Measurements of the Energy Spectrum and the Mass
Composition of Ultra-High Energy Cosmic Rays with
Telescope Array Fluorescence Detectors
in Monocular Mode(テレスコープアレイ大気蛍光望遠鏡の単眼解析による極高エネルギー宇宙線のエネルギースペクトルと質量組成の測定)

理学研究科
数物系専攻

平成 24 年度

Toshihiro Fujii(藤井 俊博)Abstract
In 1912, just one century ago, V.F.Hess discovered energetic elementary particles injected from the universe, so called “Cosmic Rays”. However, their origins
are still unknown. Among them, ultra-high energy cosmic rays (UHECRs) with
E > 1019 eV are the most energetic particles in the universe, and their origins
are related with energetic astronomical phenomena or exotic physics. Moreover,
if assumed UHECRs are pure protons, an existence of the cosmic microwave
background radiation (CMBR) leads the energy spectrum above 1019.5 eV to be
suppressed through photo-nucleon interactions with CMBR, called GZK cutoff. Additionally, cosmic rays with energies around 1018.7 eV are expected tointeract with CMBR through pair creations of electrons and positrons. Since
cosmic rays are charged particles, they are bended by galactic magnetic fields
in our galaxy. However cosmic rays with larger kinetic energies, > 1018.5 eV,
are propagated without bending. Thus, because a transition from galactic toextra-galactic origins is expected at their energies, measurements of the masscomposition and the energy spectrum with broad energies are important to ruleout several theoretical models.
In order to conclude origins of cosmic rays, we steadily observe UHECRs by
the Telescope Array (TA) experiment in Utah of U.S.A. The TA is the largest
detector in the northern hemisphere, and it consists of 38 fluorescence detectors
and 507 surface detectors covering with 700 km2 effective area. I report ananalysis technique of TA fluorescence detectors in monocular mode and resultsof the mass composition and the energy spectrum with energies from 1017.5 eV
to 1020.0 eV analyzed data during 3.7 years. The measured mass compositionindicated a transition of dominated components from heavy to light nuclei
from 1017.5 eV to 1018.5 eV, and protons were dominant above 1018.5 eV. We
measured the energy spectrum with broad energies from 1017.5 eV to 1020.0 eV,
which was in good agreement with results of TA surface detectors and Middle
Drum fluorescence detectors transported from the HiRes experiment.
Keyword: ultra-high energy cosmic rays, energy spectrum, mass composition, extensive air showers, Telescope Array experiment, fluorescence light, active galactic nuclei, gamma-ray bursts, large scale structureiii

Acknowledgments
I am deeply thankful to my supervisor Shoichi Ogio for the much I have learned
from him and the full support given during the development of my thesis. And
to Yoshio Hayashi, Koji Kojima and Nobuyuki Sakurai, that accompanied atclose distance the whole work and given their valuable advice.
I would like to thank all of the Telescope Array collaborators for great help
about the science work and pleasant days. At first, I am grateful to Masaki
Fukushima and Hiroyuki Sagawa for the great management and giving me theopportunity to participate in the Telescope Array experiment.
Next, as the same analysis group of the Telescope Array fluorescence detectors, I would like to thank to Yuichiro Tameda, Daisuke Ikeda and Takayuki
Tomida. I’m very happy to work with you, enjoy many tourist spots and get
precious memories all over the world. I would also like to express my gratitude
to Sean Stratton and Elliott Barcikowski for the helpful discussion and crosscheckings of my analysis. I would like to thank to Yoshiki Tsunesada for theiradvice and guidance for my work as an organizer of our analysis group. And
to Hisao Tokuno and Shigeharu Udo, Masahiro Takeda and Tatsunobu Shibata
for their valuable support and helpful comments. I am also very grateful to
Pierre Sokolsky, Gordon Thomson, Charlie Jui, John Matthews and Douglas
Bergman for precious discussions and their kindly support at Utah. I would
like to thank to Toshiyuki Nonaka, Takeshi Okuda, Eiji Kido and Akimichi
Taketa for their important advice and leaning the experimental technique at
the Telescope Array site, Utah of U.S.A.
As the members of our laboratory including graduated students, I would
like to thank to Akitoshi Oshima, Mayuko Minamino, Hitoshi Miyauchi, Yu
Yamashita, Eri Usui, Katsuya Yamazaki, Kazuyuki Kuramoto, Daisuke Matsumiya, Yasuhisa Yoneda, Ryo Yamane, Takashi Goto and Shogo Kobayashi
for their pleasant communications and encouragements. As the collaborators ofother institutes including graduated students, I’m grateful to Takanori Fukuda,
Kentaro Hayashi, Yusaku Kobayashi, Rie Ishimori Yoshiaki Takahashi, Daisuke
Oku, Fumiya Shibata, Kanetsugu Kitamoto, Kazuki Tsutsumi, Takanori Matsuura, Seiji Kitamura and Yuki Kitamura for their discussions and delightful
drinking sessions.
I gratefully acknowledge the valuable financial support by the Japan Society
for the Promotion of Science (JSPS). I also gratefully thank the contributions ofcomputing system at Institute for Cosmic Ray Research (ICRR) of Universityvvi
of Tokyo and the University of Utah Center for High Performance Computing(CHPC).
Finally, I am very grateful to my family, especially Nobuyuki Fujii and
Akemi Fujii, for putting up with me and supporting my research life. I would
also like to thank to my dear friends for their encouragements.

皆さんに出会え、成長できたことに深く感謝しています。

2012 年 9 月

藤井 俊博

Contents
1 Introduction

1

2 Ultra-High Energy Cosmic Rays
2.1 Overview of UHECR Physics . . . . . . . . . . . . . . . . . . .
2.2 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Energy Spectrum . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Acceleration Mechanism . . . . . . . . . . . . . . . . . .
2.3 Ultra-High Energy Cosmic Rays . . . . . . . . . . . . . . . . .
2.3.1 GZK Cutoff . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Origin of UHECRs . . . . . . . . . . . . . . . . . . . . .
2.4 Extensive Air Shower . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Air Shower Cascades . . . . . . . . . . . . . . . . . . . .
2.4.2 Longitudinal Development of EAS . . . . . . . . . . . .
2.4.3 Lateral Distribution of EAS . . . . . . . . . . . . . . . .
2.4.4 Techniques for EAS Measurement . . . . . . . . . . . .
2.4.5 Photon Emissions, Scattering and Attenuation . . . . .
2.5 Recent Results and Mysteries of UHECRs . . . . . . . . . . . .
2.5.1 Energy Spectrum Measurements . . . . . . . . . . . . .
2.5.2 Mass Composition Measurements . . . . . . . . . . . . .
2.5.3 Arrival Direction Distribution . . . . . . . . . . . . . . .

5
5
5
6
8
10
10
12
16
17
18
20
21
23
27
28
30
35

3 Telescope Array Experiment
3.1 Aims of the Telescope Array Project . . . . . . . . . . . . . . .
3.2 Overview of the TA hybrid detector . . . . . . . . . . . . . . .
3.3 Fluorescence Detectors . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Telescope and Optics . . . . . . . . . . . . . . . . . . . .
3.3.2 Photomultiplier Tube (PMT) and Camera . . . . . . .
3.3.3 Calibration of PMT Gain . . . . . . . . . . . . . . . . .
3.3.4 Trigger Electronics . . . . . . . . . . . . . . . . . . . . .
3.4 Atmospheric Monitoring . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Radiosonde . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 LIDAR . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 CLF . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Cloud Monitoring . . . . . . . . . . . . . . . . . . . . .

41
41
42
42
44
45
50
51
60
60
61
62
64

vii

viii

CONTENTS
3.4.5 Star Analysis . . . . . . . . . . . . . . . . . . . . . . . .
3.4.6 The End-to-End Absolute Energy Calibration . . . . . .
Surface Detector . . . . . . . . . . . . . . . . . . . . . . . . . .

65
67
68

4 TA FD Detector Simulation Software
4.1 Extensive Air Shower Generation . . . . . . . . . . . . . . . . .
4.1.1 CORSIKA shower simulation . . . . . . . . . . . . . . .
4.1.2 Fluorescence Light Emission . . . . . . . . . . . . . . .
4.1.3 Direct Čerenkov Light . . . . . . . . . . . . . . . . . . .
4.1.4 Scattered Čerenkov Light . . . . . . . . . . . . . . . . .
4.2 TA FD Detector Simulation . . . . . . . . . . . . . . . . . . . .
4.2.1 Ray-tracing technique . . . . . . . . . . . . . . . . . . .
4.2.2 Night Sky background . . . . . . . . . . . . . . . . . . .
4.3 Cross Checking of Simulation Software . . . . . . . . . . . . . .
4.3.1 Comparison of Photon Emission Processes and Atmospheric Model . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Comparison of Ray-Tracing . . . . . . . . . . . . . . . .

75
75
75
78
79
79
82
82
83
83

5 TA FD Reconstruction Software
5.1 PMT Selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 1st Selection . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 2nd Selection . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 3rd Selection . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 4th Selection . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Geometry Reconstruction . . . . . . . . . . . . . . . . . . . . .
5.2.1 Estimation of the Line of Sight for Each PMT . . . . .
5.2.2 Shower-Detector Plane . . . . . . . . . . . . . . . . . . .
5.2.3 Monocular Geometry Reconstruction . . . . . . . . . . .
5.3 Shower Profile Reconstruction – Inverse Monte Carlo – . . . . .
5.3.1 Xmax Determination . . . . . . . . . . . . . . . . . . . .
5.3.2 Nmax Determination . . . . . . . . . . . . . . . . . . . .
5.3.3 Energy Determination . . . . . . . . . . . . . . . . . . .

87
88
88
89
91
92
93
94
94
96
97
97
98
98

3.5

84
85

6 Performance Evaluation
101
6.1 Resolution and Aperture of the Monocular Mode . . . . . . . . 101
6.1.1 Simulation Conditions . . . . . . . . . . . . . . . . . . . 101
6.1.2 Resolutions in the Monocular Mode . . . . . . . . . . . 102
6.1.3 Estimations of Apertures . . . . . . . . . . . . . . . . . 107
6.2 Mass Composition Study . . . . . . . . . . . . . . . . . . . . . 109
6.2.1 Xmax Technique . . . . . . . . . . . . . . . . . . . . . . 109
6.2.2 Acceptance Biases on Xmax Limited Fields of View of FDs110
6.2.3 Fiducial Volume Cuts . . . . . . . . . . . . . . . . . . . 111

CONTENTS

ix

7 Data Analysis
117
7.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.1.1 Calculation of Live Time . . . . . . . . . . . . . . . . . 117
7.1.2 Number Spectrum . . . . . . . . . . . . . . . . . . . . . 119
7.2 Data/MC Comparison . . . . . . . . . . . . . . . . . . . . . . . 121
7.3 Pull Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4 Mass Composition Analysis . . . . . . . . . . . . . . . . . . . . 123
7.4.1 Mass Composition Results in BRM or LR Station . . . 123
7.4.2 Mass Composition Results in Combined Mode . . . . . 124
7.4.3 Compatibility of Xmax Distribution on Kolmogorov-Smirnov
Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.5 Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.5.1 Combined Exposure . . . . . . . . . . . . . . . . . . . . 133
7.6 Study of Systematic Uncertainty . . . . . . . . . . . . . . . . . 135
7.6.1 Fluorescence Yields . . . . . . . . . . . . . . . . . . . . 136
7.6.2 Atmospheric parameters . . . . . . . . . . . . . . . . . . 137
7.6.3 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.6.4 Geometry of Fluorescence Telescopes . . . . . . . . . . . 138
7.6.5 Reconstruction Methods . . . . . . . . . . . . . . . . . . 138
7.6.6 Total Systematic Uncertainty . . . . . . . . . . . . . . . 139
8 Discussion
141
8.1 Mass Composition Measurement . . . . . . . . . . . . . . . . . 141
8.1.1 Transition of Mass Composition from 1017.5 eV to 1018.5
eV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.1.2 Proton Dominant above 1018.5 eV . . . . . . . . . . . . 144
8.2 Energy Spectrum Measurement . . . . . . . . . . . . . . . . . . 145
8.3 Combined Interpretation . . . . . . . . . . . . . . . . . . . . . . 148
8.4 Future Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9 Conclusions

153

Appendix155
A.1 Observed EAS Events . . . . . . . . . . . . . . . . . . . . . . . 155
A.2 Data/MC comparison . . . . . . . . . . . . . . . . . . . . . . . 156
Bibliography

171

List of Figures
2.1

Overview of the cosmic ray spectrum. Approximate energies of
the two breaks commonly referred to as knee and the ankle are indicated by arrows. Data are from LEAP [7], Proton [8], AKENO[9], KASCADE [10],Auger surface array [11], Auger hybrid [12],AGASA [44], HiRes-I Monocular [50], HiRes-II Monocular [50].
2.2 Attenuation lengths of UHECR particles. The thick solid lines
shows attenuation lengths for UHE protons, the thin solid lines
are for UHE photons and the dotted line is for UHE iron nuclei.
2.3 Expected energy spectra of UHE protons [13] [14]. The left figure shows the expected spectra from a single source of several
different red shift(z = 0.004 ∼ 1.0). The right figure shows expected energy spectra assuming uniform source distribution with
with different source evolution models. . . . . . . . . . . . . . .
2.4 UHECR spectrum to be expected from a two component model,
where UHECRs consist of protons and iron nuclei and they areaccelerated with a statistical process, with assumptions that, theinjection power law index is γg = 2.0 and the maximum energy
is Emax = 4Z × 1018 eV. The data plot of energy spectrum ismeasured by Auger [15]. . . . . . . . . . . . . . . . . . . . . . .
2.5 The Hillas plot, a relation between magnetic field strengths andscales of astronomical objects. The solid and dashed lines show
the maximum energies by statistical accelerations estimated by(2.17) [59]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 A schematic views of an extensive air shower. . . . . . . . . . .
2.7 Longitudinal developments of protons and irons for a EAS simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 The lateral distribution of electron number density in air shower
whose primary is proton with energy 1019 eV at the shower maximum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 The schematic view of stereoscopic observations. . . . . . . . .
2.10 The relative spectrum of air fluorescence light measured by FLASH[92]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 The parameters for (2.43). . . . . . . . . . . . . . . . . . . . . .
xi

7

11

12

13

14
19
20

21
23
25
27

xii

LIST OF FIGURES
2.12 UHECR spectra measured by Yakutsk, AGASA, HiRes and Auger[35] [44] [50] [51]. . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.13 The averaged Xmax for Stereo Fly’s Eys (left) and HiRes/MIA
and HiRes (right) compared with predictions for primary protons
and irons with several hadron interaction models after full Monte
Carlo detector simulations [38] [37]. . . . . . . . . . . . . . . . .

31

2.14 Preliminary results of the averaged Xmax measured by the Telescope Array experiment compared with the prediction rails for
protons and irons using three types of hadron interaction models: QGSJet-I (a solid line) QGSJet-II (a dash-doted line) andSIBYLL (a dotted line) [39]. . . . . . . . . . . . . . . . . . . . .

32

2.15 Auger measured hXmax i compared with air shower simulations
using different hadronic interaction models[40]. . . . . . . . . .

32

2.16 Distribution of Xmax observed by the Pierre Auger Observatory[41]. The values of the energy limits and the number of events
selected are indicated for each panel. . . . . . . . . . . . . . . .

33µ
2.17 Averaged Xmax
values as a function of the energy measured byAuger surface detectors [42]. The number of real data eventsin each energy bin is indicated. The predictions for primary
protons and irons following different hadronic models are shownas well. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.18 Arrival directions of cosmic rays with energies above 4 × 1019 eV
observed by AGASA. Red squares and green circles represent
cosmic rays with energy of > 1020 eV, and (4 − 10) × 1019 eV,
respectively. Shaded
circles indicate event cluster within 2.5◦ .
hm◦
At 10 29 , 57 , three 4 × 1019 cosmic rays are observed againtexpected 0.06 events. [46] . . . . . . . . . . . . . . . . . . . . .
2.19 Aitoff projection o the celestial sphere in galactic coordinateswith circles of radius 3.1◦ centered at the arrival directions of the
27 cosmic rays with highest energy detected by the Pierre Auger
Observatory [29]. The position of the 472 AGN(318 in the fieldof view of the Observatory) with the redshift z ≤ 0.018 (D < 75Mpc) from the 12th edition of the catalog of quasars and active
galactic nuclei by Véron-Cetty and Véron (VCV catalog) [62] areindicated by red asterisks. The solid line represents the borderof the field of view (zenith angle smaller than 60◦ ). Darker color
indicates larger relative exposure. Each colored band has equal
integrated exposure. The dashed line is the supergalactic plane.
Centaurus A, one of our closet AGN, is marked in white. . . . .

36

36

LIST OF FIGURES

xiii

2.20 The 69 arrival directions with energy E ≤ 55 EeV detected by
the Pierre Auger Observatory up to 31 December 2009 are plotted as black dot in an Aitoff-Hammer projection of the sky ingalactic coordinates [30]. The solid line represents the field ofview of the Southern Observatory for zenith angles smaller than60◦ . Blue circles of radius 3.1◦ are centered at the positions of
the 318 AGNs in the VCV catalog [62] that lie within 75 Mpc
and that are within the field of view of the Observatory. Darker
blue indicates larger relative exposure. The exposure-weighted
fraction of the sky covered by the blue circles is 21%. . . . . . .
37
2.21 The ratio between total number of UHECRs and UHECRs direction correlated with AGN observed by Auger. Pdata = N correlated /N total[30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.22 Hammer projection of the UHECRs with E > 57 EeV observedby TA and nearby AGNs in the Galactic coordinates. Correlating and non-correlating events are shown by filled red and empty
blue circles, respectively. AGNs are represented by black dots.
The dashed line shows the boundary of the TA exposure [31]. .
38
2.23 The number of the UHECRs with E > 57 EeV observed by TAcorrelating with AGNs from VCV catalog as a function of thetotal number of events. The expectation according to the originalAuger claim is represented by the blue line together with the 1and 2-sigma significance bands. The black dashed line shows the
expected number of random coincidences [31]. . . . . . . . . . .
38
3.1

3.2

3.3
3.4

3.5

3.6

3.7

The detector configuration of TA. The red square plots: surface
detector, the yellow pentagon-shaped plots: station of fluorescence detectors, the blue cross shape: the Central Laser Facility. 43
The BRM station (top-left), the florescence detectors of BRM
station (top-right) and the MD station and MD fluorescence detectors transported from HiRes-I and HiRes II experiment (down). 44
The newly developed telescopes and their designs at BRM andLR site. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
The variation of the reflectance of the LR mirror in June 2008.
Colors on the left figures correspond to the colors on the right figure. The vertical axis is the variation from installing. It depends
on the height of mirrors. . . . . . . . . . . . . . . . . . . . . . .
46
The spectral reflectance of the camera 06 of BRM station (left)
and a picture in mirror washing (right). Open circles are thereflectance before washing and filled circles are after washing .
47
Variation in the mirror reflectance at 360 nm of a typical lower
FD (FOV: 17.5-33 in elevation) of camera 04 at LR. The mirror
was washed after these measurements in July 2007, August 2009
and May 2010 [53]. . . . . . . . . . . . . . . . . . . . . . . . . .
47
TA camera (left) and PMT of R9508 attached the UV filter (right). 48

xiv

LIST OF FIGURES
3.8

The typical transmittance of the KURARAY paraglas on thefront of camera. . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
3.9 A typical transmittance of the UV filter in the front of phototubes. Data points are the medians for all the sampled filterswith the bars corresponding the on standard deviation. . . . . .
49
3.10 The typical quantum efficiency of photo-tubes. The data plotshows the median with one standard deviation error of all PMTs
measured by HAMAMATSU PHOTONICS. . . . . . . . . . . .
49
3.11 The typical non-uniformity map with 1 mm × 1 mm resolutionof the photo-cathode of our photo-tube. It is normalized withthe bins inside a circle with 36 mm diameter. The obtained
map show an asymmetry long the x axis caused by the dynode
structure of the PMT. . . . . . . . . . . . . . . . . . . . . . . .
50
3.12 The comparison of results between the HAMAMATSU data andthe data measured by XY-scanner. The left and right figure show
the result along X axis and Y axis, respectively. The definitionof the coordinate of x and y axis is the same as Fig. 3.11. Filled
circle are the HAMAMATSU data and open circles are XY’s
scanners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.13 The schematic view and photograph of XY-scanner. The covering area of each LED is 2.5 PMTs vertically and 16 PMTs
horizontally. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
3.14 Measurement set up of CRAYS [75] . . . . . . . . . . . . . . . .
53
3.15 The UV pulsed light source located in front and center of thestandard PMT, named YAP. . . . . . . . . . . . . . . . . . . .
53
3.16 The image of Xe flasher. . . . . . . . . . . . . . . . . . . . . . .
54
3.17 Block diagram of electronics and trigger system of the TA FD .
54
3.18 Photos of the trigger modules of TA fluorescence detector . . .
55
3.19 Block diagram of TA Track Finder module. . . . . . . . . . . .
55
3.20 Schematic diagram of the track finding process. . . . . . . . . .
55
3.21 Schematic diagram of the partial track search near the boundaryof a camera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.22 Block diagram of TA Central Trigger Distributor module. . . .
57
3.23 The time table of a single triggering cycle. . . . . . . . . . . . .
58
3.24 The ratio of triggered events before and after airplane veto installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.25 The histogram of typical dead time durations in log scale forsome observation terms on Apr/2008, Oct/2008, Apr/2009, Oct/2009. 59
3.26 The overview of LIDAR system. A left picture is LIDAR’s optical system (telescope, laser, etc), a right picture is a connection
block diagram of device of LIDAR. . . . . . . . . . . . . . . . .
61
3.27 The histogram of the extinction coefficient for Mie scattering on
the ground. The median value 0.034 km−1 is equivalent to theattenuation length of 29.411 km. . . . . . . . . . . . . . . . . .
63

LIST OF FIGURES
3.28 The CLF system located at the center of TA (left) and the inside
picture of CLF (right). . . . . . . . . . . . . . . . . . . . . . . .
3.29 The image of LIDAR system installed at the CLF location (left)
and VAOD relationship measured by CLF and LIDAR (right).
3.30 The overview of IR camera (left). The right figure is the 12 photographs taken by each telescope directions of FD. The number
shows the analyzed cloud score on 4 horizontally categorized regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.31 The photo of CCD fish-eye at LR station and picture taken at
CLF, BRM and LR location. The yellow region shows the FOVof each FD, the green region shows the cover of CLF-LIDAR for
online monitoring. . . . . . . . . . . . . . . . . . . . . . . . . .
3.32 Simulation results of time variance of BG level with the different
SSPs. Red square: SSP = 0.0 degree, Blue circle: SSP = 0.1
degree, Black triangle: SSP = 0.2 degree. . . . . . . . . . . . .
3.33 Fitting sample of BG level time variance (BRM00). Error barsof observed data show their statistical errors. Circle: observed,
Square: simulated. . . . . . . . . . . . . . . . . . . . . . . . . .
3.34 The photos of ELS installed at BRM site. . . . . . . . . . . . .
3.35 The schematic view of ELS system. . . . . . . . . . . . . . . . .
3.36 The event display of the first ELS beams observed by FD. . . .
3.37 The surface detector deployed TA site. . . . . . . . . . . . . . .
3.38 Inside of a scintillator box with scintillator plates, WLS fibers
and PMTs. A total 104 WLS fibers are laid on each layer tocollect and transmit scintillation light. . . . . . . . . . . . . . .
3.39 The electronics of TA SD. . . . . . . . . . . . . . . . . . . . . .
3.40 The Black Rock Mesa communication tower, one of three in thearray. There are there stands each with solar panels. Thosestands contain batteries, data acquisition PC and network instruments for long distance link. . . . . . . . . . . . . . . . . .
3.41 The long-distance links for all the facilities and three FD stations in the entire TA site. The open triangles represent thecommunication towers where the trigger decision electronics for
sub-arrays are installed. The lines that connect the towers andfacilities represent the links between antennas. The red lines areused for trigger decision. The dotted line shows the border ofthe entire surface detector array [82]. . . . . . . . . . . . . . . .
3.42 Trigger pattern taken at the TA surface array. If any three adjacent SDs have timing difference within 8 µsec the trigger will
be generated. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.43 Typical air shower event and recorded waveforms triggered acrossthe border of sub-array. The event display of observed air shower(left) and observed waveforms (right). . . . . . . . . . . . . . .

xv

63
64

65

66

67

67
68
68
69
69

70
70

71

72

72

73

xvi

LIST OF FIGURES
4.1

4.2

4.3
4.4

4.5

4.6
4.7

4.8

4.9

5.1
5.2
5.3

5.4

5.5

The ratio between calorimetric energies and primary energies
as a function of primary energies for primary protons and irons
using the QGSJet-II hadron interaction model. The calorimetricenergies are estimated from an integration of energy deposits
fitted by the Gaisser-Hillas function. . . . . . . . . . . . . . . .
77
The photon emission processes from extensive air showers. Not
only fluorescence light, but also direct Čerenkov light and scattered Čerenkov light. . . . . . . . . . . . . . . . . . . . . . . . .
78
The phase function of Mie scattering observed at the HiRes site,
Dugway [83]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
The number of fluorescence, direct Čerenkov, Rayleigh scatteredČerenkov and Mie scattered Čerenkov photons injected into telescope. The top figure is the shower geometry across the FOV,
the bottom figure is the geometry going toward FD. . . . . . .
81
The structure of FD implemented in TA FD simulation softwarewith the ray-tracing trajectory emitted from line assumed shower
axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
The response function of SDF. The time constant is 50 ns. . . .
84
The example of the database for the background observed by
BRM camera 06. The upper figure shows the mean for 214 “bundles”. The bundle consists of the sum of 16 bins of FADC countand is continuously recorded by SDF. The lower figure represents the dispersion for the same telescope. The black line is theaveraged value of the pedestal. The horizontal axis shows themeasured data (year/month). . . . . . . . . . . . . . . . . . . .
85
the photon density of fluorescence, direct Čerenkov, Rayleighand Mie scattered Čerenkov photons as a function of slant depth.
The black line represents another result with perfectly agreement. 86
The two-dimensional histogram at the PMT camera by 10000
photons ray-tracing using our software(left) and another independently developed software (right). Our results is reasonableagreement with another result. . . . . . . . . . . . . . . . . . .
86
The typical waveforms recorded by FD. . . . . . . . . . . . . .
87
The schematic diagram of the weighted triangle filter. . . . . .
88
The distribution of significance calculated the weighted triangle
filter. The left figure is the distribution without air shower signal,
the right figure is one with air shower signal. . . . . . . . . . .
90
The shower track (left) and the distribution of separate angle β(right). While the data from air shower are concentrated at thesmaller separate angle, the noise data are not located around zero. 90
Shower track (left) and timing fitting to search for noise (right).
In the right figure, isolated PMT (-2.5◦ , 19 µs) is judged to noise
signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91

LIST OF FIGURESThe event display observed by FD comparing before(left) andafter(right) PMT selections. The noise PMTs are removed by
the PMT selection. . . . . . . . . . . . . . . . . . . . . . . . .
5.7 The total directional characteristic of all PMTs in camera00 at
BRM (top) and of each PMTs located center, edge and corner.
The direction is the relative angle from the line of sight of thetelescope. The color map indicates the sensitivity calculated by
Ray-Trace simulation. . . . . . . . . . . . . . . . . . . . . . . .
5.8 Stereo geometry reconstruction. The shower axis is determinedby intersecting two SDPs. . . . . . . . . . . . . . . . . . . . . .
5.9 Geometry reconstruction in monocular mode . . . . . . . . . .
5.10 The shower signals injected from longitudinal development curvesof IMC fitting result and an observed air shower signal. The plotis the observed data, the red show the contribution of fluorescence light, the blue indicates of the direct Čerenkov light, thepurple and green shows the scattered Čerenkov light of Rayleighand Mie process, respectively. . . . . . . . . . . . . . . . . . . .

xvii

5.6

6.1

6.2

6.3
6.4
6.5
6.6

6.7

6.8
6.9

93

95
96
96

99

Core location distribution of Monte Carlo showers. (0, 0) shows
the center of the distribution corresponding to the location of
CLF. The vertical axis, Y-axis, is the direction from south tonorth, the horizontal axis, X-axis, is from east to west. The
yellow triangles indicate the FD station locations. . . . . . . . . 102
Averaged Xmax of protons and irons generated by CORSIKA
QGSJet-II and SIBYLL model without detector simulation. The
solid line shows the QGSJet-II, the dashed line shows the SIBYLL,
the red line is the result of protons, the blue line is the result ofirons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
The open angle distribution comparing between thrown arrival
directions and reconstructed ones. . . . . . . . . . . . . . . . . 104
The resolutions of the impact parameter estimation. It is a comparison between simulated and reconstructed values. . . . . . . 105
The angle resolution on SDP compared between simulated andreconstructed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
The resolution of Xmax including protons of different energies
under the simulation condition of section 6.1.1(left). The energy
dependence for the Xmax resolutions (right). . . . . . . . . . . . 106
The energy resolution including protons of different energies under the simulation condition of section 6.1.1(left). The energy
dependence for the energy resolutions (right). . . . . . . . . . . 106
The energy systematics are fitted by a linear function. Plots
indicate the means and error bars indicate the errors of the mean.107
The corrected energy resolution reconstructed by the monocularmode as a function of energy. The systematic bias was removed. 107

xviii

LIST OF FIGURES

6.10 The weighted histogram of simulated and reconstructed energy
estimated from protons of QGSJET-II model. . . . . . . . . .
6.11 The left figure is an aperture in BRM and LR only monocularmode. The iron and proton simulated results are shown. The
right plot shows the BRM and LR combined aperture comparing
with BRM and LR monocular aperture assumed pure proton
primary. The bottom plot shows the comparison of combined
apertures estimated by protons and irons. . . . . . . . . . . . .
6.12 Longitudinal development curves simulated for primary protons
and irons with the energy of 1018 eV. The red curves show longitudinal developments of protons, the blue curves are of irons.
6.13 Showers which can not be observed by FD caused by limited afield of view. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.14 Averaged values of simulated and reconstructed Xmax under only
standard cuts. Reconstructed averaged Xmax has large biases
caused by limited fields of view. The red line and blue dashedline indicate averaged Xmax with acceptance biases for primary
protons and irons, respectively. The pink dash-dotted line andsky-blue two-dotted line indicates thrown averaged Xmax for primary protons and irons, respectively. . . . . . . . . . . . . . . .
6.15 Averaged Xmax as a function of Xstart and Xend in order to determine the optimum range for Xstart and Xend . The red andblue plots indicate results for primary protons and irons, respectively. The pink plots indicate results for a mixed composition
which consists of 50% protons and 50% irons. . . . . . . . . . .
6.16 Simulated and reconstructed of averaged Xmax under FVC. Reconstructed averaged Xmax is much close to thrown one. Theselines are the same definitions shown in Fig. 6.14. . . . . . . . .
6.17 Averaged Xmax with acceptance biases for primary protons andirons with QGSJet-II and SIBYLL model under FVC. The solidlines indicate results using QGSJet-II model. The dashed lines
indicate results using SIBYLL models. The red and blue color
indicate primary protons and irons, respectively. . . . . . . . .
7.1

7.2

7.3

The schematic view of calculation of BRM and LR live time.
There are 3 types of live time: stereo (blue), BRM monocular(orange), LR monocular (green). . . . . . . . . . . . . . . . . .
The three types of live times with the WEAT code cut. These
broken lines indicate the total live time durations in the stereo(blue), the BRM station (orange) and the LR station (green).
The growth rates of live times vary with the seasons. . . . . . .
Number spectra under the standard cuts (a) and under the FVC(b). There are three types of reconstructed energy histogramsfor the BRM station (red), the LR station (blue) and combined
them (green). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

110

111
112

112

113

114

115

118

118

120

LIST OF FIGURES
7.4

xix

Pull plots of energies (a) and Xmax (b). The peak energy ofreconstructed EASs including pull plots is 1018.6 eV. . . . . . .

122

Scatter plot of reconstructed energy and Xmax applied the fiducial volume cut in BRM and LR monocular analysis. . . . . . .

123

The measured and expected of averaged Xmax in the monocularanalyses at the BRM station (a) and the LR stations (b) under
the fiducial volume cuts. The pink and sky blue lines indicatesthe averaged Xmax of thrown MC which are estimated only to
use CORSIKA simulations. The red and blue lines indicates theaveraged Xmax which are calculated in our MC simulations withacceptance biases of limited FOV of FDs. The MC lines are
estimated using the QGSJet-II model as a hadron interaction
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

124

Scatter plots of energies and Xmax reconstructed at both the
BRM and LR stations under the fiducial volume cuts. . . . . .

125

The averaged Xmax as a combination of both BRM and LR reconstructed events under the fiducial volume cuts. The pink andsky blue lines indicates the averaged Xmax of thrown MC estimated by only CORSIKA shower generations. The red and bluelines indicates the averaged Xmax with the acceptance bias ofeach FD station. The MC lines are estimated using the QGSJetII model as a hadron interaction model. . . . . . . . . . . . . .

126

The comparison with data and MC line estimated from QGSJetII model and SIBYLL model under the fiducial volume cuts. The
number symbols indicates the number of EASs in each bin. . .

127

7.10 Xmax distribution in several energy ranges compared with the
expected distribution estimated from MC simulation for primary
protons (red), irons (blue) or mixed compositions (pink) under
the fiducial volume cuts. Three types of the vertical axis indicate
the linear scale, the logarithmic scale and its ratio between data
and MC simulations. . . . . . . . . . . . . . . . . . . . . . . . .

128

7.11 The Xmax distribution of the observed data and MC simulated byprotons and irons with 1018.4 eV ≤ E < 1018.6 eV under the fiducial volume cuts, which is the same data shown in Fig. 7.10(e).

129

7.5
7.6

7.7
7.8

7.9

7.12 The probabilities estimated by KS test using several compositions of QGSJet-II and SIBYLL. Red: proton, Blue: iron, Pink:
mixed composition assuming 50% proton and 50% iron primaries.130
7.13 The proton fraction and the averaged < ln A > measured by the
BRM and the LR stations under the fiducial volume cuts. . . .

131

xx

LIST OF FIGURES
7.14 The measured and expected of averaged Xmax with only the standard cuts. The pink and sky blue lines indicates the averaged
Xmax of thrown MC estimated by only CORSIKA shower generations. The red and blue lines indicates the averaged Xmax
with the acceptance bias of each FD station. The MC lines are
estimated using the QGSJet-II model as the hadron interaction
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

132

7.15 Energy Spectra. In the right figure, the size of binning is changed
from dlog E = 0.1 step to dlog E = 0.2. . . . . . . . . . . . . .

134

7.16 The proton fraction measured by HiRes/MIA experiment [84].

134

7.17 TA combined spectra assuming several compositions: pure proton, HiRes/MIA composition and measurement result in TA
monocular mode. . . . . . . . . . . . . . . . . . . . . . . . . . .

135

7.18 Energy spectra in the TA measurement. The blue plots show
the spectrum analyzing data collected at the BRM and the LR
stations, the open squares show the spectrum measured at the
Middle Drum station [71], the pink triangles indicate the spectrum measured by TA SD with 27% scaled as the same energies
with TA FD energies [72] . . . . . . . . . . . . . . . . . . . . .

136

7.19 The fluorescence yield comparisons between several measurements with US standard atmosphere [60] [61] [92] [93] [94]. . . .

137

8.1

The measured averaged Xmax fitted by two types of line functions
using the least square method. . . . . . . . . . . . . . . . . . .

142

8.2

The averaged Xmax for Stereo Fly’s Eys (a) and HiRes/MIA and
HiRes (b) [38] [37]. Auger measured hXmax i compared with air
shower simulations using different hadronic interaction models[40]. They are the same figures shown in Fig. 2.13and Fig. 2.15. 143

8.3

Energy spectra of several composition observed by several experiments around the knee region. The dotted lines indicate theexpected flux assuming a rigidity dependent acceleration modelusing the results of the Tibet group [97]. . . . . . . . . . . . . .

144

The measured energy spectrum fitted by three types of powerlaw function using the method of least squares. . . . . . . . . .

145

The energy spectra compared with several measurements [9] [11][12] [44] [50] [71] [72]. . . . . . . . . . . . . . . . . . . . . . . . .

146

The compariton of fitted values measured by AGASA, Yakutsk,
HiRes and TA(SD) reported at UHECR2012 Symposium and by
BRM and LR monocular mode [98]. . . . . . . . . . . . . . . .

147

8.4
8.5
8.6

LIST OF FIGURES

xxi

Propagated spectra, f (E) · E 3 , for pure proton extra-galactic
cosmic ray sources (left). The injection spectral index is E −2.6
for the HiRes data. Two different propagated spectra and thecorresponding inferred galactic cosmic ray component are shown,
for an injection spectrum either with or without a low energy
cut [99]. UHECR spectra to be expected from a two component
model (right) [15], which is the same figure shown in Fig. 2.4. . 147
8.8 The scaled energy spectra measured by AGASA, Yakutsk, HiRes
and TA(SD) reported at UHECR2012 Symposium [98]. The TA
SD, HiRes and Auger are in agreement well within the systematic
uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.9 The schematic view of the TALE experiment. The yellow circle
shows newly constructed dense SDs, the red circle shows the SDsof TA. The green hexagon indicates the TALE FD at the same
location of TA MD. . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.10 The comparison of effective area of UHECR observations: AGASA,
Auger, TA SD and TA-2. . . . . . . . . . . . . . . . . . . . . . 151
8.11 Overview of JEM-EUSO project [101]. . . . . . . . . . . . . . . 151
8.7

The observed UHECRs : E = 19.77 eV, Xmax = 796 g/cm2 . . 155
The observed UHECRs : E = 19.75 eV, Xmax = 758 g/cm2 . . 155
The observed UHECRs : E = 19.67 eV, Xmax = 743 g/cm2 . . 156
The distribution of Energy between data and MC simulation
under the standard cut. At the highest region, there is slightly
difference caused by the assumption of spectrum index, E −3.1 . . 157
A.5 The distribution of the track length between data and MC simulation under the standard cut. . . . . . . . . . . . . . . . . . . 157
A.6 The distribution of the number of selected PMTs between data
and MC simulation under standard cut. The result indicates thedifference of physics model of the lateral distribution of EAS.
The observed lateral distribution is wider than one expected from
NKG function used in our software. . . . . . . . . . . . . . . . . 158
A.7 The distribution of the number of photo-electrons divided bytrack length between data and MC simulation under the standard cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
A.8 The distribution of the number of selected PMTs divided by timeextent between data and MC simulation under the standard cut. 159
A.9 The distribution of the impact parameter between data and MC
simulation applied under the standard cut. At the highest region, there is slightly difference caused by the assumption ofspectrum index, E −3.1 . . . . . . . . . . . . . . . . . . . . . . . . 159
A.10 The distribution of the angle on SDP between data and MC
simulation applied under the standard cut. . . . . . . . . . . . 160
A.11 The distribution of core location of West-East direction between
data and MC under the standard cut. . . . . . . . . . . . . . . 160
A.1
A.2
A.3
A.4

xxii

LIST OF FIGURES

A.12 The distribution of core location of South-North direction between data and MC simulation under the standard cut. . . . .

161

A.13 The distribution of zenith angle between data and MC simulation under the standard cut. . . . . . . . . . . . . . . . . . . . .

161

A.14 The distribution of azimuth angle between data and MC simulation under the standard cut. . . . . . . . . . . . . . . . . . . .

162

A.15 The distribution of Xstart between data and MC simulation under the standard cut. . . . . . . . . . . . . . . . . . . . . . . . .

162

A.16 The distribution of Xend between data and MC simulation under
the standard cut. . . . . . . . . . . . . . . . . . . . . . . . . . .

163

A.17 The distribution of Xmax between data and MC simulation under
the standard cut. Since the discrepancy of difference between
protons and irons is large, Xmax is the most sensitive parameterto evaluate the mass composition of EASs. . . . . . . . . . . . .

163

A.18 The distribution of energy between data and MC simulation
under the fiducial volume cut. At the highest region, there isslightly difference caused by the assumption of spectrum index,
E −3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

164

A.19 The distribution of the track length between data and MC simulation under the fiducial volume cut. . . . . . . . . . . . . . .

164

A.20 The distribution of the number of selected PMTs between data
and MC simulation under the fiducial volume cut. The result
indicates the difference of physics model of the lateral distribution of EAS. The observed lateral distribution is wider than one
expected from NKG function used in our software. . . . . . . .

165

A.21 The distribution of the number of photo-electrons divided bytrack length between data and MC simulation under the fiducial
volume cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

165

A.22 The distribution of the number of selected PMTs divided bytime extent between data and MC simulation under the fiducial
volume cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

166

A.23 The distribution of the impact parameters between data and MC
simulation under the fiducial volume cut. At the highest region,
there is slightly difference caused by the assumption of spectrum
index, E −3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

166

A.24 The distribution of the angle on SDP between data and MC
simulation under the fiducial volume cut. The angle of Ψ > 120
are excluded because of Čerenkov contaminations. . . . . . . .

167

A.25 The distribution of the core location of West-East direction between data and MC simulation under the fiducial volume cut. .

167

A.26 The distribution of the core location of South-North direction
between data and MC simulation under the fiducial volume cut. 168

LIST OF FIGURES
A.27 The distribution of the zenith angle between data and MC simulation under the fiducial volume cut. The inclined shower isdisappeared under the fiducial volume cut to avoid the acceptance bias of Xmax . . . . . . . . . . . . . . . . . . . . . . . . . .
A.28 The distribution of the azimuth angle between data and MC
simulation under the fiducial volume cut. . . . . . . . . . . . . .
A.29 The distribution of Xstart between data and MC simulation under the fiducial volume cut. We applied the selection rule as 150
g/cm2 < Xstart < 700 g/cm2 . . . . . . . . . . . . . . . . . . . .
A.30 The distribution of Xend between data and MC simulation under
the fiducial volume cut. We applied the selection rule as 900
g/cm2 < Xend . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.31 The distribution of Xmax between data and MC simulation under the fiducial volume cut. Since the discrepancy of difference
between protons and irons is large, Xmax is the most sensitive
parameter to evaluate the mass composition of EASs. . . . . .

xxiii

168
169

169

170

170

List of Tables
2.1

Efficiencies of fluorescence emissions relative intensity with wavelengths of 300 ∼ 400 nm under a collisionless condition [60]. . .

24

4.1
4.2

Parameters of the U.S. standard atmosphere . . . . . . . . . . .
Parameters of air shower simulation using CORSIKA. . . . . .

76
76

5.1
5.2

The criteria for selecting the candidate PMTs in the 4th selection. 92
The criteria for judgement by the linear fitting in the 4th PMT
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93

7.1
7.2

The number of reconstructed EASs under both selection rules.
The total systematic uncertainty of energy and Xmax . . . . . .

xxv

121
139

Abbreviation
AGASA Akeno Giant Air Shower Array
Auger Pierre Auger Observatory
BRM Black Rock Mesa (name of FD station)
CCD Charge Coupled Device
C.L. Confidence Level
CLF Central Laser Facility (a center of TA site)
CMBR Cosmic Microwave Background Radiation
CORSIKA COsmic Ray SImulations for KAscade
CRAYS Calibration using RAYleigh Scattering
CTD Central Trigger Distributor
EAS Extensive Air Shower
ELS Electron Light Source
FD Fluorescence Detector
FVC Fiducial Volume Cut
GH function Gaisser-Hillas function
GPS Global Positioning System
GZK cutoff Greisen, Zatsepin and Kuzmin
HiRes High Resolution Fly’s Eye
IMC Inverse Monte Carlo (reconstruction method)
ICRC International Cosmic Ray Conference
ISS International Space Stationxxvii

xxviii

ABBREVIATION

JEM-EUSO Extreme Universe Space Observatory on board Japanese Experiment Module

KS test Kolmogorov-Smirnov test
LIDAR LIght Detection And Ranging
LR Long Ridge (name of FD station)
MC Monte CarloMD Middle Drum (name of FD station)
MPD Muon Production Depth
NKG function Nakamura-Kamata-Greisen function
NS Neutron Star
PMT Photo-Multiplier TubePPS Pulse Per Second
SD Surface Detector
SDP Shower Detector Plane
SDF Signal Digitizer and Finder
SN SuperNova
SSP Spot Size Parameter
TA Telescope Array
TALE Telescope Array Low energy Extension
TF Track Finder
UHE Ultra-High Energy
UHECR Ultra-High Energy Cosmic Ray
VAOD Vertical Aerosol Optical Depth
VCV catalog The 12th edition of the catalog of quasars and active galactic
nuclei by Véron-Cetty and Véron

VEM Vertical Equivalent Muon

Chapter 1

Introduction
In 1912, V.F.Hess discovered cosmic rays which are elementary particles andnuclei with relativistic kinetic energies in the universe. The energy spectrumof cosmic rays are measured in energies from 108 eV to beyond 1020 eV inthis recent one hundred. Since the power-law index is about -3 arriving of
ultra-high energy cosmic rays (UHECRs) exceeding 1019.5 eV on the ground arevery rare events, and the event rate is about once per year within an effective
area of 100 km2 . We believe that UHECRs are the most energetic particles
in the universe and that their origins are related with energetic astronomical
phenomena or other exotic phenomena, for example decays or annihilationsof super heavy relic particles created at early phase of the development of
the universe. Therefore, research on origins of UHECRs and revealing theiracceleration mechanisms are one of the most exciting and important subjects
in the research field covering astrophysics, cosmology and elementary particle
physics.
In order to measure the energy spectrum, the mass composition and theanisotropy of UHECRs, Telescope Array (TA) experiment has been constructedin the desert in the Utah State of U.S.A., with the collaboration of scientists
from Japan, US, Korea, Russia and Belgium and it has been started with fulloperations in 2008. The TA consists of an array of 507 Surface Detectors (SDs)
deployed 1.2 km separation covering with the effective area above 700 km2 andof three stations of Fluorescence Detectors (FDs) looking inward over the array.
The one station located north is moved from HiRes-I and II experiment, andthe other two stations located south-east and south-west are newly constructed
for TA experiment. In total we have 38 fluorescence telescopes for FDs. TA
experiment observes UHECRs using two air shower detection techniques independently and simultaneously. In this paper, I analyze data collected by the
new developed fluorescence detectors located two stations.
When a cosmic ray enters Earth’s atmosphere, a huge number of secondary
particles are generated via hadronic and electromagnetic interactions with atmospheric nuclei, and this swarm of secondary particles is called Extensive AirShower(EAS). The SD array detects EAS’s particle densities and arrival times
1

2

CHAPTER 1. INTRODUCTION

on SDs. On the other hand the FD telescopes detect air fluorescence photons
emitted by atmospheric molecules excited by EAS particles. A simulationindependent determination of primary energies provided by FD observations
gives an advantage on this technique, because FDs measure the energy deposit
to the atmosphere through energy losses by electro-magnetic particles which
are dominant in EAS and less dependent of hadron interaction models.
In this thesis, I report the development of a set of data analysis code for
FDs in monocular mode including a new method for the shower profile determination, called “Inverse Monte Carlo (IMC)”, and I evaluate the performanceof this monocular analysis procedure and aperture of FDs through analyzing
Monte Carlo (MC) simulated events. In order to measure the mass compositionof UHECRs, the maximum depth (Xmax ) of EAS’s longitudinal development
is important parameter, because it depends on primary particle types. Since
the FDs have a limited FOV in elevation ranging from about 3◦ to 33◦ , thelimitation makes on observational bias in the distribution of Xmax from theobserved showers. However, we can establish un-biased Xmax distribution applying a sophisticated event selection, called fiducial volume cut[67], and theresulted un-biased Xmax distribution is useful for comparing with MC. In order
to apply this selection in my analysis, I evaluated selection conditions and confirmed the efficiency with MC. Moreover, my analysis procedure was confirmedby cross-checking with the other independently developed software.
The data collected by 2 station of TA FD from January 2008 to September
2011 in monocular mode are analyzed by the completed software, and finallyremained more than twenty thousand EASs. For the purpose of checking a
reproduction in our MC simulation with observed data, I confirmed that several
parameters, such as an impact parameter and core position distribution, arereasonable agreement between data and MC simulation. After that, I evaluate
the mass composition through the averaged Xmax of UHECRs compared withMC predictions. Moreover I calculated the averaged Xmax measurement applied
without fiducial volume cut in both data and MC due to study the dependenceof the fiducial volume cut in the Xmax technique.
As the result, the observed Xmax indicates there is a transition of the dominated components from heavy to light nuclei from 1017.5 eV to 1018.5 eV, andprotons are dominant above 1018.5 eV. The interpretations with and without
fiducial volume cut are consistent, because the MC predicted lines without fiducial volume cut are shifted as same as measured data. Thus, we conclude thatthe estimated mass composition result and its energy dependence is independent of the fiducial volume cut. Moreover, the obtained energy spectrum isgood agreement with the result of TA surface detectors.
In this thesis, Chapter 2 is an review of UHECR physics, detection techniques and latest results. In Chapter 3, details of the TA experiment are
explained. The detailed MC simulations and reconstruction method used here
are described in Chapter 4 and 5, respectively. Systematic errors, apertures andexpected Xmax distributions are evaluated with reconstructing and analyzing
MC events, and the results are shown in Chapter 6. The result for the data of3
3.7 year observations is shown in Chapter 7. Chapter 8 and 9 are discussion
and conclusions.

Chapter 2

Ultra-High Energy Cosmic
Rays
2.1

Overview of UHECR Physics

In a research field of ultra-high energy cosmic rays (UHECRs) physics, there arethree important measurements : the energy spectrum, the mass composition
and the anisotropy of UHECRs. We shortly discuss the relation between energy
spectrum and mass composition because fluorescence technique as focused inthis thesis has the advantage to measure them. The observed energy spectrum
almost follows a simple power-law. However it has a structure with several
slopes of power-law. When mass composition of cosmic rays are proton dominant at ultra-high energy, protons interact with CMBR photons though pion
productions above 1020 eV and pair creations above 1018.5 eV, which is causedby the structure. If so, the transition from heavy to light component should
be observed at less than 1018.5 eV. Based on the magnetic field strength in our
local galaxy, it indicates that the origin moves from galactic to extra-galactic.
Therefore, we have to observe both mass composition and energy spectrum inorder to discuss the origin of cosmic rays.
In Sec. 2.2 we discuss the introduction of cosmic ray physics and acceleration
mechanism with energies less than 1015 eV. The origin models of UHECRs areshown in Sec. 2.3. We induct methods and techniques to observe UHECRs byextensive air showers in Sec. 2.4. In Sec. 2.5, we discuss the latest results andmysteries of UHECRs.

2.2

Cosmic Rays

Cosmic rays are high energy particles traveling in the universe and large amountof cosmic rays are continuously entering the Earth’s atmosphere. In 1912
V.F.Hess carried out balloon flight measurements as high as 5 km above theground to measure levels of ionizing radiation [1]. This was a clear evidenceof the fact that sources of the ionizing radiations must be located above the56

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

atmosphere. Before this discovery, people believed that all the high energy
particles are emitted from radioactive isotopes in the air, on and under the
ground. Ironizing radiations from the universe are called “Cosmic Rays”, due
to the achievement, V.F.Hess were award the Novel Prize in 1936.
In 1930, the East-West effect, flux asymmetry, because of the terrestrial
magnetic field was found so then it was clear that the major component ofcosmic rays are not neutral particles, but charged particles. In 1932, the electron and positron pair creation was discovered in the cloud chamber. Strong
penetrating particles called muon meson were discovered in 1937. In 1941, witha balloon measurement, cosmic rays consist of several nuclei groups, such as
proton, boron, carbon, nitrogen and iron. Recent measurements show cosmic
ray consists of 90% of proton, 9% of α particles and heavy nuclei.

2.2.1

Energy Spectrum

Around 1945, scientists have started to measure the energy spectrum of cosmic
rays. The observed energy spectrum in the range from 108 eV to 1021 eV isshown in Fig. 2.1. In the energy range above 101 1 eV, cosmic rays flux is
not affected by the solar activity, the spectrum follows the power-law structureof dN/dE ∝ E −γ . The index value is γ ∼ 2.7 up to 1015 eV,and it changedγ ∼ 3.0 above 1015 eV. Again the spectrum becomes hardened γ ∼ 2.7 above
1019 eV. The two broken on the spectrum are, in order of increasing energy,
called “knee” and “ankle”. At the highest energy around 1020 eV, cosmic ray
flux reaches quite low, once per year on 100 km2 area, then a huge effective area
and a large exposure are essential to measure cosmic rays with such energies.
One idea to explain the spectral break at the knee is based on the differenceof acceleration mechanisms below and above the knee energy. There is anothertheory for the knee to be explained by the cosmic ray’s leakage from the galaxy.
For cosmic ray protons of 1015 eV the Larmor radius is 0.3 pc in the galacticmagnetic field of 3 µG. This is smaller than the galactic disk thickness, but
above this energy the confinement in the galaxy by the diffusion dynamics
becomes less efficient to confine cosmic rays.
There are two models for cosmic rays at the ankle energy. In one model
the ankle structure reflects the transition from galactic to extragalactic origins
with increasing energy. Since the Larmor radius is larger than the radius of
the galaxy above the ankle energy, the confinement with magnetic field is notefficient. If this model is correct, we expect to observe that anisotropy of arrival
directions and the chemical composition change at ankle energy.
On the other hand, in the other model the ankle is due to cosmic ray
flux decreasing by energy loss. The interaction of pair creations p γ → p e+ e−
between cosmic rays protons and 3 K Cosmic Microwave Background Radiation(CMBR) is opened at around the ankle energy. The origin should have alreadychanged the outer-galaxy before the ankle region. Thus, the mass composition
remains the proton across the ankle energy. In this case, this would give an
increasingly light composition associated with 1017.5 eV , called “2nd knee”.

2.2. COSMIC RAYS

7

Figure 2.1: Overview of the cosmic ray spectrum. Approximate energies of thetwo breaks commonly referred to as knee and the ankle are indicated by arrows.
Data are from LEAP [7], Proton [8], AKENO [9], KASCADE [10],Auger surface
array [11], Auger hybrid [12], AGASA [44], HiRes-I Monocular [50], HiRes-II
Monocular [50].

8

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Therefore, to conclude the ankle model, it is important to observe the masscomposition measurement at these energy.

2.2.2

Acceleration Mechanism

The studies of cosmic-ray acceleration mechanisms are not understood very
well. In general, the acceleration mechanism should produce cosmic ray flux
following the power-law spectrum, described before.
Fermi Acceleration
The Fermi acceleration mechanism was proposed by E.Fermi in 1949, which is amodel of the statistical acceleration of charged particles which gain large kinetic
energies repeatedly interacting with molecular clouds. In this model, although
directions of the interaction is statistical random, the averaged energy gain per
encounter is positive. This value is proportional to its energy, ∆E = αE. Since
α is proportional to square of the velocity of the cloud, this acceleration are
called ”2nd Fermi acceleration”.
Cosmic rays are also accelerated by a plasma termination shock. Basedon a geometry of the shock, the plasma acceleration is superior to 2nd Fermi
acceleration. In this case, α is proportional to a velocity of the shock wave
considering a structure of the acceleration region, called 1st Fermi acceleration.
Then, if ∆E = αE per encounter, after n encounters,
En = E0 (1 + α)n(2.1)

where E0 is the energy at injection of the acceleration. The number of encounters n needed to reach an energy E,n=ln (E/E0 ).
ln (1 + α)

(2.2)

If the probability of escape from the acceleration region is Pesc per encounter,then the probability of remaining in the acceleration region after n is (1−Pesc )n .
Thus, the proportion of particles accelerated to energies greater than E is
N (≥ E) ∝

∞
X

m=n

(1 − Pesc )m =(1 − Pesc )n
,
Pesc

(2.3)

with n given by (2.2). Substitution of (2.2) into (2.3) gives,N (≥ E) ∝with

1 E −γ,Pesc E0ln (1 − Pesc )−1
Pesc
γ=
≈
.
ln(1 + α)
α

(2.4)

(2.5)

Thus, the Fermi mechanism naturally leads to a desired power law spectrum.

2.2. COSMIC RAYS

9Supernova blast wave
Ejected materials from a supernova (SN) explosion spread out through theinterstellar medium driving a shock wave at which acceleration can occur. Here
we express the diffusion coefficient and its velocity in D and u, respectively,
as long as the characteristic length for diffusion in the plasma, D/u, is muchless than the radius of curvature of the shock, the plane shock approximation
can be used. The life time of the SN blast wave is estimated as the time fortaking the expanding shell to sweep out interstellar medium of its own mass.
For shell of 10 M⊙ , expanding at mean velocity of 5 × 108 cm/sec into theinterstellar medium with average density of 1 proton/cm3 , and then the life
time is TA ∼ 1000 yrs and the shell size reaches 5 pc.
The finite lifetime of SN blast wave as a strong shock also limits the maximum energy per particle that can be achieved with 1st order Fermi acceleration
mechanism. The acceleration rate is written as
dE
αE
=
,
dt
Tcycle(2.6)

with the characteristic time for a single back and forth acceleration cycle, Tcycle .
For the estimation of Emax with integrating (2.6), we need to know Tcycle .
Firstly, let’s consider the upstream region. The particle current with theconvection is given by
J = −D∆N + uN.
(2.7)
In the upstream region the fluid velocity u1 is negative relative to the shock
front, and there is no net current in equilibrium,dN= −u1 N.
dz

(2.8)

N (z) = ρcr exp (−zu1 /D1 ) ,

(2.9)

D1
Then in the upstream region

where ρcr is the number density of cosmic rays at the shock. The total number ofparticles per unit area in the upstream region is ρcr D1 /u1 . The particle crossing
rate per unit area on the shock plane is ρcr c/4. Thus the mean residence timeof a particle in the upstream region is(ρcr D1 /u1 ) (ρcr c/4)−1 = 4D1 / (u1 c) .

(2.10)The downstream region is somewhat more complicated to analyze because it isnecessary to average the residence time only over those particles that do notescape. The analysis is straightforward and is shown explicitly by Drury [16].
The mean residence time in downstream region is identical with that in the
upstream region, 4D2 / (c u2 ), where u2 is the fluid velocity in the downstream
region. Thus,
4 D1 D2
Tcycle =+.
(2.11)
c u1
u2

10

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Next, we need to estimate the diffusion coefficient. Lagage and Cesarsky argue
the the diffusion length of charged particles, λD , cannot be smaller than its
Larmor radius, rL [17]. The Larmor radius is given by
rL =

p
ZeB

(2.12)

where e is the elementary charge, Z is the charge of the particle, p is its total
momentum and B is the magnetic field strength. Then the minimum diffusion
coefficient Dmin is calculated from rL as
Dmin =

rL c
1 Ec
∼
.
3
3 Z eB(2.13)

Here, Tcycle ≥ 20E/ (3u1 ZeB) for a strong shock with u2 = u1 /4. Substituted
to D1 = D2 = Dmin , the maximum energy of the nucleus being accelerated,
Emax ,
3 u1
Emax ≤ZeB (u1 TA ) .
(2.14)
20 c
For SN which ejects 10M⊙ at 5 × 108 cm/sec during TA ∼ 1000 years, into ainterstellar medium with the density of one proton per cubic centimeter, andwith the galactic magnetic field of 3 µG, the maximum energy reaches
Emax ≤ Z × 3 × 1013 eV.

(2.15)

Therefore, cosmic rays can be accelerated by the SN blast shock up to only
1015 eV.

2.3

Ultra-High Energy Cosmic Rays

In the field of cosmic ray physics, one of the most interesting topics is ultrahigh energy cosmic rays (UHECRs). UHECRs are the most energetic particles,
above 1019 eV, in the universe. Here, I briefly describe and discuss theoreticalpredictions about propagations and origins of UHECRs, and also introduce
related unsolved problems about UHECR physics.

2.3.1

GZK Cutoff

In 1963, as soon as Cosmic Microwave Background Radiation (CMBR) was
discovered, Greisen、Zatsepin and Kuzmin pointed out that this relic photons
make the universe opaque for cosmic rays with sufficiently high energies [13][14]. Since UHECRs have large Lorentz factors, energies of CMBR photons(∼ 10−3 eV) are converted very high energies, 100 MeV, in the rest frame of
the cosmic rays. The interaction of proton at rest with CMBR of such highenergy usually excites the protons to nucleon resonance condition. Since the2.3. ULTRA-HIGH ENERGY COSMIC RAYS

11

Figure 2.2: Attenuation lengths of UHECR particles. The thick solid lines
shows attenuation lengths for UHE protons, the thin solid lines are for UHE
photons and the dotted line is for UHE iron nuclei.

resonance decays with emitting pion through the following process, the protonenergy decreased.
γ(∼ 150MeV) + p → ∆(1232) → p + π 0 , n + π +(2.16)The pair creation with CMBR photons (γ p → p e+ e− ) can also occur for
protons above 1018.5 eV
Fig. 2.2 shows attenuation lengths of UHECRs simulated by propagations ofseveral types of charged particles in CMBR. In this Figure, attenuation lengthof protons above 1020 eV is less than 50 Mpc. Thus, protons above 1020 eV
observed on the Earth must have their origin within 50 Mpc from the Earth.
UHE protons which are ejected at origins more than about 50 Mpc from the
Earth with primary energies of more than 1020 eV reduce their own energies
through the interactions with CMBR. So then, at the Earth these protons aredetected as more lower energy protons.
However, if there is a violation of relativity at ultra-high energies, the GZKmechanism is absent [27]. That’s why anyone could not confirm the validity of
the relativity at the energy range with Lorentz factor above γ ≥ 1011 .
Fig. 2.3 shows expected energy spectra using a several type of the source
model of cosmic rays. For example, if it is assumed that UHECR sources are
uniformly distributed on the universe, the energy spectrum must have the cutoff

12

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Figure 2.3: Expected energy spectra of UHE protons [13] [14]. The left figure
shows the expected spectra from a single source of several different red shift(z =0.004 ∼ 1.0). The right figure shows expected energy spectra assuming uniform
source distribution with with different source evolution models.

structure at about 4×1019 eV, called GZK cutoff. Therefore, detailed measurements of energy spectrum to reveal its structure give us the most important
hint for identifying origins of UHECRs.
If cosmic rays are not protons rather than heavier nuclei, another interaction, photo-disintegration process, should be considered during their propagations in CMBR field [15]. Heavy nuclei with energies more than 2 × 1019
eV loose 3-4 nucleons per 1 Mpc travel. Thus, if UHECRs consisted of heavy
nuclei, the origins for nuclei at high energy end is within 20 Mpc from the
Earth. With the same reason, if the origins of UHE nuclei existed uniformity
in the universe, the observed energy spectrum would have a sharp cutoff at a
certain energy. Fig. 2.4 shows the propagated spectrum with the assumptionof the two component model, which has the suppression structure above 1019.5
eV [15].

2.3.2

Origin of UHECRs

Origins of UHECRs are still unknown. There are two different types of proposedmodels for explanation of the existence of UHECRs. One type is called the“bottom-up model”, and the other is called “top-down model”.
Bottom-up Model
The bottom-up model describes that UHECRs originate from lower energy, andthey gain their energies with repeating acceleration processes, such as Fermi
accelerations. Then, finally their energies reach ultra-high energies of larger
than 1020 eV when they escape from the acceleration regions. The upper limit2.3. ULTRA-HIGH ENERGY COSMIC RAYS

13

Figure 2.4: UHECR spectrum to be expected from a two component model,
where UHECRs consist of protons and iron nuclei and they are accelerated witha statistical process, with assumptions that, the injection power law index isγg = 2.0 and the maximum energy is Emax = 4Z × 1018 eV. The data plot ofenergy spectrum is measured by Auger [15].

of accelerated energy Emax is expressed as,
Emax ≤ γeZBR,(2.17)

where γ is the Lorentz factor of a shock wave, Z is the atomic number of acosmic ray, B is the magnetic field on the acceleration region and R is the sizeof the region. Fig. 2.5 is the Hillas plot, which shows the relations between
strength of the magnetic field strength and the scale of astronomical objects
which have each maximum acceleration energy [59]. From Fig. 2.5, it is clearlyshown that most objects in our galaxy are not candidates of UHECR sources
expect for gamma-ray bursts and neutron stars. Source candidates located outside of our galaxy are active galactic nuclei, gamma-ray bursts, radio galaxies
and galactic clusters.
Here, I summarize discussions about possibilities as UHECR sources forseveral types of astronomical objects.
• Neutron stars : Since a typical neutron star has strong magnetic fields
with strength of more than 1013 G, iron nuclei could be accelerated up
to 1020 eV if they did not suffer any efficient energy loss processes [18].
However, If in the magnetic fields 1013 G, the energy loss via synchrotron
radiations is not negligible. In fact, cosmic rays cannot be accelerated
to ultra-high energy. The energy loss rate via synchrotron radiations
depends on magnetic field strength, so then depends on the distance fromthe neutron star surface. If acceleration regions are apart more than 109

14

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Magnetic Field Strength
12

10 G

Neutron Stars

6

10 G
LHC
TEVATRON
SppS

GRBs
20 e

10

V
at
β

at

1G

20 eV

10

White Dwarfs
AGNs
Sunspots

=

β

1/

=

30

1

12

10

0

eV
Radio Galaxy
SNRs

-6

10 G

Interplanetary space
Galactic Cluster
Galactic Halo

1km

6

1pc

10 km
1AU

1kpc

1Mpc 1Gpc

Size

Figure 2.5: The Hillas plot, a relation between magnetic field strengths andscales of astronomical objects. The solid and dashed lines show the maximum
energies by statistical accelerations estimated by (2.17) [59].

2.3. ULTRA-HIGH ENERGY COSMIC RAYS

15

cm from the surface, any nuclei can escape without suffering large energy
losses [19].
This model predicts most UHECR origins exist inside our galaxy. Moreover it also predicts particles accelerated by neutron stars consist largelyof heavy nuclei, so then the mass composition and anisotropy measurements are very important for confirmation of the model.
• Active galactic nuclei (AGN) : AGN is an astronomical system which
consists of a super heavy rotating black hole and accretion disk, andin the system gravitational potential energies are converted to kinetic
energies of matters, heat of the disk and magnetic field energies, andthen finally they are emitted as radiations and outflows of magnetizedplasma particles [20]. Changed particles are accelerated by the electricfields induced by rotating magnetic fields. The maximum accelerationenergy of AGN is limited at 1019 eV, because charged particles suffer
energy losses through the interactions with radiation fields [21].
• Radio lobes : Radio lobes are normally accompanied by AGN, and they
are emission regions of charged particles accelerated and excited by termination shocks of jets with intergalactic matter. The typical size of radio
lobes is 100 kpc [20]. In a radio lobe, the radio hot spot, which is emitting
radiations with higher radio intensity than other lobe region, is usuallyseen, and this hot spot region is expected to have a strong magnetic fields
enough to confine charged particles accelerated to ultra-high energies [22].
However, AGN with the hot spots are very rare and usually exist far fromthe earth. Moreover, it is found that the positions of hot spot AGN do
not agree with the observed UHECR arrival direction distribution. If weassumed that M87, which is 18.4 Mpc away, is a UHECR source, the arrival direction of UHECRs would have a clearly anisotropy concentrating
toward the object. The next nearest candidate NGC315, which is 100
Mpc away, is too far from the earth beyond GZK horizon for UHECRs
to reach us.
• Gamma-ray bursts (GRB) : The GRB are also promising candidates of
UHECR accelerators. The average rate of energy release rate as gammarays by GRBs is comparable to that by sources UHECRs with energies
above 1019 eV, 1044 ergs Mpc−3 yr−1 [23]. Since for highest energy UHECRs sources are required to exist within GZK horizon of about 50 Mpc,
and the rate of GRBs is 1 per 100 years in such volume, the arrival direction distribution would have a strong anisotropy for highest energy
UHECRs.
• Galactic clusters : The spatial size of the typical cluster is about 500 kpc,
and the typical magnetic field strength is estimated to be 0.1 µG. So thenthe maximum acceleration energy can reach 1020 eV from the relationof (2.17) [24]. However, propagating to the earth for a long distance,

16

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS
accelerated UHECRs suffers effective energy losses via GZK mechanism
because the distance from the earth is longer than any other candidates.

Top-down ModelIn contract to the bottom-up models, top-down models are associated with thenew physics beyond the standard model, for instance, the existence of superheavy relic particles or topological defects.
• Topological defects and annihilations of super heavy particles : In thesemodels, UHECR sources are hypothetical particles of topological defects
which are expected to be generated at beginning of the universe. Decays or annihilations of super heavy particles or high density topologicaldefects can induce cascades of UHE particles [25].
Topological defects are expected to decay to super heavy gauge bosons or
Higgs bosons. Succeeding hadron jet induced by these particles decay to
gamma-rays, electrons and neutrinos with only a few percent of nucleons.
When these contribution effects the spectrum beyond the GZK cutoff,a transition of mass composition is expected at GZK energy, 4 × 1019
eV because the UHE protons with this energies suffer effective ionization
losses. Thus, the topological defect scenario suggests that proton is thedominate component in energy region less than GZK energy and gammarays are dominant above this energy.
When the super heavy relic particles are rich abundance at galactic halo,
the mass composition is not changed as a function of energy, because ofenough short distance to avoid the GZK mechanism.
• Z-burst model : In Z-burst model, UHECRs are generated via interactions
between UHE neutrinos and cosmic background relic neutrinos [26]. In
general, these interactions via the decay of Z0 products UHE photons.

2.4

Extensive Air Shower

As discussed in Sec. 2.2, since the flux of cosmic rays follows E −3 , there are thethirty orders of magnitude difference for fluxes between 109 eV and 1020 eV.
In less than 1014 eV, the relative low energy cosmic rays are observed by direct
measurements with balloons and satellite measurements. However, the higher
energy cosmic rays is very rare, so that we need the enough large effective areaand exposure to measure UHECRs. Thus, it is difficult to observed UHECRs
by direct measurements. Then, we measure extensive air showers in which thehuge numbers of secondary particles are generated via interactions between
primary cosmic rays and the atmospheric nuclei.

2.4. EXTENSIVE AIR SHOWER

2.4.1

17

Air Shower Cascades

When a primary cosmic ray proton or a nucleus enters the earth’s atmosphere,
it interacts with a nucleus in the air (nitrogen, oxygen, etc) and generates secondary particles. The each generated particles also interacts with a nucleus andgenerated the huge numbers of secondary particles. Repeating this interactions,the phenomena in which many secondary particles are generated by primarycosmic rays is called extensive air showers (EAS). In general, an extensive air
shower consists of the electromagnetic cascades and hadron cascades.
Electromagnetic Cascades
The electromagnetic cascades are the result of a series of electromagnetic interactions of electrons and photons with atmosphere. Electrons and positrons are
created from high energy gamma-rays. Gamma-rays are emitted via bremsstrahlung
from electrons and positrons. Bremsstrahlung is a process by which a high energy electron emits a photon when a photon interacts with the electromagnetic
field of the nucleus in the medium. The cross section of bremsstrahlung for aelectron, σbrems. , with E provides
 


 1
4Z 2 re2 dv
22− 13
σbrems. (E, v)dv =+ (1 − v)
1 + (1 − v) − (1 − v) ln 184Z
137 v
3
9
(2.18)
where v = hν/E, Z is the atomic number of the target, re is the classicalelectron radius. Thus, the energy loss (dE/dX)brems. per a atmospheric depth
is


dE
E
(2.19)≃− ,dX brems.
X0
where X0 is the radiation length, it defined as
1
4Z 2 re2 N 
1=
ln 184Z − 3
X0
137 A

(2.20)

where N is Avogadro’s number, A is the atomic mass number of the target. In
the air, X0 is approximately 38 g/cm2 .
Then, the cross section of electron-positron pair creation, σpp , is

 

 1
4Z 2 re2222− 13
σpp (hν, u)du =+ (1 − u) ,du u + (1 − v) − (1 − v) ln 184Z
137
3
9(2.21)
where , u = E/hν and E are energies of a generated electron. The interaction
length of pair creation is calculated from σpp ,


dE
7 E
≃−
.
(2.22)
dX pair
9 X0
Therefore, the interaction lengths of a pair creation and a bremsstrahlung arealmost similar. Thus, primary cosmic rays create more and more electrons,

18

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

positrons and photons propagating down in the atmosphere. Through interactions, their numbers increase while their energies decrease. The resulting
avalanche of electrons and photons are called electromagnetic cascades or electromagnetic showers. While secondary particles decreases their own energies,
ionization losses are dominant. Since low energy charged particles are capturedby the atmosphere, the total number of particles decreases. The critical energyof electrons is 84 MeV in the air.
When hadrons, which major component of cosmic rays are interacted withatmospheric nuclei, the multiple productions of hadrons, pions and Kaons are
happened. Most of secondary particles are pions. π 0 is shortly decay with thelife time of 8.4×10−17 sec into two gamma-rays which generate electromagnetic
cascades. The decay mode of π ± is
π + → µ+ + νµ−−

π → µ + ν̄µ(2.23)(2.24)(2.25)

with the life time of τ = 2.60 × 10−8 sec, µ± is also decay with the life time ofτ = 2.20 × 10−6 sec, with modes ofµ+ → e+ + ν̄µ + νe−−

µ → e + νµ + ν̄e .

(2.26)(2.27)

Hadrons induce nuclear cascades. Since the atmospheric depth is 10 times
larger than the mean free path of hadron multiple productions or 25 times
larger than the radiation length of electrons.As the result, the huge number ofparticles are generated through the hadronic interactions and electromagnetic
interactions. Fig. 2.6 shows a schematic vies of extensive air showers.

2.4.2

Longitudinal Development of EAS

While the huge number of secondary particles are created, energies per particles
are smaller. When EAS particles have less than critical energies Ecri , Ecri = 84
MeV in the air, their energies are lost and absorbed through energy losses
without generating secondary particles. As the result, the total number ofparticles in EAS are decreased. The increase and decrease of the number ofparticles as a function of slant depth is called longitudinal development.
When a gamma-ray with an energy of E0 enters the atmosphere, a longitudinal development is described as,
 

0.31
3
Ne (t) ∼ √ exp t 1 − ln s
(2.28)y2E0(2.29)
y = lnEcri
3ts=(2.30)
t + 2y19
Primary cosmic ray

2.4. EXTENSIVE AIR SHOWER

π

γ

π

0

π

γ

-

+

ν

µ

µ

-

+

-

e

-

Electromagnetic
shower

µ

ν

+

ν
ν

µ

ν
θ

e

θ

-

µ

e

+

Electromagnetic
showereeElectromagnetic
shower+Nucleonic cascadeeFigure 2.6: A schematic views of an extensive air shower.

where t is a unit of radiation length in the air 38 g/cm2 , s is the shower age
parameter represented a level of shower longitudinal development. The shower
age parameter indicates s = 1 at the maximum development.
Longitudinal developments of EAS are described by Gaisser and Hillas as

Ne (X) = Nmax

X − X0
Xmax − X0 Xmax −X0
λ

exp



Xmax − Xλ(2.31)

where Nmax is the number of particles at the maximum development, Xmax
g/cm2 is the slant depth at the maximum development, X0 is the first interaction point and λ is the attenuation length, typically λ = 70 g/cm2 .
Nmax approximately corresponds to the primary energy, Nmax ∼ 2 × E0 ×
−910 , where E0 is the primary energy. At an identical energy, the differenceof mass composition appears a first interaction point, X0 , and a slant depth
at the maximum of a longitudinal development, Xmax . X0 of heavier nuclei
are smaller than those of protons, because they have bigger cross sections andstart interactions at higher altitude. Since iron nuclei consists of 56 nuclei,
the energy per nucleon of heavier nuclei is smaller than the same energy of
proton. Since Xmax is roughly proportional to an energy, averaged Xmax valuesof heavier nuclei are also smaller than those of protons with an identical energy.
In a toy model, Xmax ∝ ln(E0 /A), where A is atomic mass number. Fig.
2.7 shows the longitudinal development simulated protons and irons EAS.

20

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Figure 2.7: Longitudinal developments of protons and irons for a EAS simulation.

2.4.3

Lateral Distribution of EAS

A particle distribution spread on a plane perpendicular to an arrival direction of
EAS is called a lateral distribution. The lateral distribution of electromagnetic
cascades are analytically-calculated and approximated by Nishimura-KamataGreisen(NKG) function, as follows,f (r, s) = C (s)



r
rM

ρ (r, s) =

s−2 

s−4.5r+1,
rM

Ne f (r, s),2
rM(2.32)(2.33)

where r is a distance from a shower core of EASs, C(s) is a normalization factor,
Ne is the total number of secondary particles, rM is a Molière unit, which is thecharacteristic unit of length in a high energy electron scattering. rM is definedasEscatt[g/cm2 ](2.34)
rM = X0
Ec
where Escatt is a constant called the scattering energy (21.2 MeV) and X0 is
the radiation length of the medium. It is approximately 1/4 radiation unit or
9.5 g/cm2 and rM ≃ 79 m at sea level. Fig. 2.8 shows the lateral distributionof an EAS induced by a cosmic ray proton with E = 1019 eV at its shower
maximum.

2.4. EXTENSIVE AIR SHOWER

21

Figure 2.8: The lateral distribution of electron number density in air shower
whose primary is proton with energy 1019 eV at the shower maximum.

2.4.4

Techniques for EAS Measurement

There are two types of EAS measurement techniques, which is called air shower
array and fluorescence technique.
Air Shower Array
The technique, called air shower array, traditionally measures the cosmic ray
using a lot of surface detectors (SDs) spread on the ground. A best meritof an air shower array is to observe UHECRs with the duty 100%. 90% of
EAS particles are electromagnetic particles, 10% of them are muons and a few
percent of them are hadron components. A typical detector is a scintillation
counter sensitive to charged particles and muons. To measure muons, we canuse special scintillation counters shielded by lead, soils, rocks or other densematerials. Moreover, to measure a hadron flux in the vicinity of shower axis,
hadron calorimeters had been used in several experiments.
In air shower array, an arrival direction of EASs is reconstructed from atiming distribution of each surface detector because a front of EAS has a thinplane like pan cakes. The energy of a primary particle is estimated from the air
shower size which is estimated by the shower lateral distribution of the shower.
However, it is difficult to avoid an uncertainty of from hadron interaction models, because a particle distribution of EASs is relatively large dependent on
hadron interaction models.
Fluorescence Technique
In fluorescence technique, we measures the fluorescence photons emitted byatmospheric molecules excited by air shower particles. After high energy particles penetrate the atmosphere, atmospheric molecules, for example nitrogens

22

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

or oxygens, are excited and emitted ultra-violet fluorescence photons. In other
word, the atmosphere plays a role of scintillators. When a single electron withthe kinetic energy of 80 MeV passes through 1 m in the unit atmosphere of 1
atm, 4 fluorescence photons are emitted. From a detailed Monte Carlo calculation, 2 × 1015 photons integrated over the all slant depth are emitted from a
EAS with the energy 1020 eV, and the time duration is about 30 µs.
Since the fluorescence photon emission is isotropic, we observed the fluorescence photons from all direction of UHECRs within effective area.
In general, there are two steps of data analysis in the fluorescence technique
to obtain the information of primary cosmic rays, as follows,
1. geometrical reconstruction
2. longitudinal development reconstruction
In the geometrical reconstruction, the arrival direction of a primary cosmic
ray is calculated from recorded signals at the camera installed at the focal
plane of a fluorescence telescope. In particular, when a EAS is observed by
two separated telescopes stereoscopically, the shower axis is determined as theintersection of the two planes including the position of fluorescence telescopes
and the shower axis, called shower detector plane (SDP), shown in Fig. 2.9. If
fluorescence telescopes of a station detect fluorescence photons enough to reconstruct the information of a primary cosmic ray, after determined a SDP, arrival
timing differences injected photons on each photomultiplier tubes are used forreconstruction of the shower geometry. To determine shower geometries using
fluorescence telescopes of a single station is called a monocular mode. However, the monocular mode is slightly hard to reconstruct a geometry of EASs,
because arrival timing differences are relatively small.
After the determination of the shower geometry, the longitudinal development are reconstructed with a following procedure.
i. Expected number of the photons on camera planes are calculated considering the reconstructed geometry of Ethe AS and atmospheric scattering
attenuations. The expected photons include not only fluorescence photons but also Čerenkov photons.
ii. Comparing between the real observed signals on the cameras and expectedsignals, the optimum shower parameters of Gaisser-Hillas function (2.31)
fitted to the event are reconstructed.
Since 90% of a primary energy is converted into electromagnetic particles,
the primary energy E0 is provided from integration of the longitudinal development of Ne (X) shown in (2.31),
Z
Ecri
E0 =
Ne (X) dX(2.35)
X0
where X0 is the radiation length in the atmosphere 38.0 g/cm2 and Ecri is thecritical energy, Ecri = 84 MeV.

2.4. EXTENSIVE AIR SHOWER

23

Figure 2.9: The schematic view of stereoscopic observations.

Therefore, the fluorescence technique provides a rich information of primary cosmic rays compared with the air shower array technique. However, inorder to measure the primary energy and Xmax , we estimate fluorescence yields,
scattering of ultra-violet photons, reflectivities of mirror, the transmittance offilters and quantum efficiencies of photomultiplier tubes.

2.4.5

Photon Emissions, Scattering and Attenuation

Air Fluorescence Photon Yield
When high energy particles pass through the atmosphere, the atmosphericmolecule are exited and fluorescence photons are emitted. After passing theparticles, rapidly emitted photons within 10−3 s are called fluorescence light.
Slowly emitted photons are called phosphorescence. Here, we discuss thephysics processes for emissions of fluorescence photons with wavelengths, 300 ∼
400, which are our nm for our target wavelength.
For near violet region, the excited states are mainly N+
2 first negative (1N)
3 +
2
+
2
+
band system (B IIu → X IIg ) and N2 second positive (2P) band system(C3 II+
u → B IIg ).
The deactivation processes of excited molecules have following three processes.
1. nonradiative process (internal conversion)
2. radiative process (fluorescence, phosphorescence)
3. intermolecular energy transfer
In nonradiative processes, energies of excited molecules are lost by vibration
relaxations or internal conversions without emitting fluorescence and phosphorescence photons. In radiative process, molecules move from exited to stable

24

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

wavelength (nm)
297.7
311.7
313.6
315.9
328.5
330.9
333.9
337.1
346.9
350.0
353.7
357.7
367.2
371.1
375.6
380.5
389.4
391.4
394.3
399.8
405.9

band system
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
2P
1N
2P
2P
2P

initial state(v ′ )
2
3
2
1
3
2
1
0
3
2
1
0
3
2
1
0
3
0
2
1
0

final state(v ′′ )
0
2
1
0
3
2
1
0
4
3
2
1
5
4
3
2
6
0
5
4
3

E0 (×10−2 )
0.016
0.005
0.029
0.050
0.015
0.002
0.004
0.082
0.006
0.004
0.029
0.062
0.005
0.010
0.027
0,021
0.003
0.330
0.006
0.016
0.007

Table 2.1: Efficiencies of fluorescence emissions relative intensity with wavelengths of 300 ∼ 400 nm under a collisionless condition [60].

conditions via photon emissions. In fluorescence emissions, the spin multiplicity is invariant, but in phosphorescence, it is changed. In intermolecular energy
transfers, molecules lose their energies to collide with other molecules. In fact,a deactivation process includes all three processes. Fig. 2.1 and Fig. 2.10 showsthe efficiencies of fluorescence photon emissions and the relative intensity [60][92]. The relative intensity spectrum has some emission lines between 300 nm
and 400 nm.

Čerenkov Light
When a fast charged particle moves through a medium at a constant velocity v
greater than the speed of light in that medium, c/n where c is the light speed
in the vacuum and n is the refractive index of the medium, the particle emitsČerencov radiation. The process is used as threshold detectors, because theČerenkov radiation is only emitted if the particle has velocity greater than c/n.
The Čerenkov radiation is only observed at a particular angle θ with respect2.4. EXTENSIVE AIR SHOWER

25

Figure 2.10: The relative spectrum of air fluorescence light measured by FLASH[92].

to the track of a particle. The angle is described by c 
θ = cos−1
nv(2.36)

which is known as the Čerenkov relation. Since the refractive index of the air
with a pressure of one atm is n ∼ 1.00029, θ is 1.4◦ , and for electrons thethreshold energy for the Čerenkov light is 21 MeV.
The number of photons with wavelength λ nm,
d2 N
2παz 2c2=
1− 2 2(2.37)dx dλλ2n v
2παz 2=sin2 θ.
(2.38)
λ2

where α = e2 /4πǫ0 ~c = 1/137 is the fine structure constant, z is the atomic
number of the medium. When an electron above 21 MeV passes through theatmosphere 1 m, 30 photons are radiated.
Though θ is small in real showers, Čerenkov photons spread over following
angular distributions of shower particles. Moreover, the photons are scatteredby the atmosphere. In fluorescence techniques, the Čerenkov photons and theirscatted photons are noise, because it causes a large systematic uncertainty forenergy determinations. Therefore, we need to estimate a contamination ofČerenkov photons.
Night Sky BackgroundPhotons from the sky at night are called night sky background. There are three
types of emitted sources.

26

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS
1. airglow : photons emitted from molecules and nucleons at the upperarea of atmosphere, which are excited by low energy cosmic rays or are
chemiluminescencce process.
2. zodiacal light : the solar photons scattered by dusts in the interplanetary
space.
3. stellar light : photons from stars and other astronomical objects.

These photons are measured in every photomultiplier tube as DC currents.
From a sciencecatalog, the brightness of the night sky background is 320
S10 (vis)◦ −1

1S10 (vis) = 1.20 × 10−9 erg cm−2 sec−1 sr−1 A.

There is a peak at wavelength 557.7 nm emitted by oxygen nucleon. The
continuous spectrum is a large contribution in long wavelengths. Thus, since
there are many night sky background photons in wavelengths longer than 400
nm and fluorescence process emits photons with a wavelength of 300 ∼ 400 nm,
the solution to measure fluorescence photons is observations in 300 ∼ 400 nm.
Rayleigh and Mie Scattering

Scattering by atmospheric molecules are called “Rayleigh scattering”, the probability of scattering are provided
8π 4 N α 1 + cos2 θIntensity of scattered wave=
Intensity of incident wave
λ4 r 2(2.39)

where N is the number of molecules , α is a polarizability and θ is a scatteredangle, λ is a wavelength, r is a distance between a observed point and a scatteredplace.
For the Rayleigh process, photons are scattered by small dielectric spheres.
In contrast to the Rayleigh process, for a Mie process, photons are scattered bydielectric spheres larger than wavelengths of photons, called the Mie scattering.
The Mie scattering occurs by aerosols which are fogs, dusts or smokes.
For each process, transmittances are approximately calculated by the following formula.
For Rayleigh scattering,"

XtransTRayleigh = exp −XRayleigh



400
λ

4 #

(2.40)

where, Xtrans is the slant depth through the atmosphere in the unit of g/m2 ,XRayleigh is the radiation length of the Rayleigh scattering, which is 2974 g/cm2 ,λ is the wavelength of light.

2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

27

111
000
000
111
000
111

X_transhv
detector

111111000000000000111111000000111111000000111111000000111111h_hillh_det

Figure 2.11: The parameters for (2.43).

For Mie scattering,"
TMie = exp

heff
− hv
m

e

−

heff
− hd
m

−e

hm tan θ
Rlm cos θ!

hmlm cos θ
hm tan θ
1−
R
!#

heff
v

heff
d

−h
eff − hm
m − h
heff
v e
d e

(2.41)(2.42)

where hm is a scale height of an aerosol distribution and lm is a mean free patheffof the Mie scattering, R is the radius of the earth and heffv and hd areeff
heff
v = hv (hdet − hhill ) , hd = hd (hdet − hhill ) .

(2.43)

Fig. 2.11 shows the explanation of other variables.
The transmittance of the Rayleigh scattering can be estimated with astraightforward calculation from a known of a density of the atmosphere. However, since there are large time variations in a transmittance of the Mie scattering, we need to measure conditions of aerosols by atmospheric monitoring
systems.

2.5

Recent Results and Mysteries of UHECRs

We consider origins of UHECRs to be associated with explosive phenomena
and/or new unknown physics, such as super heavy relic particles or topologicaldefects, which are products at early universe. However, origins are still unknown attributed to difficulties to measure EASs because of extraordinary low
fluxes and their extrimely high energies of UHECRs. Here, we discus recent
results and outstanding mystery in the research field of UHECRs.

28

2.5.1

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Energy Spectrum Measurements

Figure 2.12: UHECR spectra measured by Yakutsk, AGASA, HiRes and Auger[35] [44] [50] [51].

Firstly, energy spectra reported by akeno - AGASA (Akeno Giant Air
Shower Array), HiRes (High Resolution Fly’s Eye) I - HiRes-II, Auger (Pierre
Auger Observatory) and Yakutsk are displayed in Fig. 2.12 [35] [44] [50] [51].
The vertical axis indicates cosmic ray fluxes of Fig.=2.1 multiplied by E 3 inorder to see detail of structures on the energy spectra, such as variations of
the index, break points, etc. We can clearly see that there are large systematicdifferences among experiments about 20% on energy. Here, we briefly review
methods and characteristics to measure UHECRs for several experiments.
AGASA (Akeno Giant Air Shower Array)
The AGASA experiment is an air shower array consisting of 111 scintillation
detectors with the effective area of 100 km2 located in Yamanashi, Japan withthe altitude of 900 m. The air shower array technique was adopted in the
AGASA experiment. In the air shower array technique, although we can observe UHECRs with 100% duty cycle, there are two large systematic uncertainties attributed to primary species and shower ages of EASs depending on
zenith angles of EASs. Because of the zenith angle dependence of the column
density of the atmosphere with respect to a given observation level, EASs are
subject to increasing absorption with increasing zenith angle.
In the AGASA experiment, particle density detectors consisting of plastic

2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

29

scintillators of 2.2 m2 area are spread over 100 km2 with inter detector separations of about 1 km. The plastic scintillator is sensitive to detect all charged
particles, electromagnetic components and muons. In order to estimate cosmic
ray energies above 1019 eV, the particle density observed at a distance of 600 m
from the shower axis, S600, has been widely used as a good energy estimator,
because the S600 value is almost independent of primary species. The observed
particle densities are fitted to an empirical formula for the lateral distributionfunction for determining S600. In the AGASA, a conversion factor from S600
values to primary energies is estimated from MC simulations. Further, theestimated Sθ 600 for a shower arriving at zenith angle θ is transformed to theequivalent value in the vertical direction, S0 600, using the attenuation curvefor S600 which is estimated from observed EASs with an energy at 2 × 1019
eV and 9 × 1018 eV [45]. The method is called “equi-intensity cuts” and thesystematic uncertainty on energy determination is estimated to be 18% for the
AGASA experiment [47]. The AGASA spectrum indicates an evidence for acontinuation of the spectrum beyond the GZK cutoff.
HiRes (High Resolution Fly’s Eye)The HiRes experiment observe UHECRs by the fluorescence technique at twosites (HiRes I and II) 12.6 km apart, located at Dugway providing ground in
Utah [50]. Each site consists of fluorescence telescope units (22 at HiRes I
and 42 at hiRes II) The fluorescence detectors (FDs) observe the full 360◦ inazimuth but cover from 3◦ to 16.5◦ (HiRes I) and from 3◦ to 30◦ (HiRes II) in
elevation. The FDs observe longitudinal developments of EASs and determine
the calorimetric energies of primary particles. However, we need to measure a
lot of calibration factors such as fluorescence yields, atmospheric parameters,
gains of PMTs, reflectivities of mirrors and so on. The total systematic uncertainty of the HiRes experiment is estimated to be 17% on energies [50]. The
HiRes spectrum clearly shows the existence of a termination in the cosmic ray
flux consistent with the GZK cutoff prediction.
Auger (Pierre Auger Observatory)
The Pierre Auger Observatory is the largest detector located in Argentina tomeasure cosmic rays by combinations of the air shower array and the air fluorescence technique, so called “hybrid technique” [3]. The air shower array ofAuger consists of 1600 water Čerenkov detectors, each of which consists of 10
m2 water tank and three 9-inch PMTs, and detects Čerenkov photons emitted
by mainly muons into the water. The number of muons is more sensitive on
hadron interaction models than electromagnetic components. Thus, impactsof uncertainties attributed to uncertainties on hadron interaction models forAuger are larger than those for TA [109].
The magnitude of the signal in each tank is measured in “vertical equivalent muons” (VEM), a quantity easily inferred by the abundant single muons

30

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

passing through each tank. The values of VEM measured at 1000 m from areconstructed core of EAS are used as an energy scaler. Since this quantity
varies with zenith angles of EASs, an effective attenuation is determined fromthe data assuming that intensity of cosmic rays for a fixed energy must be independent of the zenith angle, which is the same with the equi-intensity cuts
method adopted in the AGASA experiment. Using the equi-intensity cut, thesignal that each shower produces at 1000 m is adjusted to the signal that would
have been produced at z zenith angle of 38◦ which is the median angle for cosmic rays with zenith angle ≤ 60◦ . The hybrid showers which are triggered byboth the surface array and the fluorescence detectors of Auger are used for absolute energy determinations. The absolute energies measured by the surface
array of Auger are calibrated by those measured by FDs. The systematic error
in the energy determination is estimated to be 22%. There is also a suppression
structure in the Auger spectrum as same as the HiRes spectrum.

A possible interpretation of 20% discrepancy on energies among AGASA, HiRes
and Auger measurements might be attributed to the difference of detection
methods between the air shower array technique and the fluorescence technique. Additionally, all energy systematic uncertainties are large, 18% for the
AGASA, 17% for the HiRes, 22% for the Auger, and these uncertainties arecomparable with the systematic discrepancy on energies among them. Therefore, in order to understand a reason of the discrepancy, we need to measured
UHECR flux with a smaller systematic uncertainty and more statistics thancurrent measurements, and then conclude whether the GZK mechanism occurs
or not at high energies above 1019.5 eV.

2.5.2

Mass Composition Measurements

Secondly, recent results on mass composition studies for UHECRs with Xmax
technique by fluorescence detectors are reported in this section. The maximum
depth of longitudinal developments of EAS, Xmax is an important paramter
to measure mass composition of UHECRs, because Xmax depends on primary
species as shown in Fig. 6.2. The difference of averaged Xmax is about 100
g/cm2 between primary protons and irons, and more than 300 g/cm2 between
primary protons and gamma rays or neutrinos, and these values are larger thanresolutions of fluorescence detectors. Thus, we distinguish primary species by
the Xmax technique of fluorescence detectors.
Fig. 2.13 shows the averaged Xmax measured by the Stereo Fly’s Eye (left)
and the HiRes/MIA and the HiRes experiments (right), which are comparedwith the prediction rails estimated from Monte Carlo simulations for primary
protons and those for irons [38] [37]. There are transitions of dominant components from heavy to light nuclei with energies from 1017.5 eV and 1018.5 eV in
Fly’s Eye experiments. The transit energy measured by the Fly’s Eye experi-

2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

31

Figure 2.13: The averaged Xmax for Stereo Fly’s Eys (left) and HiRes/MIA and
HiRes (right) compared with predictions for primary protons and irons withseveral hadron interaction models after full Monte Carlo detector simulations[38] [37].

ment indicates a half order of magnitude large compared with that measured
by the HiRes/MIA experiment. However, HiRes collaborators reported averaged Xmax values measured by the HiRes/MIA experiment are in reasonableagreement with those measured by the Fly’s Eye experiment with 13 g/cm2
systematic shift on Xmax within systematic uncertainties [38]. In energy ranges
above 1018.0 eV, the averaged Xmax values measured by the HiRes experimentare consistent with the expectation line estimated from MC simulations for
proton primaries using the QGSJet model as hadron interaction models.
The latest preliminary results on the mass composition observed by Telescope Array (TA) are shown in Fig. 2.14 [39]. The averaged Xmax is consistent
with the red line calculated with assuming purely primary protons, which issame with the result of light components above 1018 eV measured by the HiRes
experiment. The rails are also averaged Xmax from full Monte Carlo simulations for primary protons and irons using QGSJet-I, QGSJet-II and SIBYLL
models.
Fig. 2.15 shows the averaged Xmax measured by Auger in the southernhemisphere [40]. The total systematic uncertainty in Xmax measured by Auger
goes from 10 g/cm2 at low energies to 13 g/cm2 at high energies [41]. The
results by Auger indicate the mass composition of UHECRs shows a transition
from protons to heavier nuclei in energies above 1018.5 eV. Fig. 2.16 shows
distributions of Xmax in several energy ranges measured by Auger [41]. The
reduction in the width of Xmax distributions as the energy increases can beclearly observed from the figures. The distributions are also compatible withthe transition from light components to significant fraction of nuclei (CNO or
heavier).

32

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Figure 2.14: Preliminary results of the averaged Xmax measured by the Telescope Array experiment compared with the prediction rails for protons andirons using three types of hadron interaction models: QGSJet-I (a solid line)
QGSJet-II (a dash-doted line) and SIBYLL (a dotted line) [39].

Figure 2.15: Auger measured hXmax i compared with air shower simulations
using different hadronic interaction models[40].

Moreover, Auger reports mass composition results estimated from surface
detectors to achieve more statistics than FD measurements at high energies
above 1019.3 eV. In Auger, muon production depth (MPD) distributions forinclined showers are reconstructed from FADC traces of the surface detectors
far from the core. Since the MPD distributions depend on longitudinal develµto estimate theopments of EASs, Auger group defined a new observable Xmax
mass composition of UHECRs. Auger group selects showers with zenith angles
between 55◦ to 65◦ and with reconstructed energies above 2×1019 eV consists ofµµ427 events. Fig. 2.17 shows observed Xmax
values and expected rails of Xmax
estimated from MC simulations for primary protons and irons using several
hadron interaction models [42]. The uncertainties on the MPD reconstruction

2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

33

Figure 2.16: Distribution of Xmax observed by the Pierre Auger Observatory[41]. The values of the energy limits and the number of events selected are
indicated for each panel.

34

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYSµ
values as a function of the energy measured by
Figure 2.17: Averaged Xmax
Auger surface detectors [42]. The number of real data events in each energy bin
is indicated. The predictions for primary protons and irons following different
hadronic models are shown as well.

µand event selection translate into a systematic uncertainty on averaged Xmaxµof 11 g/cm2 [42]. The result of observed Xmax
is in good agreement with theAuger results obtained with other completely independent methods.
Note that strong quality cuts were applied in the Auger analysis of fluorescence detectors in order to avoid acceptance biases caused by FDs limited fieldsof views. In contrast, such the strong quality cuts were not adopted in TA and
HiRes analyses. Thus, although detectors and methods of data acquisition are
similar, details of analyses are different each other. In general, shower events
the Xmax is observed outside of fields of view of FDs are removed with quality
cuts to obtain reasonable resolutions. Since fluorescence detectors have the limited field of view, a distribution of observed Xmax is changed from an original
distribution. The prediction lines of averaged Xmax for primary protons andthat of irons corresponding to HiRes and TA results are obtained by MC data
calculated with full Monte Carlo simulations of air showers and the HiRes andTA experiments and analyzed with the identical analyses procedures applied
on real observed data, and then these prediction lines include the acceptancebiases due to the detector and the analysis process of each experiment. Therefore, even though the principle of the detections and the analysis is identicalbetween HiRes and TA FD, the predictions are different between the two experiments, because they are different experiments. Thus, it is difficult to makegraphical comparisons of the prediction lines, and also of the averaged Xmax oftwo experiments by plotting these values on a chart.
On the other hand, in order to avoid the acceptance bias of FDs, Auger2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

35

group applied strong quality cuts on the observed data and Monte Carlo simulations, called the “fiducial volume cuts”. With the fiducial volume cuts only
well contained events in the field of view of the FDs were selected and remained
for analyses, and then, for example, many nearly vertical showers are removed
from the analyses. Thus, the event statistics becomes much lower than without
it. As a result, Xmax distributions are obtained without acceptance biases.
Thus, since each experiment reported their result analyzed with their own
rules and methods, and each results has their own bias caused by detectors,
analysis methods and event selections, then these biases are different each other.
So then it is not possible to compare these results by simply plotting data points
on one chart. For comparisons, we need special care about their observation andanalysis biases. To check the discrepancy between the results by TA and thoseby Auger, and also in order to compare results by two experiments, here I apply
the fiducial volume cut to FD data detected by the TA FDs and corresponding
MC data to avoid acceptance biases.

2.5.3

Arrival Direction Distribution

Thirdly, we report recent results for point source searches and anisotropy studies. Fig. 2.18 shows arrival direction plots of UHECRs with energies above
4 × 1019 eV observed by the AGASA experiment [46]. The red squares andthe green circles represent arrival directions of UHECRs with energies above
1020 eV, and (4 − 10) × 1019 eV, respectively. The red and blue lines indicate
the galactic plane and the super galactic plane. AGASA group reported that
this arrival direction distribution is compatible with an isotropic random distribution [46]. Moreover, they reported that there is no clear correlation withalready known astronomical objects [46]. However, they report that they foundsix “event clusters” which the shaded
circles indicate the event clustering within
2.5◦ . Specially, at 10h 29m , 57◦ , three 4 × 1019 eV cosmic rays are observed
against expected 0.06 events. The chance probability of observing such triplet
under an isotropic distribution is only 0.9%.
On the other hand, correlations between arrival directions of UHECRs andnearby AGN are published by the Auger group in 2007 [29]. Fig. 2.19 shows
Aitoff projections of the celestial sphere in galactic coordinates with circles of
3.1◦ radius centered at the arrival directions of 27 events with energies above 57
EeV detected by the Pierre Auger SD array. The positions of 472 AGN (318 in
the field of view of the Observatory) with the redshift z ≤ 0.018 (D < 75 Mpc)
from the 12th edition of the catalog of quasars and active galactic nuclei byVéron-Cetty and Véron (VCV catalog) [62][62] are indicated by red asterisks.
The solid line represents the border of the field of view (zenith angle smaller
than 60◦ ). Darker blue indicates larger relative exposure. Each colored bandhas an equal integrated exposure.
However, after that, up to December in 2009, the significance of the correlations between arrival directions of UHECRs and positions of nearby AGN
decreased [62]. The sky map observed 69 cosmic rays with energies above 55

36

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS

Figure 2.18: Arrival directions of cosmic rays with energies above 4 × 1019
eV observed by AGASA. Red squares and green circles represent cosmic rays
with energy of > 1020 eV, and (4 − 10) × 1019 eV, respectively. Shaded circles
indicate event cluster within 2.5◦ . At 10h 29m , 57◦ , three 4 × 1019 cosmic rays
are observed againt expected 0.06 events. [46]Figure 2.19: Aitoff projection o the celestial sphere in galactic coordinateswith circles of radius 3.1◦ centered at the arrival directions of the 27 cosmic
rays with highest energy detected by the Pierre Auger Observatory [29]. The
position of the 472 AGN(318 in the field of view of the Observatory) with theredshift z ≤ 0.018 (D < 75 Mpc) from the 12th edition of the catalog of quasars
and active galactic nuclei by Véron-Cetty and Véron (VCV catalog) [62] areindicated by red asterisks. The solid line represents the border of the fieldof view (zenith angle smaller than 60◦ ). Darker color indicates larger relative
exposure. Each colored band has equal integrated exposure. The dashed lineis the supergalactic plane. Centaurus A, one of our closet AGN, is marked inwhite.

2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

37

Figure 2.20: The 69 arrival directions with energy E ≤ 55 EeV detected by the
Pierre Auger Observatory up to 31 December 2009 are plotted as black dot inan Aitoff-Hammer projection of the sky in galactic coordinates [30]. The solidline represents the field of view of the Southern Observatory for zenith angles
smaller than 60◦ . Blue circles of radius 3.1◦ are centered at the positions of
the 318 AGNs in the VCV catalog [62] that lie within 75 Mpc and that arewithin the field of view of the Observatory. Darker blue indicates larger relative
exposure. The exposure-weighted fraction of the sky covered by the blue circles
is 21%.

Figure 2.21: The ratio between total number of UHECRs and UHECRs direction correlated with AGN observed by Auger. Pdata = N correlated /N total[30].

EeV is shown in Fig. 2.20. As shown in Fig. 2.21, the amount of correlation
observed has decreased 69+11−13 %, from 9 out of 13 correlations, to its current
+7estimate of 38−6 %, based on 21 correlations out of a total of 55 events. The

38

CHAPTER 2. ULTRA-HIGH ENERGY COSMIC RAYS
degree of observed correlation 38+7
−6 % is compatible with 21% expected tooccur by chance if flux were isotropic.

Figure 2.22: Hammer projection of the UHECRs with E > 57 EeV observedby TA and nearby AGNs in the Galactic coordinates. Correlating and noncorrelating events are shown by filled red and empty blue circles, respectively.
AGNs are represented by black dots. The dashed line shows the boundary of
the TA exposure [31].

Figure 2.23: The number of the UHECRs with E > 57 EeV observed by TAcorrelating with AGNs from VCV catalog as a function of the total number of
events. The expectation according to the original Auger claim is represented
by the blue line together with the 1- and 2-sigma significance bands. The black
dashed line shows the expected number of random coincidences [31].

2.5. RECENT RESULTS AND MYSTERIES OF UHECRS

39

Recently, TA reported the anisotropy of UHECRs collected by the TA SD
in the first 40 months of operation [31]. The sky map of UHECRs with E > 57
EeV observed by TA and nearby AGNs from the VCV catalog is represented
in Fig. 2.22 in Galactic coordinates. The UHECRs are shown by filled red(correlating events) and empty blue circles (non-correlating events). AGN are
shown by black dots.
Fig. 2.23 shows the number of UHECRs observed by TA correlating with
AGNs as a function of the total number of events with E > 57 EeV orderedaccording to arrival time. The black dashed line represents the expected numberof random coincidences in case of a uniform distribution calculated via Monte
Carlo simulation. The blue line shows the expected number of correlating
events as derived from the original Auger claim [29]. Shaded regions represent
68% and 95% C.L. deviations from this expectation calculated by the maximum
likelihood method of Ref. [32]. As is seen from Fig. 2.23, present TA data arecompatible with both isotropic distribution and the AGN hypothesis.
In the full TA data set, there are 11 correlating events out of 25 total, , while
the expected number of random coincidence for this total number of events is5.9. Making use of the binomial distribution with the probability of a single
event to correlate 24%, one finds that such an excess has probability of ∼ 2%
to occur by chance with isotropic distribution of arrival directions.
Here, I briefly summarize recent results of UHECR measurements.
• The mass composition measurement is the proton dominant above 1018.5
eV at north hemisphere, against the transition from light to heavy nuclei
above 1018.5 eV at south hemisphere.
• In the energy spectrum measurement, there are large systematic difference
among measurements. The presence or absence of the GZK cutoff is still
unknown considering the mass composition measurements.
• In the anisotropy, there is not still clear significant correlation between
arrival direction of UHECRs and already known astronomical objects.
Everyone hopes enough statistics of UHECRs to understand the physics of
UHECRs and to conclude their origins.

Chapter 3

Telescope Array Experiment
In order to conclude origins of cosmic rays, the Telescope Array(TA) experiment has been started in 2003. TA experiment has the largest detector in thenorthern hemisphere to observe UHECRs, consisting of two types of detectors:
507 surface detectors (SDs) arrayed with a spacing of 1.2 km between each SD
in a area of approximately 700 km2 , and 38 air fluorescence detectors (FDs)located around the SDs facing inward and looking over the array. The TAexperiment has been constructed at Utah desert in United States (at latitude
39.3◦ north and longitude -112.91◦ weat and at 1382 m above sea level) withan international collaboration of AGASA, HiRes and more scientists in Japan,
US, Korea, Russia and Belgium.

3.1

Aims of the Telescope Array Project

Principle purposes of the TA experiment are listed as follows.
• In order to detect a clue to the mystery of origins of UHECRs, we measure
the energy spectrum of UHECRs with the world’s best accuracy and withthe highest statistics in the north hemisphere.
• We measure the UHECR flux precisely in the super GZK energy regionand settle the contradiction between AGASA’s super-GZK continuationand HiRes’s cutoff, with the “hybrid” detector which consists of AGASA
type, i.e., a plastic scintillation detector array and HiRes type, i.e., fluorescence telescopes.
• To confirm weather the GZK mechanism occurs at the cutoff region ornot, we observe the mass composition of UHECRs to measure a maximum depth, Xmax , of extensive air showers, because the Xmax depends
on the mass composition of the primary cosmic rays. If the mass composition is proton dominant above 1019.0 eV, it indicates an evidence of the
GZK mechanism via interaction with UHE protons and CMBR. On theother hand, if the mass composition is iron dominant above 1019.0 eV, it
41

42

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT
shows a photo-disintegration mechanism for iron nuclei occurs above thisenergy. Moreover, the composition in the ankle region around 1018.8 eV
is important to determine a reason of the ankle structure. For a point
source search, the mass composition is also essential because the bending
attributed to galactic magnetic fields is proportional to a charge of the
primary species.
• In order to search for the clusterings of UHECRs observed by AGASA
and a correlation between arrival directions of UHECRs and known astronomical objects, we observe enough statistics of UHECRs using thelargest effective area in the north hemisphere. Moreover, we search foran anisotropy as a function of energies or the transition of cosmic ray
origins. As a result, we establish a charged particle astronomy as a nextgeneration astronomy.

3.2

Overview of the TA hybrid detector

The construction of the TA detectors started at the end of 2003. Fig. 3.1
shows layouts of the detectors for the TA experiment. The 507 SDs with 1.2
km separation are spread in the area of about 700 km2 . The total 38 FDs
are installed in the three stations, called the Black Rock Mesa (BRM) station,
the Long Ridge (LR) station and the Middle Drum station (MD), and theselocations are east, west and north from the array, respectively. The field ofview of three FD stations are also shown in Fig. 3.1 covering with the effective
area of the SD array.
In March 2008, we have finished the constructions of the full TA detectors,
and we started the full operations. Moreover, the observation at the LR station
was improved to operate and monitor from the BRM station, and we havestarted unmanned operation in May 2010.

3.3

Fluorescence Detectors

Fluorescence technique is to collect fluorescence photons emitted from atmosphere excited by air shower particles using spherical mirrors, and to detect bycameras consisting of 256 photomultiplier tubes (PMTs) located at the focal
plane. At the north of the TA site, 14 fluorescence detectors of the MD station
are transported from HiRes-I and HiRes-II experiments. The effective mirror
area transported from HiRes-II is 3.75 m2 and the curvature radius is 4.74 m.
The field of view is 15.5◦ in azimuth and 16◦ in elevation. The sample and holdsystem of the HiRes-I electronics is applied [74].
On the other hand, the BRM station and LR station contained 12 fluorescence detectors, respectively, are newly designed and constructed for the TAexperiment. The total field of view of each station is 108◦ in azimuth and 3-33◦
in elevation overlapping the effective area of SD array. The fluorescence detector consists of 18 segments of spherical mirrors with diameter of 3.3 m and a3.3. FLUORESCENCE DETECTORS

43

Figure 3.1: The detector configuration of TA. The red square plots: surface
detector, the yellow pentagon-shaped plots: station of fluorescence detectors,
the blue cross shape: the Central Laser Facility.

44

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.2: The BRM station (top-left), the florescence detectors of BRM station (top-right) and the MD station and MD fluorescence detectors transported
from HiRes-I and HiRes II experiment (down).

camera assembled by 256 PMTs as shown in Fig. ). More details are describedin following sections.

3.3.1

Telescope and Optics

The field of view of each TA fluorescence telescope is 18◦ in azimuth, 15.5◦ inelevation with two lines consisting of upper 6 telescopes and lower 6 telescopes.
The field of view of upper layer is 3◦ ∼ 15.5◦ and the lower is 18.5◦ ∼ 33◦ withtotal 3◦ ∼ 33◦ . The locations of each telescopes are fanned out covering total
108◦ in azimuth.
We use spherical mirror optics to obtain a wide field of view with reasonablefocusing power. The support and adjustment mechanism for the segmented
mirrors is also simple for the spherical mirror compared with the parabolic
system. According to ray-tracing simulations, the spot size of 30 mm at the
focal plane is obtained in the field of view when the spot size of each mirror

3.3. FLUORESCENCE DETECTORS

45

Figure 3.3: The newly developed telescopes and their designs at BRM and LR
site.

at the curvature center is within 20 mm. For all of the segment mirrors, wemeasured the curvature radius and the spot size at the curvature center before
installing.
The BRM and LR telescopes have a spherical mirror with a diameter of 3.3
m which is composed of 18 hexagonal segment mirrors. The design of the segment mirror is shown in Fig. 3.3. The mirrors are made 10.5 mm thick Tempax
glass coated with 200 nm thick aluminum produced by the vacuum deposition.
A hard protection surface of Al2 O3 crystal with thickness of 5 nm is producedin the solution containing ammonium hydroxide, tartaric acid and ethylene glycol. Reflectivities of greater than 90% of the mirrors are obtained between 300∼ 400 nm wavelength. The spectral reflectivities can be adjusted to a peakaround 350 nm by tuning the thickness of anodization. The anodized surface
is stable and the degradation of the reflectivity is ∼ 1% / year from the experience of the Fly’s Eye experiment and Utah Seven Telescope groups. However,dusts on the mirror surface leads to make less reflectivities due to the expose to
the outer air directly. In order to monitor time tendencies of reflectivities, wemeasures the reflectivities by a portable reflectance spectrophotometer at regular intervals. The measured reflectivities of each layers are shown in Fig. 3.4
are divided by the height. Results indicate the decreasing tendency proportinal
to exposed time and the localization in which the reflectivities become worse
as lower layers. The mirrors can be washed by pure water for regular maintenances. After washing the mirrors, reflectivities of the mirrors were completely
recovered as shown in Fig. 3.6.

3.3.2

Photomultiplier Tube (PMT) and Camera

TA cameras are installed on a focal plane of the spherical mirrors, and the sizeof camera is 1 m by 1 m a shown in Fig. 3.7. The camera of FDs consists of 256
hexagonal PMTs arranged in 16×16 array to form an imaging plane which are

46

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.4: The variation of the reflectance of the LR mirror in June 2008.
Colors on the left figures correspond to the colors on the right figure. The
vertical axis is the variation from installing. It depends on the height of mirrors.

protected by the acrylic filter, KURARAY paraglas. Typical transparencies of
the acrylic filter are >90% above 300 nm shown in Fig. 3.8. Each camera covers
with the FOV of 18◦ in azimuth, 15.5◦ in elevation with a pixel acceptance of
1.1◦ corresponding to directional resolutions for PMTs. A Ultra-Violet transparent filter (BG3) with a thickness of 6 mm is attached in front of the PMT toreduce the number of night sky background photons with an extra wavelengthof our interest. The night sky background is about ∼ 30 photoelectrons within
100 ns.
HAMAMATSU R9508 is adopted for the photon sensor of the FD camera
in TA, which has a hexagonal bialkali photo-cathode and borosilicate glass
window. The dimensions of the PMT and a typical quantum efficiency are
25% shown in Fig. 3.10. The PMT has 8 dynodes of a box-line focus and they
are set to have an equal gain of 8 × 104 . The PMT adopts a DC-coupling tomeasured the variation of night sky background directly.
In the PMT camera, PMTs are arranged in zigzag with 1 mm spacing.
The sensitive area of PMTs is not uniform and the spot size on the focal
plane is less than 30 mm. Therefore, output signals of PMT suffer from thenon-uniformity effect. Fig. 3.11 shows the averaged non-uniformity map over
253 PMTs measured by the XY-scanner which consists of the eight UV LEDs
(NSHU590B, NICHIA). The wavelength of UV LEDs is 365 ± 10 nm with 400
ns pulse width and 1000 photoelectrons per pulse. The result is consistent3.3. FLUORESCENCE DETECTORS

47

Figure 3.5: The spectral reflectance of the camera 06 of BRM station (left)
and a picture in mirror washing (right). Open circles are the reflectance before
washing and filled circles are after washing

Figure 3.6: Variation in the mirror reflectance at 360 nm of a typical lower FD(FOV: 17.5-33 in elevation) of camera 04 at LR. The mirror was washed after
these measurements in July 2007, August 2009 and May 2010 [53].

48

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.7: TA camera (left) and PMT of R9508 attached the UV filter (right).

Figure 3.8: The typical transmittance of the KURARAY paraglas on the frontof camera.

3.3. FLUORESCENCE DETECTORS

49

Figure 3.9: A typical transmittance of the UV filter in the front of phototubes. Data points are the medians for all the sampled filters with the bars
corresponding the on standard deviation.

Figure 3.10: The typical quantum efficiency of photo-tubes. The data plotshows the median with one standard deviation error of all PMTs measured by
HAMAMATSU PHOTONICS.

50

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

with the HAMAMATSU data shown in Fig. 3.12, and the non-uniformity is
considered in detector Monte Carlo simulation discussed in the next chapter.

Distance from the center of PMT [mm]

40

1.2

30
1

20
0.8

10
0

0.6

-10
0.4

-20
0.2

-30
-40
-40

-30

-20
-10
0
10
20
Distance from the center of PMT [mm]

30

40

0

Figure 3.11: The typical non-uniformity map with 1 mm × 1 mm resolution of
the photo-cathode of our photo-tube. It is normalized with the bins inside acircle with 36 mm diameter. The obtained map show an asymmetry long thex axis caused by the dynode structure of the PMT.

3.3.3

Calibration of PMT Gain

The calibration and monitoring of the PMT gains are achieved in three steps:
the absolute measurement of standard PMT, the relative gain monitoring foreach camera and the correction by the PMT temperature [52].
The absolute gain of standard PMTs are measured by CRAYS (calibration
using Rayleigh scattering) in a laboratory [75]. The standard light source of
CRAYS is Rayleigh scattered photons emitted from a pulsed laser(N2 = 337.1nm) in nitrogen molecule gas (see Fig. 3.14). The absolute gain is acquired
to measure scattered photons with the 10 MHz FADC readout system as thesame with TA FD. The total systematic uncertainty of the CRAYS calibration isestimated to be 7.2% and an additional uncertainty of 3.7% is introduced by thetransport of the calibrated PMTs from the laboratory to the TA experimentalsite [75]. Two or three “standard” PMTs whose gain was measured by CRAYS
are installed in each camera.
In order to monitor the gain of standard PMTs, a small light pulser of
YAP(YAIO3 : Ce) scintillator with 241 Am [79] is mounted in a BG3 filter ofthem. The temperature dependence of an intensity is measured about -0.2% /degree from -10 to 40 ◦ C. The typical intensity is equivalent to 450 p.e. with afluctuation of 10% and an individual difference of less than 5%.

3.3. FLUORESCENCE DETECTORS

51

Figure 3.12: The comparison of results between the HAMAMATSU data andthe data measured by XY-scanner. The left and right figure show the result
along X axis and Y axis, respectively. The definition of the coordinate of x andy axis is the same as Fig. 3.11. Filled circle are the HAMAMATSU data andopen circles are XY’s scanners.

The gain of other PMTs can be monitored relatively to compare with intensities of Xe flash lamps which are installed in the center of each mirror [52].
Fig. 3.16 shows the relative light intensities of Xe flashers which consist of
the Xe lamp (L4646), socket (E2418) and the electric circuit (C3484) made by
HAMAMATSU and a teflon diffuser. The Xe flasher emits pulsed photons withan intensity equivalent to 2 × 104 p.e. with time width 2 µs and frequency 25
Hz. We monitor once per hour during observations with the Xe flusher. As theresult, the standard deviation of the adjusted relative gains for each camera isabout 1% [52].

3.3.4

Trigger Electronics

Fig. 3.17 shows the block diagram of the TA fluorescence detector electronics
and trigger systems in the FD station. The system consists of three type
modules: 1) signal digitizer and finder (SDF), 2) track finder (TF) and 3)
central trigger distributor (CTD) [54] shown in Fig. 3.18. The SDF module
digitizes and records the signal from PMT and calculate S/N to find fluorescencesignals from EAS. The FD modules recognize the air shower track based on the
result of SDF. The CTD module unifies all of the modules and controls the
DAQ process.
Signal Digitizer and Finder
The SDF module digitizes the signal from PMT by 12 bit 40 MHz FADC andrecords the output of FADC added up with 4 bins as a waveform. Each SDF
has 16 input channel from PMTs and 16 SDFs are assigned for each telescopefor each channel,

52

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.13: The schematic view and photograph of XY-scanner. The covering
area of each LED is 2.5 PMTs vertically and 16 PMTs horizontally.

In order to find large excess signals over the night sky background, SDF
calculates moving average in several time windows of 1.6, 3.2, 6.4 and 12.8
µs. The average and the standard deviation are also calculated from past
1.6 ms, to normalize moving average counts. The SDF module examines themoving average counts to find fluorescence signals by comparing with a pre-set
threshold level. The results of SDF on each PMT are sent to the TF.
Track Finder
The TF module processes the hit patterns of one camera in every frame. The
hit patterns are the map of results of the first level trigger of each channels.
When it recognizes the hit patterns as an air shower track, it sends the second

3.3. FLUORESCENCE DETECTORS

53

Figure 3.14: Measurement set up of CRAYS [75]Figure 3.15: The UV pulsed light source located in front and center of thestandard PMT, named YAP.

level trigger to the CTD. The major components of the TF are one CPLD(XC95288XL), one FPGA (XC3S400E), one configuration ROM (XC18V04)
and nine SPAMs (CY7C1041). These devices are assembled onto 9U VME
printed circuit board. The block diagram of the TF module is shown in Fig.
3.19.
At each camera, one TF module communicates with the 16 SDFs via the
VME bus lines. To form the second level trigger, the TF searches through the
PMT hits, determined by the SDFs, looking for patterns in space and time.
It recognizes shower tracks on the camera or rejects accidental coincidences
caused by night sky backgrounds or other artificial sources such as light from
airplanes. The TF scans over hits in the camera, as identified by the SDFs, in
sub arrays of 5 by 5 PMTs. The sub array window scans over all camera at agiven observatory site for 25.6 µs search window every 12.8 µs. Those observed
patterns are compared with the lookup table for possible track recognition.
At the same time, the TF module receives “Non-Conditional” (NC) trigger
information from the SDFs, which are set when significantly large signals are

54

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.16: The image of Xe flasher.

Figure 3.17: Block diagram of electronics and trigger system of the TA FD

3.3. FLUORESCENCE DETECTORS(a) SDF(b) TF

55(c) CTD

Figure 3.18: Photos of the trigger modules of TA fluorescence detector

Figure 3.19: Block diagram of TA Track Finder module.

Figure 3.20: Schematic diagram of the track finding process.

56

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.21: Schematic diagram of the partial track search near the boundaryof a camera.

found in the PMTs. The TF module can also generate trigger signals by using
the NC information without track identifications for calibration runs. The
trigger signals generated by the TF (“second level” triggers) are sent to the
CTD module. Each TF has two inputs on its front panel for veto and external
triggers, and also has an output pulse indicating a second level trigger.
The track recognition criterion for a “complete track” condition is that five
adjacent PMTs in the camera are above threshold within a coincidence windowof 25.6 µs, as shown in Fig. 3.20. The TF crops a hit pattern into a 5 × 5 submatrix and searches for complete tracks in the sub-matrix. The sub-matrix is
shifted column by column, row by row across the face of the camera repeating
the search for a track. The number of hit patterns of 5 × 5 pixels is 225 , thelookup table is programmed in the 8 static RAMs (CY7C1041, 256k × 16).
The processing time is 3.5 µs, corresponding to 25 ns × 155, for the patternmatching of 155 sub-matrices in a camera.
An additional trigger condition implemented in the TF helps it to recognize
showers which straddle two cameras leaving short tracks in each. These “partial
tracks” are identified if there are three adjoining PMTs above threshold in a 4 ×
4 sub-matrix at the boundaries of two adjacent cameras, (see Fig. 3.21). Thisis equivalent to the complete track condition, because there is an overlap witha width of one PMT (FOV ≃ 1◦ ) between the field of view of two neighboring
cameras.
The TF can generate the second level trigger in other two cases: first when
the NC trigger initiated by a large signal in the SDF and second when an
external trigger is induced by a pulse input to the TF front-panel. When one of
the trigger criteria is fulfilled, the TF sends the second level trigger information
to CTD with a frame ID.

3.3. FLUORESCENCE DETECTORS

57

Central Trigger Distributer
The CTD module generates the final trigger judgment for the FD DAQ system
to record air shower candidates. It also serves as the controller of the FD station
system distributing the system clock to keep all of SDFs and TFs synchronized.
It also sends the “reset” signals to initialize the frame counters.
The CTD module is a VME-9U single width board. Its major components
are nine CPLD (one XC95288XL and eight XC95144), one FPGA (XC2S200E)
and a configuration ROM (XC18V02). A GPS module (Motorola M12 + Timing Oncore (P283T12T1X)) is also installed on the CTD to provide precise
timing of the shower events. The block diagram of CTD is shown in Fig. 3.22.
The CTD module receives and examines the second level trigger codes from

Figure 3.22: Block diagram of TA Central Trigger Distributor module.

all TFs at an observatory station. When the CTD receives the second level
trigger with the code of a complete track from one or more TFs, it generates
and distributes a “final trigger” to all TFs to record the waveform data of all
the PMTs in the station. Aside from this condition, the CTD also triggers
the DAQ system when two neighboring TFs send second level triggers withthe code of a partial track. The CTD can generate the final trigger if TFs sent
trigger codes of NC triggers or external trigger for calibration runs, for example
to acquire a reference light source to monitor the PMT gain [52]. A final trigger
signal consists of a trigger pulse with a readout mask which is a 12-digit binary
number indicating a second level trigger in the telescopes as well as a trigger
ID. At the moment of the generation of final trigger signals, the CTD and TFs
supply DAQ signals for each VME control PC to start a DAQ cycle.
Event times are calculated from the difference between the rise time of thelatest 1 pulse per second (PPS) signal from GPS module and the beginningof the frame. The time difference is counted with 40 MHz system clock, theresolution of absolute time is 25 ns. The accuracy of absolute times depends

58

CHAPTER 3. TELESCOPE ARRAY EXPERIMENTon the stability of 1 PPS signals, which is 20 ns from our measurement.
The time table of a signal DAQ cycle, from the beginning of the signal
finding process to the end of data transmissions into readout buffers, is shown in
Fig. 3.23. It is dominated by the time required for the track finding process andFigure 3.23: The time table of a single triggering cycle.

data transmissions of trigger information between modules. The total process
time is smaller than the frame interval of 12.8 µs. If the readout buffers of SDFs
and TFs are full, CTD suspends trigger distributions. In order to measure thedead time in operations, the CTD recored the IDs and the absolute times ofthe first and last frame in each suspended period, and also it calculates the sum(length) of those periods. This information is transferred to the VME control
PC for the CTD.
The CTD module supplies 40 MHz system clock pulse to all the trigger
electronics modules and sends the reset pulse to synchronize all of them. If
TF misses to receive the system clock, TF switches to the TF inner clock andstands the error bit.
The absolute time information can be known for each triggered data by
GPS time and the number of clock pulse from the latest 1 PPS. This time isimportant in analysis other FD station’s and the SD array’s triggered eventsand accuracy of less than µsec order is essential.
By track finding algorithm, aircraft exterior light is also triggered. In astable run, trigger rate is about 2 ∼ 3 Hz. However, once airplane flights into
the FOV of telescope, trigger rate become higher to the maximum of DAQ rate
∼ 30 Hz. The CTD module can distinguish airplane trigger from others. If
there are a continuous trigger whose duration is over 100 µs, the CTD regard
them as airplane’s light. After than in ∼ 10 µs trigger is vetoed. Before
installation of airplane veto, the ratio of airplane was about 1/3 shown in Fig.
3.24. Currently, most of the signal from air plane are vetoed by the CTD.
Because of the read out and airplane veto, dead time is included in a observation time. Dead time is essential to be accounted for to estimate an accurate
exposure. The CTD module can calculate the accurate dead time. Th buffer isprepared, which is less then 0.1 Hz. If the trigger rate becomes more than 30
Hz temporally, the data are left in the buffer not to be acquired. At this time
the buffer becomes full (8 or predetermined limit more event data are stored)3.3. FLUORESCENCE DETECTORS

59

Figure 3.24: The ratio of triggered events before and after airplane veto installation

and we can not acquire the air shower data, even though there is a triggered
air shower. This interval should be add up as a dead time. The TF modules
send the buffer status which means that buffer is full or not to CTD. The CTD
module counts the number of dead time frames and records the start and end
frame ID of dead time interval. By this information we can know the accurate
dead time Fig. 3.25. The first group is caused by the airplane veto, and the

Figure 3.25: The histogram of typical dead time durations in log scale for someobservation terms on Apr/2008, Oct/2008, Apr/2009, Oct/2009.

second group is caused by the read out, 30 ms is the minimum time to readout the data.

60

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

3.4

Atmospheric Monitoring

TA has the several methods to monitor an atmospheric condition. Air shower
measurement by FD is achieved to detect fluorescence photons emitted along
the air shower axis apart from several kilo meters. Then, the intensity of fluorescence photons are attenuated by the atmospheric scattering in propagating
through the atmosphere. In order to estimate the primary energy of air showers
from detected fluorescence photons, it is quite important to study the atmospheric profile.
The TA FD analysis are used the following three parameters.
• Atmospheric parameters (temperature, pressure and humidity)• Transmittance (horizontal attenuation length)• Cloud
The atmospheric parameters such as temperature, pressure and humidity
are used for estimation of a yield of the fluorescence light and transmittanceby the Rayleigh scattering. Those parameters are measured by the radiosonde.
Since the transmittance of the atmospheric affects the reconstructed energy
directly, this is one of the most important calibration factors. The main uncertainty of the transmittance is caused by the Mie scattering. Since it depends on
the time, the transmittance has to be measured frequently. In FD analysis, thetransmittance is measured by Light Detection And Ranging (LIDAR) systemat the start and the end of daily operation of FD.
The aperture of FD is affected by the cloud, because the cloud shields
the fluorescence photons emitted from EAS. In TA, there are three methods
to measure the amount of the cloud: the weather code (WEAT code) visually
recorded by the operator in the MD station, the picture taken by the IR camera
at the BRM station, and CCD-fisheye camera installed at BRM, LR and CLF
locations. The WEAT code is adopted in FD analysis because almost all datasetof FD observations are recorded.

3.4.1

Radiosonde

The atmospheric parameters such as pressure, temperature and humidity areimportant for the FD analysis. These parameters are used for the calculationof the fluorescence yield, atmospheric depth, transparency of the atmosphereand so on. Since the atmosphere is changed by time, these parameters shouldbe measured periodically. For each altitude, the measurement is done by aballoon up to 30 km above sea level. There are six launching the site for theradiosonde around the TA site by meteorological instrument. At each site,
the characteristics of the atmosphere are measured every 12 hours and they
are opened to the public on the web site [96]. The atmospheric parameters
measured by ELKO site (40.87 North, 115.73 West) are adopted in FD analysis
because the climate of ELKO is similar to the experimental site of TA. All of

3.4. ATMOSPHERIC MONITORING

61

the data are prepared as a database to use for the analysis. The detailed study
for the radiosonde is written in [76] [108].

3.4.2

LIDAR

For measurements of the attenuation in atmosphere, TA has a laser systemcalled light detection and ranging (LIDAR) [77] which is located 100 m far
from the BRM station. The overview of LIDAR system is shown in Fig. 3.26.
It consists of the YAG laser with 355 nm wavelength, 4 mJ power and 1 Hz
frequency (ORION made by ESI), the energy prob with a UV sensitive (J50LP1A made by Coherent) and a 30 cm diameter telescope (LX200GPS-30 madeby MEADE) on the steerable mounting and a PMT (R3479, HAMAMATSU)
with a UV filter. The remote operation can be done from the FD station.
The atmospheric attenuation is measured using the photons scattered backward in the laser shooting. The photons are detected by the PMTs with thetelescope and digitized by the oscillo scope (WaveRunner6039 made by Lecroy).
The LIDAR system operated before and after observation with 4 types of measurement: 500 vertical shots and 500 horizontal shots with two types of energy,
respectively. The details of the operation and analysis are written in [77]Figure 3.26: The overview of LIDAR system. A left picture is LIDAR’s opticalsystem (telescope, laser, etc), a right picture is a connection block diagram ofdevice of LIDAR.

The atmosphere has two main components for the attenuation. One ismolecules in the atmosphere, another is aerosols. The scattering phenomenon
caused by molecules is called Rayleigh scattering. It is well known by atmospheric parameters corresponding to temperature and pressure. Thus, the important things for measurement of the atmospheric attenuation is the scattering

62

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

caused by aerosols, called Mie scattering. The factor of Mie scattering for theaerosol scattering can be measured by LIDAR system through detecting backscattered photon. Additionally, the component of the Rayleigh scattering canbe calculated by the atmospheric parameters measured by Radiosonde. Therefore, the component of the Mie scattering can be obtained by the measured
total attenuation subtracted by the calculated attenuation for the Rayleighscattering.
The LIDAR system measures the extinction coefficient which is the inverseof the horizontal attenuation length for each height for every observation day.
The data obtained by the horizontal shots can measure the extinction coefficienton the ground. The distribution of the attenuation for the component of theMie scattering is shown in Fig. 3.27. The typical attenuation length on the
ground is 29.4 km. For the index of the attenuation, we define the verticalaerosol optical depth (VAOD)
TMie = exp(−VAOD),(3.1)

where TMie is the transparency by the Mie scattering. The typical VAOD ofthe measured data is about 0.034 shown in Fig. 3.27, and then TMie is 0.967.
The amount of the aerosol is reduced as the altitude increases. So theextinction coefficient Mie(h) at the several heights h is expressed asMie(h) = exp(−h/H)(3.2)

where H is the scale height for the aerosol distribution. This parameter canbe obtained by fitting for the attenuation length on the ground and VAOD ateach height. The fitted scale height is obtained for 1.0 km, the VAOD at the
3.5 km or 5.0 km is 0.033, 0.034 respectively. It shows in good agreement withthe measured VAOD. The obtained value is also in reasonable agreement withthose of HiRes [78]. In the FD analysis, the typical value shown in Fig 3.27 areused for the attenuation of the Mie scattering.

3.4.3

CLF

The central laser facility (CLF) was installed at the center of TA site with thesame distance 20.85 km far from all three stations and shooting the vertical UV
laser same as LIDAR (355 nm, 5 mJ). Side scattered photons can be measured
by three stations to monitor the relative gain and atmospheric condition every
30 minute. Fig. shows the CLF system and inside picture of CLF.
Additionally, the LIDAR system has been installed at CLF location in
September 2010. When shooting the laser, the back-scattered photons aredetected at the ground. Thus, the telescope system same as LIDAR was set up
to measure back scattered photons from CLF laser. Fig. 3.29 shows the imageof LIDAR system and the typical result of VAOD measured by both LIDAR
systems located at BRM and CLF. While the LIDAR at BRM operates in thetime to start and finish every observation, CLF is shooting the laser every 30

3.4. ATMOSPHERIC MONITORING

63

Figure 3.27: The histogram of the extinction coefficient for Mie scattering on
the ground. The median value 0.034 km−1 is equivalent to the attenuation
length of 29.411 km.

Figure 3.28: The CLF system located at the center of TA (left) and the inside
picture of CLF (right).

64

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

minutes. Since these results are consistent and complementary, we can use theatmospheric parameter with better time resolution in near future.

Figure 3.29: The image of LIDAR system installed at the CLF location (left)
and VAOD relationship measured by CLF and LIDAR (right).

3.4.4

Cloud Monitoring

When the sky is covered with the cloud, the fluorescence light cannot be measured by fluorescence detector caused by cloud shielding. Thus we need to knowwhether there is cloud or not in the FOV.
WEAT CodeIn order to know the cloud existence in the sky, an operator of the MD station ismonitoring the mount of cloud by own eyes every one hour. The recorded codeis called as the “WEAT code”. The code consists of whether there is the cloud
or not in the North, East, South, West and Overhead recorded 0 or 1, the ratioof area covered by cloud recorded from 0 to 4, 4 is full sky, and haze recordedby 0 or 1. The monitoring method is the same as that of HiRes experiment [50].
Since the measurement have been started at the beginning of MD observation,
the code is available in all observation term. Thus the information of WEAT
code of the cloud South and East is used in BRM and LR FD analysis. We
analyze the data with which the total score of south and east direction is lessthan 2.
IR Camera
The TA has been installed the infrared camera (Avio TV S-600) which is sensitive in a infrared wavelength of 8 ∼ 14 µm to monitor a temperature of theatmosphere inside FOV. The camera and taken pictures are shown in Fig. 3.30.
If there is the cloud in the sky, the cloud region is relative higher temperature3.4. ATMOSPHERIC MONITORING

65

than the sky area. The camera measured the temperature in a field of view
25.8◦ × 19.5◦ moving to 14 direction every 1 hour. The 12 directions are thealmost same direction with the FOV of FD, and the others are horizontal andvertical pictures.

Figure 3.30: The overview of IR camera (left). The right figure is the 12
photographs taken by each telescope directions of FD. The number shows theanalyzed cloud score on 4 horizontally categorized regions.

The IR camera and photograph taken by IR camera are shown in Fig. 3.30.
In the data analysis each IR picture is divided into 4 regions in the horizontal
direction. Using temperature information, the each picture is scored from 0
to 4.The score of 4 means full cloud while 0 is clear night. Although the IR
camera is not always operating all observation because of a trouble and a repairof device, we confirmed the score of WEAT code is consistent with IR camera
score [80].
CCD Fish-eye
In Jan 2012, the charge coupled device fish-eye has been installed at CLF, BRM
and LR station. The CCD fish-eye consists of the CCD (1/2” WAT-120N+,
Watec Vedeo output), fish-eye lens (FE185C057HA-1, Fujinon). During themoonless night, the camera takes pictures with the full sky FOV. Fig. 3.31
shows the overview of CCD fish-eye and photographs taken at CLF, BRM andLR with the star name and the FOV of FD. If the sky is covered with someclouds, we cannot see the star so that we recognized whether there is cloud inthe sky or not. Moreover the “stereo” observation which is used more than two
CCD fish-eye data can be reconstructed the altitude of cloud. Since recently
started full operations, we are steadily collecting the data enough to analyze.

3.4.5

Star Analysis

Stars are a useful light source to calibrate the line of sight direction of eachtelescope and PMT. When FD station is triggered with 2-4 Hz, all PMT waveforms of 12 camera are collected at short intervals. Thus, a variation of BG

66

CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.31: The photo of CCD fish-eye at LR station and picture taken at
CLF, BRM and LR location. The yellow region shows the FOV of each FD,
the green region shows the cover of CLF-LIDAR for online monitoring.

level from star light are steadily observed by FD. In general, since each PMT
has the FOV about 1◦ , the BG level of FADC are increased during 5 minute.
Since we can evaluate star directions from star catalogs at given time, geometries of FD are calibrated from these directions. May types of star catalogs
from various star observations ware already released. In this analysis, we useda planet position catalog [89], a visible star catalog [90] and stellar flux catalog
in ultra-violet catalog [91].
Parallel rays from a star inside FD FOV make a spot on the camera. Fromray-tracing simulation discussed in section 4.2.1, the spot radius is estimated of
21 mm (68% C.L.) on the camera center with the ideal alignment accuracy. The
actual spot radius might be larger than the ideal value owing to the alignment
accuracies of FD. To evaluate these accuracies by ray-tracing simulation, mirror
reflected photons are a 2-dimensional Gaussian distribution with a standard
deviation. This standard deviation is called as Spot Size Parameter (SSP).
Fig 3.32 shows the simulation of star transition by of the ray-tracing of parallel
photons with several SSP. The red square, blue circle and black triangle indicate
the simulation result with SSP = 0.0, 0.1 and 0.2, respectively.
To obtain SSPs for each FD, we compare observed time variance of BGlevel with these simulated ones. Fig. 3.33 shows an example of fit result, andthis fitting provides the best fit SSP value of 0.200 degree. From the fitting, we
obtained SSP value for each FD. As result of the star analysis, the accuracy of
FD telescope direction is 0.01 degree, and the accuracy of each PMT direction
is within 0.1 degree.

3.4. ATMOSPHERIC MONITORING

67

Figure 3.32: Simulation results of time variance of BG level with the different
SSPs. Red square: SSP = 0.0 degree, Blue circle: SSP = 0.1 degree, Black
triangle: SSP = 0.2 degree.

Figure 3.33: Fitting sample of BG level time variance (BRM00). Error bars ofobserved data show their statistical errors. Circle: observed, Square: simulated.

3.4.6

The End-to-End Absolute Energy Calibration

The electron light source (ELS) is an unique and first of it’s kind apparatus
that can be used for end-to-end absolute energy calibration at BRM [36].
Fig. 3.34 shows the ELS located 100 m far from BRM station, and can firea upward going electron beam through the FOV of the telescopes. The typical
output beam consists of about 40 MeV ×109 electrons per pulse with 0.5 Hz andits water cooling system in 40-ft and 20-ft container, respectively (see Fig. 3.35).
The fluorescence light from ELS corresponds to photons emitted from 1020 eV
shower injected 20 km far from BRM. Since the fluorescence photons fromelectron beams are the identical phenomena emitted from EAS, the FDs canbe calibrated all detector components, for example, fluorescence yield, mirror
reflectance, filter transmittance, PMT gain. When the ELS calibration can be

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CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

achieved at BRM site, a systematic uncertainty of FD is dramatically smaller
than before. We have started the ELS beam operation in September, 2010.
The event display observed by FD from the first shot of ELS is shown in Fig.
3.36

Figure 3.34: The photos of ELS installed at BRM site.

Figure 3.35: The schematic view of ELS system.

3.5

Surface Detector

The 507 surface detector (SD) have been deployed 1.2 km separations in Utah
desert with covering 700 km2 . Fig. 3.37 shows the deployed SD which consistsof a scintillator box, a communication antenna and solar panels [82]. The
schematic view of inside the scintillator box is shown in Fig. . Each surface
detector consists of two layer of plastic scintillator which has 3 m2 effective area
and a thickness of 1.2 cm. A 1 mm stainless-steel plate is inserted in between
layers. A scintillation light is collected through 104 wavelength shifting (WLS)

3.5. SURFACE DETECTOR

69

Figure 3.36: The event display of the first ELS beams observed by FD.

fibers that are 5 m distance (Y-11, KURARAY Co. Ltd.) and laid on eachlayer. The fibers along the grooves connect to a PMT (9124SA, Electron TubesLtd.) and convert the photons to signal.

Figure 3.37: The surface detector deployed TA site.

Fig. shows the detector electronics for the scintillator counter installed ina stainless-steel box under the solar panel. The output signals from PMTs are
digitized by a 12 bit FADC (AD9235RU-65, Analog Devices Co.) with a 50
MHz sampling rate on the CPU board (SH4, Renesas Electronics Co.). Signals
grater than approximately 0.3 minimum ionizing particles (MIP) are stored in amemory buffer on CPU board as LEVEL-0 trigger data. The stored waveformis 2.56 µsec long (128 FADC bins). Signals greater than 3.0 MIP are recorded

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CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.38: Inside of a scintillator box with scintillator plates, WLS fibers and
PMTs. A total 104 WLS fibers are laid on each layer to collect and transmit
scintillation light.

Figure 3.39: The electronics of TA SD.

as Level-1 trigger events which are sent to the trigger decision electronics atthe communication tower via a wireless LAN modem (ADLINK540F, ADTEC.
Co) using a custom made communication protocol [81]. The local trigger rateof single SD is ∼ 750 Hz for Level-0 trigger and ∼ 30 Hz for Level-1 trigger.
The synchronization of electronics of the surface detectors is done by 1
PPS signal received by GPS units (Motorola M12+ oncore module) like FD.
A time stamp with a precision of about 20 nsec is created by the 50 MHz subclock on the main board. Each SD is powered from one solar panel (KC125J,
KYOCERA corp.) and one deep cycle battery (DCS100, C&D Technologies,
Inc). The charging battery is controlled by home made charge control boardthat works with main CPU board. The solar panel system provides a sufficient
power required from the electronics (∼ 5 W).
One of the three communication towers of TA is shown in Fig. 3.40, which islocated at near BRM FD station. The schematic view of three tower locations

3.5. SURFACE DETECTOR

71

and connections is shown in Fig. 3.41. They play a role of the collection of
trigger informations from the SDs and providing communications for the FD
stations and CLF site. The data communication between the trigger decisionelectronics at communication towers and SDs is done by 2.4 GHz wireless LAN.
The trigger decision electronics at each communication tower requests the SD
to send its Level-1 trigger list and the total counts of the sub-clock between
PPS signals. From the lists, an air shower trigger is generated when threeadjacent SDs are coincident within 8 µsec.

Figure 3.40: The Black Rock Mesa communication tower, one of three in thearray. There are there stands each with solar panels. Those stands containbatteries, data acquisition PC and network instruments for long distance link.

Fig. 3.42 shows a current trigger pattern of three adjacent SDs with Level1 trigger, called Level-2 trigger. With this trigger, the data of waveform of
SDs will be collected to the communication towers. The trigger electronics
collects waveforms coincident within ±32 µsec from the trigger timing. Whenthe Level-2 trigger is generated within one sub-array, the trigger time information is transmitted to the central trigger decision process running at the dataacquisition PC (TS7800, Technologic System Co. Ltd.) in the tower. From
the one tower triggered, the trigger signal is distributed to the other towers.
Thus, when the air shower impacts at the border of sub-array, data of the othersub-array were collected by the board-casting of trigger. Fig. 3.43 is an event
display and measured waveforms of a typical air shower triggered across theborder of sub-array.

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CHAPTER 3. TELESCOPE ARRAY EXPERIMENT

Figure 3.41: The long-distance links for all the facilities and three FD stationsin the entire TA site. The open triangles represent the communication towers
where the trigger decision electronics for sub-arrays are installed. The linesthat connect the towers and facilities represent the links between antennas.
The red lines are used for trigger decision. The dotted line shows the borderof the entire surface detector array [82].

Figure 3.42: Trigger pattern taken at the TA surface array. If any three adjacentSDs have timing difference within 8 µsec the trigger will be generated.

3.5. SURFACE DETECTOR

73

Figure 3.43: Typical air shower event and recorded waveforms triggered acrossthe border of sub-array. The event display of observed air shower (left) andobserved waveforms (right).

Chapter 4

TA FD Detector Simulation
Software
In order to estimate performance and aperture in monocular mode, we developed a detector Monte Carlo software. In this chapter, we explain how tosimulate the signal detected on PMT camera. The simulation software consists of the shower generation, photon emission processes and each waveform
calculation on the PMT considering the details of detector structure.

4.1

Extensive Air Shower Generation

4.1.1

CORSIKA shower simulation

At first, we simulate air shower developments. Air shower developments in theatmosphere are given by the CORSIKA air shower simulation [33]. CORSIKA(cosmic ray simulations for kascade) is the most popular to simulate the EASs
initiated by high energy cosmic ray particles originally made for KASCADE
experiment. CORSIKA can treat many kind of primary particles as protons,
light nuclei up to iron and photons, take various model of particle interaction.
For hadron interaction models, GHEISHA and FLUKA are available at low
energy region and VENUS, QGSJET, DPMJET, SIBYLL, neXus and EPOS
are adopted at high energy region. For electromagnetic interactions, EGS4
or the analytical NKG formula can be used. Options for the generation ofČerenkov radiation and neutrinos are also available in CORSIKA.
In the FD shower library, the primary particles are considered as only protons or irons because the resolution of composition is not enough clear to separate in the nuclei level. Thus, the composition model is assumed as pure
protons or pure irons. Moreover QGSJET-II and SIBYLL models are adopt
as the hadron interaction model. The QGSJET model is based on the GribovRegge theory [85] [86], wile SIBYLL is a mini-jet model [87]. The most influence factor of shower developments are an inelastic cross-section and the energy
spectrum of forward emitted particles. However, those cannot be measured by75

76

CHAPTER 4. TA FD DETECTOR SIMULATION SOFTWARE

the present accelerator and are just extrapolated. In near future, it is expected
to measure the cross-section and the energy spectrum of forward particles inthe energy region up to 1017 eV by the LHCf experiments [88].
In general, U.S. standard atmosphere are adopted, in which atmosphericdensity is given by
T (h) =

ai + bi exp( −bci ), i = 1, 2, 3, 4

(4.1)

ai − bi chi , i = 5

where h is the height and parameters are shown in Tab. 4.1.
Layer i12345altitude h km
0-4
4 - 10
10 - 40
40 - 100100 <ai g/cm2-186.5562-94.9190.6128900.01128292

bi g/cm2
1222.6562
1144.9069
1305.5948
540.1778
1

ai cm
994186.38
878153.55
636143.04
772170.16
109

Table 4.1: Parameters of the U.S. standard atmosphere

To reduce a computing time, the thinning option is applied in which particles with energy below the thinning factor of primary energy are grouped as
the weighted particle. Moreover, particles with energy below the Ecut are nottraced. In the case of FD shower library, thinning factor of 10−4 is enough tosimulate the shower developments because the distribution of shower parameters such as Xmax almost the same as the case of 10−5 , 10−6 . The parametersof air shower simulation are shown in Table 4.2.
Model
Energy range
Zenith angle
Azimuth angle
Thinning factor
Ecut
Number of showers

QGSJET-II, SIBYLL
1017 ∼ 1020 eV
0 ∼ 65 degree, uniformly
0 ∼ 360 degree, uniformly
10−4
100 keV for electromagnetic component
100 MeV for hadronic component
500 events per d log E = 0.1

Table 4.2: Parameters of air shower simulation using CORSIKA.

CORSIKA gives particle distributions at the ground and longitudinal profiles. Longitudinal profiles at each atmospheric depth are mainly divided in
two parts, the number of particles and energy depositions. For the number ofParticles, γ, e+ , e− , µ+ , µ− , hadrons and nuclei are taken into account. In theenergy deposits, γ energy cut, ionization and energy cut of e± , µ± , hadrons

4.1. EXTENSIVE AIR SHOWER GENERATION

77

and nuclei are given, where energy cut is the total energy of particles withenergy below the given threshold level. For the fluorescence technique, the energy deposits can be applied because they are proportional to the number offluorescence photons in principle. Thus, the information for each slant depth isdefined as “segment” and stored energy deposit, position, shower age and slant
depth which use in the calculation of photon emission. Some characteristic
parameters of longitudinal profile, Xmax , Nmax , Xint , are also given as fitting
parameters of Gaisser-Hillas function.
Missing Energy
Neutral particles, mainly neutrinos and neutrons, do not emit fluorescence photons. Thus, FD can not measure energies of these neutral particles and the total
calorimetric energies, Ecal , are smaller than primary energies E0 . The discrepancy of energy is defined as “Missing Energy” Emiss which is given by
Ecal = E0 − Emiss .

(4.2)

The missing energies are estimated from the CORSIKA simulation and correct
1
0.95

Ecal / E0

0.9
0.85
0.8

Proton (QGS-II)

0.75
0.7
17

Iron (QGS-II)

17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 4.1: The ratio between calorimetric energies and primary energies as afunction of primary energies for primary protons and irons using the QGSJetII hadron interaction model. The calorimetric energies are estimated from an
integration of energy deposits fitted by the Gaisser-Hillas function.

to calorimetric energies observed by FD. In the CORSIKA simulation discussed
as section 4.1.1, missing energies for primary protons and irons are shown in
Fig. 4.1. Fig. 4.1 also indicates the ratio between an integration of energy
deposits fitted by the Gaisser-Hillas function and primary energies for primary
protons (red) and irons (blue) using the QGSJet-II hadron interaction model.
In FD analysis, the missing energies for primary protons are adopted to estimate the primary energies. Thus, the discrepancy of missing energies between

78

CHAPTER 4. TA FD DETECTOR SIMULATION SOFTWARE

primary protons and irons is 5%, which is considered as systematic uncertaintyof the primary energy.
In next step, the number of photons emitted from fluorescence and Čerenkov
physical processes is calculated from each segment information. There are three
processes for photon emission from EAS: fluorescence light, direct Čerenkov
light and scattered Čerenkov light Fig. shown in 4.2).

Figure 4.2: The photon emission processes from extensive air showers. Not
only fluorescence light, but also direct Čerenkov light and scattered Čerenkov
light.

4.1.2

Fluorescence Light Emission

Fl for each wavelength λ are calculated
The number of fluorescence photons NiλdEdep.
from the energy deposit dX stored in each segment.
Fl
Niλ
=

dEdep. Fl
Yiλ (Hi ) SλFl (Hi ) dli
dX

(4.3)

where i is the ID of segments, YiλFl (Hi ) and SλFl (Hi ) are the fluorescence yieldand emitted spectrum on its height Hi , dli is the length of segment. Since
Fl,telthe fluorescence photons are emitted isotropy, the number of photon Niλinjected to telescope is calculated by
Fl,telFl Rayleigh
Mie
Niλ
= Niλ
Tiλ
(ri ) Tiλ
(ri )

Ai
,
4πri2

(4.4)

Rayleighwhere ri is the distance from the segment to the telescope, Tiλ(ri ) andMie
Tiλ (ri ) are a transmittance for the wavelength λ propagating the distance riof Rayleigh scattering and Mie scattering, respectively. Ai is an effective areaof the telescope. The effective area discussed here is defined as an area assumed
the combined mirror as a single spherical mirror.

4.1. EXTENSIVE AIR SHOWER GENERATION

4.1.3

79

Direct Čerenkov LightThe number of Čerenkov photons is also estimated from energy deposit stored
segment same as fluorescence. The calculation of Čerenkov needs the numberof electrons, and then the energy deposit should be divided the mean ionization
loss rate αeff (s) simulated by CORSIKA.
αeff (s) =c1+ c4 + c5 · s,
(c2 + s)c3

(4.5)

where c1 = 3.90883, c2 = 1.05301, c3 = 9.91717, c4 = 2.41715 and c5 = 0.13180[63].
In contract to fluorescence photon, the emitted spectrum depends on theshower age parameter in Čerenkov. Moreover only electrons with energies above
their threshold radiates Čerenkov photons. Thus, the energy spectrum fe (E, s)of an individual shower with shower age s and energy E is parameterized asfe (E, s) = a0 ·E
(E + a1 )(E + a2 )s(4.6)

where a0 , a1 , a2 are the same parameter described in [63]. Then, the numberof photon is calculated byZ
1 dEdep (x)CC
YiλC (Hi , si , E) Siλ(Hi , si , E) ∆li fe (E, s) d ln E.
Niλ =αeff (s) dX
ln Ethr(4.7)
C (H , s ) is Čherenkov yield and emitted spectrum
where YiλC (Hi , si ) and Siλi iwith shower age si and energy E, Hi is the altitude of the segment. Moreover
the Čerenkov light depends on the angular distribution. Therefore the good
approximation are applied in the Čherenkov angular distribution DiC ,


1
θi
C
Di (θi ) =
exp −
(4.8)
θ0
θ0
where θi is the angle between shower axis and emitted direction, θ0 is a pa−b
rameter determined from an threshold energy of Čerenkov light, θ0 = a EC
thr 、
(a, b) = (0.83, 0.67) [63]. Additionally considering the atmospheric scattering,C,telthe number of Čerenkov photons Niλis estimated as
C,tel
C Rayleigh
Mie
Niλ
= Niλ
Tiλ
(ri ) Tiλ
(ri )

4.1.4

2
Ai
DC (θi ) .
sin θi 4πri2 i(4.9)

Scattered Čerenkov Light

The observed Čerenkov photons at PMT camera include not only the direct injected photons but also scattered photons by atmospheric molecule and aerosol,
called scattered Čerenkov photons. Since Čerenkov photons are accumulated
by each segments, the scattered photons number is proportional to an integration of Čerenkov photons along the shower axis from the top of atmosphere.

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CHAPTER 4. TA FD DETECTOR SIMULATION SOFTWARE

Figure 4.3: The phase function of Mie scattering observed at the HiRes site,
Dugway [83].

The total number of Čerenkov photons N C Total with i segment is calculated thesum of emitted Čerenkov photons in this segment and the integrated Čerenkov
photons before this segments,
C passC TotalCNiλ= Niλ+ Ni−1,(4.10)C Total , scattered photons by Rayleigh process
From total integrated photons Niλ
RayC
MieC and photons transmissive photons to next segment
Niλ, Mie process Niλ
C passNiλare calculated.
C passC Total RayleighMieT(dli ) Tiλ(dli )
Niλ
= Niλ
h iλ
i
RayC
Rayleigh
C Total
Mie
Niλ
= Niλ
1 − Tiλ(dli ) Tiλ(dli )hi
MieC
C Total Rayleigh
Mie
Niλ
= Niλ
Tiλ
(dli ) 1 − Tiλ(dli )(4.11)(4.12)(4.13)

and, considering difference of angular distribution, called phase function, ofRayleigh and Mie processes, we calculate the number of photons injected fromthe segment to telescopes.
Ai Ray(θi )D
4πri2 iAi MieMieC Rayleigh
Mie
= Niλ
Tiλ
(ri ) Tiλ
(ri )
D
(θi )
4πri2 i

RayC,tel
RayC Rayleigh
Mie
Niλ
= Niλ
Tiλ
(ri ) Tiλ(ri )(4.14)

MieC,telNiλ(4.15)

Here, the phase function of Rayleigh scattering, DRay , is theoretically given by
DRay =

3(1 + cos2 θ),
16π(4.16)

4.1. EXTENSIVE AIR SHOWER GENERATION

81

and, the phase function of Mie scattering measured at near the TA site, Dugway
where HiRes located, is adopted in MC simulations. Fig.4.3 shows the phasefunction observed at the HiRes site, Dugway [83].
As discussed before, we estimate the number of fluorescence photons, directČerenkov and scattered Čerenkov photons from a longitudinal development
simulated by CORSIKA. In next step, waveforms detected at PMT camera issimulated using the detector simulation considering the lateral distribution of
EAS.

Figure 4.4: The number of fluorescence, direct Čerenkov, Rayleigh scatteredČerenkov and Mie scattered Čerenkov photons injected into telescope. The
top figure is the shower geometry across the FOV, the bottom figure is thegeometry going toward FD.

Fig. 4.4 represents the contributions of fluorescence, direct Čerenkov, Rayleighscattered Čerenkov and Mie scattered Čerenkov photons injected to the telescope. The red area shows the number of fluorescence photons, the blue areashows the direct Čerenkov photons, the purple area shows Rayleigh scattered

82

CHAPTER 4. TA FD DETECTOR SIMULATION SOFTWARE

photons and the green area shows the Mie scattered Čerenkov photons. The
top figure shows the result with the geometry across the FOV of FD which is almost fluorescence light and slightly Rayleigh scattered photons at the large slant
depth. The bottom figure shows the result with the geometry coming toward
FD which has large direct Čerenkov contamination and scattered Čerenkov
photons. Thus, the Čerenkov photon is systematic background photons in fluorescence technique.

4.2

TA FD Detector Simulation

4.2.1

Ray-tracing technique“Ray-tracing” technique is used in TA FD detector simulation in order to estimate the signal detected at PMT camera. In the ray-tracing simulation, a
trajectory for each photon is simulated on the reflected point on the mirror
and injected point on the PMT camera. Owing to reproduce the real response,the detail structure should be implemented in the software. Fig. 4.5 shows a

Figure 4.5: The structure of FD implemented in TA FD simulation softwarewith the ray-tracing trajectory emitted from line assumed shower axis.

detail structure of the FD station developed in the simulation software. The
combined spherical mirror, supporting columns are implemented in the sameas the actual FD station.
The ray-tracing calculation should need the computing power, because allof enormous photons should simulate their trajectory. For the purpose of ashorter calculation time, the number of photons for ray-tracing is multipliedby the factor of the mirror reflectance and the paraglas transmittance for eachtelescope which depend on the observation time. In concrete terms, the number

4.3. CROSS CHECKING OF SIMULATION SOFTWAREof photons injected to PMT camera NiRayTrace is given byZ
p,tel mirror para BG3
NiRayTrace = NiλRiλ τiλ τiλ Qiλ dλ83(4.17)

p,tel
mirror is the rewhere Niλis already derived from (4.4), (4.9) and (4.15), Riλpara
BG3flectance of the mirror, τiλ and τiλ are the transmittance of the paraglas andthe BG3 filter, Qiλ is the quantum efficiency of PMT. Since a non-uniformity of
the PMT cathode is dependent on the injected position, the factor is consideredafter ray-tracing.
In the beginning of ray-tracing, the position emitted photon is determinedby NKG function shown in (2.32). Next, the reflect point is determined arandom point inside the mirror effective area. The line is calculated by theemitted point and reflect point and it corresponding to “ray” of the photon.
The ray reflects at the mirror and enters PMT camera by tracing. Since themirror is the combined mirror, when the reflect point is selected the dip ofsegment mirror or the obscuration structure like the supporting column, theray-tracing of the photon is finished. Effects of the detector shielding andcombined mirror are considered by repeating NiRayTrace ray-tracing, and theinjection point at the PMT cathode is fixed.
After that, to calculate the non-uniformity of the PMT, we multiplied thenon-uniformity factor depending on the position of PMT, which is measured
by XY-scanner and shown in Fig. 3.11 section 3.3.1.
The injected photons are converted to the photo-electrons, amplified byeach PMT gain and digitized by the SDF through the response function. The
response function of SDF is shown in Fig. 4.6), the time constant is 50 ns.
After injected time is determined by the trajectory of ray, considered the response function, the waveform of PMT is generated by the sum of these signals.
Repeating the procedure, all PMT signal from the air shower is calculated andstored in each PMTs.

4.2.2

Night Sky backgroundThe background light is important to calculate the resolution and the performance in fluorescence technique. Thus, the value of mean and dispersion of
the background recorded SDF are stored in the database of every 10 minutes.
The 10 minutes corresponds to the time during which a star goes through the
FOV of a PMT. We use the database to obtain the actual background in our
detector simulation. The example of the data in the database is shown in Fig.
4.7.

4.3

Cross Checking of Simulation Software

In the TA collaborator, there are two developed softwares in official. We havecompared the results with another independently developed software in order
to confirm more confident in our analysis.

84

CHAPTER 4. TA FD DETECTOR SIMULATION SOFTWARE
0.2

ratio

0.15
0.1
0.05
0
0

200

400
600
time [ns]

800

1000

Figure 4.6: The response function of SDF. The time constant is 50 ns.

4.3.1

Comparison of Photon Emission Processes and Atmospheric ModelFirst of all, an identical air shower cascade are generated by identical GaisserHillas function with the same parameters. When we implemented the exactly
same function, our result should be in perfectly agreement within the computing
error. The common parameters are• Gaisser-Hillas function,• geometry of shower axis,• fluorescence yield and spectrum,• Čerenkov yield and spectrum and• U.S. atmosphere and the transmittance of aerosol.
By the same method to integrate, we generate the identical “standard” shower
using own software. Calculated the factor of attenuation by atmosphere andthe contribution from scattered Čerenkov light, the comparison figure of photon
density arrived at the mirror is shown in Fig. 4.8. The figure represent thephoton density of fluorescence, direct Čerenkov, Rayleigh and Mie scatteredČerenkov photons as a function of slant depth. The another software result isoverwriting as the black line with the perfectly agreement. As the result, we
confirmed that the exactly same physics model and parameters are implemented
in our software.

4.3. CROSS CHECKING OF SIMULATION SOFTWARE

85

Figure 4.7: The example of the database for the background observed by BRM
camera 06. The upper figure shows the mean for 214 “bundles”. The bundle
consists of the sum of 16 bins of FADC count and is continuously recorded by
SDF. The lower figure represents the dispersion for the same telescope. The
black line is the averaged value of the pedestal. The horizontal axis shows themeasured data (year/month).
.

4.3.2

Comparison of Ray-Tracing

After comfirmed perfectly agreement in the photon densities at the mirror, wemove to the comparison of ray-tracing. Note that, the ray-tracing is randomly
selected the injected point and reflected point to consider the effects of shielding
and the dip of segment mirrors. Thus, the standard light source is defined in oursoftware independently, and we compared the injected photon distribution at
the camera. Fig. 4.9 show the two-dimensional histogram at the PMT cameraby 10000 photons ray-tracing each other. The point of standard light is localedat CLF with altitude 4 km (0 km, 0 km, 4 km). Since the telescope direction
and structure is compared in this step, the calibration factor, for example
reflectance and transmittance, is 100%. While the left figure of Fig. 4.9 is our
result, the right figure is another result. We checked the result from the othertwo point light sources located at (10 km, 0 km, 4 km) and (0 km, -10 km,
4 km). The number of photons injected to camera is in reasonable agreement

86

CHAPTER 4. TA FD DETECTOR SIMULATION SOFTWARE

Areal Density at Mirror [m2]25

Fluorescence
Direct Cherenkov
Ray. Scattered Ckv
Mie Scattered Ckv
Another Results

20
15
10
5
0
0

100

200

300

400

500

600

700

800

2

Slant Depth [g/cm ]Figure 4.8: the photon density of fluorescence, direct Čerenkov, Rayleigh andMie scattered Čerenkov photons as a function of slant depth. The black line
represents another result with perfectly agreement.

within 2 % and the distribution of photons is also very similar. Therefore wehave confirmed that the telescope directions and the PMT camera alignments
are in agreement each other.

(a) Our result(b) Another result

Figure 4.9: The two-dimensional histogram at the PMT camera by 10000 photons ray-tracing using our software(left) and another independently developed
software (right). Our results is reasonable agreement with another result.

Chapter 5

TA FD Reconstruction
Software
The data measured and recorded by FD consists of digitized waveforms of 51.2
µs length from the PMT for each image pixel shown in Fig. 5.1. There are
90

30

80
25

60

FADC COUNTSFADC COUNTS

70

50
40
30

20

15

10

20
5
10
0

0
0

10

20

30

40

50

0

TIME [us]

10

20

30

40

50

TIME [us]Figure 5.1: The typical waveforms recorded by FD.

three processes to reconstruct an information of primary cosmic rays as follows:
1. PMT Selection,
2. Geometry Reconstruction, and
3. Shower Profile Reconstruction (Inverse Monte Carlo).
For each shower image we distinguish and select air shower signals for further
analysis and separate them from noise signals, for example night sky background and artificial light. In the geometry reconstruction, we determine thearrival direction and the core position of air showers. In shower profile reconstruction, we evaluate the energy and the depth of maximum development of
air showers. Here, we describe an “Inverse Monte Carlo” method in which we87

88

CHAPTER 5. TA FD RECONSTRUCTION SOFTWARE

search for an optimum solution via repeating Monte Carlo (MC) simulations
and comparing observed data with MC simulation.
When the FD station is triggered and stored the data, all PMT waveforms
are recorded for 12 files of each telescope separately. Since the recorded data
are too large (∼ 1 TB / month), only waveforms of PMT with a significant
signal are picked up, and combined 12 files to a single file. The threshold levelof significant is 3 σ, and by this procedure, the data size is reduced to about
10%.

5.1

PMT Selection

When a fluorescence light is incident on a PMT, the output current of the
PMT is increased during 1 ∼ 10 µs. At first, we selected the PMT which injects fluorescence photons emitted from EAS, and judged to use in the nextreconstruction. Moreover, the signal timing and the number of photo-electrons
are estimated in this step, which are important in the geometrical reconstruction and the shower profile reconstruction.

5.1.1

1st Selection

The waveform with air shower signal has the triangle shape as shown in Fig.
5.1, called “triangle filter”. Fig. 5.2 shows the schematic diagram of weighted

Figure 5.2: The schematic diagram of the weighted triangle filter.

triangle filter in order to search for an maximum significance σ(w, p) with peak

5.1. PMT SELECTION

89

p and width w in the waveform,
Pp+w

i=p−w
σ(w, p) = Pp+w

Fsub (i)W (i)i=p−w Prms (i)W (i)W (i) = w − |p − i|

(5.1)
(5.2)

where Fsub is the i-th bin of waveform subtracted by a pedestal mean, W (i)is the weight, Prms is the pedestal fluctuation. The mean and fluctuation ofeach pedestal are recorded by SDF. Th filter searches for the width w from 0 to
30-th bin and the peak bin p in all of the bins. When the pair of p and w withmaximum significance are found, the timing T and its error σT are calculated
by
T =
σT2 =

Pp+w

i=p−w i×Fsub (i)Pp+w
i=p−w Fsub

× 100 nsPp+w

2
i=p−w (T −i) ×Fsub (i)Pp+w
i=p−w Fsub

× 100 ns.

(5.3)
(5.4)

Here, 100 ns is the bin width corresponding to the 10 MHz sampling. The
timing T indicates the center of gravity in the assigned width. If the selected
width of a PMT is 30 bins, the PMT is treated as failed fitting for noise PMT
and is not used for the analysis. The number of photo-electrons Npe is given
by
p+3w
X
Npe = Gain ×
Fsub (i)(5.5)
i=p−3wwhere Gain is the conversion factor from the FADC count to the number ofphoto-electrons which is obtained by calibration as discussed in section 3.3.3.
The integration area between p ± w is enough larger than the width of thedetected pulse.
The distribution of significance of wighted triangle filter is shown in 5.3 comparing without and with shower signals. The significance distribution without
air shower signal is almost less than 6σ, but one with shower signals has a tailat the region of more than 6σ. Thus, we pick up the PMTs with significancemore than 6σ as the initial parameters for next step. The PMTs with a slightly
significance less than 6σ are used in the 4-th selection as discussed later.

5.1.2

2nd Selection

Although the 1st selection can remove almost all noise PMTs, the larger signal
noise caused by night sky background is selected by only 1st selection. When
air shower signals inject on the PMT camera, the PMTs with shower signals are
spatially continued distribution along a line. The line structure can be used in
the 2nd selection. In general, a line in X-Y plane is represented by a parameter
pair (ρ, ω) as
ρ = x cos ω + y sin ω
(5.6)

90

CHAPTER 5. TA FD RECONSTRUCTION SOFTWARE
1000

NUMBER OF DATANUMBER OF DATA

1000

100

10

100

10

1

1
0

2

4

6

8

10

12

14

16

0

2

4

6

8

S/N

10

12

14

16

S/N

Figure 5.3: The distribution of significance calculated the weighted triangle
filter. The left figure is the distribution without air shower signal, the rightfigure is one with air shower signal.

The ρ − ω space is called Hough space and this parameterization is called
Hough transform. A line group which goes through the same point (xi , yi ) isshown as the curve line in the Hough space. Therefore the cross point of all
curved lines which corresponds to all positions of PMTs is shown as the trackline on the PMT direction plane.
70

20

500

18
16

400

75

80
200

Number Of Data

theta [deg]

14
300

12
10
8
6

85
100

4
2

90
140 135 130 125 120 115 110 105 100 95
phi [deg]

0

0
0

5

10

15

20

25

30

35

40

45

beta [deg]Figure 5.4: The shower track (left) and the distribution of separate angle β(right). While the data from air shower are concentrated at the smaller separate
angle, the noise data are not located around zero.

The number of electron is the most around a shower axis, and the number
decreases the location far from the axis. Since fluorescence lights emit isotropic
photons, the PMT far from shower axis can not inject the fluorescence photons.
Therefore the shower track approximately considers the shower line, and theseparate angle between line and PMT direction are calculated. The larger
separate angle of PMT is defined as the noise PMT, and removed in next step.
However, the distribution of separate angle is dependent on a primary energy

5.1. PMT SELECTION

91

and geometry. Thus, the isolated PMT is removed using calculated distributionof separate angle as shown in Fig. 5.4.

5.1.3

3rd Selection

Although the isolated PMTs far from shower axis were excluded in 2nd selection, the noise PMTs beside shower axis are passed through 2nd selection.
Since timings of all selected PMTs are fitted in geometry reconstruction, a geometrical resolution is worse when we select the noise PMT. In the 3rd selection,
we use the timing information Ti estimated in 1st selection.
The injected timing of each PMT depends on arrival directions and core
locations of air showers. The expected arrival time ti is represented asti = t∗ +1 sin ψ − sin αi ∗rc sin (ψ + αi )(5.7)

where ψ is the angle between the FOV direction of PMT and shower coredirection, αi is elevation angle of PMT direction, t∗ is timing when the shower
core hits on the ground, r0 is the distance from FD station to shower core.
In the case of φ − θ of the Cartesian coordinates, (5.7) is not exactly approved. However, when α is enough small, it is approximately approved. The
separate angle αi , between the direction vector toward the center of shower
track, nc and the PMT viewing direction vector nproj
is given byiαi = cos−1 nproj
·
n
c
i

(5.8)

The αi of each PMTs and Ti estimated by (5.7) are fitted, and the isolated
PMTs are removed.
50

θ
shower axis

αitime [us]ψ

40track center

30

20

10

track line

φ

0
-10

-5

0

5
alpha [deg]

10

15

20

Figure 5.5: Shower track (left) and timing fitting to search for noise (right). In
the right figure, isolated PMT (-2.5◦ , 19 µs) is judged to noise signal.

92

5.1.4

CHAPTER 5. TA FD RECONSTRUCTION SOFTWARE

4th Selection

In this step, we select PMTs by timing information almost same as monoculargeometrical reconstruction. By 1st, 2nd, 3rd selection, only PMTs with > 6σsignificance are selected. Here, we include the PMT with small signals like lessthan < 6σ. Moreover the 4th selection works not only for the rejection but also
for the addition of the rejected PMTs in the previous selections.
First of all, the elevation angles of the PMT directions on the obtained
Shower Detector Plane (SDP) and timing of all selected PMTs are fitted bytiming fitting in monocular mode. The details for the timing fit and how to
obtain the SDP are described in section 5.2.3.
Next, the timing difference Ri from fitted function, pseudo χ2 and separate
angle with SDP βi are calculated for all PMTs, including all rejected PMTs in
the previous steps.
Ri = |f (αi ) − Ti |
(5.9)


Ri 2
χ2 =
(5.10)σTi~SDP
βi = P~i · V(5.11)

where αi is projected elevation angle to the SDP of i-th PMT, f (αi ) is theobtained timing form the fitted function at αi , σTi is the error of the peak
~SDP is the pertiming obtained by the 1st selection, P~i is the pointing vector, Vpendicular direction on the SDP. These parameters are used for the judgment
for addition/rejection of PMTs. These PMTs are categorized by the criteria,
which is shown in Tab. 5.1. There are two types of criteria: SOFT and HARD.
item
Ri
χ2
βi

SORT
< 1.2 µs
< 20
< 4◦

HARD
< 0.8 µs
< 15
< 2◦

Table 5.1: The criteria for selecting the candidate PMTs in the 4th selection.

Firstly, the SOFT criterion is applied in 4th selection. After finished SOFT
selection, the same routine is applied again with HARD criterion for the precise
selection.
Each categorized PMT is judged by the “linear” fitting of αi and Ti with theneighboring PMTs, which are selected by the separate angle with the judged
PMT < 5◦ and timing difference < 5 µs. The time difference from fitted
function Rlinear , pseudo χ2linear and the number of used PMTs Nlinear are used
for this judgement. The criteria are shown in Tab. 5.2 The judgement works forrejections for PMTs which have isolated position and timing. When the PMT
which is fulfilled in these criteria, this PMT is picked up and the 4th selection
starts again. If a PMT which is not in these two criteria, the PMT is rejected,

5.2. GEOMETRY RECONSTRUCTION
item
Nlinear
Rlinearχ2linear

93

THRESHOLD>3
1.2 µs20

Table 5.2: The criteria for judgement by the linear fitting in the 4th PMT
selection.

and then the 4th selection is also restarted. This iteration is continued until
there is no candidate for the addition or rejection of PMT.

Figure 5.6: The event display observed by FD comparing before(left) and after(right) PMT selections. The noise PMTs are removed by the PMT selection.

Fig. 5.6 shows the event display of actually observed shower candidate at
BRM. The data plot represents the PMT viewing direction, the color indicatesthe injected timing, the size shows the number of photo-electrons. The left figure is the data with > 3σ before all selections, and there are many noise PMTs
caused by night sky background. In the right figure after applied with 1th to
4th selections, the removed PMTs shows × mark. Therefore these selection are
valid for noise reductions.

5.2

Geometry Reconstruction

In the geometry reconstruction, we determine a shower geometry which is a core
position and an arrival direction of air showers. The methods reconstructed bydata of two FD stations, called “Stereo mode”, and by data of only 1 station,
called “Monocular mode”, are described here. In the both cases, first of all, thestation should be determined the Shower-Detector Plane (SDP) which consistsof the shower axis and the detector location. In general, the stereo mode is better resolution than the monocular mode, because the two SDPs are estimated

94

CHAPTER 5. TA FD RECONSTRUCTION SOFTWARE

by each station separately.

5.2.1

Estimation of the Line of Sight for Each PMT

In order to estimate the SDP, we must know the line of sight for each PMT.
These the line of sight is dependent on not only the location of PMT andthe combined mirror, but also the supporting column, the whole structure, its
shielding and non-uniformity of PMT. Therefore it is estimated from ray-tracing
using the detector simulation.
The simulation is simple, in which the parallel photons inject on the mirror,
and hence we estimate the directional characteristic of each PMT. The obtained
the directional characteristics are shown in Fig. 5.7. Although the each PMT
FOV of the camera is 1◦ , a distribution of sensitive direction is difference foreach PMT caused by a spherical aberration. We calculate a center of gravityof the distribution and use the direction as the line of sight for each PMT. The
directional characteristic is also important to calculate faster in Inverse Monte
Carlo as discussed later.

5.2.2

Shower-Detector Plane

Shower-Detector Plane (SDP) is the plane consisting of the FD station and ashower axis. The location of FD station is assumed as the single point because
the distance between the shower axis and FD station is enough large comparedwith the distance among telescopes. When the i-th PMT injects photons emitted from EAS, a normal vector of the SDP is perpendicular to all PMT of lineof a sight ki . Since the air shower photons are detected by several PMTs, theoptimal normal vector of SDP is estimated from the minimum value ofχ2 =X wi (n · ki )2i

σi2(5.12)

where σi is the normalize factor of the PMT FOV, σi = sin 0.8◦ 、wi is the wightof PMT. The PMTs with larger photons near the shower axis are weighted by
wi =

Nipe
N pe

.

(5.13)

where Nipe is the number of photo-electrons of i-th PMT, N pe is the averaged
value of all selected PMTs.
The geometry of stereo event is calculated from an intersection line of two
SDPs. Once the shower planes are determined, finding the stereo geometry
reconstruction is a very simple matter by simply intersecting the two SDPs as
shown in Figure 5.8. Thus, the shower axis s is given bys = n1 × n2
where n1 and n2 are the two SDP normal vectors.

(5.14)

95

0.5

Elevation Angle [deg]

10

0.4

5

Sensitivity

5.2. GEOMETRY RECONSTRUCTION

0.3

0
0.2

-5
0.1

-10
-10

-5

0

5

0

10

Azimuth Angle [deg]

5

0.2

0

0.15
0.1

-5

10

0.45
0.4

5

0.35
0.3
0.25

0

0.2
0.15

-5

0.1

0.05

-10
-5

0

5

10

0

-10

-5

0

5

Azimuth Angle [deg](b) PMT 247(c) PMT 119

0.2

5
0.15

0
0.1

-5
0.05

-10

10

0.3

5

0.25
0.2

0

0.15

-5

0.1
0.05

-10
-10

-5

0

5

10

0

0

0.35

10
Elevation Angle [deg]0.25

Sensitivity

Azimuth Angle [deg]10
Elevation Angle [deg]

0.05

-10
-10

Sensitivity

0.25

Sensitivity

0.3

Elevation Angle [deg]Elevation Angle [deg]10

Sensitivity(a) Total

-10

-5

0

5

Azimuth Angle [deg]Azimuth Angle [deg](d) PMT 255(e) PMT 127

100

Figure 5.7: The total directional characteristic of all PMTs in camera00 at
BRM (top) and of each PMTs located center, edge and corner. The directionis the relative angle from the line of sight of the telescope. The color map
indicates the sensitivity calculated by Ray-Trace simulation.

96

CHAPTER 5. TA FD RECONSTRUCTION SOFTWARE

Station2

Station1

Figure 5.8: Stereo geometry reconstruction. The shower axis is determined byintersecting two SDPs.

Shower Axist = tPrit = tiαir*Telescopet = t*

ψShower Core

Figure 5.9: Geometry reconstruction in monocular mode

5.2.3

Monocular Geometry Reconstruction

On the other hand, a shower geometry by mono reconstruction in which we use
data from a single station is estimated by taking account of signal timings ofeach PMTs, as shown in Figure 5.9. where r ∗ is a vector of the core position
and t∗ is the timing which the air shower injects on the ground. When timingtP emitted photon at the location ri is measured on i-th PMT at the timing
ti , the relation of these parameters is
ti = tP + 1c |ri |t∗ = tP + 1c |r ∗ − ri |,removing tP value,ti − t∗ =1(|ri | − |r ∗ − ri |) .
c

(5.15)(5.16)(5.17)

5.3. SHOWER PROFILE RECONSTRUCTION – INVERSE MONTE CARLO –97
Since the line of the sight of each PMT is already calculated, the elevation
angle ri toward the emitted location of photon is also known. The (5.17) istransformed to
1 sin ψ − sin αi ∗ti = t∗ +r(5.18)
c sin (ψ + αi )where ψ is the elevation angle on SDP toward the shower axis. The formula issame as 3th selection one. In the reconstruction routine, the optimal solutionsof t∗ , r∗ and ψ are determined by the minimized χ2 considering the error of
injection time σi .
"
2 . #X 
1∗
2∗ti − t − si (ψ)rχ =σi2
(5.19)ci

where si (ψ) issi (ψ) =sin ψ − sin αi.
sin (ψ + αi )(5.20)The r ∗ and ψ are estimated in (5.20) so that the shower axis and the core
location are determined.

5.3

Shower Profile Reconstruction – Inverse Monte
Carlo –As discussed in chapter 4, the fluorescence technique detects not only fluorescence light but also the Čerenkov light and its scattered. In TA, the reconstruction of shower profile is estimated by an “Inverse Monte Carlo” (IMC)
method. The IMC method is newly developed in TA and searched for an optimum solution via repeating Monte Carlo (MC) simulations and comparing
observed data with MC simulation including all photon emission and scatteredprocesses.
In this IMC procedure, we use the Gaisser-Hillas function as the longitudinaldevelopment curve. The first interaction point, X0 , and the interaction length,
λ, are fixed at 0 g/cm2 and 70 g/cm2 , respectively. The scanned values are
the optimum Xmax , the slant depth of maximum development and Nmax , theshower size at Xmax .

5.3.1

Xmax Determination

Initially, we obtain a optimum solution of Xmax . We calculate energy deposited along the shower axis from Gaisser-Hillas function with Xmax , X0 , λand Nmax = 1.0 and the mean ionization loss rate, αeff [63].
We adopt the fluorescence yield measured by Kakimoto et al. [61] as theabsolute value, the emitted fluorescence spectra measured by FLASH [92] andČerenkov yield estimated in [63]. Using atmospheric parameters measured by
the radiosonde and the LIDAR system, we evaluate the number of fluorescence

98

CHAPTER 5. TA FD RECONSTRUCTION SOFTWARE

photons, Čerenkov photons and scattered Čerenkov photons along the shower
axis.
Next, we simulate signals on all the FDs by ray-trace taking into the calibration constants, an atmosphere transmittance, a mirror reflectivity and QE× CE [52]. Moreover in order to increase the speed of the calculations, we use
a database of the directional characteristic shown in Figure 5.7. The number
on i-th PMT is simulated byof photo-electrons nsim
i
Z Z
sim
N (x, λ) × fi (~rx ) dλdx
(5.21)ni =x

λwhere N (x, λ) is the number of photons incident upon a telescope from aeach slant depth x, fi (~rx ) is the sensitivity of i-th PMT. Then, we calculate
and simulated
the following likelihood using the observed photo-electrons nobsiones nsim
from(5.21),
i
X
nsim
i
L=
{nobs
log
}
(5.22)
i
nsim,stiXnsim,st =nsim(5.23)ii

where nsim,stis the total number of photo-electrons on a station from MC
calculations, and ni /nsim,st is a probability for one photo-electron to enter thei-th PMT. While changing Xmax , we search for the optimum Xmax with the
maximum likelihood value.

5.3.2

Nmax Determination

After Xmax is determined, we estimate Nmax which is the scale of shower developments. Since the number of simulated photo-electrons, nsim
i , is calculated
under a condition of Nmax = 1, we determine Nmax from the ratio of the total
number of detected photo-electrons to the simulated one,P pe,datai niNmax = P(5.24)
pe .
i niFig. 5.10 shows an observed longitudinal development curve superimposedon the corresponding IMC fitting result. The contributions of the different
emission and scattering mechanisms are shown by different colors.

5.3.3

Energy Determination

The primary energy of an UHECR can be estimated from the sum of energy
deposited along the shower axis. In our analysis, we first calculate the calorimetric energy, Ecal , from the integration of the Gaisser-Hillas function with the
optimum Xmax and Nmax and minimum ionization loss rate αeff ,Z ∞Ecal =Ne (x, Nmax , Xmax , X0 )αeff (x)dx.
(5.25)
X0

5.3. SHOWER PROFILE RECONSTRUCTION – INVERSE MONTE CARLO –99
160

160

140

140

120

120

100

100
Npe

Npe

NPE detected by PMT

80

80

60

60

40

40

20

20

0

Fluorescence
Mie Cherenkov
Direct Cherenkov
Rayleigh Cherenkov
NPE detected by PMT

0
0

200

400

600

800

1000

1200

1400

1600

0

200

2

400

600

800

1000

1200

1400

1600

2

slant depth [g/cm ]slant depth [g/cm ]Figure 5.10: The shower signals injected from longitudinal development curvesof IMC fitting result and an observed air shower signal. The plot is the observed
data, the red show the contribution of fluorescence light, the blue indicates ofthe direct Čerenkov light, the purple and green shows the scattered Čerenkov
light of Rayleigh and Mie process, respectively.

By the way, Gaisser-Hillas function is transformed by
X − X0λXmax − X0
ξ=
,
λ
t=

and we obtain ξe
Ne (t) = Nmax
e−t tξ .
ξ

(5.26)(5.27)(5.28)As the result, the primary energy Ecal is estimated by the integration with Γfunction, 
dE e ξ
Ecal = λNmax
Γ(ξ + 1)
(5.29)dX ξ
Next, as discussed in section 4.1.1, we correct missing energy which does notdeposit in the atmosphere, such as neutral particles and their kinetic energies
and then we obtain estimate the primary energy E0 .

Chapter 6

Performance Evaluation
In this chapter, we evaluate a performance of the monocular mode of TA FD
with the simulation and reconstruction software developed by our collaboration.
In order to measure the energy spectrum and the mass composition of UHECRs,
we estimate the aperture of the monocular mode of TA FD and the resolutionis also estimated using the same way. In the mass composition analysis of
UHECRs, we simulate expectation lines of a averaged Xmax and its energy
dependence for primaries of protons and irons. After analyzed observed data,
an observed Xmax is compared with their expectation lines.

6.1

Resolution and Aperture of the Monocular Mode

6.1.1

Simulation ConditionsFirst of all, simulation conditions were defined for the MC simulation software.
EASs were simulated under the following conditions for both BRM and LR
trigger modes.
• Energy, E0 : 1017.5 ∼ 1020.0 eV random.
• Spectral index : γ = −1.
• Zenith angle : 0◦ ∼ 65◦ with isotropic distributions.
• Azimuth angle : 0◦ ∼ 360◦ with isotropic distributions.
• Core position : uniformly distribution within the circle of 35 km radiusfrom the CLF location.
• Hadron interaction models : two types of models, QGSJet-II or SIBYLL.
• Mass composition : two types of nuclei, protons or irons.
• Background photon : database of observed background photons generated
from means and standard deviations of FADC counts.
101

102

CHAPTER 6. PERFORMANCE EVALUATION• Calibration : calibration factors dependent on times as same as thoseused for data analysis.

Figure 6.1: Core location distribution of Monte Carlo showers. (0, 0) shows thecenter of the distribution corresponding to the location of CLF. The verticalaxis, Y-axis, is the direction from south to north, the horizontal axis, X-axis,
is from east to west. The yellow triangles indicate the FD station locations.

Fig. 6.1 shows locations of the FD stations and core positions of the simulated
EASs. The area of the core locations for MC was defined having enough sizeof area compared with an effective area of FDs.
Fig. shows the averaged Xmax of MC air showers induced by primary protons or irons generated by CORSIKA QGSJet-II and SIBYLL. The solid lines
indicate averaged Xmax values for the QGSJet-II interaction model, the dashedlines indicate those for the SIBYLL, the red lines are averaged Xmax values forprimary protons, the blue lines are those for irons. The difference of averaged
Xmax between protons and irons is about 100 g/cm2

6.1.2

Resolutions in the Monocular Mode

Resolutions in the monocular mode are estimated with analysis and studies
of MC events by comparing the MC thrown information with reconstructed
ones in event by event manner. Before comparisons, the following quality cuts
are applied in the monocular analysis, because faint shower signals with short

6.1. RESOLUTION AND APERTURE OF THE MONOCULAR MODE 103

1000<Xmax> (g/cm2)

950

Proton QGS-II

900

Proton SIBYLL
Iron QGS-II

850

Iron SIBYLL

800
750
700
650
600
550
500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 6.2: Averaged Xmax of protons and irons generated by CORSIKA
QGSJet-II and SIBYLL model without detector simulation. The solid line
shows the QGSJet-II, the dashed line shows the SIBYLL, the red line is theresult of protons, the blue line is the result of irons.

tracks are difficult to reconstruct to determine their geometries. Thus, short
tracks and small time extent events were removed with the following quality
cut.
• The geometrical and the longitudinal fittings are converged.
• The number of selected PMTs is larger than 10.
• The track length is larger than 10◦ .
• The time extent is larger than 2 µs.
• The reduced χ2 for the geometrical fitting is less than 20.
• The maximum depth of EAS is observed inside the field of view of FD,
Xstart < Xmax < Xend where Xstart is the start of slant depth detected
photons inside FOV, Xend is the end of slant depth detected photons
inside FOV.
When we reconstruct data triggered by head or edge of air showers without
Xmax inside the FOV FD, their showers are difficult to fit by shower profile
reconstructions, introducing large uncertainties of energies. The energy areoverestimated from reconstructed shower events which don’t observed Xmax
inside of FOV. In traditionally, we select air showers which Xmax positions are
inside of FOV.

104

CHAPTER 6. PERFORMANCE EVALUATION

We defined the simulation conditions of zenith angles and core locations,which are less than 55◦ , within 35 km, respectively. In order to avoid a contamination caused by geometrical resolutions in monocular mode, we applied
two addition cuts for consistencies with observed data and MC simulations.
• The reconstructed zenith angle is less than 55◦ .
• The reconstructed core location is within a circle with 25 km radius fromthe location of CLF.
Here, we define the set of eight quality cuts is a “standard cut”.
As discussed in simulation conditions, simulated showers are independently
triggered by both BRM and LR stations. When cosmic rays with energies
above 1019 eV inject within FD effective area, air showers induced by them
are triggered by both stations and hence are reconstructed from data recordedby both stations. When EASs are reconstructed by both stations, we adopt a
result of the station with the larger number of photo-electrons than that of theother station, because bright shower signals are easy to reconstruct geometries.
Here, resolutions in the monocular mode are estimated by comparing MC
thrown information with reconstructed one. At first, an open angle distribution,comparing arrival directions between thrown values and reconstructed ones, isshown in Fig. 6.3. The one sigma region which includes 68% of data is from0◦ to 7.4◦ . So then, the geometrical resolution is determined as 7.4◦ in the
monocular mode and it is worse than stereo reconstructions which is about 1◦ .
Histogram
Entries 48201
Mean
6.79
RMS
6.287

3500

Number of Events

3000
2500
2000
1500
1000
500
0
0

5

10
15
20
OpenAngle [deg]25

30

Figure 6.3: The open angle distribution comparing between thrown arrival
directions and reconstructed ones.

Fig. 6.4 and Fig. 6.5 show resolutions of the impact parameter and the Ψangle which is the angle in SDP shown in Fig. 5.9. The mean of the reconstructed impact parameter is -130 m and the averaged difference of the Ψ angle
is -2.9◦ . As a result, the monocular analysis has a tendency to reconstructinclined geometries at a shorter distance than actual ones.
The resolutions of other parameters in shower profile reconstructions areevaluated by the same way. The left figure of Fig. 6.6 shows comparisons6.1. RESOLUTION AND APERTURE OF THE MONOCULAR MODE 105
Histogram
Entries
48201
Mean-0.1104
RMS
2.217

8000
Number of Events

7000
6000
5000
4000
3000
2000
1000
0
-10

-8

-6

-4

-2

0

2

4

6

8

10

Rpreco - Rpsimu [km]Figure 6.4: The resolutions of the impact parameter estimation. It is a comparison between simulated and reconstructed values.

Histogram
Entries 48201
Mean-2.837RMS
10.47

Number of Events

6000
5000
4000
3000
2000
1000
0
-50 -40 -30 -20 -10

0

10

20

30

40

50

Ψreco - Ψsimu [deg]Figure 6.5: The angle resolution on SDP compared between simulated andreconstructed.

between thrown values of Xmax and reconstructed ones. The average is almost
zero and the RMS is 104 g/cm2 . The Gaussian fitted mean and the standard
deviation for the histogram from -150 g/cm2 to +150 g/cm2 is 9 g/cm2 and 66
g/cm2 , respectively. The right figure of Fig. 6.6 shows the energy dependenceof Xmax resolutions. The plot shows the mean and the error-bar shows thestandard deviation. The standard deviation is small at low energies, because
FD triggers low energy showers at only short distances so that these showers
are better geometrical resolutions than showers with a large distance. While
the mean of low energies is almost zero, those of high energies above 1019.0
eV is slightly systematic smaller than zero. Since EASs with high energies
have deep Xmax , these Xmax are usually located at an edge of FOV. Moreover,a reconstructed Xmax fluctuates within Xmax resolutions in monocular modeand must be observed within a FOV of FD. Showers with Xmax reconstructed
out of the FOV are removed under standard cuts. As a result, air showers

106

CHAPTER 6. PERFORMANCE EVALUATION

Number of Events

3000
2500

Histogram
Entries
48201
Mean-7.256105.1
RMS
χ2 / ndf
1451 / 27
2484 ± 17.6
Constant
Mean
9.378 ± 0.359
Sigma
66.44 ± 0.39

2000
1500
1000
500

Xmax(reco) - Xmax(simu) [g/cm22]

reconstructed smaller Xmax compared with the thrown Xmax are selected, andthen it causes the systematic small averaged Xmax in high energy region.

400
200
0
-200
-400
17.5

0
-500 -400 -300 -200 -100 0 100 200 300 400 500
Xmaxreco - Xmaxsimu [g/cm2]

18

18.5
19
log10 (E (eV))

19.5

20

Figure 6.6: The resolution of Xmax including protons of different energies under
the simulation condition of section 6.1.1 (left). The energy dependence for the
Xmax resolutions (right).

3000

Number of Events

2500

Histogram
Entries
48201
Mean-6.13821.75
RMS
χ2 / ndf
944.5 / 27
2572 ± 17.8
Constant
Mean-4.183 ± 0.072
Sigma
12.76 ± 0.07

2000
1500
1000
500
0
-100 -80 -60 -40-20 0 20 40 60( E0reco - E0simu ) / E0simu [%]80 100(E0(reco) - E0(simu)) / E0(simu) [%]Fig. 6.7 shows the energy resolutions and its energy dependence. The average of reconstructed energies are smaller than corresponding thrown energies at
the higher energy region. It is consistent with the tendency of the geometricalreconstruction which estimate inclined shower geometries at a shorter distances.
At high energies, the effect is large caused by the geometrical resolution in the
monocular mode. RMS of residual energy distributions are almost same at allenergy ranges. Since the systematic difference on the energy reconstructions are

80
60
40
20
0
-20
-40
-60
-80
17.5

18

18.5
19
log10 (E (eV))

19.5

20

Figure 6.7: The energy resolution including protons of different energies under
the simulation condition of section 6.1.1 (left). The energy dependence for theenergy resolutions (right).

caused by the systematics on the geometrical reconstruction, observed shower
energies are also underestimated. Therefore, we correct the systematic difference. Fig. 6.1.2 shows a linear fitting result of energy systematics. The error

6.1. RESOLUTION AND APERTURE OF THE MONOCULAR MODE 107√
bar shows the error of the mean, σ/ N , where σ is the standard deviation and
N is the number of events for each bins. Reconstructed energies are additionally corrected by the fitted results to avoid geometrical reconstruction biases
in monocular mode.
50

Mono Reconstructed Bias [%]

40
30
20
10
0
-10
-20
-30
-40
-50

17

17.5

18
18.5
19
Log (E0[simu] [eV])

19.5

20

10

Figure 6.8: The energy systematics are fitted by a linear function. Plots indicate
the means and error bars indicate the errors of the mean.

Number of Events

2500
2000

Histogram
Entries
48201
Mean
-1.06
RMS
22.93
χ2 / ndf
709.9 / 27
Constant
2424 ± 16.6
Mean
0.7765 ± 0.0743
Sigma
13.59 ± 0.08

1500
1000
500
0
-100 -80 -60 -40-20 0 20 40 60( E0reco - E0simu ) / E0simu [%]80 100(E0(reco) - E0(simu)) / E0(simu) [%]After the correction for the geometrical bias on energies, the energy resolutions were calculated and shown in Fig. again. We can see that the systematic
bias was corrected. Of course, the energy correction is applied in both MC
simulation and data in the same way.

80
60
40
20
0
-20
-40
-60
-80
17.5

18

18.5
19
log10 (E (eV))

19.5

20

Figure 6.9: The corrected energy resolution reconstructed by the monocularmode as a function of energy. The systematic bias was removed.

6.1.3

Estimations of Apertures

Here, we estimate a geometrical factor, called aperture, of FD stations which
is an important factor for calculation of energy spectra. The aperture of FDs
can not be estimated by analytical calculations, and it must be estimated by

108

CHAPTER 6. PERFORMANCE EVALUATION

the Monte Carlo simulation. The geometrical aperture AΩG simulated under
the MC condition discussed in section 6.1.1 is analytically calculated by,Z θmaxAΩG = πR2 ×2π sin θ cos θdθ(6.1)
0= (πR sin θmax )2(6.2)

where R is the radius of a thrown circle area of MC simulations on the groundand θmax is the maximum of a thrown zenith angle of MC simulations. Here,
substituting from R = 35 km and θmax = 65◦ in section 6.1.1, therefore AΩG =9930.87 km2 ·sr.
In order to obtain the correct aperture, detection efficiencies which are
the ratios between the simulated number of events and the corresponding reconstructed number of events with the standard cuts are needed. Then, theaperture, AΩ(E), is given byAΩ(E) = AΩG ×

MC )Nreco (Ereco
MC
Nthrown (Ethrown
)

(6.3)

where Nthrown is the thrown number of events within an energy bin calculatedMCfrom MC thrown (true) energies, Ethrown. Nreco is the reconstructed numberof events within the same energy bin calculated from reconstructed energies,
MC .
Ereco
To estimate the aperture by Monte Carlo simulation, the aperture depends
on the primary cosmic rays. Here, we used protons and irons for the QGSJet-II,and estimated the systematic difference of apertures for primary nuclei.
Nreco /Nthrown is calculated from our MC simulation which is generated by aspectral index, γ = −1.0 under simulation conditions. Reconstructed energies
fluctuate within the energy resolution shown in Fig 6.9. Thus, if the spectral index assumed in MC simulations differs from an observed one, effects ofbin-to-bin movements also make a discrepancy. Since observed UHECR spectrum almost follows spectral index about -3.1, the simulated showers are also
weighted with γ = −3.1 shown in Fig. 6.10.
Finally, FD aperture, AΩ(E), is obtained from AΩG multiplied by the ratio,
Nreco /Nthrown , shown in Fig. 6.10. The aperture is fitted by a empirical function
shown in (6.4) in order to avoid irregular variations on the aperture caused byfluctuations in the MC simulations.
B − log10 (E)log10 AΩ(E) = A 1 − exp(6.4)
CThe left plot of Fig. 6.11(a) shows the apertures for BRM and LR FD
stations in the monocular mode. The solid red and blue lines show the apertures
assuming proton primaries of BRM and LR, respectively, the dotted yellow andgreen lines show the aperture assuming iron primaries observed by the BRM
and LR stations, respectively. The difference of apertures indicate the difference
between detection efficiencies for protons and irons.

6.2. MASS COMPOSITION STUDY

109

109
108

Number of Events

107
106
5

10

104
103
102
10
1
16

16.5

17

17.5

18
18.5 19log (E (eV))

19.5

20

20.5

21

10

Figure 6.10: The weighted histogram of simulated and reconstructed energy
estimated from protons of QGSJET-II model.

The difference between the aperture for primary protons and that for irons
is large in the low energy region, because an averaged Xmax of irons is 100 g/cm2
smaller than that of protons. Although the detectors in the BRM station is
identical as the detectors in the LR station, the discrepancies in the aperture
come from the difference of the site altitudes. The altitude of the LR station
is 150 m higher than that of the BRM station. Thus, the BRM station favors
detectors of deeper Xmax showers than the LR station.
The right plot of Fig. 6.11(b) shows the combined aperture of the monocularmode analysis for the BRM and LR data.This curve was carefully calculated
for avoiding double counting with two stations for high energy EASs. The
green curve shows the combined aperture comparing the monocular aperturesby BRM and LR, respectively. Since both the BRM and the LR aperture
have a common sensitive area near the center of the array, the growth rate of
the combined aperture is smaller than the single station apertures in higher
energies. Fig. 6.11(c) indicates a comparison of combined aperture calculated
for primary protons or irons. The aperture for protons is systematic larger
than that for irons in less than 1018.0 eV. Since averaged Xmax values of ironprimaries are 100 g/cm2 smaller than those of proton primaries with the sameenergy, more iron showers with low energies are removed under the standard
cut of Xmax , Xstart < Xmax < Xend , than proton showers.

6.2

Mass Composition Study

6.2.1

Xmax Technique

Depth of the maximum developments, Xmax , is an important parameter todistinguish primary species of UHECRs.

110

CHAPTER 6. PERFORMANCE EVALUATION

BRM (P, QGS-II)
LR (P, QGS-II)
BRM (Fe, QGS-II)
LR (Fe, QGS-II)

LR (P, QGS-II)

103
Aperture [km2 sr]

Aperture [km2 sr]

103

BRM (P, QGS-II)

102

10

BRM + LR (P, QGS-II)

102

10
17.5

18

18.5
log (E (eV))

19

19.5

17.5

18

10

18.5
log (E (eV))

19

19.5

10

(a) BRM and LR (proton and iron)(b) BRM, LR and Combined (proton)

Combined (P, QGS-II)
3

Combined (Fe, QGS-II)

Aperture [km2 sr]

10

102

10
17.5

18

18.5
log (E (eV))

19

19.5

10

(c) Combined (proton and iron)Figure 6.11: The left figure is an aperture in BRM and LR only monocularmode. The iron and proton simulated results are shown. The right plot shows
the BRM and LR combined aperture comparing with BRM and LR monocular
aperture assumed pure proton primary. The bottom plot shows the comparisonof combined apertures estimated by protons and irons.

As shown in Fig. 6.2, an averaged Xmax is proportional to a primary energies. Since an iron consists of 56 nucleons, an iron with an energy, E, assumes
56 proton with an energy of E/56. Therefore, Xmax of irons are smaller thanthat of protons with the same primary energies of irons. Fig. 6.12 shows longitudinal development curves of protons ans irons at E = 1018 eV. The red
curves show longitudinal developments of protons, the blue curves are those ofirons. Xmax of irons are tend to be smaller than that of protons. The averaged
Xmax as a function of energy from 1017.5 eV to 1020 eV is already shown in
Fig. 6.2.

6.2.2

Acceptance Biases on Xmax Limited Fields of View of FDs

Since the FOV of the FD’s is limited in an elevation from about 3◦ to 33◦ ,observed Xmax distribution is an irregular distribution which is difference from

6.2. MASS COMPOSITION STUDY

111

Figure 6.12: Longitudinal development curves simulated for primary protons
and irons with the energy of 1018 eV. The red curves show longitudinal developments of protons, the blue curves are of irons.

an actual Xmax distribution, unless acceptance bias-free selections are applied.
This bias is amplified under the standard cut of Xmax within an observed FD
FOV, Xstart < Xmax < Xend . The reason for this bias in the Xmax distribution
is that most showers landing close to the FD have their Xmax at upper sideof the FOV and Xmax of observed developments is not located inside FOV or
deeper developed showers simply are not detected, as shown in Fig. 6.13. As
a result, the averaged Xmax appears to be larger i.e., deeper, than the averageof thrown or the unbiased values. A similar bias happens for high energy
showers. High energy showers develop as their Xmax deeper in the atmospherethan showers by lower primary energies, then for some near vertical showers
Xmax are below the station’s FOV, as shown in Fig. 6.13, and then, those deep
showers are removed and not used for further analysis. Therefore, the averaged
Xmax appears to be smaller.
In the monocular mode, the biases are evaluated from Monte Carlo simulations. Fig. 6.14 shows the averaged values of the simulated and reconstructed
Xmax with lines obtained by linear fittings of the plotted points. At the highenergy of 1019.5 eV, there is the acceptance bias of -60 g/cm2 and at the low
energy of 1017.5 eV, there is that of +10 g/cm2 .

6.2.3

Fiducial Volume Cuts

Under the standard cuts, there are large biases in reconstructed averaged Xmaxcaused by acceptance of FDs. Since averaged Xmax of data observed by FD
already includes these biases, we can compare the observed averaged Xmax
with the expected lines calculated from MC simulations for primary protons

112

CHAPTER 6. PERFORMANCE EVALUATION

Figure 6.13: Showers which can not be observed by FD caused by limited afield of view.

1000
Proton MC

950

Iron MC

900

Proton Reconstructed
Iron Reconstructed<Xmax> (g/cm2)

850
800
750
700
650
600
550
500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 6.14: Averaged values of simulated and reconstructed Xmax under only
standard cuts. Reconstructed averaged Xmax has large biases caused by limited
fields of view. The red line and blue dashed line indicate averaged Xmax withacceptance biases for primary protons and irons, respectively. The pink dashdotted line and sky-blue two-dotted line indicates thrown averaged Xmax forprimary protons and irons, respectively.

and irons.
However, we can determine selection rules to remove biased geometries ofshowers using MC simulations and apply bias-free cuts in a FD monocularanalysis with a similar way developed by Pierre Auger group [67], called fiducial
volume cut (FVC). In FVC, important parameters are not only Xmax , but also
Xstart and Xend . Xstart and Xend are upper and lower limits of the slant depth6.2. MASS COMPOSITION STUDY

113

along a shower axis that is inside the FD files of view. These limits are definedat where a shower axis intercepts the FD field of view limit or where a shower
axis intercepts the maximum distance which a shower with an energy is stilldetectable. Note that values for Xstart and Xend depend only on geometries ofshowers and not on a particular depth of shower profiles. In order to determine
optimum ranges for Xstart and Xend , we use a averaged Xmax as a functionof Xstart and Xend in Fig. 6.15. The pink plots indicates results of mixed
composition which consists of 50% protons and 50% irons.

Figure 6.15: Averaged Xmax as a function of Xstart and Xend in order to determine the optimum range for Xstart and Xend . The red and blue plots indicate
results for primary protons and irons, respectively. The pink plots indicate
results for a mixed composition which consists of 50% protons and 50% irons.

For 700 g/cm2 < Xstart and Xend < 900 g/cm2 , the averaged Xmax haslarge biases compared with the other averaged Xmax . Moreover averaged Xmax
at a small Xstart is systematic smaller than thrown one caused by a Čerenkov
contamination. Biased ranges of Xstart and Xend should be excluded for biasfree measurements of Xmax .
Therefore, we determined selection rules on addition to standard cuts discussed in section 6.1.2.
• The minimum viewing angle is larger than 20◦ .
• The Ψ angle within SDP is smaller than 120.
• The Xstart is larger than 150 g/cm2 .
• The value of Xstart − Xend is larger than 150 g/cm2 .
• The Xstart is smaller than 700 g/cm2 and Xend is larger than 900 g/cm2 .
A set of cuts with the criteria listed above is defined as “fiducial volume cut(FVC)”. These criteria are determined to fulfill small acceptance biases within

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CHAPTER 6. PERFORMANCE EVALUATION

10 g/cm2 for all energy ranges and to leave as many EASs as possible. The first
three cuts are effective to remove EASs with geometries of a large Čerenkov
contamination. The last two cuts are impacts to avoid biased geometries of
EASs.
After applied with FVC, the same plot of Fig. 6.14 is shown in Fig. 6.16
using showers survived in FVC. The red and blues lines of averaged Xmax withthe acceptance bias for primary protons and irons are close to the pink andsky-blue lines of thrown averaged Xmax for them. To compare at 1019.5 eV,
the acceptance bias under FVC, 10 g/cm2 , is much smaller than that understandard cuts, 60 g/cm2 .
1000
Proton MC

950

Iron MC

900

Proton Reconstructed
Iron Reconstructed<Xmax> (g/cm2)

850
800
750
700
650
600
550
500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 6.16: Simulated and reconstructed of averaged Xmax under FVC. Reconstructed averaged Xmax is much close to thrown one. These lines are thesame definitions shown in Fig. 6.14.

We estimated the averaged Xmax with acceptance biases under FVC using
not only QGSJet-II, but also SIBYLL model as shown in Fig. 6.17.
However, although we have successfully developed and applied the bias-free
analyses of averaged Xmax , large percentages, about 50%, of observed EASs are
removed under FVC. Although the acceptance bias is larger in measurements
applied with only the standard cuts, more statistic is achieved than one applied with FVC. Therefore, we also compare the results FVC with the results
only with the standard cuts to check whether both results are consistent or
not. It is also essential important to understand the discrepancy between masscomposition analyses and results by the TA and those by the Pierre Augergroup.

6.2. MASS COMPOSITION STUDY

115

1000

<Xmax> (g/cm2)

950

Proton QGS-II Rec.

900

Proton SIBYLL Rec.
Iron QGS-II Rec.

850

Iron SIBYLL Rec.

800
750
700
650
600
550
500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 6.17: Averaged Xmax with acceptance biases for primary protons andirons with QGSJet-II and SIBYLL model under FVC. The solid lines indicate
results using QGSJet-II model. The dashed lines indicate results using SIBYLL
models. The red and blue color indicate primary protons and irons, respectively.

Chapter 7

Data Analysis
In this chapter, we report analyzed results for data collected by BRM andLR from January 2008 to September 2011. Firstly, we confirm that the several
distribution of the shower parameters obtained data reconstructions are in good
agreement with MC expectations not only with the standard cut, but also withthe fiducial volume cut. Secondly, the observed averaged Xmax are comparedwith the expectations simulated by the primary protons and irons, and thirdly
we discuss about mass composition. Moreover, we evaluate the energy spectrumwith after careful studies about the estimation of the aperture and the live time.

7.1

Data Set

In this analysis, the data collected with FDs in the BRM and in the LR stations
are analyzed with the monocular mode analysis described in Chapter 5 during
3.7 year from January 2008 to September 2011. Some of the data includes
cloudy days. As discussed in section 3.4.4, the data for the analysis is selectedbased on weather at that time recorded as the WEAT code because the WEAT
code monitoring covers observation period of the data.

7.1.1

Calculation of Live Time

When FD stations are making event triggers for data acquisitions, there aredead times, ∼ 4 ms, to collect data from all telescopes. Since the BRM and LR
stations are independently making event triggers, we can calculate the following
three different live times.
• Stereo live time
• BRM monocular live time
• LR monocular live time
Fig. 7.1 shows the schematic diagram of the three different types of dead time
appearances. There are live times and dead times for the BRM and the LR
117

118

CHAPTER 7. DATA ANALYSIS

Figure 7.1: The schematic view of calculation of BRM and LR live time. Thereare 3 types of live time: stereo (blue), BRM monocular (orange), LR monocular(green).

Figure 7.2: The three types of live times with the WEAT code cut. These
broken lines indicate the total live time durations in the stereo (blue), theBRM station (orange) and the LR station (green). The growth rates of live
times vary with the seasons.

stations, independently. When both BRM and LR stations are operating without dead times to observe showers at the same time, the time durations areaccumulated as the stereo live time shown as the blue area in Fig. 7.1. When
only a single station observes without dead times, operating time durations
are accumulated as a live time of the single station. Even if both stations areoperating, when there are dead times in one station, the time durations are calculated as the live time of the other station, not as the stereo live time. Thus,
to accumulate as the stereo live time, the BRM and the LR stations need to
be operated without dead times at both stations.

7.1. DATA SET

119

Using the method to calculate live times, the three types of live times are
estimated without the WEAT code cut.
• Stereo live time : 2307.1 hours• BRM monocular live time : 985.1 hours• LR monocular live time : 486.0 hours
After we apply the WEAT code cut with the criteria discussed in section 3.4.4,• Stereo live time : 1716.7 hours (74%)• BRM monocular live time : 681.9 hours (69%)• LR monocular live time : 337.7 hours (70%)
where the values in the parentheses are the percentages compared with live
times before WEAT code selections. The about 70% observation time aresurvived after the WEAT code cuts.
The accumulate observation times are shown in Fig. 7.2. These brokenlines indicate the total live time in the stereo (blue), the BRM station (orange)
and the LR station (green). All of the growth rates variates depending on theseasons, because the observation time per night in the winter is longer thanthat in the summer. As the other importance thing, the live time of LR isapparently shorter than that of BRM and the growth rate of LR is also smaller
than that of BRM. It is for this reason that when we have started LR remote
operations from May 2009, the finish times of LR observation are one hourearlier than that of the BRM stations for the safety operations. Thus, the live
time of LR is shorter than that of BRM.

7.1.2

Number Spectrum

After the event selections based on a weather evaluated as the WEAT code areapplied, the selected data measured at the BRM or the LR stations are analyzed
in each monocular mode. Number spectra corresponding to the histograms ofreconstructed primary energies are shown in Fig. 7.3(a). The red line showsa histogram of energies reconstructed in BRM monocular mode, the blue line
shows a histogram of energies reconstructed in LR monocular mode.
At higher energies above 1019 eV, most EASs are reconstructed at boththe BRM and the LR stations because they have the common detectable area.
Thus, if EASs are successfully analyzed by both stations, in order to avoid adouble-counting of EASs, we select results reconstructed at a station with thelarger number of photo-electrons than the other station in the same way ofMonte Carlo simulations.
The three types of the number of reconstructed showers under the standard
cuts are shown in Tab. 7.1. From the number of reconstructed EASs and thelive times shown in Fig. 7.2, we observe EASs every 10 minute by the roughly

120

CHAPTER 7. DATA ANALYSISBlack Rock Mesa
Long Ridge

3

10
Number of Events

BRM + LR

102

10

1
16

16.5

17

17.5

18
18.5 19log (E (eV))

19.5

20

20.5

21

10

(a) Standard cut

Black Rock Mesa
Long Ridge

103
Number of Events

BRM + LR

102

10

1
16

16.5

17

17.5

18
18.5 19log (E (eV))

19.5

20

20.5

21

10

(b) Fiducial volume cut

Figure 7.3: Number spectra under the standard cuts (a) and under the FVC(b). There are three types of reconstructed energy histograms for the BRM
station (red), the LR station (blue) and combined them (green).

estimation from the number of showers and the live time in the TA experiment.
Additionally, to avoid the acceptance biases on averaged Xmax in the masscomposition analysis, we apply the FVC to the observed shower candidates as7.2. DATA/MC COMPARISON
item
BRM
LR
Combinedstandard cut
10929
11756
22417

121
+fiducial volume cut (FVC)
5711 (62%)
5575 (47%)
11127 (50%)

Table 7.1: The number of reconstructed EASs under both selection rules.

discussed section 6.2.3. The number of showers after FVC are also shown in
Tab.7.1. Thus, the 50% EASs are removed by the FVC in return for the biasfree measurement on averaged Xmax . The number spectra after the FVC isshown in Fig. 7.3(b). Comparing the histogram before the FVC with that after
the FVC, there are the similar reductions of EASs at all energies, although the
reductions are slightly large at low energies.

7.2

Data/MC Comparison

As further enhancement of our reliability in our analysis, the distributions of theseveral parameters obtained from the reconstructions of the observed data arecompared with the expected ones estimated from MC simulations. Moreover,
we apply the two types of selection rules which are the standard cut and theFVC, and we compare the observed distributions of the several parameters withthe expected ones not only under the standard cut, but also under the FVC.
In our MC simulations, we generate EASs events with the spectral index,
γ = −1.0 with energies from 1017 eV to 1020 eV as discussed in section 6.1.1.
Since observed spectra almost follow a spectral index, γ = −3.1, and hence weassume that the spectrum index is -3.1 in all energy ranges in the Data/MC
comparisons.
Results of Data/MC comparisons are shown in appendix at the end of thethesis. In these figures, the black plots indicates the distributions observed at
the BRM or LR station, the red or blue histograms indicates the expected distributions estimated from MC simulations at the BRM or LR station for primary
protons and irons, respectively. The distributions of each MC is normalized to
the number of observed data. These plots are in reasonable agreements between
data and MC simulations not only under the standard cut, but also under the
FVC.

7.3

Pull Plots

Air showers reconstructed by both stations are useful to confirm accuracies
of a reconstructed energy and Xmax . Comparing each detectors installed at
the BRM and the LR stations respectively, they are completely identical eachothers, and hence we consider that both stations have same resolutions on

122

CHAPTER 7. DATA ANALYSIS

Number of Events

30

Data
MC (QGS-II)

25
20
15
10
5
0
-2.5

-2

-1.5

-1 -0.5 0 0.5 1
ln( E0BRM / E0LR )

1.5

2

2.5

(a) Energy

Number of Events

50
40

Data
MC (QGS-II)

30
20
10
0
-500 -400 -300 -200 -100 0 100 200 300 400 500(XmaxBRM - XmaxLR) / 2 [g/cm2](b) Xmax

Figure 7.4: Pull plots of energies (a) and Xmax (b). The peak energy of reconstructed EASs including pull plots is 1018.6 eV.

reconstructed energies and Xmax . Therefore, the standard deviation from distributions of the difference between both reconstructed results are given by
q
2
2 .
+ σLR
(7.1)
σBRM+LR = σBRM
Thus, we can estimate resolutions from distributions of a difference of reconstructed results in the BRM and the LR stations, called as “pull plot”. Thereare 234 events reconstructed by both stations, and pull plots for reconstructedenergies and Xmax are shown in Fig. 7.4. Since the distance between BRM and7.4. MASS COMPOSITION ANALYSIS123

LR is 35 km, only cosmic ray above at least 1018.5 eV can be reconstructed atboth stations. Therefore, a peak energy of EASs reconstructed at both stations
including pull plots is 1018.6 eV.
The gaussian fitted mean and sigma of pull plot are• Energy (Data) : Mean = -0.08 ± 0.04, Sigma 0.46 ± 0.05
• Energy (MC) : Mean = -0.03 ± 0.01, Sigma 0.47 ± 0.01
• Xmax (Data) : Mean = 12 ± 8 g/cm2 , Sigma 116 ± 7 g/cm2• Xmax (MC) : Mean = 3 ± 1 g/cm2 , Sigma 120 ± 1 g/cm2 ,respectively. The energies reconstructed at the LR station are 8% higher thanones reconstructed at the BRM station, and 8% is smaller than systematic
uncertainties of TA FD. From these result, we evaluated the robust energy
and Xmax resolutions without MC simulations, which are 40% and 120 g/cm2 ,respectively.

7.4

Mass Composition Analysis

Since MC simulations have been confirmed reasonable agreement with measured data, the averaged Xmax values reconstructed at the BRM and LR stations are compared with the expectation ones estimated from MC simulations
for primary protons and irons.
1200

1100

1100

1000

1000

Xmax (g/cm2)

Xmax (g/cm2)

1200

900
800
700
600
500

900
800
700
600
500

400
17

17.5

18

18.5

19

log10( E(eV))(a) BRM

19.5

20

400
17

17.5

18

18.5

19

19.5

20

log10( E(eV))(b) LR

Figure 7.5: Scatter plot of reconstructed energy and Xmax applied the fiducial
volume cut in BRM and LR monocular analysis.

7.4.1

Mass Composition Results in BRM or LR Station

At first, mass composition measurements under the FVC are shown in thissection, and next, ones under the standard cuts are shown in section 7.4.3.

124

CHAPTER 7. DATA ANALYSISThe scatter plots of energy and Xmax reconstructed at the BRM and the LR
station under the FVC are shown in Fig. 7.5. From the measured data in Fig.
7.5, averages are calculated and compared with the expected lines estimatedfrom MC simulations for primary protons and irons using the QGSJet-II model
as a hadron interaction model. The results are shown shown in Fig. 7.6. The
plots are √the average of Xmax , the error bars are mean errors of the averaged
Xmax , σ/ NData where NData is the number of events. In Fig. 7.6, the pink andsky blue lines indicates the averaged Xmax of thrown MC simulations which are
estimated only to use CORSIKA simulations. The red and blue lines indicate
the averaged Xmax which are calculated in our MC simulations with acceptancebiases of limited FOV of FDs.
The mass composition in the energy range of 1017.5 eV ≤ E ≤ 1018.5 eV
indicated an evidence of the transition from heavy to light compositions. The
mass composition above 1018.5 eV was consistent with the pure proton expectation.
1000

1000
Proton MC

950

Proton Reconstructed

900

Data

<Xmax> (g/cm2)

750
700

Iron Reconstructed
Data

800
750
700

650

650

600

600

550

550
18

Proton Reconstructed

850

800

500
17.5

Iron MC

900

Iron Reconstructed

850<Xmax> (g/cm2)

Proton MC

950

Iron MC

18.5
19log (E (eV))10(a) BRM

19.5

20

500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

(b) LR

Figure 7.6: The measured and expected of averaged Xmax in the monocularanalyses at the BRM station (a) and the LR stations (b) under the fiducial
volume cuts. The pink and sky blue lines indicates the averaged Xmax ofthrown MC which are estimated only to use CORSIKA simulations. The redand blue lines indicates the averaged Xmax which are calculated in our MC
simulations with acceptance biases of limited FOV of FDs. The MC lines are
estimated using the QGSJet-II model as a hadron interaction model.

7.4.2

Mass Composition Results in Combined Mode

Next, in order to calculate the averaged Xmax with more statistics of EASs,
we evaluate the averaged Xmax from a combination of observed EASs analyzed
at both the BRM and the LR stations. As the same way of MC simulations,
we select results reconstructed at a station with the larger number of photoelectrons than the other station.

7.4. MASS COMPOSITION ANALYSIS

125

1200

Xmax (g/cm2)

1100
1000
900
800
700
600
500
400
17

17.5

18

18.5

19

19.5

20

log10( E(eV))
Figure 7.7: Scatter plots of energies and Xmax reconstructed at both the BRM
and LR stations under the fiducial volume cuts.

With the criteria, a scatter plot of energies and Xmax reconstructed at both
stations under the FVC is shown in Fig. 7.7, and the combined averaged Xmax
are shown in Fig. 7.8 with the expected lines estimated from MC simulations
with the same criteria as shown in Fig. 6.16 In Fig. 7.8, the plots indicate theaveraged Xmax , and the pink and sky blue lines indicates the averaged Xmaxof thrown MC which are estimated only to use CORSIKA simulations. The
red and blue lines indicates the averaged Xmax which are calculated in our MC
simulations with acceptance biases of limited FOV of FDs. The MC lines are
estimated using the QGSJet-II model as a hadron interaction model.
These results indicate the same tendency as the BRM and LR monocularanalysis results shown in the previous section, which have transitions at low
energy around 1018.0 eV and the proton dominant at high energies above 1019
eV.
Moreover, measured averaged Xmax values are compared with ones obtainedfor MC events simulated using a hadron interaction model of QGSJet-II or
SIBYLL. The result is shown in Fig. 7.9 with the number of observed EASs.
The interpretation for the mass composition is not changed when we adopt the
SIBYLL MC simulation. Comparing observed averaged Xmax values with the
QGSJet-II or the SIBYLL model, measured averaged Xmax values are better
agreements with expected averaged Xmax values for the QGSJet-II model thanthose of SIBYLL model in high energies above 1018.5 eV.
To discuss mass composition results using Xmax technique, it is important
to compare not only averaged Xmax , but also distributions of observed Xmax

126

CHAPTER 7. DATA ANALYSIS

1000
Proton MC

950

Iron MC
Proton Reconstructed

900

Iron Reconstructed
Data<Xmax> (g/cm2)

850
800
750
700
650
600
550
500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 7.8: The averaged Xmax as a combination of both BRM and LR reconstructed events under the fiducial volume cuts. The pink and sky bluelines indicates the averaged Xmax of thrown MC estimated by only CORSIKA
shower generations. The red and blue lines indicates the averaged Xmax withthe acceptance bias of each FD station. The MC lines are estimated using the
QGSJet-II model as a hadron interaction model.

with expectations estimated from MC simulations for primary protons or irons.
We can compare shapes of observed Xmax distributions with expected ones including averaged Xmax values. Therefore, distribution of Xmax are shown in
Fig. 7.10 under several energy ranges. The plots indicate the measured Xmax
analyzing observed data, and the red and blue histograms of Xmax are estimated in MC simulations with primary protons, irons, respectively. The pink
histogram of Xmax indicates results of mixed composition which are estimatedfrom MC simulations for 50% proton and 50% iron primaries. In results withenergies of 1017.5 eV ≤ E < 1017.8 eV, the observed distribution of Xmax agrees
with the mixed one. Until results with energies of 1018.4 eV ≤ E < 1018.6 eV,
the measured distribution of Xmax moves from the mixed one to the proton
one. Above 1018.6 eV, the observed distribution of Xmax is consistent with the
expected distribution for proton primaries. Thus, these figures also indicatethat there are transitions of dominant components from heavy to light nuclei
from 1017.5 eV to 1018.5 eV and proton dominants above 1018.5 eV.

7.4. MASS COMPOSITION ANALYSIS

127

Figure 7.9: The comparison with data and MC line estimated from QGSJet-IImodel and SIBYLL model under the fiducial volume cuts. The number symbols
indicates the number of EASs in each bin.

7.4.3

Compatibility of Xmax Distribution on Kolmogorov-Smirnov
TestHere, we apply Kolmogrov-Smirnov test (KS test) to the evaluation of compatibility between the observed Xmax distribution and Xmax distribution expectedby proton, iron or mixed mass composition.
The KS test is a standard method to use to estimate quantitatively whether
two distribution functions differ stochastically or not [95]. In the KS test, a
statistical value of compatibility is calculated using the difference of cumulative
probabilities. Fig. 7.11 shows the cumulative probabilities for observed Xmax
compared with expected distributions of Xmax estimated from MC simulation
for primary protons, irons, mixed compositions with energies from 1018.4 eV to1018.6 eV shown in Fig. 7.10(e). In order to evaluate the compatibility, the Dvalue is calculated byD=

max−∞<x<∞|SN (x) − P (x)|(7.2)

where SN (x) and P (x) are the cumulative probabilities of observed Xmax distribution and expected distributions estimated from MC simulations, respectively. Hence, the D values are also shown in Fig. 7.11 using the plots witha broken line. In the energy range from 1018.4 eV to 1018.6 eV, the observed
Xmax distribution is compatible with the expected distribution estimated from
MC simulations for primary protons. From the D value, the probability P is

128

CHAPTER 7. DATA ANALYSIS
Data
P (MC)Fe (MC)
Mixed (MC)

700
500
400
300

400
300
200

550

600

650

700

750

800

850

900

950

0
500

1000

200
150

50
550

600

Reconstructed Xmax [g/cm2]

650

700

750

800

850

900

950

0
500

1000

550

600

Reconstructed Xmax [g/cm2]
10

3

Data
P (MC)Fe (MC)
Mixed (MC)Data
P (MC)Fe (MC)
Mixed (MC)

700

750

800

850

900

950

1000

10

Data
P (MC)Fe (MC)
Mixed (MC)102

Entries

102

650

Reconstructed Xmax [g/cm2]

3

102

Entries

Entries

250

100

100

10

Data
P (MC)Fe (MC)
Mixed (MC)

300

100

200
0
500

350

Data
P (MC)Fe (MC)
Mixed (MC)500

Entries

Entries

600

Entries

800

10

10
1

1
500

550

600

650

700

750

800

850

900

950

500

1000

550

600

P (MC)Fe (MC)
Mixed (MC)

750

800

850

900

950

1000

1.5
1
0.5

P (MC)Fe (MC)
Mixed (MC)

2

600

650

700

750

800

850

1.5
1

900

950

0
500

1000

550

600

650

700

750

800

850

900

950

750

800

850

900

950

60
40

0
500

550

600

Reconstructed Xmax [g/cm2]

700

750

800

850

900

950

10

1000

1

550

600

650

700

750

800

850

900

950

1000

Data
P (MC)Fe (MC)
Mixed (MC)

40
35
30
25
20
15
10
5
0
500

1000

550

600

650

700

750

800

850

900

950

1000

Reconstructed Xmax [g/cm2]
Data
P (MC)Fe (MC)
Mixed (MC)

Entries

Entries

Entries

650

102

Data
P (MC)Fe (MC)
Mixed (MC)950

P (MC)Fe (MC)
Mixed (MC)Reconstructed Xmax [g/cm2]

102

900

45

Data
P (MC)Fe (MC)
Mixed (MC)

80

1000

850

(c) 18.0 ≤ log(E) < 18.2,
1755 events
Entries

Entries

100

Entries
700

800

Reconstructed Xmax [g/cm2]

20
650

750

1.5

0
500

1000

(a) 17.5 ≤ log(E) < 17.8, (b) 17.8 ≤ log(E) < 18.0,
3590 events
2482 events

600

700

2

Reconstructed Xmax [g/cm2]

Data
P (MC)Fe (MC)
Mixed (MC)

650

0.5

Reconstructed Xmax [g/cm2]

550

600

2.5

0.5
550

550

Reconstructed Xmax [g/cm2]

2.5

Data / MC

2

200
180
160
140
120
100
80
60
40
20
0
500

500

Data / MC

2.5

Data / MC

700

Reconstructed Xmax [g/cm ]Reconstructed Xmax [g/cm ]

0
500

650

2

2

10

Data
P (MC)Fe (MC)
Mixed (MC)

10

1
1
1
500

550

600

650

700

750

800

850

900

950

500

1000

550

600

Reconstructed Xmax [g/cm2]
P (MC)Fe (MC)
Mixed (MC)

700

750

800

850

900

950

1000

500

1.5
1

P (MC)Fe (MC)
Mixed (MC)

2.5

0.5

2

600

650

700

750

800

850

1.5
1

900

950

0
500

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550

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650

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950

1000

6

2
0
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Reconstructed Xmax [g/cm ]

550

600

650

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950

1000

3
2

0
500

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1000

Reconstructed Xmax [g/cm2]
Data
P (MC)Fe (MC)
Mixed (MC)Data
P (MC)Fe (MC)
Mixed (MC)10

Entries

1

650

Data
P (MC)Fe (MC)
Mixed (MC)Reconstructed Xmax [g/cm ]Entries

Entries12

Data
P (MC)Fe (MC)
Mixed (MC)

1000

1
550

2

10

950

P (MC)Fe (MC)
Mixed (MC)

4

4

0
500

900

5

Entries

85850(f) 18.6 ≤ log(E) < 18.8,
234 events

Data
P (MC)Fe (MC)
Mixed (MC)10

Entries

Entries

10800

Reconstructed Xmax [g/cm2](e) 18.4 ≤ log(E) < 18.6,
504 events

Data
P (MC)Fe (MC)
Mixed (MC)

15

750

1.5

0
500

25
20

700

2

Reconstructed Xmax [g/cm2](d) 18.2 ≤ log(E) < 18.4,
1028 events

650

0.5

Reconstructed Xmax [g/cm2]

550

600

2.5

0.5
550

550

Reconstructed Xmax [g/cm2]

Data / MC

2

Data / MC

Data / MC

2.5

0
500

650

Reconstructed Xmax [g/cm2]

1

1

10-1
500

550

600

650

700

750

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850

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950

10-1
500

1000

550

600

2

750

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950

P (MC)Fe (MC)
Mixed (MC)1
0.5

P (MC)Fe (MC)
Mixed (MC)

2
1.5
1
0.5

650

700

750

800

850

600

900

950

1000

Reconstructed Xmax [g/cm2](g) 18.8 ≤ log(E) < 19.0,
123 events

0
500

650

700

750

800

850

900

950

1000

P (MC)Fe (MC)
Mixed (MC)

2.5

Data / MC

1.5

600

550

Reconstructed Xmax [g/cm2]

2.5

Data / MC

2

550

500

1000

Reconstructed Xmax [g/cm ]2.5

Data / MC700

2Reconstructed Xmax [g/cm ]

0
500

650

2
1.5
1
0.5

550

600

650

700

750

800

850

900

950

Reconstructed Xmax [g/cm2](h) 19.0 ≤ log(E) < 19.3,
62 events

1000

0
500

550

600

650

700

750

800

850

900

950

1000

Reconstructed Xmax [g/cm2](i) 19.3 ≤ log(E), 33 events

Figure 7.10: Xmax distribution in several energy ranges compared with the
expected distribution estimated from MC simulation for primary protons (red),irons (blue) or mixed compositions (pink) under the fiducial volume cuts. Threetypes of the vertical axis indicate the linear scale, the logarithmic scale and its
ratio between data and MC simulations.

7.4. MASS COMPOSITION ANALYSIS

129

Figure 7.11: The Xmax distribution of the observed data and MC simulated byprotons and irons with 1018.4 eV ≤ E < 1018.6 eV under the fiducial volume
cuts, which is the same data shown in Fig. 7.10(e).

evaluated as follows.
P (D > observed) = QKS

r

N1 N2
D
N1 + N2!

(7.3)

where QKS is the function given by
QKS (λ) = 2∞
X(−1)j−1 exp(−2j 2 λ2 ).

(7.4)

j=1

Fig. 7.12 shows the probabilities calculated from KS tests with each energy bin comparing observed Xmax distribution calculated from observed data
analysis with expected Xmax distribution estimated from MC simulations forprimary protons and irons using the QGSJet-II model and the SIBYLL model
as a hadron interaction model. At the lowest plot of reconstructed energies at
1017.65 eV, the measured Xmax distribution was compatible with the expecteddistribution estimated from MC simulations for mixed composition primaries.
In the energy region above 1018.5 eV, the measured Xmax distribution calculated from observed data analysis was only compatible with primary protons
and incompatible with primary irons or the mixed compositions. The result
was also consistent with the transition from a heavy dominant composition toa light dominant at the energy of 1018.5 eV.
Evaluation of Proton Fraction and Mean Logarithmic Mass
From measurements of averaged Xmax , we estimate proton fractions using thetwo component model, assuming a mixed composition of purely protons andirons. The proton fraction Pfraction is calculated with
Pfraction =Obs. − X Fe
Xmax
max
.
p
Fe
Xmax
− Xmax

(7.5)

130

CHAPTER 7. DATA ANALYSIS

P-value

1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12
10-13
10-14
10-15
17.5

P QGS-IIFe QGS-II
Mixed QGS-II
P SIBYLLP SIBYLL
Mixed SIBYLL

18

18.5
19
log (E (eV))

19.5

20

10

Figure 7.12: The probabilities estimated by KS test using several compositionsof QGSJet-II and SIBYLL. Red: proton, Blue: iron, Pink: mixed composition
assuming 50% proton and 50% iron primaries.

However, estimations of proton factions need to correct differences of acceptance biases between primary protons and irons. The acceptance difference
corresponds to the difference of apertures shown in Fig. 6.11(c). In low energies less than 1018.0 eV, the acceptance of primary irons is smaller than thatof primary protons, because the averaged Xmax for primary irons is smaller
than one for primary protons. Here, acceptance differences between primary
protons and irons are calculated from apertures shown in Fig. 6.11. A ratio ofacceptance difference, R, is calculated from
 Fe

Fe
Nreco. /Nthrown
AΩFe
R=
=
(7.6)
p
p
AΩp
Nreco.
/Nthrown
where Nreco. is the number of reconstructed events, Nthrown is the number ofthrown events. AΩp and AΩFe indicate the apertures for primary protons andirons, respectively.
Therefore, (7.5) is modified to use R of (7.6),
Obs. − X Fe
Xmax
max · R
Corr.
(7.7)
Pfraction =pFe ) + (R − 1) · X Obs.
− Xmax(Xmax
max
Corr. is the proton fraction corrected the acceptance bias.
where Pfraction
Moreover the mean of logarithm natural of atomic mass number is evaluatedCorr. assuming the two component model,
from PfractionCorr.
< ln A >= 1 − Pfraction
× ln 56.
(7.8)

7.4. MASS COMPOSITION ANALYSIS

131

Corr.
Fig. 7.13 shows Pfractionand < ln A > calculated from the averaged Xmax
and the expected lines from MC simulations using primary protons and irons.

1.4

QGS-II
QGS-II correctedProton fraction

1.2
1

SIBYLLSIBYLL corrected

0.8
0.6
0.4
0.2
0
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Mean logarithmic mass <ln A>(a) Proton fraction

4

QGS-II
QGS-II corrected
SIBYLL3

SIBYLL corrected

2
1
0
-1
17.5

18

18.5
19
log (E (eV))

19.5

20

10

(b) < ln A >Figure 7.13: The proton fraction and the averaged < ln A > measured by the
BRM and the LR stations under the fiducial volume cuts.

132

CHAPTER 7. DATA ANALYSIS

Mass Composition Results under the Standard Cuts
For the purpose of the cross-checking of mass composition measurements, theFVC is removed in the combined data and MC simulations. Fig. 7.14 shows
the averaged Xmax for observed and MC events selected with the standard cut
only. In Fig. 7.14, the pink and sky blue lines indicates the averaged Xmaxof thrown MC estimated by only CORSIKA shower generations. The red andblue lines indicates the averaged Xmax with the acceptance bias of each FD
station. The MC lines are estimated using the QGSJet-II model as the hadroninteraction model.
The averaged Xmax valuse only under the standard cuts have the similartendency with those under the FVC. The averaged Xmax values in the energy
range of 1017.5 eV ≤ E ≤ 1018.5 eV indicate transitions of dominant components
from heavy to light nuclei and are consistent with the pure proton expectation
above 1018.5 eV. These interpretations of the results are the same with thosewith the FVC shown in Fig. 7.8. Therefore, we demonstrated the systematic
shift caused by acceptance biases of limited FOV of FD in MC simulations.
Moreover, we confirmed that the interpretation on the mass composition obtained from our observations and analyses does not depend on whether weapply the FVC as bias-free Xmax measurements or not.

1000
Proton MC

950

Iron MC
Proton Reconstructed

900

Iron Reconstructed
Data<Xmax> (g/cm2)

850
800
750
700
650
600
550
500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

Figure 7.14: The measured and expected of averaged Xmax with only the standard cuts. The pink and sky blue lines indicates the averaged Xmax of thrown
MC estimated by only CORSIKA shower generations. The red and blue lines
indicates the averaged Xmax with the acceptance bias of each FD station. The
MC lines are estimated using the QGSJet-II model as the hadron interaction
model.

7.5. ENERGY SPECTRUM

7.5

133

Energy Spectrum

Next, we obtain the energy spectrum based on the detector aperture, the live
time and the number spectrum estimated in section 6.1.

7.5.1

Combined ExposureFirstly, we use the results from BRM and LR data obtained independent analyses, and we calculated the energy spectra assuming independent observationfrom the BRM and the LR stations. Secondly, we calculate a combined spectrum. Since the BRM and LR stations with the common sensitive area are
independently operated, some of EASs with high energies above 1018.5 eV arereconstructed at both stations. Thus, we carefully select results of both reconstructed EASs to avoid a double-counting of EASs. As a result, the reconstructed EASs include results reconstructed three types of observation mode:both the BRM and the LR stations mode, monocular mode of only the BRM
or LR station. Therefore, considering three types of the apertures and the live
times, we estimate the combined exposure, ω(E). The exposures of the BRM
and the LR stations are simply given by
ω(E) = AΩ(E) · t(7.9)

where t indicates the live time and aperture, AΩ(E), is already estimated inFig. 6.11. The fluxes measured at the BRM and the LR stations are straightforward to evaluate with the following formula.
J(E) =

N (E).
ω(E) · ∆E(7.10)

However, we consider the three types of the apertures shown in Fig. 6.11(b)and the three types of the live times. Thus, the combined aperture are modifiedasω ALL (E) = AΩBRM (E) · tBRM + AΩLR (E) · tLR + AΩcombined (E) · tStereo (7.11)
where AΩBRM , AΩrmLR and AΩCombined shows the aperture of only the BRM
station, only the LR station and the combined aperture, respectively, tBRM ,tLR and tStereo show their live times. Here, we assume pure proton primaries
as the mass composition.
The combined flux J(E) is given by (7.11) substituting ω ALL (E) for ω(E).
Fig. 7.15 shows BRM, LR and the combined spectra multiplied by E 3 in orderto check details of a spectrum structure. The red, blue and green plots indicate
the energy spectra measured at the BRM station and√ the LR stations, and their
combination, respectively. The error bars indicate N with the assumption of
the Poisson distribution, where N is the number of EASs in each energy bin.
Since the data in high energies above 1019 eV have not enough statistics,
the size of binning is changed from dlog E = 0.1 step to dlog E = 0.2, theresults are shown in the right figure of Fig. 7.15.

134

CHAPTER 7. DATA ANALYSIS

102
Black Rock Mesa

Black Rock Mesa

Long Ridge

Long Ridge

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

102

Combined

10

1

10-1
17.5

18

18.5

19
log (E (eV))

19.5

20

20.5

Combined

10

1

10-1
17.5

18

18.5

10

19
log (E (eV))

19.5

20

20.5

10

Figure 7.15: Energy Spectra. In the right figure, the size of binning is changed
from dlog E = 0.1 step to dlog E = 0.2.

Energy Spectra considering Mass Composition Measurements
Estimated apertures depend on assumed primary composition, as shown in
Fig. 6.11. Once the proton fraction is obtained, the aperture based on themixed composition, AΩf , can be obtainedAΩf = AΩp (R + f · (1 − R))(7.12)

where f is the proton fraction, R is difference of acceptance shown in (7.5) [84].

Figure 7.16: The proton fraction measured by HiRes/MIA experiment [84].

Fig. 7.16 shows the proton fraction measured by HiRes/MIA experiment[38]. On the other hand, we have already obtained the proton fraction fromthe TA monocular analyses for data measured with the BRM and LR stations
described in section 7.4, and the results are shown in Fig. 7.13. The apertures
for primary protons and irons are already estimated in Fig. 7.13. We calculate

7.6. STUDY OF SYSTEMATIC UNCERTAINTY

135

two apertures assuming proton fractions obtained from HiRes/MIA experimentor from TA monocular analyses. Using the estimated apertures, energy spectra are re-calculated as shown in Fig. 7.17. Although obtained fluxes in low

102
Combined (Pure Proton composition)

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

Combined (HiRes/MIA composition)
Combined (TA Mono composition)

10

1

10-1
17.5

18

18.5

19
log (E (eV))

19.5

20

20.5

10

Figure 7.17: TA combined spectra assuming several compositions: pure proton,
HiRes/MIA composition and measurement result in TA monocular mode.

energies less than 1018 eV are large differences between composition assumptions, the fluxes in high energies above 1018.5 eV is almost independent on
assumptions of the proton fraction.
Fig. 7.18 shows the comparisons of other spectra measured by the TA
surface detector and by the FDs at the TA Middle Drum station transported
from HiRes experiment. In the Fig. 7.18, the spectrum labeled as BRM+LR
under the assumption of the HiRes/MIA proton fraction is shown, because thespectrum of Middle Drum assumes the HiRes/MIA composition. The blue plotsshow the spectrum analyzing data collected at the BRM and the LR stations,the open squares show the spectrum measured at the Middle Drum station[71], the pink triangles indicate the spectrum measured by TA SD with 27%
scaled as the same energies with TA FD energies [72]. These spectra are ingood agreement with each other.

7.6

Study of Systematic Uncertainty

In this section, we discuss systematic uncertainties on energies and Xmax determined with FD measurements [73].

136

CHAPTER 7. DATA ANALYSIS

102
BRM + LR

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

Middle DrumTA SD (ICRC2011)

10

1

10-1
17.5

18

18.5

19
log (E (eV))

19.5

20

20.5

10

Figure 7.18: Energy spectra in the TA measurement. The blue plots show
the spectrum analyzing data collected at the BRM and the LR stations, theopen squares show the spectrum measured at the Middle Drum station [71],the pink triangles indicate the spectrum measured by TA SD with 27% scaled
as the same energies with TA FD energies [72]7.6.1

Fluorescence Yields

Firstly, the uncertainty attributed to the fluorescence yields is discussed. Fig. 7.19
shows several measurements of the fluorescence yields as a function of altitudein the US standard atmosphere [60] [61] [92] [93] [94]. In TA FD analysis,
we adopt an absolute value of the number of fluorescence photons measured
by Kakimoto et al. [61], and also we adopt the relative intensity spectrum
measured by FLASH measurements [92]. Comparing total yield measured by
Kakimoto et al, (blue triangles) with that measured by Nagano et al. (purple squares) at an altitude of 10 km, the difference to other measurements is11%, and this is the systematic error attributed to the uncertainties of thefluorescence yields.
The fluorescence yields are independent of longitudinal developments of
EASs, Thus, uncertainties on Xmax caused by the systematic error attributed tothe uncertainties of fluorescence yields can be estimated from the averaged Xmax
and its energy dependence shown in Fig. 6.2. If the energy are shifted 11%, theshift on the averaged Xmax is less than 5 g/cm2 in all models. Therefore weestimated 5 g/cm2 as Xmax systematic uncertainty caused by the fluorescence
yield systematic error.

7.6. STUDY OF SYSTEMATIC UNCERTAINTY

137

Figure 7.19: The fluorescence yield comparisons between several measurementswith US standard atmosphere [60] [61] [92] [93] [94].

7.6.2

Atmospheric parameters

Secondly, we estimate the uncertainty attributed to the uncertainties on atmospheric parameters. In FD analysis, we adopt a typical value of the horizontal
attenuation length (29.4 km, VADO = 0.034), and as the other atmosphericcondition parameters we adopt the monthly average values obtained from radiosonde observations at ELKO. In order to study systematic differences, MC
simulations using daily values of the horizontal attenuation length measured
by the LIDAR system and also using daily values of parameters measured byradiosondes lunched daily are used as an event generator. The obtained MC
events are reconstructed by two different ways. One is the reconstruction process using the typical VAOD and the monthly averaged parameters. The otheris the reconstruction process using daily values which are used in the corresponding MC simulations. The distribution of differences on reconstructedenergies and on Xmax between two analyses for the identical MC events indicate the systematics uncertainties. The systematic uncertainties on energies
and on Xmax caused by atmospheric parameter uncertainties are ±11.2% and±12.4 g/cm2 , respectively [108].

7.6.3

Calibrations

Thirdly, we estimate the uncertainty caused by detector calibrations which
directly effects the uncertainty of reconstructed energies. The major systematic
error caused by the detector calibrations is attributed to the uncertainty on theabsolute calibrations using CRAYS. The systematic error on a primary energy
estimation is 7.2% attributed to the accuracy of the energy probe in CRAYS forthe laser power measurement. Additionally the uncertainty on primary energies

138

CHAPTER 7. DATA ANALYSIS

of 3.7% is attributed to systematic gain drifts caused by the transports of thecalibrated PMTs to TA experimental site [75].
Gains of PMTs vary caused by aging effects. We monitor the gain drifts on
the absolutely calibrated PMTs by the aging effects by YAP as the calibration
sources. The results of the gain drift monitoring using YAP pulsars show thatno apparent gain drift is observed on any cameras. The standard deviation ofdrifting gains is less than 3%.
Another source of the systematic error on primary energy estimations is
the mirror reflectance uncertainty attributed to the systematic uncertainty on
the spectrophotometer and interpolation errors on the time variation curves ofthe monitored mirror reflectance. The contribution from the mirror reflectanceuncertainty is the systematic energy shift of 3% and the fluctuation of lessthan 2% . The mirror areas also have uncertainties at the edges and the center
attributed to the fluctuations on the anodization process, which is estimatedto be 2%.
We adopt an average value of the transmittances of the filters on each PMT
photocathode as the typical transmittance for all filters. The standard deviation for all the measured filters is 1%, and the same amount contributes to theenergy uncertainty. The other source is the time variations of the transmittance of the camera windows damaged by dusts and fogs. However, we havenot detected any apparent decreases, and it is estimated to be less than 1%.
From the square root of the quadratic sum of the uncertainties mentioned
above, the total uncertainty attributed to the uncertainties on the detector
calibrations is estimated to be 10%. Also we evaluated contributions from thesame sources on the systematic error of Xmax , and it is 5 g/cm2 .

7.6.4

Geometry of Fluorescence Telescopes

As discussed in section 3.4.5, the directions of the telescopes are calibrated withobservations and analyses of star tracks on the focal planes. The directions of
the telescopes are determined with an accuracy of 0.01 degree, and the accuracyof each PMT direction is 0.1 degree. Using these values, the systematic uncertainties on energies and Xmax attributed to the uncertainties on telescope’sand PMT’s pointing directions are estimated less than 4% and 9 g/cm2 with
MC simulation studies.

7.6.5

Reconstruction Methods

As shown in Fig. 4.1, the averaged missing energy is difference between primary
protons and irons. In our analysis, every estimated primary energy is correctedwith averaged missing energy calculated for primary protons. Thus, it causes
the systematic error on primary energies of 5%.
Moreover, primary energies reconstructed in the monocular analysis are
systematic smaller than the thrown energies caused by geometrical accuracies
in the monocular mode. Thus, we correct the systematic shift of reconstructed7.6. STUDY OF SYSTEMATIC UNCERTAINTY

139

energies estimated from MC simulations as shown in Fig. 6.1.2. The correction
factor is estimated as 7% at 1019.5 eV.
As shown in section 7.2 of Data/MC comparisons, the shapes of lateral
distributions are slightly difference for observed showers and MC simulated
showers based on the NKG function. Thus, we reconstruct the observed data
without lateral distributions, and compare the reconstructed energies without
lateral distributions with energies considering lateral distribution based on the
NKG function. The contribution on the systematic error on energy estimations
is 3% with our reconstruction software.
As discussed in section 6.1.2 of accuracies on Xmax estimated from MC
simulations, there are systematic differences between thrown Xmax values andreconstructed ones in the monocular analysis. The averaged systematic bias is
10 g/cm2 estimated from MC simulations shown in Fig. 6.6. Since the reconstructed Xmax values are not corrected in the monocular analysis, hence we use
10 g/cm2 attributed to systematic uncertainty on Xmax .

7.6.6

Total Systematic Uncertainty

Table 7.2 shows the systematic uncertainties attributed to several sources.
The total systematic uncertainties on energies and Xmax are summarized inthis table. As the result, we conclude that the total systematic uncertainty onenergy and Xmax are 21% and 19 g/cm2 , respectively. The energy systematic
error is almost same as the other experiments (AGASA: 18%, HiRes: 17%,
Auger: 22%).
item
Fluorescence Yield
Atmosphere
Calibration
Detector Geometry
Reconstruction
Total

Energy
11%
11%
10%
4%
10%
21%

Xmax
5 g/cm2
12 g/cm2
5 g/cm2
9 g/cm2
10 g/cm2
19 g/cm2

Table 7.2: The total systematic uncertainty of energy and Xmax .

Chapter 8

Discussion
In this chapter, we summarize the analysis results for the mass composition
and the energy spectrum based on the monocular analysis for TA FDs, and we
discuss possible interpretations for the results and for UHECR origins.

8.1

Mass Composition Measurement

At first, we discuss interpretations of the mass composition measurement.
Fig. 8.1 shows the fitting results of averaged Xmax estimated from MC simulations for two primary species and two hadron interaction models and calculated
from observed data analysis under the FVC. The left figure and the right figre
of Fig. 8.1 are fitted by different types of linear functions using the least square
method of a single line fitting (a) and of two lines and a break energy (b),respectively. The point at the highest energy includes only three EASs, andthese points are located at adjacent positions. Although a standard deviation
calculated from these points was small, the standard deviation is much smaller
than those estimated from MC simulations for all primary speices and interaction models using enough statistics. In order to avoid the accidental bias
attributed to small statistics, we exclude the point at the highest energy fromthe fittings.
Comparing reduced χ2 of a single line function, χ2 /ndf = 9.682/16 ≃ 0.61,
with that of a two lines function, χ2 /ndf = 5.434/14 ≃ 0.39, the fitting result
using two lines connecting at a break point are better than that with a single
line. When we apply two line fit on the averaged Xmax plots, we define thelow and D highbreaking energy, EB , and elongation rates below/above EB , D1010
low = 74 ± 5 and[g/cm2 /decade]. Then we obtained log(EB ) = 18.6 ± 0.2, D10
high= 30 ± 24.
D10
On the other hand, the elongation rates for MC results, with the hadron inP,sibyll
P,qgsII== 38±1 and D10
teraction model of QGSJet-II and SIBYLL, are D10
42 ± 2, respectively, for protons. For primary irons, the MC calculated elongaFe,sibyll
Fe,qgsII= 43 ± 2 for irons. The measured= 37 ± 1 and D10tion rates are D10
low = 74±5, is larger than the MC predicted values
elongation rate below EB , D10
141

142

CHAPTER 8. DISCUSSION

1000<Xmax> (g/cm2)

900
850

Proton QGS-II Rec.
Proton SIBYLL Rec.
Iron QGS-II Rec.

1000
950
900

Iron SIBYLL Rec.
Data

<Xmax> (g/cm2)950

χ2 / ndf
ndf
39.68 / 16
44.88
9.682
19
20
48.44
31.55
p0
37.67
43.24
1.315
41.54
37.28±±±1.532
68.62
1.533
1.16
3.66
p1
55.16
-136.1±±±24.72
28.6-524.5-9.496-15.92
65.94
28.69
21.78

800
750
700
650

850

650
550

19.5

10

(a) single line fitting

20

Iron SIBYLL Rec.
Data

700
600

18.5
19
log (E (eV))

30.47 ± 24.11
18.59 ± 0.1764

750

550
18

p2
p3

800

600
500
17.5

Proton QGS-II Rec.
Proton SIBYLL Rec.
Iron QGS-II Rec.

5.434 / 2014ndf
χ22 // ndf
ndf
39.68
44.88
19
48.44
31.55
73.75
5.146
p0
37.67
43.24
1.315
41.54
37.28±±±1.532
1.533
1.16
p1
-616.3±±±±24.72
92.41
p1
55.16
-136.1
28.6-9.496-15.92
28.69
21.78

500
17.5

18

18.5
19
log (E (eV))

19.5

20

10

(b) fitting with two lines and a break point

Figure 8.1: The measured averaged Xmax fitted by two types of line functions
using the least square method.

with assuming a constant composition, regardless of hadron interaction models.
Thus, the result strongly suggests the transition of the dominant component
from heavy to light nuclei in the energy range from 1017.5 eV to 1018.5 .
At higher energies above EB , the measured elongation rate above EB ,high
D10 = 30 ± 24, is consistent with expected elongation rates with assuming a
constant composition, regardless of the hadron interaction models within thestatistical error. Therefore, the result is compatible with a constant composition in the mass composition of UHECRs from 1018.6 eV to 1019.6 eV.

8.1.1

Transition of Mass Composition from 1017.5 eV to 1018.5
eV

As shown in Fig. 7.9 and Fig. 8.1, the measured averaged Xmax shows the clear
evidence of the transition from the heavy dominant components to the lightdominant components from 1017.5 eV to 1018.5 eV. Moreover, distributions of
Xmax also indicate the same tendency in Fig. 7.10. The observed proton fractionof Fig. 7.13 calculated from averaged Xmax values and acceptance biases is 20%
at 1017.5 eV and 90% at 1018.5 eV.
Compared with the Stereo Fly’s Eye and the HiRes/MIA and HiRes measurements shown in Fig. 8.2(a)(b), the observed transition of the mass composition of the TA monocular analysis seems to be consistent with that measured
by the Fly’s Eye experiment. From the result of the HiRes/MIA experiment,
the transition energy of HiRes/MIA is smaller than that of TA monocular analysis. However, the HiRes collaborator claims the observed Xmax of Fly’s Eye
is in agreement well with that of HiRes/MIA considering the systematic shiftof 13 g/cm2 on Xmax within their systematic uncertainty [38]. Thus, since asystematic uncertainty of TA monocular analysis is 19 g/cm2 , the Xmax measurement of TA monocular analysis is also consistent with those of the Fly’s
Eye and HiRes/MIA.

8.1. MASS COMPOSITION MEASUREMENT(a) Stereo Fly’s Eye143(b) HiRes/MIA and HiRes(c) Auger

Figure 8.2: The averaged Xmax for Stereo Fly’s Eys (a) and HiRes/MIA and
HiRes (b) [38] [37]. Auger measured hXmax i compared with air shower simulations using different hadronic interaction models [40]. They are the same
figures shown in Fig. 2.13 and Fig. 2.15.

As a possible interpretation, we discuss the transition of the mass composition of UHECRs. The result indicates cosmic rays are accelerated on two
different types of origins: sources accelerated for iron nuclei around 1018.0 eV,
and source accelerated for protons above 1018.0 eV.
If we assume rigidity dependent acceleration models such as Fermi accelerations in which maximum acceleration energies are dependent on a charge of
nuclei, we can consider iron nuclei are accelerated to ∼ 1018.0 eV on a origin.
Fig. 8.3 shows the observed energy spectra around knee region for several masscompositions. The Tibet group reported heavy elements dominate at the knee
and beyond [97]. Additionally, cosmic rays with energies around the knee believe to be accelerated in our local galaxy. Since, we observed iron dominant at
1017.5 eV, we can consider the maximum acceleration energy reaches to 1017.5

144

CHAPTER 8. DISCUSSION

Figure 8.3: Energy spectra of several composition observed by several experiments around the knee region. The dotted lines indicate the expected flux
assuming a rigidity dependent acceleration model using the results of the Tibet
group [97].

eV for irons in our galaxy. In origins of higher energies, cosmic rays are accelerated above 1018.0 eV in extra-galactic sources, such as GRB, neutron star,
AGN, galactic cluster and so on. Therefore, as a possible interpretation, theobserved mass composition indicates a transition of origins of cosmic rays fromgalactic to extra-galactic sources.
If we assume cosmic rays are accelerated by neutron stars with distances
enough short to avoid bending of galactic magnetic fields in our galaxy, a clear
anisotropy should be observed around 1018.0 eV at the direction of astronomical
objects. Therefore, it is important to observe an anisotropy of UHECRs in order
to conclude origins of UHECRs.

8.1.2

Proton Dominant above 1018.5 eVSecondly, as shown in the averaged Xmax of Fig. 7.9, the monocular analyses
for the mass composition indicate proton dominant above 1018.5 eV.
Comparing with other measurements, the proton dominant result is also
consistent with the HiRes measurement. However, the Auger claims that themass composition is getting heavier nuclei above 1018.5 eV, which is shownin Fig. 8.2(c). Thus, there is still the contradiction between TA and Auger
measurements. In this thesis, we applied the FVC on Xmax measurements tounderstand our discrepancy. Compared with the mass composition under the
standard cut, an interpretation of the mass composition is the identical withthe result under the FVC, because acceptance biases are also demonstrated

8.2. ENERGY SPECTRUM MEASUREMENT

145

in the MC predicted lines as same as observed data as shown in comparisons
between Fig. 7.8 and Fig. 7.14. Therefore, we confirmed the mass composition
measurement by Xmax technique is independent of selection rules.
The TA and the Auger collaborators should understand the discrepancy
on the mass composition between north hemisphere and south hemisphere.
Therefore, we have plans to exchange common calibration sources or analysis
softwares as future plans as world-wide international collaborations between
the TA and the Auger.
χ2 / ndf
59.75 / 18
p0-0.2002 ± 0.01327
p1
3.983 ± 0.2388

102

BRM + LR Mono

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

BRM + LR Mono

10

1

10-1
17.5

18

18.5

χ2 / ndf
14.8 / 16
p0-0.2453 ± 0.01809
p1
4.789 ± 0.3249
p2
0.216 ± 0.06668
p3
18.58 ± 0.06149

102

19
log (E (eV))

19.5

20

10

1

10-1
17.5

20.5

18

18.5

10

19.5

20

20.5

10

(a) Power-law fitting(b) Two power-law fitting
χ2 / ndf
11.67 / 14
p0-0.2349 ± 0.01636
p1
4.604 ± 0.2941
p2
0.4014 ± 0.1093
p3
18.71 ± 0.05671
p4-1.061 ± 1.874
p5
19.58 ± 0.2375

102

BRM + LR Mono

Flux*E3/10 24 (eV2 m-2 sr-1 s-1)

19
log (E (eV))

10

1

10-1
17.5

18

18.5

19
log (E (eV))

19.5

20

20.5

10

(c) Three power-law fitting

Figure 8.4: The measured energy spectrum fitted by three types of power-law
function using the method of least squares.

As discussed in section 2.3.2, The top-down modes predict gamma-ray dominant composition above 1019.0 eV, such as the Z-burst model or annihilations/decays of dark matters. Therefore, we exclude the top-down models, andthe result is consistent with bottom-up models instead of top-down models.

8.2

Energy Spectrum Measurement

In the TA monocular analysis, we measured the energy spectrum with broad
energies from 1017.5 eV to 1020.0 eV. Firstly, we discuss systematic uncertain-

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E3 J(E) [eV2/m2/s/str]

Akeno
AGASA

1025

HiRes-1
HiRes-2
Auger (ICRC2011)1024
TA FD: BRM+LR
TA FD: MD

1023

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1018

1019
Energy [eV]1020

Figure 8.5: The energy spectra compared with several measurements [9] [11][12] [44] [50] [71] [72].

ties caused by the assumption of a proton fraction. Fig. 7.17 shows the energy
spectra assuming proton fractions of pure proton, HiRes/MIA and TA monocular measurements. The difference is large at low energies less than 1018.0 eV,
but it is negligible at high energies above 1018.5 eV. Thus, an assumption of
the proton fraction impacts only at low energies less than 1018.0 eV.
Secondly, the measured spectrum in the TA monocular analysis is fitted
by three types of power-law formulas shown in Fig. 8.4. The single powerlaw fitting is excluded by a value of the reduced χ2 , χ2 /ndf = 59.75/18 ≃ 3.32.
The reduced χ2 of three power-law fitting, χ2 /ndf = 11.67/14 ≃ 0.83, is slightly
better than one of two power-law fitting, χ2 /ndf = 14.8/16 ≃ 0.93.
Next, we compare the measured energy spectrum in the TA monocular analysis with other measurements shown in Fig. 8.5. The TA monocular spectrum
is in good agreement with the HiRes measurements at all energy ranges. Moreover, the fitted values are compared with other measurements shown in Fig. 8.6
reported at UHECR 2012 Symposium [98]. The definition of fitting parameters
are also described in the same figure. The fitted values in the TA monocular
spectrum is consistent with values of the HiRes spectrum. The HiRes col-

8.2. ENERGY SPECTRUM MEASUREMENT

147

Figure 8.6: The compariton of fitted values measured by AGASA, Yakutsk,
HiRes and TA(SD) reported at UHECR2012 Symposium and by BRM and LR
monocular mode [98].

laborators conclude a detection of the GZK suppression caused by photo-pion
interactions and e+ e− pair-creations between UHE protons and CMBR throughγ + p → p + π 0 + π ± ... and γ + p → p + e+ + e− , respectively.

Figure 8.7: Propagated spectra, f (E)·E 3 , for pure proton extra-galactic cosmic
ray sources (left). The injection spectral index is E −2.6 for the HiRes data. Two
different propagated spectra and the corresponding inferred galactic cosmic raycomponent are shown, for an injection spectrum either with or without a low
energy cut [99]. UHECR spectra to be expected from a two component model(right) [15], which is the same figure shown in Fig. 2.4.

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The left figure of Fig. 8.7 shows the propagated spectra for pure proton
extra-galactic cosmic ray sources. The injection spectral index is E −2.6 for the
HiRes data. Since the TA monocular spectrum is in agreement with the HiRes
spectrum, the spectrum is also consistent with the GZK cutoff.
At suppression energies shown in Fig. 8.6, ES , there is a discrepancy beyond
the fitted errors between TA SD and Auger. However, the suppression energy of
the TA monocular analysis has a large fitted error attributed to low statistics.
The suppression energy of the TA monocular analysis is consistent with both
TA SD and Auger within the fitted error. Therefore, there is not enoughstatistics for the TA monocular spectrum to distinguish the suppression energies
measured by TA and Auger.
The ankle energy and the spectral indexes around ankle estimated fromthe TA monocular spectrum are consistent with those of TA SD. When theAuger energies are scaled to fit the ankle energy, the scaled Auger spectrum isalso consistent with the TA SD except for the suppression energy as shown in
Fig. 8.8. As a result, considering energy scales, the TA monocular spectrum isconsistent with all spectra within the error.

Figure 8.8: The scaled energy spectra measured by AGASA, Yakutsk, HiRes
and TA(SD) reported at UHECR2012 Symposium [98]. The TA SD, HiRes
and Auger are in agreement well within the systematic uncertainties.

8.3

Combined Interpretation

The clever advantage to observe UHECRs in the TA monocular analysis ismeasurements of both the energy spectrum and the mass composition withbroad energies from 1017.5 eV to 1020 eV.
The structure of the measured energy spectrum is consistent with the interaction between UHE protons and CMBR, and the measured mass composition is proton dominant above 1018.5 eV. Therefore, we claim the ankle struc-8.4. FUTURE PLANS

149

ture of the energy spectrum is generated through e+ e− pair-creations between
UHE protons and CMBR. In contrast, these results are clearly contradictions
with the dip transition model from galactic to extra-galactic sources shown in
Fig. 2.4.
As a result, since the position of ankle is universal, we can apply the ankle
structure as an energy calibrator as shown in Fig. 8.8. Furthermore, the observed energy spectrum and mass composition results are also consistent withexpectation estimated from GZK feature. However, since there are low statistics above 1019.6 eV in the mass composition analysis, and the spectral index
of the energy spectrum above the suppression energy has large statistical error,
we can not significantly claim the observation of the GZK cutoff.
If GZK neutrinos which are generated though GZK processes are observedin neutrino detectors, such as the IceCube experiment [102], it is a significant
evidence to exist the GZK mechanism. If the mass composition of UHECRs
with energies above 1020 eV is still protons, we could measure an correlation
between arrival directions of UHECRs and large scale structures or known
astronomical objects, and observe a recovering from the GZK suppression above
1021 eV in next-generation observations.
In order to conclude proton dominant of cosmic rays with energies above
19.6
10
eV, we need more statistics of UHECRs under the FVC. The measured
mass composition under the standard cuts with twice statistic also indicates
proton dominant above 1019.6 eV, although the acceptance biases are large.
These result is consistent with acceleration models of extra-galactic sources
such as GRB, AGN, galactic cluster. However, we can not distinguish these
origin models to observe the mass composition and the energy spectrum, andneed to observe an anisotropy of UHECRs. If these sources are origins of
UHECRs, the correlation between arrival directions and known astronomical
objects should be clearly observed by surface detectors to collect more statistics
of UHE protons in near future.

8.4

Future Plans

The TA experiment has been started constructing a dense of surface detector array and new fluorescence detectors, called Telescope Array low energy
extension (TALE) [100]. The schematic view of TALE is shown in Fig. 8.9.
The TALE consists of 105 SDs same as the TA SD with three types of
spacing: 400 m, 600 m and 1200 m, respectively, and 14 FDs with a upper fieldof view to observe UHECRs from low energies, above 1016.5 eV, using hybrid
techniques. Using collected data, we will measure the mass composition withhigh resolution due to the hybrid technique, and an anisotropy measurement
above 1016.5 eV by the dense deployed SDs.
Moreover, the TA experiment has started “hybrid triggers” in the end of2010 at three FD stations [107]. The hybrid trigger has been shown from our
MC studies that geometry determination accuracies of monocular FD events are

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Figure 8.9: The schematic view of the TALE experiment. The yellow circle
shows newly constructed dense SDs, the red circle shows the SDs of TA. The
green hexagon indicates the TALE FD at the same location of TA MD.

significantly improved using SD information. However, in lower energy region
below 1018.5 eV, trigger efficiency for the TA SD is small compared with that ofFD, therefore some showers have no SD information. Then to collect the small
SD signals, we have installed an FD driven SD trigger system: this introduces
en external triggering scheme to the TA SD using triggering signals from FD.
We have already measured the FD and SD data collected by the hybrid trigger
more than 1 years. In near future, the mass composition are measured withhigh accuracies and statistics using the hybrid technique.

Telescope Array 2
We have started the research and development of Telescope Array 2 (TA-2) as
the future plan of TA. The TA-2 will be the world record of UHECR detectors
which consists of 10,000 SDs with 2.0 km spacing and covers with ∼ 40,000
km2 effective area. The comparison of effective area of UHECR observations
are shown in Fig. 8.10. You see that TA-2 is the largest detector to observeUHECRs.
In the TA-2, we concentrate on the UHECR detections with energies above
1019.5 eV. Therefore, we can identify UHECR sources and conclude the UHECR
origins using TA-2 measurements.

8.4. FUTURE PLANS

151

Figure 8.10: The comparison of effective area of UHECR observations:
AGASA, Auger, TA SD and TA-2.

JEM-EUSO
An other future plan to observe UHECRs is the Extreme Universe Space Observatory on board Japanese Experiment Module (JEM-EUSO) [101]. JEM-EUSO
is a new type of observatory that uses the earth’s atmosphere as a detector.
As shown in Fig.8.11, JEM-EUSO will be installed on the International Space
Station (ISS) located on the orbit, and observe UHECRs with energies above
3 × 1019.0 eV using a super wide-field telescopes from the space.

Figure 8.11: Overview of JEM-EUSO project [101].

The JEM EUSO telescopes has a super-wide-field of view ±30◦ , with two
double side curved Fresnel lenses and records the track of an EAS with a time

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resolution 2.5 µs and a spatial resolution of about 0.75 km, corresponding
to 0.1◦ . The time-segmented images allow a determination of energies anddirections of UHECRs. The light receiving section of the JEM EUSO telescope
is formed by about 6000 multi-anode PMTs. The number of pixels is about two
hundred thousand. The observational aperture of the ground area is a circle
with 250 km radius, and its atmospheric volume above it with a 60◦ field ofview is one tera-ton or more.
The remote-sensing JEM-EUSO orbits around the earth every 90 minutes
on a board of the ISS at the altitude of 400 km with a huge effective area.
Thus, in addition to the significant increase of the overall exposure by about
an order of magnitude compared with Auger as of today, the orbiting JEMEUSO telescope will cover the entire Celestial Sphere. Such advantage is more
pronounced if UHECRs from a single source are observed with angular spread,and more important to open up “particle astronomy” through the investigationof UHECR origins.

Chapter 9

Conclusions
In order to conclude origins of cosmic rays, the Telescope Array experiment has
started stable observations in 2008, and it consists of 38 Fluorescence detectors
located in three stations and 507 surface detectors with 1.2 km separations
covering with 700 km2 of effective area. We explained our MC simulations
and reconstruction methods of fluorescence detectors, and then evaluated an
performance of FD in monocular mode though analyzing simulated shower
events. In order to evaluate the energy spectrum and the mass compositionof UHECRs, an aperture of FD and an averaged Xmax expected for primary
protons or irons are estimated from the MC simulations. Moreover, since FDs
have the limited field of view and the observed average Xmax has the bias, we
determined the fiducial volume cut and almost confirmed bias-free of averaged
Xmax in the MC simulation.
Using the developed reconstruction, we analyzed the data collected at the
BRM and LR stations during 3.7 years in monocular mode. As a result, twenty
thousand showers are analyzed, and then we confirmed reasonable agreements
between observed data distribution of several parameters and the expected
one estimated from MC simulations. Moreover, our developed software wascompared with independently developed software for the cross-checking, and we
confirmed consistencies within expected errors.
As further enhancement of our reliability in our analysis, the measured
averaged Xmax was compared with the expectation value estimated from MC
simulations for primary protons or irons using the QGSJet-II hadron interaction model or the SIBYLL one. The measured Xmax indicated a transition of
dominant components from heavy to light nuclei from 1017.5 eV to 1018.5 eVand proton dominant with energies above 1018.5 eV. The proton fraction andthe mean of ln A were also evaluated from averaged Xmax assuming a mixed
composition of purely protons and irons. Moreover, the averaged Xmax values
under fiducial volume cuts was compared with those under only standard cuts,
corresponding to biased Xmax . Since both results were consistent, we confirmed
the mass composition is not dependent on the selection rules.
We measured the energy spectrum of UHECRs with a broad energies from
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1017.5 eV to 1020.0 eV, and observed spectrum is in good agreement with TA
SD and TA MD transported from the HiRes experiment. Finally, we evaluated that systematic uncertainties of energy and Xmax are 21% and 19 g/cm2 ,respectively.

Appendix
A.1

Observed EAS Events

We show event displays of the top-three highest observed EASs shownin Fig. 7.7 under the fiducial volume cut (FVC). The left side of eachfigures show observed photon signails emitted from EASs for all PMTsof a station. The colors indicate timings entering photons emitted from
EASs and sizes of plots show the number of detected photo-electrons oneach PMT. The right side of each figures indicate detected signals on PMT
cameras. The plots indicate observed signals analyzing date observed at
FD stations, and the color histograms show a contribution of fluorescencephotons (red) and contamination of direct Čerenkov photons (green), its
Rayleigh scatted photons (blue) and its Mie scattered photons (purple).

Figure A.1: The observed UHECRs : E = 19.77 eV, Xmax = 796 g/cm2

Figure A.2: The observed UHECRs : E = 19.75 eV, Xmax = 758 g/cm2

155

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Figure A.3: The observed UHECRs : E = 19.67 eV, Xmax = 743 g/cm2

A.2

Data/MC comparison

As further enhancement of our reliability in our analysis, distributions of
the several parameters obtained from the reconstructions of the observed
data are compared with the expected ones estimated from MC simulations.
In analyses of this thesis, there are two types of selection rules as discussed
in Sec. 6.1.1. One is called as the standard cuts, and The other is called as
the fiducial volume cuts to achieve a bias-free analysis on Xmax measurements. Here, we compare distribution of several parameters of observed
UHECR with energies above 1017.5 eV under both of the selection rules
between observed data and MC simulations. Results under the standard
cuts are shown in Fig. A.4 to A.17 and under the fiducial volume cuts in
Fig. A.18 to A.31.
There are discrepancies caused by differences of a mass composition, assumption of a spectral index and a lateral distribution of EASs assuming
the NKG function. At highest energies region above 1019 eV, the energy
spectrum does not follow the spectral index of -3.1, and then it attributes
to discrepancies of far showers. At measurements of cosmic rays with energies less than 1018.0 eV, which has the largest statistic, we measure transitions of dominant components from heavy to light nuclei with energies
from 1017.5 eV to 1018.5 eV. Therefore, compositions were mixed in theenergy range. Differences of the number of selected PMTs are caused bydiscrepancies of physics models of lateral distributions of EASs. The results indicate the lateral distribution estimated from NKG function usedin our analysis software is wider than that obtained from observed data reconstructions. However, the differences are enough small, and we included
as systematic uncertainties as discussed in Sec. 7.6. As a result, the distributions estimated from MC simulations are in reasonable agreements withthe distributions obtained from reconstructions of observed data.

A.2. DATA/MC COMPARISON

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length between data and MC simulation under the standard cut.

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CoreX [km](a) BRM

10

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30

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10

20

30

CoreX [km](b) LR

Figure A.11: The distribution of core location of West-East direction between
data and MC under the standard cut.

A.2. DATA/MC COMPARISON

1600

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Data
P (MC)Fe (MC)

1400
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CoreY [km]P (MC)Fe (MC)

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P (MC)Fe (MC)

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Entries

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30

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CoreY [km]

0

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CoreY [km](a) BRM(b) LR

Figure A.12: The distribution of core location of South-North direction between
data and MC simulation under the standard cut.

500

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P (MC)Fe (MC)

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Entries

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P (MC)Fe (MC)

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40

Zenith angle [degree](a) BRM

50

60

0
0

10

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30

40

50

60

Zenith angle [degree](b) LR

Figure A.13: The distribution of zenith angle between data and MC simulation
under the standard cut.

162

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Data
P (MC)Fe (MC)

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P (MC)Fe (MC)

Entries

EntriesFigure A.14: The distribution of azimuth angle between data and MC simulation under the standard cut.

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P (MC)Fe (MC)

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700

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1000

0
0

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Xstart [g/cm2](b) LR

Figure A.15: The distribution of Xstart between data and MC simulation under
the standard cut.

A.2. DATA/MC COMPARISON

163

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P (MC)Fe (MC)

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Data
P (MC)Fe (MC)

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Xend [g/cm ]

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P (MC)Fe (MC)

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P (MC)Fe (MC)2

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1100 1200 1300 1400 1500

600

700

800

Xend [g/cm2]

900

1000

1100 1200 1300 1400 1500

Xend [g/cm2](a) BRM(b) LR

Figure A.16: The distribution of Xend between data and MC simulation under
the standard cut.

800

500
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Data
P (MC)Fe (MC)

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P (MC)Fe (MC)

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P (MC)Fe (MC)

102

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Reconstructed Xmax [g/cm2]
P (MC)Fe (MC)

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P (MC)Fe (MC)

2.5

Data / MC

Data / MC750

3Reconstructed Xmax [g/cm2]

0
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700

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Reconstructed Xmax [g/cm2]

Reconstructed Xmax [g/cm ]

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900

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1000

0
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550

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650

700

750

800

850

900

950

1000

Reconstructed Xmax [g/cm2](b) LR

Figure A.17: The distribution of Xmax between data and MC simulation under
the standard cut. Since the discrepancy of difference between protons and irons
is large, Xmax is the most sensitive parameter to evaluate the mass composition
of EASs.

164

APPENDIX

700

Data
P (MC)Fe (MC)

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P (MC)Fe (MC)

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P (MC)Fe (MC)

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P (MC)Fe (MC)

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Data / MC18

log (E (eV))

log (E (eV))

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P (MC)Fe (MC)

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log (E (eV))

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log (E (eV))1010(a) BRM(b) LR

Figure A.18: The distribution of energy between data and MC simulation under
the fiducial volume cut. At the highest region, there is slightly difference causedby the assumption of spectrum index, E −3.1 .

Data
P (MC)Fe (MC)Data
P (MC)Fe (MC)

800
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Entries

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Data
P (MC)Fe (MC)

102

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P (MC)Fe (MC)

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P (MC)Fe (MC)

2.5

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1.5
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P (MC)Fe (MC)

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Data / MC

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Track length [degree]

Track length [degree]

Data / MC

20

Track length [degree]

2
1.5
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10

20

30

40

Track length [degree](a) BRM

50

60

0
0

10

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30

40

50

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Track length [degree](b) LR

Figure A.19: The distribution of the track length between data and MC simulation under the fiducial volume cut.

A.2. DATA/MC COMPARISON

165
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Data
P (MC)Fe (MC)

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P (MC)Fe (MC)

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P (MC)Fe (MC)

102

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# of selected PMTs

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# of selected PMTs
P (MC)Fe (MC)

2.5

P (MC)Fe (MC)

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Data / MC

Data / MC150# of selected PMTs

1.5
1
0.5

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1.5
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0.5

0
0

50

100

150

200

0
0

250

50

100

# of selected PMTs

150

200

250

# of selected PMTs(a) BRM(b) LR

Figure A.20: The distribution of the number of selected PMTs between data
and MC simulation under the fiducial volume cut. The result indicates thedifference of physics model of the lateral distribution of EAS. The observed
lateral distribution is wider than one expected from NKG function used in oursoftware.

1000

Entries

Entries

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P (MC)Fe (MC)

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P (MC)Fe (MC)

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P (MC)Fe (MC)P (MC)Fe (MC)

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4.5

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P (MC)Fe (MC)

10

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1
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4

3

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2.5

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102

Entries

Entries10

Data
P (MC)Fe (MC)

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log (# of p.e. / track length [deg-1])

10

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log (# of p.e. / track length [deg-1])
10(a) BRM

4.5

5

0
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3.5

4

4.5

5

log (# of p.e. / track length [deg-1])
10(b) LR

Figure A.21: The distribution of the number of photo-electrons divided bytrack length between data and MC simulation under the fiducial volume cut.

APPENDIX

2400
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P (MC)Fe (MC)

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P (MC)Fe (MC)

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# of PMTs / time extend [us -1]
Data
P (MC)Fe (MC)

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P (MC)Fe (MC)

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# of PMTs / time extend [us -1]
P (MC)Fe (MC)

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# of PMTs / time extend [us -1]

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10

# of PMTs / time extend [us -1]

15

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25

30

35

40

45

50

# of PMTs / time extend [us -1](a) BRM(b) LR

Figure A.22: The distribution of the number of selected PMTs divided by timeextent between data and MC simulation under the fiducial volume cut.

1400

1200

Data
P (MC)Fe (MC)

1200

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102

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P (MC)Fe (MC)

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Data / MC

Data / MC

2.5

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Rp [km]Rp [km]

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Rp [km](a) BRM

25

30

35

40

0
0

5

10

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25

30

35

40

Rp [km](b) LR

Figure A.23: The distribution of the impact parameters between data and MC
simulation under the fiducial volume cut. At the highest region, there is slightly
difference caused by the assumption of spectrum index, E −3.1 .

A.2. DATA/MC COMPARISON

600

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P (MC)Fe (MC)

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P (MC)Fe (MC)

102

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Entries100Ψ [degree]

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160

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P (MC)Fe (MC)

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1

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Data / MC

2.5

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100

Ψ [degree]Ψ [degree]

2
1.5
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100

120

140

0
20

160

40

60

80

Ψ [degree]

100

120

140

160

Ψ [degree](a) BRM(b) LR

Figure A.24: The distribution of the angle on SDP between data and MC
simulation under the fiducial volume cut. The angle of Ψ > 120 are excluded
because of Čerenkov contaminations.

Data
P (MC)Fe (MC)

1200

800
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P (MC)Fe (MC)

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CoreX [km]P (MC)Fe (MC)

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P (MC)Fe (MC)

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10Data
P (MC)Fe (MC)CoreX [km]

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10

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CoreX [km](b) LR

Figure A.25: The distribution of the core location of West-East direction between data and MC simulation under the fiducial volume cut.

168

APPENDIX

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P (MC)Fe (MC)

700

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30

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CoreY [km]

0

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20

30

CoreY [km](a) BRM(b) LR

Figure A.26: The distribution of the core location of South-North direction
between data and MC simulation under the fiducial volume cut.

450

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300
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102

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P (MC)Fe (MC)

2

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50

60

0
0

10

20

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40

50

60

Zenith angle [degree](b) LR

Figure A.27: The distribution of the zenith angle between data and MC simulation under the fiducial volume cut. The inclined shower is disappeared under
the fiducial volume cut to avoid the acceptance bias of Xmax .

340
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P (MC)Fe (MC)

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P (MC)Fe (MC)

2.5

0

50

100

150

1.5
1

P (MC)Fe (MC)

2.5

Data / MC

2

0.5
0

-50

Azimuth angle [degree]

Azimuth angle [degree]

Data / MC

150

Azimuth angle [degree]

2
1.5
1
0.5

-150

-100

-50

0

50

100

0

150

-150

-100

-50

0

50

100

Azimuth angle [degree]

Azimuth angle [degree](a) BRM(b) LR

150

Figure A.28: The distribution of the azimuth angle between data and MC
simulation under the fiducial volume cut.

600

600

Data
P (MC)Fe (MC)

400
300
200

400
300
200

100
0
0

Data
P (MC)Fe (MC)

500

Entries

Entries

500

100
100

200

300

400

500

600

700

800

900

0
0

1000

100

200

300

Xstart [g/cm2]
10

400

500

600

700

800

3

10

1000

3

Data
P (MC)Fe (MC)

EntriesData
P (MC)Fe (MC)

Entries900

Xstart [g/cm2]

102

102

10
0

100

200

300

400

500

600

700

800

900

0

1000

100

200

300

P (MC)Fe (MC)

2

500

600

700

800

900

1000

1.5
1
0.5

P (MC)Fe (MC)

2.5

Data / MC

Data / MC

2.5

0
0

400

Xstart [g/cm2]

Xstart [g/cm2]

2
1.5
1
0.5

100

200

300

400

500

600

Xstart [g/cm2](a) BRM

700

800

900

1000

0
0

100

200

300

400

500

600

700

800

900

1000

Xstart [g/cm2](b) LR

Figure A.29: The distribution of Xstart between data and MC simulation under
the fiducial volume cut. We applied the selection rule as 150 g/cm2 < Xstart <700 g/cm2 .

170

APPENDIX

1200

800
600
400

800
600
400

200
0
500

Data
P (MC)Fe (MC)

1000

Entries

Entries

1200

Data
P (MC)Fe (MC)

1000

200
600

700

800

900

1000

0
500

1100 1200 1300 1400 1500

600

700

800

Xend [g/cm2]

1000

1100 1200 1300 1400 1500

Xend [g/cm2]

3

10

Data
P (MC)Fe (MC)

102

3

Data
P (MC)Fe (MC)

102

Entries

Entries

10

900

10
1

10

10-1
500

600

700

800

900

1000

500

1100 1200 1300 1400 1500

600

700

800

P (MC)Fe (MC)

2

1000

1100 1200 1300 1400 1500

1.5
1P (MC)Fe (MC)

2.5

Data / MC

Data / MC

2.5

0.5
0
500

900

Xend [g/cm2]

Xend [g/cm2]

2
1.5
1
0.5

600

700

800

900

1000

0
500

1100 1200 1300 1400 1500

600

700

800

Xend [g/cm2]

900

1000

1100 1200 1300 1400 1500

Xend [g/cm2](a) BRM(b) LR

Figure A.30: The distribution of Xend between data and MC simulation under
the fiducial volume cut. We applied the selection rule as 900 g/cm2 < Xend .

500

Data
P (MC)Fe (MC)

500

300
200

300
200
100

100
0
500

Data
P (MC)Fe (MC)

400

Entries

Entries

400

550

600

650

700

750

800

850

900

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0
500

1000

550

600

Reconstructed Xmax [g/cm2]
10Data
P (MC)Fe (MC)

750

800

850

900

950

1000

10

1
500

Data
P (MC)Fe (MC)

102

Entries

Entries

700

3

102

10

1
550

600

650

700

750

800

850

900

950

1000

500

550

600

Reconstructed Xmax [g/cm2]
P (MC)Fe (MC)

700

750

800

850

900

950

1000

1.5
1
0.5

P (MC)Fe (MC)

2.5

Data / MC

2

0
500

650

Reconstructed Xmax [g/cm2]

2.5

Data / MC650

Reconstructed Xmax [g/cm2]

2
1.5
1
0.5

550

600

650

700

750

800

850

Reconstructed Xmax [g/cm2](a) BRM

900

950

1000

0
500

550

600

650

700

750

800

850

900

950

1000

Reconstructed Xmax [g/cm2](b) LR

Figure A.31: The distribution of Xmax between data and MC simulation under
the fiducial volume cut. Since the discrepancy of difference between protons
and irons is large, Xmax is the most sensitive parameter to evaluate the masscomposition of EASs.

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