99.98
99.99
3rd Reduction 99.91 99.97
99.81
99.83
4th Reduction 99.51 99.51
99.68
99.00
5th Reduction 99.47 99.43
99.62
98.85

6.1.7

Event Reconstruction

Event information can be obtained by the reconstruction of the Cherenkov light cones in SK.
In this section, the event reconstruction method of high-energy event is briefly described. A
detailed explanation of the reconstruction can be found in Shiozawa et. al [114].

Vertex Reconstruction
The vertex reconstruction algorithm consists of three steps, point-fit, ring edge finding, and TDCfit. Since this step is prior to the ring counting algorithm described later, the following calculation
assumes a single-ring event and focuses on the most energetic ring. An initial vertex position isestimated by maximizing the following estimator (G), assuming all photons are emitted at thesame time and position:
(
)
1 ∑ 1
(t′ i − t0 )2
G=
exp
−
,
(6.1.5)N i σi22(⟨σ⟩ × 1.5)2
where N is the number of hit PMTs, ⟨σ⟩ is fixed to 2.5 nsec here, and t′ i is the i-th PMT’stime-of-flight subtracted residual time for an assumed vertex position. The vertex fitter searches
for a vertex position where the estimator G takes the maximum value.
The direction and the outer edge of the dominant ring are measured in the second step. A
pair consisting of the direction and the opening angle, Q(θedge ), is tested by a parameter asfollows:∫ θedgeQ(θedge ) =0PE(θ)dθ×sin(θedge )(dPE(θ)dθ θ=θedge

)2

(
× exp

(θedge − θexp )2
2σθ2

)
,

(6.1.6)

where θexp and σθ are the Cherenkov opening angle expected from the charge within the cone
and its resolution. PE(θ) is the angular distribution of the observed charge as a function of
opening angle θ from the particle direction. For the first factor, the numerator of the firstelement favors more of the charge in the reconstructed ring and the denominator is enhanced
against the narrower ring. The middle factor favors sharper rings and the last factor enhances
the estimator if it is close to the expectation. The direction and the ring edge position aredetermined to maximize the estimator. The vertex position is then determined using TDC-fit,
wherein track length of a charged particle and the scattering are taken into account. The time
residuals for PMTs inside and outside the Cherenkov ring are calculated, and the goodness of
the algorithm proceeds step by step, and the later reconstruction steps use results obtained in
the former steps.

6. EVENT RECONSTRUCTION

118

Table 6.2: Angular resolution of FC and PC for each SK phase. The resolution isdefined as the width where 68% of the events are included.
80

CHAPTER 6. SK DATA ANALYSIS◦

Angular Resolution [ ]Ring Counting

SK-I

SK-II

SK-III

SK-IV

3.2

3.4

3.2

3.2

1.0

1.2

1.0

0.9

FC : Sub-GeV
e-likeSingle-ring
When the vertex
and the first Cherenkov ring are found, the ring counting algorithm is appliedµ-like1.9
to search for other such ringsin the event. Other
rings are2.2
searched 1.9
for using an1.9
algorithm witha Hough transformation
andthelikelihood
technique.
Figure
6.3
shows
the
illustrationof theFC : Multi-GeV
method. The dashed circles centered at each hit PMT are drawn with 42◦ . The direction of
the Cherenkov ring is identified
as the intersectionof those dashede-like1.3 point1.4
1.3 circles.
1.2 By selecting
Single-ring
the ring direction
using this method, the second and subsequent ring candidates are searchedµ-like0.8 with ringfor. The likelihood method isused to determine 0.9
whether a1.0
candidate0.8
ring is consistent
properties.
PC

Single-ringµ-likeFigure6.1: Basic idea of finding ring candidates is shown. The shaded circle
Figure 6.3: Basic idea of finding ring candidates. The shaded ring represents the Cherenkov
represents
theandCherenkov
ring image,andthe dashedcircles atareeachvirtualCherenkov
ring image,the dashed circles
are virtual
Cherenkov
rings centered
PMT hit.
The
overlapping
point
is
to
be
the
centerofthereal
Cherenkov
ring.
rings centered on each PMT hit. The point of overlap is to be the center of the real
Cherenkov ring.
event, we test whether the (N + 1)-th ring candidate is true using the likelihood.
When N rings are found for an event, we test whether the (N + 1)-th ring candidate is true

6.2. LOW-ENERGY EVENT ANALYSIS

81

using the likelihood. The likelihood function is defined as
L

=

∑

(
log

prob(qiobs ,

N
+1
∑

)
exp
αn · qi,n),(6.1.7)

n=1

i


(
)
obs
exp 2

 √1 exp − (q − q )(q exp > 20 p.e.)2σprob(q obs , q exp ) =2Single p.e. and Poisson convolution (q exp ≤ 20 p.e.),(6.1.8)where hit PMTs inside N + 1 Cherenkov rings are summed. q obs is the observed p.e. in theexp
i-th PMT, αn · qi,nis the expected p.e. at the i-th PMT from the nth ring, σ is the resolution
exp
for q , and the probability function determines how well the expected charge reproduces the
charge observed in the i-th PMT. The likelihood is maximized by varying the αn factors with alower momentum constraint.

6.2

Low-Energy Event Analysis

The lowest threshold for the Super-Kamiokande detector analysis is 3.5 MeV, but in the neutrinoenergy region below 14.06 MeV, the steady-state 8 B neutrinos are dominant. Therefore theenergy region to be analyzed is above 16 MeV for the solar flare neutrino search. For low-energy
events, the vertex of the event is reconstructed from the hit timing of each PMT, the direction of
the event from the hit pattern of the PMTs, and the energy is reconstructed from the parameters
obtained from the calibration of the detector and used in the reduction processes.

6.2.1

Event Reconstruction

Vertex Reconstruction
The hit timing of each PMT is used to reconstruct the vertex. The maximum distance that acharged particle with an energy of less than 100 MeV can travel in pure water is about 50 cm,
which is small compared to the positional resolution. Therefore, the track of charged particles
is assumed to be point-like. The maximum likelihood method is used to reconstruct the vertex
position, and the likelihood function is defined as follows.
L(v, ∆ti ) ≡

N
hit
∑

log(P (∆ti (v))),(6.2.1)i=1where ∆ti is defined using TOF corrected residual time of the i-th PMT (tres,i ) and time ofoccurrence of the event (t0 ) as∆ti ≡ tres,i − t0 .

(6.2.2)P (∆ti (v)) is the probability density function of ∆ti and it is determined by the LINAC calibration. Vertex position reconstruction is done by maximizing the likelihood function in an event
reconstruction program called BONSAI (Branch Optimization Naviating Successive Annealing
Iterations).

82

CHAPTER 6. SK DATA ANALYSIS

Direction Reconstruction
Since Cherenkov light photons create a ring pattern of events, it is possible to determine thedirection of the events. The direction
reconstruction,themaximum
likelihood
methodis used,To obtain
the number of true
hits,
the number ofthe hit withinthe “off-time
window” issubtracted
that of the “on-timing window”. Since the hit rate depends on both geometricaland the likelihood function is defined
asfromfollows:
location of a PMT and the Ni calibration source position, the corrected hit rate for the i−th
Nis20defined as
PMT∑
cos θ

log(f (cos θi , E)) ×

L(d) ≡

i=1

i

,
2
a(θ
i )(i) = hi × ri
hcorr

(6.2.3)(5.1.4)a(θi )

whereofhi is
hit rate tofor thethe i−thri is asthe shown
distance between
i−th NPMT
and thewhere θi is the angle of incidence
a thephotoni-thPMT,PMTin Fig.the6.4,
20 iscalibration source position and a(θi ) is the PMT acceptance which is extracted by the MC
the maximum number of ID PMT
hits
in
a
sliding20
nsec
window
after
subtracting
thephotonsimulation as shown in Figure 5.4. This acceptance depends on the geometry of the PMT andtime-of-flight and f (cos θi , E) isthethe
distributionfunctionanglecasebetween
thedirectionof2 . The
acrylic
case. After the
installationofof thethe acrylic
in SK-II, itsvalue
was changed
PMT angulardependenceof thePMT acceptancewasvertex.
represented
as cos(θi )/a(θi )the charged particle and the directionof theobservedphotonfrom theTheterm is a correction term for the acceptance of
the i-th PMT as shown in Fig. 6.5.
a(θ ) = 0.205 + 0.524 cos θ + 0.390 cos2 θ − 0.132 cos3 θ .
(5.1.6)

Acceptance of PMT

i

i

i

i

1.2

1

0.8

0.6

0.4

0.2

0
0

10

20

30

40

50

60

70
80
90
incident angle [degree]

Figure 5.4: The incident angle dependence of the PMT acceptance. The black dotted curve
indicates the acceptance without the acrylic case. The red curve indicates the acceptance with
Figure6.5:SK-III
Angulardependence
of ofaccepthe acrylic case usedin SK-II,and SK-IV.
The difference
acceptance above 40◦ iscased by the combinationofthegeometry
of
the
PMT
and
the
acrylic
case.
tance of PMT (a(θi )). Taken from [116].

The black line is for PMT only (SK-I). The
red line indicates the case with shock wave
hcorr (i)Figureof θi and ϕi . Taken protection (SK-II
Figure 4.7: Definitionof6.4:(θi , Definition
φi ).
! later).
Ph (i) =and,hcorr (i)/Nallfrom [115]2Finally, the hit rate is normalized to obtain the hit probability as(5.1.7)

Before the installation of the acrylic case when SK-I, the angular dependence of the PMT acceptance wasdescribed asa(θi ) = 0.354 + 0.510 cos θi + 0.116 cos2 θi − 0.012 cos3 θi .
(5.1.5)

Energy Reconstruction
Since the number of emitted Cherenkov photons is essentially proportional
to the energy of the60
charged particles, the energy of the charged particles can be estimated from the observed numberof photons. However, for low-energy events, the number of PMTs which detected photons, called
hit PMTs hereafter, is used to reconstruct the energy instead of the total number of photons.
The reason for using the number of hit PMTs is as follows.
• The number of photons emitted in low-energy events is small, and the average
number of photoelectrons in each PMT is mostly one.
• The resolution of one photoelectron of PMT is not good.
The number of PMT hits depends on the vertex position and the direction of an event, thetransparency of the water, and the quantum eﬃciency of each PMT. The number of eﬀective36

6.2. LOW-ENERGY EVENT ANALYSIS

83

hits, Neﬀ , is calculated by making the following corrections to the hit PMTs of N50 which is the
maximum number of ID PMT hits in a sliding 50 nsec window.
Neﬀ =

]
N50 [
∑
RcoverNall
×× exp(ri /λ) × G(i)(Xi + εtail − εdark ) ×NaliveS(θi , ϕi )i=1

(6.2.4)

where Xi is the multiple hit correction, εtail is the delayed hit correction, εdark is the dark noisecorrection, Nall is the number of ID PMTs in SK, Nalive is the number of non bad PMTs, Rcoveris the coverage of ID PMTs, the eﬀective area of the i-th PMT’s photocathode from view ofthe direction of photon incidence, the exp(ri /λ) term is water transparency correction term andG(i) is the quantum eﬃciency correction term. From the above corrections, Neﬀ is determined.
The conversion function from Neﬀ to energy is determined by Monte Carlo simulation of monoenergitic electrons.

6.2.2

First Reduction

The 1st reduction is used to remove typical detector-derived noises and cosmic ray events. The
cutting criteria are as follows.
First of all, events with Low Energy (LE) triggers are selected for low-energy sample. In
addition, we remove events most likely due to muons by vetoing OD triggers or events with acharge deposition larger than 1000 p.e.’s.
Some well-reconstructed events in FV can be electrons from muon decays or charged particles
from showers associated with cosmic muons induced spallation events. To remove these events,
low-energy events occuring less than 50 µsec after a muon are rejected. There are many background events coming from the wall. To remove these, the fiducial volume (FV) cut is applied,which selects only events more than 200 cm away from the ID wall.
We then apply quality cuts to the remaining events by requiring the goodness of the vertex fit as defined in Eq. 6.2.6, which is called bsgoodness, and the azimuthal isotropy of thereconstructed ring as defined in Eq. 6.2.7, bsdirKS, to verify
bsgoodness > 0.5 and Ovaq = bsgoodness2 − bsdirKS 2 > 0.25.

(6.2.5)

Definition of bsgoodness is as follows:∑bsgoodness =(tres,i −t0 )2(t−t0 )2) exp( res,i
)
2w2
2σ 2
,
∑
(tres,i −t0 )2
exp(
)
2
i
2w

i exp((6.2.6)

where tres,i is the i-th PMT s hit time after subtracting the time of flight, and t0 is the fit peaktime of tres,i distribution,w is the RMS of the tres,i distribution and σ is the timing resolution of
the PMTs.
Another parameter, bsdirKS, is defined as
bsdirKS =max(Auniform,i − Adata,i ) − min(Auniform,i − Adata,i ),
2π(6.2.7)

where Auniform,i is the azimuthal angle of the i-th hit PMT, assuming that the hit PMTs are
uniformly distributed along a Cherenkov cone. Adata,i is that of the observed azimuthal angle ofthe i-th hit PMT.

84

CHAPTER 6. SK DATA ANALYSIS

6.2.3

Second Reduction

Since only half of the spallation background events are removed in the first reduction, a more indepth study of the correlations between muons and low-energy events is necessary. We therefore
pair each low-energy event that passes the first reduction with all muons up to 30 sec before andafter the low-energy event and, for each of these pairs, compute the following observables. The
former and the latter are called pre sample and post sample, respectively.
variables
dt: time diﬀerence between the muon and the low-energy event.
l t : Transverse distance of the low-energy event to the muon track.
ll : Longitudinal distance to the point of the muon track associated with the maximal energy
deposition.
muqismsk: Total charge deposited by the muon in the detector. This directly reflects how likely
oxygen nuclei are broken up by the muon track.
resQ: Residual charge deposited by a muon compared to the value expected from the minimum
ionization. This observable can be expressed as
resQ = muqismsk − qMI · L(6.2.8)where qMI and L are the number of photoelectrons per centimeter expected from the minimum
ionization and the track length, respectively. For muons with multiple tracks, L is the sum of thelengths of all tracks. This observable is not associated to an event pair but allows to determine
how likely a given muon is to induce a shower.
In order to discriminate the spallation events from the random events more eﬀectively, alikelihood is calculated from the spallation variables. For this, two probability density functions(PDFs), the spallation PDF (P DFspall ) and the random PDF (P DFrandom ), are prepared for eachdiscriminating variable i(= dt, lt, ll, muqismsk, resQ).The post sample distribution is subtracted
from the pre sample distribution and the resulting distribution is area-normalized to produceii
P DFspall. The post sample distributions are area-normalized to produce P DFrandom. The ratiosiiof P DFspall to P DFrandom are multiplied to each other to make spallation likelihood (Lspall ) as:
Lspall = log(i
∏ P DFspallii
P DFrandom)(6.2.9)The cut points are determined by the shape of likelihood distributions as shown in Fig. 6.6.

6.2.4

Third Reduction

The low energy end of the search energy window is contaminated by radioactivity events thatsurvive the fiducial volume cut. In order to reduce all these diﬀerent contributions, we consider
the following observables:
Eﬀective distance to wall deﬀ: the distance to the nearest detector wall along the event’s

6.2. LOW-ENERGY EVENT ANALYSIS

85

reconstructed direction. This observable allows to remove residual radioactivity background
events which are mostly coming perpendicular to the wall.
Cherenkov angle θc : the opening angle of the Cherenkov light cone emitted by an electron isaround 42◦ over a large energy range. Conversely, the angles heavier particles like muons andpions are significantly smaller than 42◦ in the low-energy analysis. In addition, neutral current(NC) interactions with multiple photon emissions can lead to superimposed Cherenkov cones asmultiple MeV-scale photons can accelerate more than one electron through the Compton eﬀect.
These multiple overlapping cones will then be reconstructed as a single cone with a particularly
large opening angle. Consequently, θc is one of the most powerful observables for reducing both
NC and µπ atmospheric neutrino backgrounds.
Pion likeness pilike: electrons and positrons do not follow a straight trajectory in SK due to
Coulomb multiple scatterings, which leads to fuzzy Cherenkov rings. Charged pions, on the other
hand, lead to well-delineated ring patterns. In order to discriminate pion rings from electron rings
we consider a 15 ns time-of-flight subtracted window around the main activity peak and computethe opening angles of the cones formed by the directions of all possible 3-hit combinations of
the hit PMTs. We then identify the peak of this opening angle distribution θ0 and estimate thefuzzyness of the ring by computing.

pilike =Ntriple (θ0 ± 3◦ )Ntriple (θ0 ± 10◦ )(6.2.10)

Rings with pilike close to one will be more pion-like.
Pre- and post-activity cuts: events where visible muons and pions decay into electrons canlead to two distinct activity peaks in the same trigger window. Depending on which particle
deposits more light, unusually high activity can be noticed either before or after the main peakin the trigger window. For pre-activity we compute the maximal number of hits in a 15 ns
time-of-flight subtracted window ending at least 12 ns before the main peak. We thus derive
two observables, maxpre and maxpregate, by considering hits in the whole SHE trigger window
and in the 1.3 µs gate around the main activity peak, respectively. For post-activity, we use
the muechk function elaborated by the atmospheric neutrino analysis group to identify muon
decays. This function evaluates the number of decay electrons.

6.2.5

Summary of Low-Energy Sample

After applying all reduction written above, the energy and cos θSun distribution is shown Fig. 6.7
and Fig. 6.8. θSun is the angle between the reconstructed event direction and the vector pointing
from the Sun to SK. Because of energy resolution of SK, the solar neutrino peak is seen in theright most bins of cos θSun distributions and the lowest energy bins of the energy distributions.
The overall eﬃciency of the low-energy samples for the true solar flare neutrino events is
estimated by the signal MC as shown in Tab. 6.2.5.

86

CHAPTER 6. SK DATA ANALYSIS

Table 6.2: Reduction eﬃciency after each low-energy reduction step calculated by signal MC.
Eﬃciency
SK-I
SK-II SK-III SK-IV
1st Reduction > 99% > 99% > 99% > 99%
2nd Reduction 81.8% 76.2% 81.8% 82.7%
3rd Reduction 79.3% 85.2% 90.9% 90.2%

6.3

Summary for SK Data Analysis

The rate of BG events in this search was calculated from data other than the search time window.
Table. 6.3 shows the background rate in each SK phase.
Table 6.3: Background event rate of each SK phase.
SK phase
SK-I
SK-II
SK-III
Low-energy (event/day) 0.20 ± 0.01 0.19 ± 0.02 0.20 ± 0.01
High-energy (event/day) 7.45 ± 0.07 7.33 ± 0.09 7.53 ± 0.12

SK-IV
0.20 ± 0.01
7.15 ± 0.05

6.3. SUMMARY FOR SK DATA ANALYSIS

87

Figure 6.6: Likelihood cut thresholds for misfit (top left), stopping (top right), single throughgoing along dt (middle left) and dlt (middle right), and multiple muons along dt (bottom left)and dlt (bottom right). These are the exact cut conditions for misfit and stopping muons while
give the initial points for the later scan.

0.03

0.014

Energy distribution
0.025

Event/day/bin

CHAPTER 6. SK DATA ANALYSIS
Event/day/bin

88

Relic W/O suncut

0.02

cosθSun distribution
Relic W/O suncut

0.012
0.01

0.008

0.015

0.006
0.01
0.004
0.005

0.002

0
0

10

20

30

40

50

60

70

80

0
-1 -0.8 -0.6 -0.4 -0.2

90 1000

0.2 0.4 0.6 0.8

1cosθSunReconstructed Energy [MeV]

0.03

Event/day/bin

Event/day/bin

Figure 6.7: energy(left) and cos θSun (right) distribution SK I-III final sample. Because of energy
resolution of SK, the solar neutrino peak is seen in most right bins of cos θSun distributions andthe lowest energy bin of the energy distributions.

Energy distribution
0.025

Relic W/O suncut

0.02

0.014

cosθSun distribution
Relic W/O suncut

0.012

0.01

0.008

0.015

0.006
0.01
0.004
0.005

0

0

0.002

10

20

30

40

50

60

70

80

90

100

Reconstructed Energy [MeV]0-1-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6

0.8

1

cosθSunFigure 6.8: energy(left) and cos θSun (right) distribution SK IV final sample. Because of energy
resolution of SK, the solar neutrino peak is seen in the most right bins of cos θSun distributions
and the lowest energy bin of the energy distributions.

Chapter 7

Results and Discussions
7.1

Visible Side Solar Flares

Neutrino Search with the Time Windows Determined by Derivative ofSoft X-ray light curves
As explained in Section 3.2, we selected twenty-three solar flares above X5.0 class occurringon the visible side of the solar surface. However, we can not search for solar flare neutrinos
from the three solar flares occurring on August 25th, 2001, December 13th, 2001 and July 23rd,
2002 because no SK data is available due to the reconstruction work toward SK-II after theaccident. Hence, we searched for solar flare neutrinos from the remaining twenty solar flares. As
a consequence of the search, there is no signal detected in the low-energy data sample while two
events in the high-energy data sample are detected as summarized in Table 7.1. Figures 7.1- 7.10
show the time distributions of neutrino events in SK around the search time windows. Figure 7.11
shows the time of observed events together with light curves recorded by the GOES satellite.
The event on November 4th, 2003 was observed during the impulsive phase of the solar flare,
where particle acceleration is expected to be active. In addition to this, there was an observationof the neutron associated with this solar flare [117]. On the other hand, the event on September
6th, 2017 was observed during the dimming phase after the peak of the soft X-ray light curve,
where all process of particle acceleration is likely to complete.
Figure 7.12 shows the energy of the observed event with the background energy spectrum.
Here, the background sample is the events accumulated outside the search windows and the main
component is the interaction of atmospheric neutrinos. The expected number of background
events of high-energy data samples in the search time windows is 0.20 events (0.12 events) for
solar flare event on November 4th, 2003 (September 6th, 2017). The probability of a background
event is 18.1% (11.3%).
In order to investigate whether background events come from the direction of the Sun ornot, we examined the angular distribution of θSun , which is defined as the angle between thereconstructed direction of charged particle and the direction pointing from the Sun to SK.

Neutrino Search with the Time Windows Determined by Line γ-ray
light curves
We set the search time windows by using 2.223 MeV γ-ray data that indicates hadron accelerationand neutrino existence in solar flares as described in Chap. 3. By using the search time windows89

90

CHAPTER 7. RESULTS AND DISCUSSIONS

Table 7.1: The summary of two events observed within the search window for neutrinos associatedwith the solar flare occurring on the visible side of the Sun.
Date (UTC)
November 4th, 2003 September 6th, 2017
Solar flare class
X28.0
X9.4
SK phase
SK-II
SK-IV
Observed time (UTC)
19:42:26
12:03:05
Event topology
2-ring e-like
1-ring µ-likeReconstructed energy
178.3 MeV
1.2 GeV
θSun
67.1◦
39.6◦
−1
Estimated background rate [event flare ]
0.20
0.12
Probability of background event
18.1%
11.3%

for solar flare events which occurring on November 2nd, 2003 and January 20th, 2005, the solar
flare neutrino event has been sought in SK. However, there was no candidate neutrino event
within the search time windows. For the solar flare occurring on July 23rd, 2002, we can notsearch for neutrino event because no SK data is available due to the reconstruction work toward
SK-II after the accident.

7.2

Invisible Side Solar Flares

As explained in Section 3.3, we selected ten large CMEs occurring on the invisible side of theSun by setting the criteria of their emission speed. Unfortunately, we can not search for solar
flare neutrinos from the CMEs occurring on July 19th and 20th, 2002 because no SK data isavailable due to the reconstruction work toward SK-II after the accident. Hence, we searched
for solar flare neutrinos from the remaining eight CMEs.
There is no signal in the low-energy data sample while six events in the high-energy data
sample as summarized in Table 7.2. The numbers of observed events within the search time
window are two events for the solar flares on November 7th, 2003 and July 24th, 2005 while
one event for those on June 4th, 2011 and July 23rd, 2012. Figures 7.15-7.18 show the time
distributions of neutrino events in SK around the search time windows.
In the case of two solar flares on November 7th, 2003, and on July 24th, 2005, we found
two consecutive neutrino events within their search windows. Their time diﬀerences are 1131 s
and 4065 s, respectively. We analyzed the time diﬀerence distribution between the consecutive
events in the background sample in order to verify whether their time diﬀerences are rare ornot. Figure 7.19 shows the time diﬀerence of two consecutive events observed within their searchwindows together with the time diﬀerence distribution of the background sample. Comparing thetime diﬀerence distribution of the background sample, we estimated the occurrence probabilities
for each solar flare, which corresponds to 10% and 29%. The black data points in Fig. 7.20 show
the distribution of the number of neutrino candidates in each solar flare. It is consistent with
the Poisson distribution with the estimated background rate of 0.62 event/flare as shown withthe red histograms in the figure.
Figure 7.21 shows the energy of the observed event with the background energy spectrum.
The expected number of background events of the high-energy data sample is 0.62 event/flare.
It is the same for all the solar flares on the invisible side since the search time range is uniform
for the solar flares on the invisible side.
Figures 7.22-7.27 show the angular distribution of the neutrino events from solar flares that

7.2. INVISIBLE SIDE SOLAR FLARES
occurring on the invisible side of the solar surface and that of the signal simulation sample.

91

CHAPTER 7. RESULTS AND DISCUSSIONS

Visible Energy [MeV]92

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104

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103

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04/07
00:00

04/07
03:00

04/07
06:00

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04/07
12:00

Time (UTC)

Figure 7.1: The time distributions of high-energy neutrino events around the solar flares occurringon the visible side of the Sun on November 6th, 1996 (top), July 14th, 2000 (upper-middle), April
2nd, 2001 (lower-middle), and April 6th, 2001 (bottom). The red points show the time of neutrino
events.

Visible Energy [MeV]

7.2. INVISIBLE SIDE SOLAR FLARES

93

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104

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103

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21:00

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104

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103

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104

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10/30
00:00

10/30
03:00

10/30
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10/30
12:00
Time (UTC)

Figure 7.2: The time distributions of high-energy neutrino events around the solar flares occurringon the visible side of the Sun on April 15th, 2001 (top), October 23rd, 2003 (upper-middle),
October 28th, 2003 (lower-middle), and October 29th, 2003 (bottom). The red points show thetime of neutrino events.

CHAPTER 7. RESULTS AND DISCUSSIONS

Visible Energy [MeV]94

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104

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103

11/02
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104

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104

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18:00

09/07
21:00

09/08
00:00

09/08
03:00

09/08
06:00

09/08
09:00
Time (UTC)

Figure 7.3: The time distributions of high-energy neutrino events around the solar flares occurringon the visible side of the Sun on November 2nd, 2003 (top), November 4th, 2003 (upper-middle),
January 20th, 2005 (lower-middle), and September 7th, 2005 (bottom). The red points show thetime of neutrino events.

Visible Energy [MeV]

7.2. INVISIBLE SIDE SOLAR FLARES

95

104

103

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104

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Time (UTC)

Figure 7.4: The time distributions of high-energy neutrino events around the solar flares occurringon the visible side of the Sun on September 8th, 2005 (top), September 9th, 2005 (upper-middle),
December 5th, 2006 (lower-middle), and December 5th, 2006 (bottom). The red points show thetime of neutrino events.

CHAPTER 7. RESULTS AND DISCUSSIONS

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Figure 7.5: The time distributions of high-energy neutrino events around the solar flares occurringon the visible side of the Sun on August 9th, 2011 (top), March 7th, 2012 (upper-middle),
September 6th, 2017 (lower-middle), and September 10th, 2017 (bottom). The red points show
the time of neutrino events.

Recostructed Energy [MeV]

7.2. INVISIBLE SIDE SOLAR FLARES

97

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Figure 7.6: The time distributions of low-energy neutrino events around the solar flares occurringon the visible side of the Sun on November 6th, 1996 (top), July 14th, 2000 (upper-middle), April
2nd, 2001 (lower-middle), and April 6th, 2001 (bottom). The red points show the time of neutrino
events.

CHAPTER 7. RESULTS AND DISCUSSIONS

Recostructed Energy [MeV]

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10/29
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10
0
21:00
10/28

03:00
10/29

09:00
10/29

15:00
10/29

21:00
10/29

03:00
10/30

09:00
10/30

15:00
10/30
Time (UTC)

Figure 7.7: The time distributions of high-energy neutrino events around the solar flares occurringon the visible side of the Sun on April 15th, 2001 (top), October 23rd, 2003 (upper-middle),
October 28th, 2003 (lower-middle), and October 29th, 2003 (bottom). The red points show thetime of neutrino events.

Recostructed Energy [MeV]

7.2. INVISIBLE SIDE SOLAR FLARES

99

100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

21:00
11/01

03:00
11/02

09:00
11/02

15:00
11/02

21:00
11/02

03:00
11/03

09:00
11/03

15:00
11/03
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

21:00
11/03

03:00
11/04

09:00
11/04

15:00
11/04

21:00
11/04

03:00
11/05

09:00
11/05

15:00
11/05
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

09:00
01/19

15:00
01/19

21:00
01/19

03:00
01/20

09:00
01/20

15:00
01/20

21:00
01/20

03:00
01/21
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10
0

21:00
09/06

03:00
09/07

09:00
09/07

15:00
09/07

21:00
09/07

03:00
09/08

09:00
09/08

15:00
09/08
Time (UTC)

Figure 7.8: The time distributions of low-energy neutrino events around the solar flares occurringon the visible side of the Sun on November 2nd, 2003 (top), November 4th, 2003 (upper-middle),
January 20th, 2005 (lower-middle), and September 7th, 2005 (bottom). The red points show thetime of neutrino events.

CHAPTER 7. RESULTS AND DISCUSSIONS

Recostructed Energy [MeV]

100

100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

03:00
09/08

09:00
09/08

15:00
09/08

21:00
09/08

03:00
09/09

09:00
09/09

15:00
21:00
09/09
09/09
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

21:00
09/08

03:00
09/09

09:00
09/09

15:00
09/09

21:00
09/09

03:00
09/10

09:00
09/10

15:00
09/10
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

15:00
12/04

21:00
12/04

03:00
12/05

09:00
12/05

15:00
12/05

21:00
12/05

03:00
09:00
12/06
12/06
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10
0

21:00
12/05

03:00
12/06

09:00
12/06

15:00
12/06

21:00
12/06

03:00
12/07

09:00
12/07

15:00
12/07
Time (UTC)

Figure 7.9: The time distributions of low-energy neutrino events around the solar flares occurringon the visible side of the Sun on September 8th, 2005 (top), September 9th, 2005 (upper-middle),
December 5th, 2006 (lower-middle), and December 5th, 2006 (bottom). The red points show thetime of neutrino events.

Reconstructed energy [MeV]

7.2. INVISIBLE SIDE SOLAR FLARES

101

100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Reconstructed energy [MeV]

0
09:00
08/08

15:00
08/08

21:00
08/08

03:00
08/09

09:00
08/09

15:00
08/09

21:00
08/09

03:00
08/10
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Reconstructed energy [MeV]

0

03:00
03/06

09:00
03/06

15:00
03/06

21:00
03/06

03:00
03/07

09:00
03/07

15:00
03/07

21:00
03/07
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Reconstructed energy [MeV]

0
03:00
09/05

09:00
09/05

15:00
09/05

21:00
09/05

03:00
09/06

09:00
09/06

15:00
09/06

21:00
03:00
09/06
09/07
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10
0

09:00
09/09

15:00
09/09

21:00
09/09

03:00
09/10

09:00
09/10

15:00
09/10

21:00
09/10

03:00
09/11
Time (UTC)

Figure 7.10: The time distributions of low-energy neutrino events around the solar flares occurring on the visible side of the Sun on August 9th, 2011 (top), March 7th, 2012 (upper-middle),
September 6th, 2017 (lower-middle), and September 10th, 2017 (bottom). The red points show
the time of neutrino events.

×103

3

7000
70
6000
60
5000

Solar Flare on Nov. 4th 2003

50

Derivative of Soft X-ray

4000

Soft X-ray

40

Neutrino event time3000

(19:42:26 Nov. 4 2003)

30

Search time window

2000

20
The photon detector on GOES was saturated

1000

10
0

0
11/04
19:40

11/04
19:50

11/04
20:00

Time (UTC)Soft X-ray [Count]

80 ×1080 ×10×103

3Solar flare on Sep. 6 2017

7000

Derivative of Soft X-ray

70

Soft X-ray

6000

Neutrino event time60

(12:03:05 Sep. 6 2017)

5000

Search time window

50

4000

40

3000

30
20

2000

10

1000

0

09/06
11:50

09/06
11:52

09/06
11:54

09/06
11:56

09/06
11:58

09/06
12:00

09/06
12:02

09/06
12:04

0

Time (UTC)

Figure 7.11: The time of observed neutrino events for the solar flare on November 4th, 2003 (left),and July 6th, 2017 (right). The black dotted line shows the time of neutrino event in the SK
detector. The red (green) plot shows the derivative of the light curves (original light curve)
recorded by the GOES satellite. The shaded region shows the search windows determined byusing the derivative of soft X-ray light curve according to the method described in Chap. 3. In
the case of the solar flare on November 4th, 2003 (left), the instrument on the GOES satellite
saturated due to the high intensity of soft X-rays. This did not allow the satellite to record thedata for more than 15 minutes from 19:45 to 20:00.

Soft X-ray [Count]

CHAPTER 7. RESULTS AND DISCUSSIONS

Derivative of soft X-ray [Counts/s]

Derivative of Soft X-ray [Count/s]

102Event/Search time window

7.2. INVISIBLE SIDE SOLAR FLARES

103

1.2
Solar flare on visible side
Nov. 4th 2003 19:42:26
Sep. 6th 2017 12:03:05
Background Spectrum

1

0.8

0.6

0.4

0.2

0

1000

2000

3000

4000

5000

6000
7000
Visible Energy [MeV]

Figure 7.12: The energy distribution of the two neutrino events observed in the time window
for solar flares occurring on the visible side of the Sun and that of the background sample.
The first event (a green square) was observed as 2-ring e-like event on November 4th, 2003
while the other (a magenta circle) was observed as 1-ring µ-like event on September 6th, 2017.
The background spectrum is normalized by the average duration of 700 s determined from thederivative of the soft X-ray light curve.

CHAPTER 7. RESULTS AND DISCUSSIONS

Area Normilized Entry

104

0.06
Solar Flare on the Visible Side (Nov. 4th 2003)

0.05

Signal (MC) angle distribution (100.0-500.0 MeV)
BG (DATA) angle distribution (100.0-500.0 MeV)

0.04

Neutrino signal (19:42:26 178.3 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Area Normilized Entry

Figure 7.13: The angular distribution of the neutrino events from solar flares occurring on
November 4th, 2003, and that of signal simulation sample. The green thick and the black thinline shows the angular distribution of signal MC and Background sample, respectively. The reddashed line shows the angular, θSun , of the candidate neutrino event.

0.06
Solar Flare on the Visible Side (Sep. 6th 2017)0.05

Signal (MC) angle distribution (1000.0-2000.0 MeV)
BG (DATA) angle distribution (1000.0-2000.0 MeV)

0.04

Neutrino signal (12:03:05 1178 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Figure 7.14: The angular distribution of the neutrino events from solar flares occurring on
September 6th, 2017, and that of the signal simulation sample. The green thick and the black
thin line shows the angular distribution of signal MC and Background sample, respectively. The
red dashed line shows the angular, θSun , of the candidate neutrino event.

Table 7.2: The summary of events observed within the search window for neutrinos associated with the solar flare occurring on theinvisible side of the Sun.
Date (UTC)
November 7th, 2003 July 24th, 2005 June 4th, 2011
July 23rd, 2012
SK phase
SK-II
SK-II
SK-IV
SK-IV
Number of candidates22
1
1
Observed time (UTC)00:18:34
22:07:36
06:05:07
12:03:47
00:40:45
23:15:21––
Event topology
1-ring e-like
1-ring µ-like
4-ring e-like
3-ring two µ-like, e-like
2-ring e-like
1-ring µ-like––Reconstructed energy
3.58 GeV
126 MeV
2.14 GeV
834 MeV493 MeV
1.35 GeV––
Estimated background rate [event · flare−1 ]
0.62
0.62
0.62
0.62
θSun
20.0◦
100.4◦
101.0◦
76.7◦
◦
◦
71.4
94.0
–
–
Probability of background event
12.8%
12.8%
46.2%
46.2%
from background rate
Probability of background event
10.0%
29.0%
–
–
from timing distribution

7.2. INVISIBLE SIDE SOLAR FLARES
105

106

7.3

CHAPTER 7. RESULTS AND DISCUSSIONS

Fluence Calculation

Since the number of neutrino candidates is consistent with the number of expected backgrounds,
we have converted that to the upper limit on the neutrino fluence. In this thesis, the limits ofthe solar flare neutrinos were calculated using the predictions from Fargion and Moscato [42],Kocharov et. al [43], and Takeishi et. al [44]. The probability density function of the number ofthe observed event for the low-energy data set is defined as follows:∫ ∫ ∫ −(S+B)(S + B)nobs
1eA
nobs !
× G(∆σIBD )G(∆εLow )G(∆B)d(∆σIBD )d(∆εLow )d(∆B),∫≡ Np temit F (Eν )σIBD (Eν )εLow (Eν )dEν ,PLow (S + B|nobs ) =S(7.3.1)(7.3.2)where S represents number of expected signal, A is a normalization factor representing the total
integral of PLow (S + B|nobs ), nobs is number of observed events in the search time window, Np is
the number of target proton in SK relevant to the neutrino interactions, F is predicted neutrino
flux in unit of cm−2 sec−1 MeV−1 , temit is time duration of neutrino emission in a solar flare,
which is assumed as 100 sec, σIBD = σ0,IBD + ∆σIBD is the IBD cross section as a function ofelectron anti neutrino energy derived from the simulation, σ0,IBD is the best estimate and ∆σIBD
is the deviation, εLow = ε0,Low + ∆εLow is the reduction eﬃciency of the low-energy sample,
ε0,Low is the best estimate and ∆εLow is the deviation, and B = B0 + ∆B is number of expectedbackground events in the search window, B0 is the best estimate and ∆B is the deviation.
G(∆σIBD ), G(∆εLow ), G(∆B) represent the prior probabilities for fluctuation of the IBD crosssection, the reduction eﬃciency and number of expected background event in the search time
window, respectively. They are assumed to be Gaussian functions,G(∆σIBD ) = √1(∆σIBD )2
exp(−),
2δσ2IBD2πδσ2IBD(7.3.3)1(∆εLow )2),exp(−
2δε2Low2πδε2Low(7.3.4)

(∆B)2
2 ),
2δB

(7.3.5)G(∆εLow ) = √G(∆B) = √

1

exp(−
2

2πδB

where δσIBD , δεLow and δB are systematic uncertainties of the the IBD cross section, the reduction
eﬃciency and number of expected backgound event in the search time window, respectively.
Neutrino fluence can be calculated by using flux F ,∫Φ = temit F (E)dE,(7.3.6)
With these definitions, the neutrino fluence limit at a given confidence level (C.L.) is caluculatedas∫ ΦlimPLow (S + B|nobs )dΦ
C.L. = ∫0 ∞.
(7.3.7)
PLow (S + B|nobs )dΦ0
The fluence limits obtained from low-energy data set is given in Tables 7.3 and 7.4.

Visible Energy [MeV]

7.3. FLUENCE CALCULATION

107

Neutrino events

104

Estimated CME start time
Search Time Window

103

04/18
17:00

04/18
18:00

04/18
19:00

04/18
20:00

04/18
21:00

04/18
22:00

04/18
23:00

04/19
00:00

Visible Energy [MeV]Time (UTC)

Neutrino events

104

Estimated CME start time
Search Time Window

103

11/02
06:00

11/02
07:00

11/02
08:00

11/02
09:00

11/02
10:00

11/02
11:00

11/02
12:00

11/02
13:00

Visible Energy [MeV]Time (UTC)
Nov. 7th 2003
Neutrino events

104

Estimated CME start time
Search Time Window

103

11/07
12:00

11/07
13:00

11/07
14:00

11/07
15:00

11/07
16:00

11/07
17:00

11/07
18:00

11/07
19:00

Visible Energy [MeV]Time (UTC)

Neutrino events

104

Estimated CME start time
Search Time Window

103

11/09
02:00

11/09
03:00

11/09
04:00

11/09
05:00

11/09
06:00

11/09
07:00

11/09
08:00

11/09
09:00
Time (UTC)

Figure 7.15: The time distributions of high-energy neutrino events around the solar flares occurring on the invisible side of the Sun on April 18th, 2001 (top), November 2nd, 2003 (uppermiddle), November 7th, 2003 (lower-middle), and November 9th, 2003 (bottom). The red points
show the time of neutrino events. The dashed vertical line shows the estimated start time of particular CME emission and the shaded regions show the search windows according to the method
described in Section 3.3.2.

CHAPTER 7. RESULTS AND DISCUSSIONS

Visible Energy [MeV]108

July. 24th 2005
Neutrino events

104

Estimated CME start time
Search Time Window

103

07/24
10:00

07/24
11:00

07/24
12:00

07/24
13:00

07/24
14:00

07/24
15:00

07/24
16:00

07/24
17:00

Visible Energy [MeV]Time (UTC)

Jun. 4th 2011
Neutrino events
Estimated CME start time
Search Time Window

104

103

06/04
18:00

06/04
19:00

06/04
20:00

06/04
21:00

06/04
22:00

06/04
23:00

06/05
00:00

06/05
01:00

Visible Energy [MeV]

Time(UTC)

Jul. 23rd 2012
Neutrino events
Estimated CME start time
Search Time Window

104

103

07/22
23:00

07/23
00:00

07/23
01:00

07/23
02:00

07/23
03:00

07/23
04:00

07/23
05:00

07/23
06:00

Visible Energy [MeV]

Time(UTC)

Dec. 13rd 2014
Neutrino events
Estimated CME start time
Search Time Window

104

103

12/13
10:00

12/13
11:00

12/13
12:00

12/13
13:00

12/13
14:00

12/13
15:00

12/13
16:00

12/13
17:00
Time(UTC)

Figure 7.16: The time distributions of high-energy neutrino events around the solar flares occurring on the invisible side of the Sun on July 24th, 2005 (top), June 4th, 2011 (upper-middle),
July 23rd, 2012 (lower-middle) December 13th, 2014 (bottom). The red points show the timeof neutrino events. The dashed vertical line shows the estimated start time of particular CMEemission and the shaded regions show the search windows according to the method described in
Section 3.3.2.

Recostructed Energy [MeV]

7.3. FLUENCE CALCULATION

109

100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0

03:00
04/17

09:00
04/17

15:00
04/17

21:00
04/17

03:00
04/18

09:00
04/18

15:00
04/18

21:00
04/18
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0
09:00
11/01

15:00
11/01

21:00
11/01

03:00
11/02

09:00
11/02

15:00
11/02

21:00
11/02

03:00
11/03
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Recostructed Energy [MeV]

0
15:00
11/06

21:00
11/06

03:00
11/07

09:00
11/07

15:00
11/07

21:00
11/07

03:00
11/08

09:00
11/08
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10
0

09:00
11/08

15:00
11/08

21:00
11/08

03:00
11/09

09:00
11/09

15:00
11/09

21:00
11/09

03:00
11/10
Time (UTC)

Figure 7.17: The time distributions of low-energy neutrino events around the solar flares occurring on the invisible side of the Sun on July 24th, 2005 (top), June 4th, 2011 (upper-middle),
July 23rd, 2012 (lower-middle) December 13th, 2014 (bottom). The red points show the time ofneutrino events.

CHAPTER 7. RESULTS AND DISCUSSIONS

Recostructed Energy [MeV]

110

100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Reconstructed energy [MeV]

0

15:00
07/23

21:00
07/23

03:00
07/24

09:00
07/24

15:00
07/24

21:00
07/24

03:00
07/25

09:00
07/25
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Reconstructed energy [MeV]

0
21:00
06/03

03:00
06/04

09:00
06/04

15:00
06/04

21:00
06/04

03:00
06/05

09:00
06/05

15:00
06/05

21:00
06/05
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10

Reconstructed energy [MeV]

0

03:00
07/22

09:00
07/22

15:00
07/22

21:00
07/22

03:00
07/23

09:00
07/23

15:00
07/23

21:00
03:00
07/23
07/24
Time (UTC)100
90
Neutrino events

80
Search Time Window

70
60
50
40
30
20
10
0

09:00
12/12

15:00
12/12

21:00
12/12

03:00
12/13

09:00
12/13

15:00
12/13

21:00
12/13

03:00
12/14
Time (UTC)

Figure 7.18: The time distributions of low-energy neutrino events around the solar flares occurring on the invisible side of the Sun on July 24th, 2005 (top), June 4th, 2011 (upper-middle),
July 23rd, 2012 (lower-middle) December 13th, 2014 (bottom). The red points show the time ofneutrino events.

Entry (Area normalized)

7.3. FLUENCE CALCULATION

111

0.1
0.09

Nov. 8th, 2003

0.08

July 24th, 2005

0.07

Background Sample

0.06
0.05
0.04
0.03
0.02
0.01
0
0

5000

10000

15000
20000
25000
Time Difference from Previous Event [sec]Figure 7.19: The time diﬀerence between the two events observed within the search windows forsolar flares on November 8th, 2003 (dashed blue line) and July 24th, 2005 (dotted pink line).
The red histograms show the area normalized distribution of the time diﬀerence between theconsecutive events in the background sample.

Number of solar flare112

CHAPTER 7. RESULTS AND DISCUSSIONS

6
5

Data

4

Poisson distribution, 8 × Po(x,0.62)

3

2
1
0
0

1

2

3
4
5
6
7
8
9
10
Number of neutrino candidates in the search time window [event/flare]

Figure 7.20: The distribution of the number of neutrino candidates in the search time window
per one solar flare. The black lines show the distribution of the number of neutrino candidates
from solar flares on the invisible side. The red histograms show the Poisson distribution withthe estimated background rate, 0.62 event/flare, as the mean. The red histograms is normalized
as the area to be 8, which is the number of solar flares occurring on the invisible side.

Event/Search time window

7.3. FLUENCE CALCULATION

113

1.2
Solar flares on invisible side
Nov. 7th 2003
left: 15:40:45
right: 15:18:34
Jul. 24th 2005
left: 13:07:36
right: 14:15:21
Jun. 4th 2011 22:09:37
Jul. 23rd 2012 03:03:47
Background Spectrum

1

0.8

0.6

0.4

0.2

0

1000

2000

3000

4000

5000

6000
7000
Visible Energy[MeV]

Figure 7.21: The energy distribution of the neutrino events observed in the time window forsolar flares occurring on the invisible side of the Sun and that of the background sample. The
green circle, magenta square, yellow upward triangle, blue downward triangle are the energy ofobserved events on November 7th, 2003, July 24th, 2005, June 4th, 2011, and July 23rd, 2012,
respectively. The background spectrum is normalized by the time duration of 7238 s according
to the method described in Section 3.3.1.

CHAPTER 7. RESULTS AND DISCUSSIONS

Area Normilized Entry

114

0.06
Solar Flare on the Invisible Side (Nov. 7th 2003)

0.05

Signal (MC) angle distribution (3000.0-4000.0 MeV)
BG (DATA) angle distribution (3000.0-4000.0 MeV)

0.04

Neutrino signal (15:18:34 3579 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Area Normilized Entry

Figure 7.22: The angular distribution of the neutrino events from the solar flare occurring on
November 7th, 2003, and that of the signal simulation sample. The green thick and the black
thin histograms show the angular distribution of signal MC and Background sample, respectively.
The red dashed line shows the angle from the Sun, θSun , of the candidate neutrino event.

0.06
Solar Flare on the Invisible Side (Nov. 7th 2003)

0.05

Signal (MC) angle distribution (100.0-500.0 MeV)
BG (DATA) angle distribution (100.0-500.0 MeV)

0.04

Neutrino signal (15:40:45 493.0 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Figure 7.23: The angular distribution of the neutrino events from the solar flare occurring on
November 7th, 2003, and that of the signal simulation sample. The green thick and the black
thin histograms show the angular distribution of signal MC and Background sample, respectively.
The red dashed line shows the angle from the Sun, θSun , of the candidate neutrino event.

Area Normilized Entry

7.3. FLUENCE CALCULATION

115

0.06
Solar Flare on the Invisible Side (Jul. 24th 2005)

0.05

Signal (MC) angle distribution (100.0-500.0 MeV)
BG (DATA) angle distribution (100.0-500.0 MeV)

0.04

Neutrino signal (22:07:36 126.0 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Area Normilized Entry

Figure 7.24: The angular distribution of the neutrino events from the solar flare occurring on
July 23rd, 2005, and that of the signal simulation sample. The green thick and the black thinhistograms show the angular distribution of signal MC and Background sample, respectively.
The red dashed line shows the angle from the Sun, θSun , of the candidate neutrino event.

0.06
Solar Flare on the Invisible Side (Jul. 24th 2005)

0.05

Signal (MC) angle distribution (1000.0-2000.0 MeV)
BG (DATA) angle distribution (1000.0-2000.0 MeV)

0.04

Neutrino signal (23:15:21 1350 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Figure 7.25: The angular distribution of the neutrino events from the solar flare occurring on
July 23rd, 2005, and that of the signal simulation sample. The green thick and the black thinhistograms show the angular distribution of signal MC and Background sample, respectively.
The red dashed line shows the angle from the Sun, θSun , of the candidate neutrino event.

CHAPTER 7. RESULTS AND DISCUSSIONS

Area Normilized Entry

116

0.06
Solar Flare on the Invisible Side (Jun. 4th 2011)

0.05

Signal (MC) angle distribution (2000.0-3000.0 MeV)
BG (DATA) angle distribution (2000.0-3000.0 MeV)

0.04

Neutrino signal (06:05:07 2135 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Area Normilized Entry

Figure 7.26: The angular distribution of the neutrino events from the solar flare occurring on
June 4th, 2011, and that of the signal simulation sample. The green thick and the black thinhistograms show the angular distribution of signal MC and Background sample, respectively.
The red dashed line shows the angle from the Sun, θSun , of the candidate neutrino event.

0.06
Solar Flare on the Invisible Side (Jul. 23rd 2012)

0.05

Signal (MC) angle distribution (500.0-1000.0 MeV)
BG (DATA) angle distribution (500.0-1000.0 MeV)

0.04

Neutrino signal (12:03:47 834.0 MeV)

0.03

0.02

0.01

0
0

20

40

60

80

100

120

140

160

180
θSun [°]

Figure 7.27: The angular distribution of the neutrino events from the solar flare occurring on
July 23rd, 2012, and that of the signal simulation sample. The green thick and the black thinhistograms show the angular distribution of signal MC and Background sample, respectively.
The red dashed line shows the angle from the Sun, θSun , of the candidate neutrino event.

Table 7.3: The summary of fluence limits for the low-energy sample for solar flares on the visible side. We assumed the energy spectrum
from Fargion and Moscato [42] and the neutrino interactions from Strumia and Vissani [113]. The search time windows are same as in
Table 3.9
Date
Derivative of soft X-rays Line γ-ray (RHESSI) Number of candidate Expected background Fluence limits
Start
End
Start
End
event [event]rate [event/flare][cm−2 flare−1 ]1997 Nov. 6 11:52:13
11:54:58––
00.0004< 1.7 × 107
10:28:31––
00.0027< 1.7 × 107
2000 Jul. 14 10:08:44
2001 Apr. 2
21:35:10
21:52:57––
00.0025< 1.7 × 107
19:12:32
19:21:31––00.0012< 1.7 × 107
2001 Apr. 6
2001 Apr. 15 13:43:48
13:51:03––
00.0010< 1.7 × 107
2001 Aug. 25 16:28:36
16:33:38––
No SK data
2001 Dec. 13 14:24:25
14:31:05––
No SK data
2002 Jul. 23 00:25:08
00:31:36
00:26:28
00:56:22
No SK data
2003 Oct. 23 08:20:32
08:36:03––
00.0022< 1.7 × 107
11:10:57––
00.0016< 1.7 × 107
2003 Oct. 28 10:59:30
2003 Oct. 29 20:38:46
20:50:07––
00.0016< 1.7 × 107
2003 Nov. 2 17:12:01
17:26:03
17:14:14
17:36:4100.0019< 1.7 × 107
2003 Nov. 4 19:36:59
19:56:03––
00.0026< 1.7 × 107
2005 Jan. 20 06:39:22
06:57:12
06:42:54
07:09:52
00.0025< 1.7 × 107
17:23:34
17:39:48––
00.0023< 1.7 × 107
2005 Sep. 7
21:00:27
21:08:05––
00.0011< 1.7 × 107
2005 Sep. 8
2005 Sep. 9
19:13:00
21:20:36
–
–
0
0.018
< 1.7 × 107
2006 Dec. 5
10:24:18
10:35:43––
00.0016< 1.7 × 107
18:41:29
18:47:06––
00.0008< 1.7 × 107
2006 Dec. 6
2011 Aug. 9 08:00:50
08:05:40––
00.0007< 1.7 × 107
00:25:16––
00.0029< 1.7 × 107
2012 Mar. 7 00:04:21
2017 Sep. 6
11:54:39
12:03:20––
00.0012< 1.7 × 107
16:06:32––
00.0024< 1.7 × 107
2017 Sep. 10 15:49:12

7.3. FLUENCE CALCULATION
117

118

CHAPTER 7. RESULTS AND DISCUSSIONS

Table 7.4: The summary of fluence limits for the low-energy sample for solar flares on theinvisible side. We assumed the energy spectrum from Fargion and Moscato [42] and the neutrino
interactions from Strumia and Vissani [113]. The search time windows are same as in Table 3.10
Date2001 Apr. 18
2002 Jul. 18
2002 Jul. 19
2003 Nov. 2
2003 Nov. 7
2003 Nov. 9
2005 Jul. 24
2011 Jun. 42012 Jul. 23
2014 Dec. 13

Search Time Window
Start
End
01:15:24
03:16:02
18:07:20
20:07:58
15:13:34
17:14:12
08:09:23
10:10:01
14:41:19
16:41:57
05:06:57
07:45:29
12:44:51
14:45:29
20:51:42
22:52:20
01:19:07
03:19:45
13:06:34
15:07:12

Number of candidate
event [event]0
No SK data
No SK data
0
0
0
0
0
0
0

Expected backgroundrate [event/flare]
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002

Fluence limits[cm−2 flare−1 ]< 1.7 × 107< 1.7 × 107< 1.7 × 107< 1.7 × 107< 1.7 × 107< 1.7 × 107< 1.7 × 107< 1.7 × 107

For the high-energy data set, we considered reactions of all neutrino flavors because thedistance between the Sun and the Earth is suﬃciently long compared with the oscillation lengthof neutrinos whose energy is less than 100 GeV [118]. The flavor ratio of solar flare neutrinos at
the production point is νe : νµ : ντ = 1 : 2 : 0 due to its origin from π ± and µ± decays while
the flavor ratio at the detector is approximately νe : νµ : ντ = 1 : 1 : 1, where we also assume
that the ratio of neutrino to anti-neutrino is approximately equal, as ν : ν̄ = 1 : 1. The fluence
limit of solar flare neutrino using the high-energy sample can be obtained by a similar procedure
to the one for the low-energy sample. The diﬀerence in the calculation procedure of the upper
limit between the high and the low-energy data sets is the definition of the probability density
function of the number of observed events. For the high-energy data set, it is defined as follows:∫ ∫ ∫ −(S+B)
1e(S + B)nobs
PHigh (S + B|nobs ) =A′nobs !
× G(∆σ(Eν ))G(∆εHigh )G(∆B)d(∆σ(Eν ))d(∆εHigh )d(∆B), (7.3.8))(∫∑
F (Eνi )σ(Eνi )εHigh (Eνi ), (7.3.9)
S = NT temit dEν6
i=e,µ,τ,ē,µ̄,τ̄
where NT is the number of target nuclei relevant to the neutrino interactions, F (Eν ) is the
expected energy spectrum from each theoretical model [42–44], σ(Eν ) is the combined crosssection for all interactions, and εHigh (Eν ) is the reduction eﬃciency of the high-energy sample.
Figure 7.28 shows a comparison between fluence prediction from solar flare neutrino models andthe upper limits in this study. The Fargion’s model is experimentally excluded. The Kocharov’s
model will be testified by the next-generation neutrino detector such as Hyper-K. The Takeishi’s
model is diﬃcult to test even if the next-generation neutrino detector.
Fargion and Moscato [42] define energy conversion factor, η, as the amount of energy carriedaway by π ± out of the total energy of a solar flare. If the total energy of a solar flare is known, theenergy conversion factor can be calculated by using our result, based on the following equation:()
EFL
nobs = 7.5η
(7.3.10)1031 erg

Neutrino Fluence [cm -2 flare-1]

7.3. FLUENCE CALCULATION

119

107
106
105
104
103
102

Predicted Fluence
Upper Limit with each Model

101

Fargion and Moscato (2003)

Kocharov et al. (1991)

Takeishi et al. (2013)

Models of Solar Flare Neutrino Spectrum

Figure 7.28: The comparison between predicted fluence by solar flare neutrino models and fluence
upper limits obtained in this study. Red solid lines (black dashed line) show predicted neutrino
fluence of each model (fluence upper limit).

120

CHAPTER 7. RESULTS AND DISCUSSIONS

where EFL is the total energy of solar flare and nobs is observed event in SK. According toRef. [61], The total energy of the solar flare event that occurred on November 4th, 2003 is
estimated to be 1.3 × 1034 erg. In the case of this solar flare, the energy conversion factor isdetermined as η = 0.004, which is two order of magnitude smaller than the estimation by Fargion
and Moscato [42]. Therefore, this experimental result suggests that the theoretical assumptionof energy conversion during solar flares should be re-considered. The 90% C.L. upper limits ofthe fluence for solar flare neutrino in the high-energy data sample in each flare are summarizedin Tables 7.5 and 7.6.

Table 7.5: The summary of fluence upper limits at 90% C.L. for the high-energy sample. We assumed the energy spectrum from Fargion
and Moscato [42] and the neutrino interactions from Hayato et. al [84]. The search time windows are same as in Table 3.9
Date
Derivative of soft X-rays Line γ-ray (RHESSI) Number of candidate Expected background Fluence limits
Start
End
Start
End
event [event]rate [event/flare][cm−2 flare−1 ]1997 Nov. 6 11:52:13
11:54:58––
00.04< 5.6 × 105
2000 Jul. 14 10:08:44
10:28:31––
00.20< 5.6 × 105
2001 Apr. 2
21:35:10
21:52:57––
00.20< 5.6 × 105
2001 Apr. 6
19:12:32
19:21:31––
00.10< 5.6 × 105
13:51:03––
00.08< 5.6 × 105
2001 Apr. 15 13:43:48
16:33:38––
No SK data
2001 Aug. 25 16:28:36
2001 Dec. 13 14:24:25
14:31:05––
No SK data
2002 Jul. 23 00:25:08
00:31:36
00:26:28
00:56:22
No SK data
2003 Oct. 23 08:20:32
08:36:03––
00.16< 5.6 × 105
2003 Oct. 28 10:59:30
11:10:57––
00.12< 5.6 × 105
2003 Oct. 29 20:38:46
20:50:07––
00.12< 5.6 × 105
17:26:03
17:14:14
17:36:41
00.14< 5.6 × 105
2003 Nov. 2 17:12:01
2003 Nov. 4 19:36:59
19:56:03––
1
0.20< 8.5 × 105
2005 Jan. 20 06:39:22
06:57:12
06:42:54
07:09:52
00.18< 5.6 × 105
2005 Sep. 7
17:23:34
17:39:48––
00.18< 5.6 × 105
2005 Sep. 8
21:00:27
21:08:05––
00.08< 5.6 × 105
19:13:00
21:20:36––
00.67< 5.6 × 105
2005 Sep. 9
10:24:18
10:35:43––
00.12< 5.6 × 105
2006 Dec. 5
2006 Dec. 6
18:41:29
18:47:06––
00.06< 5.6 × 105
08:05:40––
00.06< 5.6 × 105
2011 Aug. 9 08:00:50
2012 Mar. 7 00:04:21
00:25:16––
00.20< 5.6 × 105
11:54:39
12:03:20––
1
0.12< 8.9 × 105
2017 Sep. 6
2017 Sep. 10 15:49:12
16:06:32––
00.18< 5.6 × 105

7.3. FLUENCE CALCULATION
121

122

CHAPTER 7. RESULTS AND DISCUSSIONS

Table 7.6: The summary of fluence upper limits at 90% C.L. for the high-energy sample for solar
flares on the invisible side. We assumed the energy spectrum from Fargion and Moscato [42]and the neutrino interactions from Hayato et. al [84]. The search time windows are same as in
Table 3.10
Date2001 Apr. 18
2002 Jul. 18
2002 Jul. 19
2003 Nov. 2
2003 Nov. 7
2003 Nov. 9
2005 Jul. 24
2011 Jun. 42012 Jul. 23
2014 Dec. 13

Search Time Window
Start
End
01:15:24
03:16:02
18:07:20
20:07:58
15:13:34
17:14:12
08:09:23
10:10:01
14:41:19
16:41:57
05:06:57
07:45:29
12:44:51
14:45:29
20:51:42
22:52:20
01:19:07
03:19:45
13:06:34
15:07:12

Number of candidate
event [event]0
No SK data
No SK data
0
2
0
2
1
1
0

Expected backgroundrate [event/flare]
0.62
0.62
0.62
0.62
0.62
0.62
0.62
0.62

Fluence limits[cm−2 flare−1 ]< 5.6 × 105< 5.6 × 105< 1.2 × 106< 5.6 × 105< 1.2 × 106< 8.2 × 105< 8.2 × 105< 5.6 × 105

To compare the results of this work with the other experimental results, the model-independent
fluence upper limit was also calculated for the low-energy sample. In this case, the probability
density function at an energy E is defined as follows:

PLow (S + B|nobs )(E)

=
×

S(E)

=

∫ ∫ ∫ −(S(E)+B)
1e(S(E) + B)nobs
A
nobs !
G(∆σIBD )G(∆εLow )G(∆B)d(∆σIBD )d(∆εLow )d(∆B),(7.3.11)∫
Np temit F (Eν )θ(E, Eν )σIBD (Eν )εLow (Eν )dEν
(7.3.12)

where θ(E, Eν ) is a function which is defined as,{
1 (E − 5 MeV < Eν ≤ E + 5 MeV)
θ(E, Eν ) =0 (otherwise),(7.3.13)and other variables and functions are same as that used in Eq. (7.3.2). The fluence limit wascalculated every 10 MeV in the energy range from 20 to 120 MeV. Figure 7.29 shows the resultsof the upper limits of fluence for solar flare neutrinos with the model-independent method. Compared to the Kamiokande-II result [52], the sensitivity was improved by an order of magnitude in
the energy region from 20 to 110 MeV. SNO, Borexino, and KamLAND collaborations searched
for neutrinos from solar flares in the energy range of MeV by analyzing light curves from the
GOES satellite. Because their methods (as well as assumptions) diﬀer from each other, we can
not directly compare the experimental results with these results.

7.4

Discussions and Future Prospects

Neutrinos from solar flares are important to understand the mechanism of proton acceleration at
the astrophysical site. For solar flares that occurred on the visible and invisible sides, we firstly
estimated the time of neutrino emission from optical light curves and CMEs observations by theNeutrino fluence limit per flare [cm -2]

7.4. DISCUSSIONS AND FUTURE PROSPECTS

123

1017
1016

Solar flare on the visible side
SK Upper Limit (This work)
Kamland ES+IBD (νe)
Kamiokande
Borexino (νe)
SNO
Homestake (νe)

1015
1014
1013
1012
1011
1010
109
108
107
106
0

20

40

60

80

100
Neutrino energy [MeV]

Figure 7.29: The fluence limit obtained by the SK-I, II, III, and IV (red thick-solid) together withthe other experimental results by Kamiokande (black long-dashed-dotted) [52], KamLAND (pinkdashed) [119], Borexino (Green thin-solid) [54], SNO (blue dotted) [53] below 100 MeV. The
results from other experiments have been scaled to fit the definition of calculation in this study.

124

CHAPTER 7. RESULTS AND DISCUSSIONS

solar satellites. Then, we searched for neutrino events coincident with solar flares in the SuperKamiokande detector. Two neutrino events from solar flares occurring on the visible side, while
six neutrino events from solar flares that occurred on the invisible side were observed, but all ofthem are consistent with the background rate estimated from the usual data of the SK detector.
Since no significant excess of events is observed, we obtained the upper limit of the solar flare
neutrino fluence. For example, the fluence limit at 90% C.L. for the largest solar flare with theclass of X28.0 occurring on the visible side of the Sun on November 4th, 2003 is 8.5 × 105 cm−2 .
In addition, the fluence limit for the solar flare occurring on the invisible side on November 7th,
2003, which followed the largest solar flare from April 1996 to May 2018, is 1.2 × 106 cm−2 .
In order to compare the results with the other experimental fluence limits, the modelindependent fluence limit is also obtained below 100 MeV. Our result gave the most stringent
upper limit on the fluence of solar flare neutrinos.
In July 2020, 13 tons of Gd2 (SO4 )3 · 8H2 O (gadolinium sulfate octahydrate) was dissolved into
the detector’s water tank in order to improve its neutron detection eﬃciency. This Gd loading
is mainly motivated to increase the detector’s sensitivity to the diﬀuse supernova anti-electron
neutrinos by applying the delayed coincidence technique between primary neutrino interaction
and about 8 MeV γ-rays from Gd-neutron capture due to large neutron cross-section of Gd [120].
This technique also enhances the sensitivity to solar flare neutrinos as well. In addition to SK-Gd,
further searches are required to understand the production of solar flare neutrinos by the large
scale neutrino detectors such as Hyper-Kamiokande [45], IceCube gen-2 [121], and JUNO [122]during the next solar cycle 25 staring from the late 2019. The fiducial volume of Hyper-K isabout ten times that of Super-K. Assuming that the reduction eﬃciency of Hyper-K is the sameas that of Super-K, the sensitivity of the solar flare neutrino detection is estimated to be about
six times better.
In this study, we searched for solar flare neutrinos coincident with the impulsive phase of solar
flares. On the other hand, the late arrival of prompt solar charged particles results in the delayed
neutrino flux originating from the collisions with the Earth’s atmosphere. Search for neutrinos
originated from the long time-scale acceleration would be an interesting topic in future.

Chapter 8

Conclusion
We have performed searches for neutrinos associated with solar flares with the Super-Kamiokande
detector. Neutrinos from solar flares are important to understand the mechanism of proton
acceleration at the astrophysical site. When the protons are traveling downward towards thesolar core along with the magnetic field line, a beam-like acceleration of protons eﬃciently collides
with a nucleus in the dense plasma. Such a process results in enhancing the production rate of
the neutrinos. If this beam-like acceleration occurs on the invisible side of the Sun, the large
neutrino intensity at the neutrino detectors at the Earth would be expected.
The first step of the solar flare neutrino search was to select the large solar flares and estimate
the neutrino emission time for both the visible and invisible sides of the Sun. Twenty-three solar
flares on the visible side above the X5.0 class, and ten solar flares accompanied with CMEs whose
emission speed is faster than 2000 km s−1 on the invisible side occurring between April 1996 andMay 2018 were selected. For solar flares occurring on the visible side, we estimated the time ofneutrino emission from optical light curves which are observed by the solar satellites. For solar
flares occurring on the invisible side, we set the search time window from CMEs observations.
The average duration of the search windows used in this study are 700 s (derivative of soft X-ray
by GOES) and 1586 s (line γ-ray by RHESSI) for the visible side solar flares. We conservatively
set the search time window of 7238 s/flare (3060 s before the time of CMEs emission and 4178 safter the time of CME emission), where this duration is determined from the study of the visible
side solar flares, since all processes, such as acceleration, energy release, etc, occurring during asolar flare complete within this time duration. As a result, the average background rate for asolar flare in Super-Kamiokande becomes 0.24 event/flare for the visible side and 0.62 event/flare
for the invisible side.
Then, we searched for neutrino events coincident with the solar flares in the Super-Kamiokande
detector. The SK data is divided into two samples as high-energy samples (above 100 MeV) andlow-energy samples (16 - 100 MeV). For the three solar flares on the visible side, the SK data
is not available because the SK detector was under reconstruction. Therefore, the number ofsolar flares on the visible side for solar flare neutrino search is twenty. No low-energy neutrino
candidates are found in the search time windows while the backgrond rate is 0.001 event/flare.
On the other hands, there are two solar flares occurring on the visible side of the Sun with one
high-energy neutrino candidate in the search time windows. For the other solar flares on thevisible side, there are not any neutrino candidates. The solar flares with the neutrino candidate occurred on November 4th, 2003, and September 6th, 2017, and background rates are 0.20
event/flare and 0.12 event/flare, respectively. The probabilities that the neutrino candidate isfrom a background source are 18.1% and 11.3%, respectively. So we have concluded they are
125

126

CHAPTER 8. CONCLUSION

consistent with the background rate.
For the solar flares occurring on the invisible side of the Sun, the SK data is not available
for the two solar flares because of the reconstruction work of the SK detector. Hence, we havesearched for solar flare neutrinos by using eight solar flares occurring on the invisible side, finally.
No low-energy neutrino candidates are found in the search time windows while the backgrond
rate is 0.002 event/flare. There are two solar flares with two high-energy neutrino candidates andtwo solar flares with one high-energy neutrino candidate. There are not any neutrino candidates
with the other four solar flares. The background rate for each solar flare on the invisible side is
0.62 event/flare. The probabilities that the neutrino candidates are from background sources are
12.8% for solar flares with two neutrino candidates and 46.2% for solar flares with one neutrino
candidate, respectively. So we have concluded they are also consistent with the background rate.
It is the first time that the solar flare neutrino search from solar flares on the invisible side of
the Sun has been carried out.
Based on the observed events within the search window, the upper limit of the solar flare
neutrino fluence was calculated for each solar flare. The fluence upper limits at 90% C.L. for thesolar flares occurring on the visible side of the Sun without neutrino candidates are 5.6×105 cm−2 .
For the solar flares occurring on the invisible side of the Sun, The fluence upper limits at 90%
C.L. in the energy region from 100 MeV to 10 GeV are 5.6 × 105 cm−2 , 8.2 × 105 cm−2 and1.2 × 106 cm−2 for solar flares with zero, one and two neutrino candidates, respectively. The
fluence upper limit for the solar flare occurring on November 4th, 2003 is 8.5 × 105 cm−2 . This is
the largest solar flare since 1996. From the obtained fluence upper limit, the upper limit on theconversion factor, η, which is the eﬃciency of energy conversion from the total energy of solar
flare to the energy of the neutrinos, is estimated based on Fargion and Moscato [42]. In the caseof the largest solar flare on November 4th, 2003, it is determined as η < 0.004, which is twoorders of magnitude smaller than the estimation by Fargion and Moscato [42]. Therefore, thisexperimental result suggests that the theoretical assumption adopted in Ref. [42] of the energy
conversion during solar flares should be re-considered. In addition, the fluence upper limit at 90%
C.L. for the solar flare occurring on the invisible side on November 7th, 2003, which followed thelargest solar flare, is 1.2 × 106 cm−2 . From the comparison between the fluence upper limit andprediction of the solar flare neutrino fluence expected by the theoretical model [42] of Fargion
and Moscato, we have concluded the theoretical model is excluded. The fluence upper limits at
90% C.L. in the energy region from 16 to 100 MeV for the solar flares occurring on the visible
and invisible side of the Sun are 1.7 × 107 cm−2 . In order to compare the results with the fluence
limits from other experiments, the model independent fluence upper limit below 100 MeV is also
obtained. The result does not rule any theoretical models but gives the most stringent upper
limits on the fluence of solar flare neutrinos in the tens of MeV region.

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